diff --git a/library/init/coe.lean b/library/init/coe.lean
index a87a665ab1..0ddc24aad8 100644
--- a/library/init/coe.lean
+++ b/library/init/coe.lean
@@ -80,13 +80,13 @@ universes u₁ u₂ u₃
 /- Transitive closure for HasLift, HasCoe, HasCoeToFun -/
 
 instance liftTrans {a : Sort u₁} {b : Sort u₂} {c : Sort u₃} [HasLift a b] [HasLiftT b c] : HasLiftT a c :=
-⟨λ x, liftT (lift x : b)⟩
+⟨fun x => liftT (lift x : b)⟩
 
 instance liftRefl {a : Sort u} : HasLiftT a a :=
 ⟨id⟩
 
 instance coeTrans {a : Sort u₁} {b : Sort u₂} {c : Sort u₃} [HasCoe a b] [HasCoeT b c] : HasCoeT a c :=
-⟨λ x, coeT (coeB x : b)⟩
+⟨fun x => coeT (coeB x : b)⟩
 
 instance coeBase {a : Sort u} {b : Sort v} [HasCoe a b] : HasCoeT a b :=
 ⟨coeB⟩
@@ -106,7 +106,7 @@ instance coeBase {a : Sort u} {b : Sort v} [HasCoe a b] : HasCoeT a b :=
    ...
 -/
 instance coeOption {a : Type u} : HasCoeT a (Option a) :=
-⟨λ x, some x⟩
+⟨fun x => some x⟩
 
 /- Auxiliary transitive closure for HasCoe which does not contain
    instances such as coeOption.
@@ -117,18 +117,18 @@ class HasCoeTAux (a : Sort u) (b : Sort v) :=
 (coe : a → b)
 
 instance coeTransAux {a : Sort u₁} {b : Sort u₂} {c : Sort u₃} [HasCoe a b] [HasCoeTAux b c] : HasCoeTAux a c :=
-⟨λ x : a, @HasCoeTAux.coe b c _ (coeB x)⟩
+⟨fun x : a => @HasCoeTAux.coe b c _ (coeB x)⟩
 
 instance coeBaseAux {a : Sort u} {b : Sort v} [HasCoe a b] : HasCoeTAux a b :=
 ⟨coeB⟩
 
 instance coeFnTrans {a : Sort u₁} {b : Sort u₂} [HasCoeTAux a b] [HasCoeToFun.{u₂, u₃} b] : HasCoeToFun.{u₁, u₃} a :=
-{ F   := λ x, @HasCoeToFun.F.{u₂, u₃} b _ (@HasCoeTAux.coe a b _ x),
-  coe := λ x, coeFn (@HasCoeTAux.coe a b _ x) }
+{ F   := fun x => @HasCoeToFun.F.{u₂, u₃} b _ (@HasCoeTAux.coe a b _ x),
+  coe := fun x => coeFn (@HasCoeTAux.coe a b _ x) }
 
 instance coeSortTrans {a : Sort u₁} {b : Sort u₂} [HasCoeTAux a b] [HasCoeToSort.{u₂, u₃} b] : HasCoeToSort.{u₁, u₃} a :=
 { S   := HasCoeToSort.S.{u₂, u₃} b,
-  coe := λ x, coeSort (@HasCoeTAux.coe a b _ x) }
+  coe := fun x => coeSort (@HasCoeTAux.coe a b _ x) }
 
 /- Every coercion is also a lift -/
 
@@ -138,7 +138,7 @@ instance coeToLift {a : Sort u} {b : Sort v} [HasCoeT a b] : HasLiftT a b :=
 /- basic coercions -/
 
 instance coeBoolToProp : HasCoe Bool Prop :=
-⟨λ y, y = true⟩
+⟨fun y => y = true⟩
 
 /- Tactics such as the simplifier only unfold reducible constants when checking whether two terms are definitionally
    equal or a Term is a proposition. The motivation is performance.
@@ -146,7 +146,7 @@ instance coeBoolToProp : HasCoe Bool Prop :=
    Thus, we mark the following instance as @[reducible], otherwise `simp` will not visit `↑p` when simplifying `↑p -> q`.
 -/
 @[reducible] instance coeSortBool : HasCoeToSort Bool :=
-⟨Prop, λ y, y = true⟩
+⟨Prop, fun y => y = true⟩
 
 instance coeDecidableEq (x : Bool) : Decidable (coe x) :=
 inferInstanceAs (Decidable (x = true))
@@ -161,22 +161,22 @@ universes ua ua₁ ua₂ ub ub₁ ub₂
 /- Remark: we can't use [HasLiftT a₂ a₁] since it will produce non-termination whenever a type class resolution
    problem does not have a solution. -/
 instance liftFn {a₁ : Sort ua₁} {a₂ : Sort ua₂} {b₁ : Sort ub₁} {b₂ : Sort ub₂} [HasLift a₂ a₁] [HasLiftT b₁ b₂] : HasLift (a₁ → b₁) (a₂ → b₂) :=
-⟨λ f x, coe (f (coe x))⟩
+⟨fun f x => coe (f (coe x))⟩
 
 instance liftFnRange {a : Sort ua} {b₁ : Sort ub₁} {b₂ : Sort ub₂} [HasLiftT b₁ b₂] : HasLift (a → b₁) (a → b₂) :=
-⟨λ f x, coe (f x)⟩
+⟨fun f x => coe (f x)⟩
 
 instance liftFnDom {a₁ : Sort ua₁} {a₂ : Sort ua₂} {b : Sort ub} [HasLift a₂ a₁] : HasLift (a₁ → b) (a₂ → b) :=
-⟨λ f x, f (coe x)⟩
+⟨fun f x => f (coe x)⟩
 
 instance liftPair {a₁ : Type ua₁} {a₂ : Type ub₂} {b₁ : Type ub₁} {b₂ : Type ub₂} [HasLiftT a₁ a₂] [HasLiftT b₁ b₂] : HasLift (a₁ × b₁) (a₂ × b₂) :=
-⟨λ p, Prod.casesOn p (λ x y, (coe x,  coe y))⟩
+⟨fun p => Prod.casesOn p (fun x y => (coe x,  coe y))⟩
 
 instance liftPair₁ {a₁ : Type ua₁} {a₂ : Type ua₂} {b : Type ub} [HasLiftT a₁ a₂] : HasLift (a₁ × b) (a₂ × b) :=
-⟨λ p, Prod.casesOn p (λ x y, (coe x, y))⟩
+⟨fun p => Prod.casesOn p (fun x y => (coe x, y))⟩
 
 instance liftPair₂ {a : Type ua} {b₁ : Type ub₁} {b₂ : Type ub₂} [HasLiftT b₁ b₂] : HasLift (a × b₁) (a × b₂) :=
-⟨λ p, Prod.casesOn p (λ x y, (x,  coe y))⟩
+⟨fun p => Prod.casesOn p (fun x y => (x,  coe y))⟩
 
 instance liftList {a : Type u} {b : Type v} [HasLiftT a b] : HasLift (List a) (List b) :=
-⟨λ l, List.map (@coe a b _) l⟩
+⟨fun l => List.map (@coe a b _) l⟩
diff --git a/library/init/control/applicative.lean b/library/init/control/applicative.lean
index 71c7c2fe69..789e099539 100644
--- a/library/init/control/applicative.lean
+++ b/library/init/control/applicative.lean
@@ -29,6 +29,6 @@ class HasSeqRight (f : Type u → Type v) : Type (max (u+1) v) :=
 infixr *> := HasSeqRight.seqRight
 
 class Applicative (f : Type u → Type v) extends Functor f, HasPure f, HasSeq f, HasSeqLeft f, HasSeqRight f :=
-(map      := λ _ _ x y, pure x <*> y)
-(seqLeft  := λ α β a b, const β <$> a <*> b)
-(seqRight := λ α β a b, const α id <$> a <*> b)
+(map      := fun _ _ x y => pure x <*> y)
+(seqLeft  := fun α β a b => const β <$> a <*> b)
+(seqRight := fun α β a b => const α id <$> a <*> b)
diff --git a/library/init/control/estate.lean b/library/init/control/estate.lean
index 5ad9e8c02e..260b43aac1 100644
--- a/library/init/control/estate.lean
+++ b/library/init/control/estate.lean
@@ -53,49 +53,49 @@ namespace EState
 variables {ε σ α β : Type u}
 
 instance [Inhabited ε] : Inhabited (EState ε σ α) :=
-⟨λ r, match r with
+⟨fun r => match r with
       | ⟨Result.ok _ s, _⟩    := Result.error (default ε) s
       | ⟨Result.error _ _, h⟩ := unreachableError h⟩
 
 @[inline] protected def pure (a : α) : EState ε σ α :=
-λ r, match r with
+fun r => match r with
      | ⟨Result.ok _ s, _⟩    := Result.ok a s
      | ⟨Result.error _ _, h⟩ := unreachableError h
 
 @[inline] protected def set (s : σ) : EState ε σ PUnit :=
-λ r, match r with
+fun r => match r with
      | ⟨Result.ok _ _, _⟩    := Result.ok ⟨⟩ s
      | ⟨Result.error _ _, h⟩ := unreachableError h
 
 @[inline] protected def get : EState ε σ σ :=
-λ r, match r with
+fun r => match r with
      | ⟨Result.ok _ s, _⟩    := Result.ok s s
      | ⟨Result.error _ _, h⟩ := unreachableError h
 
 @[inline] protected def modify (f : σ → σ) : EState ε σ PUnit :=
-λ r, match r with
+fun r => match r with
      | ⟨Result.ok _ s, _⟩    := Result.ok ⟨⟩ (f s)
      | ⟨Result.error _ _, h⟩ := unreachableError h
 
 @[inline] protected def throw (e : ε) : EState ε σ α :=
-λ r, match r with
+fun r => match r with
      | ⟨Result.ok _ s, _⟩    := Result.error e s
      | ⟨Result.error _ _, h⟩ := unreachableError h
 
 @[inline] protected def catch (x : EState ε σ α) (handle : ε → EState ε σ α) : EState ε σ α :=
-λ r, match x r with
+fun r => match x r with
      | Result.error e s := handle e (resultOk.mk ⟨⟩ s)
      | ok               := ok
 
 @[inline] protected def orelse (x₁ x₂ : EState ε σ α) : EState ε σ α :=
-λ r, match x₁ r with
+fun r => match x₁ r with
      | Result.error _ s := x₂ (resultOk.mk ⟨⟩ s)
      | ok               := ok
 
 /-- Alternative orelse operator that allows to select which exception should be used.
     The default is to use the first exception since the standard `orelse` uses the second. -/
 @[inline] protected def orelse' (x₁ x₂ : EState ε σ α) (useFirstEx := true) : EState ε σ α :=
-λ r, match x₁ r with
+fun r => match x₁ r with
      | Result.error e₁ s₁ :=
        match x₂ (resultOk.mk ⟨⟩ s₁) with
        | Result.error e₂ s₂ := Result.error (if useFirstEx then e₁ else e₂) s₂
@@ -103,22 +103,22 @@ instance [Inhabited ε] : Inhabited (EState ε σ α) :=
      | ok                 := ok
 
 @[inline] def adaptExcept {ε' : Type u} [HasLift ε ε'] (x : EState ε σ α) : EState ε' σ α :=
-λ r, match x r with
+fun r => match x r with
      | Result.error e s := Result.error (lift e) s
      | Result.ok a s    := Result.ok a s
 
 @[inline] protected def bind (x : EState ε σ α) (f : α → EState ε σ β) : EState ε σ β :=
-λ r, match x r with
+fun r => match x r with
      | Result.ok a s    := f a (resultOk.mk ⟨⟩ s)
      | Result.error e s := Result.error e s
 
 @[inline] protected def map (f : α → β) (x : EState ε σ α) : EState ε σ β :=
-λ r, match x r with
+fun r => match x r with
      | Result.ok a s    := Result.ok (f a) s
      | Result.error e s := Result.error e s
 
 @[inline] protected def seqRight (x : EState ε σ α) (y : EState ε σ β) : EState ε σ β :=
-λ r, match x r with
+fun r => match x r with
      | Result.ok _ s    := y (resultOk.mk ⟨⟩ s)
      | Result.error e s := Result.error e s
 
diff --git a/library/init/control/except.lean b/library/init/control/except.lean
index 231b747ccd..7c0a763b87 100644
--- a/library/init/control/except.lean
+++ b/library/init/control/except.lean
@@ -94,7 +94,7 @@ ExceptT.mk $ pure (Except.ok a)
 ExceptT.mk $ ma >>= ExceptT.bindCont f
 
 @[inline] protected def map {α β : Type u} (f : α → β) (x : ExceptT ε m α) : ExceptT ε m β :=
-ExceptT.mk $ x >>= λ a, match a with
+ExceptT.mk $ x >>= fun a => match a with
   | (Except.ok a)    := pure $ Except.ok (f a)
   | (Except.error e) := pure $ Except.error e
 
@@ -102,24 +102,24 @@ ExceptT.mk $ x >>= λ a, match a with
 ExceptT.mk $ Except.ok <$> t
 
 instance exceptTOfExcept : HasMonadLift (Except ε) (ExceptT ε m) :=
-⟨λ α e, ExceptT.mk $ pure e⟩
+⟨fun α e => ExceptT.mk $ pure e⟩
 
 instance : HasMonadLift m (ExceptT ε m) :=
 ⟨@ExceptT.lift _ _ _⟩
 
 @[inline] protected def catch {α : Type u} (ma : ExceptT ε m α) (handle : ε → ExceptT ε m α) : ExceptT ε m α :=
-ExceptT.mk $ ma >>= λ res, match res with
+ExceptT.mk $ ma >>= fun res => match res with
  | Except.ok a    := pure (Except.ok a)
  | Except.error e := (handle e)
 
 instance (m') [Monad m'] : MonadFunctor m m' (ExceptT ε m) (ExceptT ε m') :=
-⟨λ _ f x, f x⟩
+⟨fun _ f x => f x⟩
 
 instance : Monad (ExceptT ε m) :=
 { pure := @ExceptT.pure _ _ _, bind := @ExceptT.bind _ _ _, map := @ExceptT.map _ _ _ }
 
 @[inline] protected def adapt {ε' α : Type u} (f : ε → ε') : ExceptT ε m α → ExceptT ε' m α :=
-λ x, ExceptT.mk $ Except.mapError f <$> x
+fun x => ExceptT.mk $ Except.mapError f <$> x
 end ExceptT
 
 /-- An implementation of [MonadError](https://hackage.haskell.org/package/mtl-2.2.2/docs/Control-Monad-Except.html#t:MonadError) -/
@@ -131,12 +131,12 @@ namespace MonadExcept
 variables {ε : Type u} {m : Type v → Type w}
 
 @[inline] protected def orelse [MonadExcept ε m] {α : Type v} (t₁ t₂ : m α) : m α :=
-catch t₁ $ λ _, t₂
+catch t₁ $ fun _ => t₂
 
 /-- Alternative orelse operator that allows to select which exception should be used.
     The default is to use the first exception since the standard `orelse` uses the second. -/
 @[inline] def orelse' [MonadExcept ε m] {α : Type v} (t₁ t₂ : m α) (useFirstEx := true) : m α :=
-catch t₁ $ λ e₁, catch t₂ $ λ e₂, throw (if useFirstEx then e₁ else e₂)
+catch t₁ $ fun e₁ => catch t₂ $ fun e₂ => throw (if useFirstEx then e₁ else e₂)
 
 @[inline] def liftExcept {ε' : Type u} [MonadExcept ε m] [HasLiftT ε' ε] [Monad m] {α : Type v} : Except ε' α → m α
 | (Except.error e) := throw (coe e)
@@ -146,11 +146,11 @@ end MonadExcept
 export MonadExcept (throw catch)
 
 instance (m : Type u → Type v) (ε : Type u) [Monad m] : MonadExcept ε (ExceptT ε m) :=
-{ throw := λ α e, ExceptT.mk $ pure (Except.error e),
+{ throw := fun α e => ExceptT.mk $ pure (Except.error e),
   catch := @ExceptT.catch ε _ _ }
 
 instance (ε) : MonadExcept ε (Except ε) :=
-{ throw := λ α, Except.error, catch := @Except.catch _ }
+{ throw := fun α => Except.error, catch := @Except.catch _ }
 
 /-- Adapt a Monad stack, changing its top-most error Type.
 
@@ -168,15 +168,15 @@ section
 variables {ε ε' : Type u} {m m' : Type u → Type v}
 
 instance monadExceptAdapterTrans {n n' : Type u → Type v} [MonadFunctor m m' n n'] [MonadExceptAdapter ε ε' m m'] : MonadExceptAdapter ε ε' n n' :=
-⟨λ α f, monadMap (λ α, (adaptExcept f : m α → m' α))⟩
+⟨fun α f => monadMap (fun α => (adaptExcept f : m α → m' α))⟩
 
 instance [Monad m] : MonadExceptAdapter ε ε' (ExceptT ε m) (ExceptT ε' m) :=
-⟨λ α, ExceptT.adapt⟩
+⟨fun α => ExceptT.adapt⟩
 end
 
-instance (ε m out) [MonadRun out m] : MonadRun (λ α, out (Except ε α)) (ExceptT ε m) :=
-⟨λ α, run⟩
+instance (ε m out) [MonadRun out m] : MonadRun (fun α => out (Except ε α)) (ExceptT ε m) :=
+⟨fun α => run⟩
 
 -- useful for implicit failures in do-notation
 instance (m : Type → Type) [Monad m] : MonadFail (ExceptT String m) :=
-⟨λ _, throw⟩
+⟨fun _ => throw⟩
diff --git a/library/init/control/functor.lean b/library/init/control/functor.lean
index b13c6f43c9..4ec5d9e8fc 100644
--- a/library/init/control/functor.lean
+++ b/library/init/control/functor.lean
@@ -10,15 +10,15 @@ universes u v
 
 class Functor (f : Type u → Type v) : Type (max (u+1) v) :=
 (map : Π {α β : Type u}, (α → β) → f α → f β)
-(mapConst : Π {α β : Type u}, α → f β → f α := λ α β, map ∘ const β)
+(mapConst : Π {α β : Type u}, α → f β → f α := fun α β => map ∘ const β)
 
 infixr <$> := Functor.map
 infixr <$  := Functor.mapConst
 
 @[reducible] def Functor.mapConstRev {f : Type u → Type v} [Functor f] {α β : Type u} : f β → α → f α :=
-λ a b, b <$ a
+fun a b => b <$ a
 infixr $>  := Functor.mapConstRev
 
 @[reducible] def Functor.mapRev {f : Type u → Type v} [Functor f] {α β : Type u} : f α → (α → β) → f β :=
-λ a f, f <$> a
+fun a f => f <$> a
 infixl <&> := Functor.mapRev
diff --git a/library/init/control/lift.lean b/library/init/control/lift.lean
index e8a0219a8f..22ae392579 100644
--- a/library/init/control/lift.lean
+++ b/library/init/control/lift.lean
@@ -34,10 +34,10 @@ export HasMonadLiftT (monadLift)
 ⟨monadLift⟩
 
 instance hasMonadLiftTTrans (m n o) [HasMonadLift n o] [HasMonadLiftT m n] : HasMonadLiftT m o :=
-⟨λ α ma, HasMonadLift.monadLift (monadLift ma : n α)⟩
+⟨fun α ma => HasMonadLift.monadLift (monadLift ma : n α)⟩
 
 instance hasMonadLiftTRefl (m) : HasMonadLiftT m m :=
-⟨λ α, id⟩
+⟨fun α => id⟩
 
 theorem monadLiftRefl {m : Type u → Type v} {α} : (monadLift : m α → m α) = id := rfl
 
@@ -63,10 +63,10 @@ export MonadFunctorT (monadMap)
 
 instance monadFunctorTTrans (m m' n n' o o') [MonadFunctor n n' o o'] [MonadFunctorT m m' n n'] :
   MonadFunctorT m m' o o' :=
-⟨λ α f, MonadFunctor.monadMap (λ β, (monadMap @f : n β → n' β))⟩
+⟨fun α f => MonadFunctor.monadMap (fun β => (monadMap @f : n β → n' β))⟩
 
 instance monadFunctorTRefl (m m') : MonadFunctorT m m' m m' :=
-⟨λ α f, f⟩
+⟨fun α f => f⟩
 
 theorem monadMapRefl {m m' : Type u → Type v} (f : ∀ {β}, m β → m' β) {α} : (monadMap @f : m α → m' α) = f := rfl
 
diff --git a/library/init/control/monad.lean b/library/init/control/monad.lean
index 69cc6367f6..1014534185 100644
--- a/library/init/control/monad.lean
+++ b/library/init/control/monad.lean
@@ -17,15 +17,15 @@ export HasBind (bind)
 infixr >>= := bind
 
 @[inline] def mcomp {α : Type u} {β δ : Type v} {m : Type v → Type w} [HasBind m] (f : α → m β) (g : β → m δ) : α → m δ :=
-λ a, f a >>= g
+fun a => f a >>= g
 
 infixr >=> := mcomp
 
 class Monad (m : Type u → Type v) extends Applicative m, HasBind m : Type (max (u+1) v) :=
-(map      := λ α β f x, x >>= pure ∘ f)
-(seq      := λ α β f x, f >>= (λ y, y <$> x))
-(seqLeft  := λ α β x y, x >>= λ a, y >>= λ _, pure a)
-(seqRight := λ α β x y, x >>= λ _, y)
+(map      := fun α β f x => x >>= pure ∘ f)
+(seq      := fun α β f x => f >>= (fun y => y <$> x))
+(seqLeft  := fun α β x y => x >>= fun a => y >>= fun _ => pure a)
+(seqRight := fun α β x y => x >>= fun _ => y)
 
 instance monadInhabited' {α : Type u} {m : Type u → Type v} [Monad m] : Inhabited (α → m α) :=
 ⟨pure⟩
diff --git a/library/init/control/monadfail.lean b/library/init/control/monadfail.lean
index 356efffc3f..50859b3bba 100644
--- a/library/init/control/monadfail.lean
+++ b/library/init/control/monadfail.lean
@@ -15,4 +15,4 @@ def matchFailed {α : Type u} {m : Type u → Type v} [MonadFail m] : m α :=
 MonadFail.fail "match failed"
 
 instance monadFailLift (m n : Type u → Type v) [HasMonadLift m n] [MonadFail m] [Monad n] : MonadFail n :=
-{ fail := λ α s, monadLift (MonadFail.fail s : m α) }
+{ fail := fun α s => monadLift (MonadFail.fail s : m α) }
diff --git a/library/init/control/option.lean b/library/init/control/option.lean
index f358f4c760..f2456ef807 100644
--- a/library/init/control/option.lean
+++ b/library/init/control/option.lean
@@ -49,18 +49,18 @@ namespace OptionT
   ⟨@OptionT.lift _ _⟩
 
   @[inline] protected def monadMap {m'} [Monad m'] {α} (f : ∀ {α}, m α → m' α) : OptionT m α → OptionT m' α :=
-  λ x, f x
+  fun x => f x
 
   instance (m') [Monad m'] : MonadFunctor m m' (OptionT m) (OptionT m') :=
-  ⟨λ α, OptionT.monadMap⟩
+  ⟨fun α => OptionT.monadMap⟩
 
   protected def catch (ma : OptionT m α) (handle : Unit → OptionT m α) : OptionT m α :=
   (do { some a ← ma | (handle ());
         pure a } : m (Option α))
 
   instance : MonadExcept Unit (OptionT m) :=
-  { throw := λ _ _, OptionT.fail, catch := @OptionT.catch _ _ }
+  { throw := fun _ _ => OptionT.fail, catch := @OptionT.catch _ _ }
 
-  instance (m out) [MonadRun out m] : MonadRun (λ α, out (Option α)) (OptionT m) :=
-  ⟨λ α, MonadRun.run⟩
+  instance (m out) [MonadRun out m] : MonadRun (fun α => out (Option α)) (OptionT m) :=
+  ⟨fun α => MonadRun.run⟩
 end OptionT
diff --git a/library/init/control/reader.lean b/library/init/control/reader.lean
index d9880b3d73..bd5251e5ec 100644
--- a/library/init/control/reader.lean
+++ b/library/init/control/reader.lean
@@ -27,34 +27,34 @@ variables {ρ : Type u} {m : Type u → Type v} [Monad m] {α β : Type u}
 pure
 
 @[inline] protected def pure (a : α) : ReaderT ρ m α :=
-λ r, pure a
+fun r => pure a
 
 @[inline] protected def bind (x : ReaderT ρ m α) (f : α → ReaderT ρ m β) : ReaderT ρ m β :=
-λ r, do a ← x r; f a r
+fun r => do a ← x r; f a r
 
 @[inline] protected def map (f : α → β) (x : ReaderT ρ m α) : ReaderT ρ m β :=
-λ r, f <$> x r
+fun r => f <$> x r
 
 instance : Monad (ReaderT ρ m) :=
 { pure := @ReaderT.pure _ _ _, bind := @ReaderT.bind _ _ _, map := @ReaderT.map _ _ _ }
 
 @[inline] protected def lift (a : m α) : ReaderT ρ m α :=
-λ r, a
+fun r => a
 
 instance (m) [Monad m] : HasMonadLift m (ReaderT ρ m) :=
 ⟨@ReaderT.lift ρ m _⟩
 
 instance (ρ m m') [Monad m] [Monad m'] : MonadFunctor m m' (ReaderT ρ m) (ReaderT ρ m') :=
-⟨λ _ f x, λ r, f (x r)⟩
+⟨fun _ f x r => f (x r)⟩
 
 @[inline] protected def adapt {ρ' : Type u} [Monad m] {α : Type u} (f : ρ' → ρ) : ReaderT ρ m α → ReaderT ρ' m α :=
-λ x r, x (f r)
+fun x r => x (f r)
 
 @[inline] protected def orelse [Alternative m] {α : Type u} (x₁ x₂ : ReaderT ρ m α) : ReaderT ρ m α :=
-λ s, x₁ s <|> x₂ s
+fun s => x₁ s <|> x₂ s
 
 @[inline] protected def failure [Alternative m] {α : Type u} : ReaderT ρ m α :=
-λ s, failure
+fun s => failure
 
 instance [Alternative m] : Alternative (ReaderT ρ m) :=
 { failure := @ReaderT.failure _ _ _ _,
@@ -62,8 +62,8 @@ instance [Alternative m] : Alternative (ReaderT ρ m) :=
   ..ReaderT.Monad }
 
 instance (ε) [Monad m] [MonadExcept ε m] : MonadExcept ε (ReaderT ρ m) :=
-{ throw := λ α, ReaderT.lift ∘ throw,
-  catch := λ α x c r, catch (x r) (λ e, (c e) r) }
+{ throw := fun α => ReaderT.lift ∘ throw,
+  catch := fun α x c r => catch (x r) (fun e => (c e) r) }
 end
 end ReaderT
 
@@ -108,14 +108,14 @@ section
 variables {ρ ρ' : Type u} {m m' : Type u → Type v}
 
 instance monadReaderAdapterTrans {n n' : Type u → Type v} [MonadFunctor m m' n n'] [MonadReaderAdapter ρ ρ' m m'] : MonadReaderAdapter ρ ρ' n n' :=
-⟨λ α f, monadMap (λ α, (adaptReader f : m α → m' α))⟩
+⟨fun α f => monadMap (fun α => (adaptReader f : m α → m' α))⟩
 
 instance [Monad m] : MonadReaderAdapter ρ ρ' (ReaderT ρ m) (ReaderT ρ' m) :=
-⟨λ α, ReaderT.adapt⟩
+⟨fun α => ReaderT.adapt⟩
 end
 
-instance (ρ : Type u) (m out) [MonadRun out m] : MonadRun (λ α, ρ → out α) (ReaderT ρ m) :=
-⟨λ α x, run ∘ x⟩
+instance (ρ : Type u) (m out) [MonadRun out m] : MonadRun (fun α => ρ → out α) (ReaderT ρ m) :=
+⟨fun α x => run ∘ x⟩
 
 class MonadReaderRunner (ρ : Type u) (m m' : Type u → Type u) :=
 (runReader {} {α : Type u} : m α → ρ → m' α)
@@ -125,8 +125,8 @@ section
 variables {ρ ρ' : Type u} {m m' : Type u → Type u}
 
 instance monadReaderRunnerTrans {n n' : Type u → Type u} [MonadFunctor m m' n n'] [MonadReaderRunner ρ m m'] : MonadReaderRunner ρ n n' :=
-⟨λ α x r, monadMap (λ α (y : m α), (runReader y r : m' α)) x⟩
+⟨fun α x r => monadMap (fun (α) (y : m α) => (runReader y r : m' α)) x⟩
 
 instance ReaderT.MonadStateRunner [Monad m] : MonadReaderRunner ρ (ReaderT ρ m) m :=
-⟨λ α x r, x r⟩
+⟨fun α x r => x r⟩
 end
diff --git a/library/init/control/state.lean b/library/init/control/state.lean
index eec4f7bdbf..d22faa94e3 100644
--- a/library/init/control/state.lean
+++ b/library/init/control/state.lean
@@ -27,22 +27,22 @@ variables {σ : Type u} {m : Type u → Type v}
 variables [Monad m] {α β : Type u}
 
 @[inline] protected def pure (a : α) : StateT σ m α :=
-λ s, pure (a, s)
+fun s => pure (a, s)
 
 @[inline] protected def bind (x : StateT σ m α) (f : α → StateT σ m β) : StateT σ m β :=
-λ s, do (a, s) ← x s; f a s
+fun s => do (a, s) ← x s; f a s
 
 @[inline] protected def map (f : α → β) (x : StateT σ m α) : StateT σ m β :=
-λ s, do (a, s) ← x s; pure (f a, s)
+fun s => do (a, s) ← x s; pure (f a, s)
 
 instance : Monad (StateT σ m) :=
 { pure := @StateT.pure _ _ _, bind := @StateT.bind _ _ _, map := @StateT.map _ _ _ }
 
 @[inline] protected def orelse [Alternative m] {α : Type u} (x₁ x₂ : StateT σ m α) : StateT σ m α :=
-λ s, x₁ s <|> x₂ s
+fun s => x₁ s <|> x₂ s
 
 @[inline] protected def failure [Alternative m] {α : Type u} : StateT σ m α :=
-λ s, failure
+fun s => failure
 
 instance [Alternative m] : Alternative (StateT σ m) :=
 { failure := @StateT.failure _ _ _ _,
@@ -50,33 +50,33 @@ instance [Alternative m] : Alternative (StateT σ m) :=
   .. StateT.Monad }
 
 @[inline] protected def get : StateT σ m σ :=
-λ s, pure (s, s)
+fun s => pure (s, s)
 
 @[inline] protected def set : σ → StateT σ m PUnit :=
-λ s' s, pure (⟨⟩, s')
+fun s' s => pure (⟨⟩, s')
 
 @[inline] protected def modify (f : σ → σ) : StateT σ m PUnit :=
-λ s, pure (⟨⟩, f s)
+fun s => pure (⟨⟩, f s)
 
 @[inline] protected def lift {α : Type u} (t : m α) : StateT σ m α :=
-λ s, do a ← t; pure (a, s)
+fun s => do a ← t; pure (a, s)
 
 instance : HasMonadLift m (StateT σ m) :=
 ⟨@StateT.lift σ m _⟩
 
 instance (σ m m') [Monad m] [Monad m'] : MonadFunctor m m' (StateT σ m) (StateT σ m') :=
-⟨λ _ f x s, f (x s)⟩
+⟨fun _ f x s => f (x s)⟩
 
 @[inline] protected def adapt {σ σ' σ'' α : Type u} {m : Type u → Type v} [Monad m] (split : σ → σ' × σ'')
         (join : σ' → σ'' → σ) (x : StateT σ' m α) : StateT σ m α :=
-λ st, do
+fun st => do
   let (st, ctx) := split st;
   (a, st') ← x st;
   pure (a, join st' ctx)
 
 instance (ε) [MonadExcept ε m] : MonadExcept ε (StateT σ m) :=
-{ throw := λ α, StateT.lift ∘ throw,
-  catch := λ α x c s, catch (x s) (λ e, c e s) }
+{ throw := fun α => StateT.lift ∘ throw,
+  catch := fun α x c s => catch (x s) (fun e => c e s) }
 end
 end StateT
 
@@ -106,8 +106,8 @@ do s ← get; modify f; pure s
 -- will be picked first
 instance monadStateTrans {n : Type u → Type w} [HasMonadLift m n] [MonadState σ m] : MonadState σ n :=
 { get := monadLift (MonadState.get : m _),
-  set := λ st, monadLift (MonadState.set st : m _),
-  modify := λ f, monadLift (MonadState.modify f : m _) }
+  set := fun st => monadLift (MonadState.set st : m _),
+  modify := fun f => monadLift (MonadState.modify f : m _) }
 
 instance [Monad m] : MonadState σ (StateT σ m) :=
 { get := StateT.get,
@@ -133,7 +133,7 @@ end
     Example:
     ```
     def withSnd {α σ σ' : Type} (snd : σ') : State (σ × σ') α → State σ α :=
-    adaptState (λ st, ((st, snd), ())) (λ ⟨st,snd⟩ _, st)
+    adaptState (fun st => ((st, snd), ())) (fun ⟨st,snd⟩ _ => st)
     ```
 
     Note: This class can be seen as a simplification of the more "principled" definition
@@ -142,10 +142,10 @@ end
     (map {} {α : Type u} : (∀ {m : Type u → Type u} [Monad m], StateT σ m α → StateT σ' m α) → n α → n' α)
     ```
     which better describes the intent of "we can map a `StateT` anywhere in the Monad stack".
-    If we look at the unfolded Type of the first argument `∀ m [Monad m], (σ → m (α × σ)) → σ' → m (α × σ')`, we see that it has the lens Type `∀ f [Functor f], (α → f α) → β → f β` with `f` specialized to `λ σ, m (α × σ)` (exercise: show that this is a lawful Functor). We can build all lenses we are insterested in from the functions `split` and `join` as
+    If we look at the unfolded Type of the first argument `∀ m [Monad m], (σ → m (α × σ)) → σ' → m (α × σ')`, we see that it has the lens Type `∀ f [Functor f], (α → f α) → β → f β` with `f` specialized to `fun σ => m (α × σ)` (exercise: show that this is a lawful Functor). We can build all lenses we are insterested in from the functions `split` and `join` as
     ```
-    λ f _ st, let (st, ctx) := split st in
-              (λ st', join st' ctx) <$> f st
+    fun f _ st => let (st, ctx) := split st in
+              (fun st' => join st' ctx) <$> f st
     ```
     -/
 class MonadStateAdapter (σ σ' : outParam (Type u)) (m m' : Type u → Type v) :=
@@ -156,18 +156,18 @@ section
 variables {σ σ' : Type u} {m m' : Type u → Type v}
 
 def MonadStateAdapter.adaptState' [MonadStateAdapter σ σ' m m'] {α : Type u} (toSigma : σ' → σ) (fromSigma : σ → σ') : m α → m' α :=
-adaptState (λ st, (toSigma st, PUnit.unit)) (λ st _, fromSigma st)
+adaptState (fun st => (toSigma st, PUnit.unit)) (fun st _ => fromSigma st)
 export MonadStateAdapter (adaptState')
 
 instance monadStateAdapterTrans {n n' : Type u → Type v} [MonadFunctor m m' n n'] [MonadStateAdapter σ σ' m m'] : MonadStateAdapter σ σ' n n' :=
-⟨λ σ'' α split join, monadMap (λ α, (adaptState split join : m α → m' α))⟩
+⟨fun σ'' α split join => monadMap (fun α => (adaptState split join : m α → m' α))⟩
 
 instance [Monad m] : MonadStateAdapter σ σ' (StateT σ m) (StateT σ' m) :=
-⟨λ σ'' α, StateT.adapt⟩
+⟨fun σ'' α => StateT.adapt⟩
 end
 
-instance (σ : Type u) (m out : Type u → Type v) [Functor m] [MonadRun out m] : MonadRun (λ α, σ → out α) (StateT σ m) :=
-⟨λ α x, run ∘ StateT.run' x⟩
+instance (σ : Type u) (m out : Type u → Type v) [Functor m] [MonadRun out m] : MonadRun (fun α => σ → out α) (StateT σ m) :=
+⟨fun α x => run ∘ StateT.run' x⟩
 
 class MonadStateRunner (σ : Type u) (m m' : Type u → Type u) :=
 (runState {} {α : Type u} : m α → σ → m' α)
@@ -177,8 +177,8 @@ section
 variables {σ σ' : Type u} {m m' : Type u → Type u}
 
 instance monadStateRunnerTrans {n n' : Type u → Type u} [MonadFunctor m m' n n'] [MonadStateRunner σ m m'] : MonadStateRunner σ n n' :=
-⟨λ α x s, monadMap (λ α (y : m α), (runState y s : m' α)) x⟩
+⟨fun α x s => monadMap (fun (α) (y : m α) => (runState y s : m' α)) x⟩
 
 instance StateT.MonadStateRunner [Monad m] : MonadStateRunner σ (StateT σ m) m :=
-⟨λ α x s, Prod.fst <$> x s⟩
+⟨fun α x s => Prod.fst <$> x s⟩
 end
diff --git a/library/init/core.lean b/library/init/core.lean
index 12ecf36a45..4be339480c 100644
--- a/library/init/core.lean
+++ b/library/init/core.lean
@@ -108,7 +108,7 @@ unsafe axiom lcUnreachable {α : Sort u} : α
 def inline {α : Sort u} (a : α) : α := a
 
 @[inline] def flip {α : Sort u} {β : Sort v} {φ : Sort w} (f : α → β → φ) : β → α → φ :=
-λ b a, f a b
+fun b a => f a b
 
 /-
 The kernel definitional equality test (t =?= s) has special support for idDelta applications.
@@ -159,16 +159,16 @@ attribute [extern cpp inline "lean::mk_thunk(#2)"] Thunk.mk
 
 @[noinline, extern cpp inline "lean::thunk_pure(#2)"]
 protected def Thunk.pure {α : Type u} (a : α) : Thunk α :=
-⟨λ _, a⟩
+⟨fun _ => a⟩
 @[noinline, extern cpp inline "lean::thunk_get_own(#2)"]
 protected def Thunk.get {α : Type u} (x : @& Thunk α) : α :=
 x.fn ()
 @[noinline, extern cpp inline "lean::thunk_map(#3, #4)"]
 protected def Thunk.map {α : Type u} {β : Type v} (f : α → β) (x : Thunk α) : Thunk β :=
-⟨λ _, f x.get⟩
+⟨fun _ => f x.get⟩
 @[noinline, extern cpp inline "lean::thunk_bind(#3, #4)"]
 protected def Thunk.bind {α : Type u} {β : Type v} (x : Thunk α) (f : α → Thunk β) : Thunk β :=
-⟨λ _, (f x.get).get⟩
+⟨fun _ => (f x.get).get⟩
 
 /- Remark: tasks have an efficient implementation in the runtime. -/
 structure Task (α : Type u) : Type u :=
@@ -178,16 +178,16 @@ attribute [extern cpp inline "lean::mk_task(#2)"] Task.mk
 
 @[noinline, extern cpp inline "lean::task_pure(#2)"]
 protected def Task.pure {α : Type u} (a : α) : Task α :=
-⟨λ _, a⟩
+⟨fun _ => a⟩
 @[noinline, extern cpp inline "lean::task_get(#2)"]
 protected def Task.get {α : Type u} (x : @& Task α) : α :=
 x.fn ()
 @[noinline, extern cpp inline "lean::task_map(#3, #4)"]
 protected def Task.map {α : Type u} {β : Type v} (f : α → β) (x : Task α) : Task β :=
-⟨λ _, f x.get⟩
+⟨fun _ => f x.get⟩
 @[noinline, extern cpp inline "lean::task_bind(#3, #4)"]
 protected def Task.bind {α : Type u} {β : Type v} (x : Task α) (f : α → Task β) : Task β :=
-⟨λ _, (f x.get).get⟩
+⟨fun _ => (f x.get).get⟩
 
 inductive True : Prop
 | intro : True
@@ -204,11 +204,11 @@ inductive Eq {α : Sort u} (a : α) : α → Prop
 
 @[elabAsEliminator, inline, reducible]
 def Eq.ndrec.{u1, u2} {α : Sort u2} {a : α} {C : α → Sort u1} (m : C a) {b : α} (h : Eq a b) : C b :=
-@Eq.rec α a (λ α _, C α) m b h
+@Eq.rec α a (fun α _ => C α) m b h
 
 @[elabAsEliminator, inline, reducible]
 def Eq.ndrecOn.{u1, u2} {α : Sort u2} {a : α} {C : α → Sort u1} {b : α} (h : Eq a b) (m : C a) : C b :=
-@Eq.rec α a (λ α _, C α) m b h
+@Eq.rec α a (fun α _ => C α) m b h
 
 /-
 Initialize the Quotient Module, which effectively adds the following definitions:
@@ -267,7 +267,7 @@ infix ≅ := Heq
 
 theorem eqOfHeq {α : Sort u} {a a' : α} (h : a ≅ a') : a = a' :=
 have ∀ (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a') (h₂ : α = α'), (Eq.recOn h₂ a : α') = a', from
-  λ (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a'), Heq.recOn h₁ (λ h₂ : α = α, rfl),
+  fun (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a') => Heq.recOn h₁ (fun h₂ : α = α => rfl),
 show (Eq.ndrecOn (Eq.refl α) a : α) = a', from
   this α a' h (Eq.refl α)
 
@@ -631,17 +631,18 @@ infix != := bne
 def implies (a b : Prop) := a → b
 
 theorem implies.trans {p q r : Prop} (h₁ : implies p q) (h₂ : implies q r) : implies p r :=
-λ hp, h₂ (h₁ hp)
+fun hp => h₂ (h₁ hp)
 
 def trivial : True := ⟨⟩
 
 @[macroInline] def False.elim {C : Sort u} (h : False) : C :=
-False.rec (λ _, C) h
+False.rec (fun _ => C) h
 
 @[macroInline] def absurd {a : Prop} {b : Sort v} (h₁ : a) (h₂ : ¬a) : b :=
 False.elim (h₂ h₁)
 
-theorem mt {a b : Prop} (h₁ : a → b) (h₂ : ¬b) : ¬a := λ ha : a, h₂ (h₁ ha)
+theorem mt {a b : Prop} (h₁ : a → b) (h₂ : ¬b) : ¬a :=
+fun ha => h₂ (h₁ ha)
 
 theorem notFalse : ¬False := id
 
@@ -654,7 +655,7 @@ theorem id.def {α : Sort u} (a : α) : id a = a := rfl
 Eq.recOn h₁ h₂
 
 @[macroInline] def Eq.mpr {α β : Sort u} : (α = β) → β → α :=
-λ h₁ h₂, Eq.recOn (Eq.symm h₁) h₂
+fun h₁ h₂ => Eq.recOn (Eq.symm h₁) h₂
 
 @[elabAsEliminator]
 theorem Eq.substr {α : Sort u} {p : α → Prop} {a b : α} (h₁ : b = a) (h₂ : p a) : p b :=
@@ -679,7 +680,7 @@ theorem ofEqTrue {p : Prop} (h : p = True) : p :=
 h.symm ▸ trivial
 
 theorem notOfEqFalse {p : Prop} (h : p = False) : ¬p :=
-λ hp, h ▸ hp
+fun hp => h ▸ hp
 
 @[macroInline] def cast {α β : Sort u} (h : α = β) (a : α) : β :=
 Eq.rec a h
@@ -704,15 +705,15 @@ theorem Ne.elim (h : a ≠ b) : a = b → False := h
 theorem Ne.irrefl (h : a ≠ a) : False := h rfl
 
 theorem Ne.symm (h : a ≠ b) : b ≠ a :=
-λ (h₁ : b = a), h (h₁.symm)
+fun h₁ => h (h₁.symm)
 
 theorem falseOfNe : a ≠ a → False := Ne.irrefl
 
 theorem neFalseOfSelf : p → p ≠ False :=
-λ (hp : p) (Heq : p = False), Heq ▸ hp
+fun (hp : p) (Heq : p = False) => Heq ▸ hp
 
 theorem neTrueOfNot : ¬p → p ≠ True :=
-λ (hnp : ¬p) (Heq : p = True), (Heq ▸ hnp) trivial
+fun (hnp : ¬p) (Heq : p = True) => (Heq ▸ hnp) trivial
 
 theorem trueNeFalse : ¬True = False :=
 neFalseOfSelf trivial
@@ -731,11 +732,11 @@ variables {α β φ : Sort u} {a a' : α} {b b' : β} {c : φ}
 
 @[elabAsEliminator]
 theorem Heq.ndrec.{u1, u2} {α : Sort u2} {a : α} {C : Π {β : Sort u2}, β → Sort u1} (m : C a) {β : Sort u2} {b : β} (h : a ≅ b) : C b :=
-@Heq.rec α a (λ β b _, C b) m β b h
+@Heq.rec α a (fun β b _ => C b) m β b h
 
 @[elabAsEliminator]
 theorem Heq.ndrecOn.{u1, u2} {α : Sort u2} {a : α} {C : Π {β : Sort u2}, β → Sort u1} {β : Sort u2} {b : β} (h : a ≅ b) (m : C a) : C b :=
-@Heq.rec α a (λ β b _, C b) m β b h
+@Heq.rec α a (fun β b _ => C b) m β b h
 
 theorem Heq.elim {α : Sort u} {a : α} {p : α → Sort v} {b : α} (h₁ : a ≅ b) (h₂ : p a) : p b :=
 Eq.recOn (eqOfHeq h₁) h₂
@@ -777,7 +778,7 @@ theorem And.elim (h₁ : a ∧ b) (h₂ : a → b → c) : c :=
 And.rec h₂ h₁
 
 theorem And.swap : a ∧ b → b ∧ a :=
-λ ⟨ha, hb⟩, ⟨hb, ha⟩
+fun ⟨ha, hb⟩ => ⟨hb, ha⟩
 
 def And.symm := @And.swap
 
@@ -800,18 +801,18 @@ theorem Iff.left : (a ↔ b) → a → b := Iff.mp
 theorem Iff.right : (a ↔ b) → b → a := Iff.mpr
 
 theorem iffIffImpliesAndImplies (a b : Prop) : (a ↔ b) ↔ (a → b) ∧ (b → a) :=
-Iff.intro (λ h, And.intro h.mp h.mpr) (λ h, Iff.intro h.left h.right)
+Iff.intro (fun h => And.intro h.mp h.mpr) (fun h => Iff.intro h.left h.right)
 
 theorem Iff.refl (a : Prop) : a ↔ a :=
-Iff.intro (λ h, h) (λ h, h)
+Iff.intro (fun h => h) (fun h => h)
 
 theorem Iff.rfl {a : Prop} : a ↔ a :=
 Iff.refl a
 
 theorem Iff.trans (h₁ : a ↔ b) (h₂ : b ↔ c) : a ↔ c :=
 Iff.intro
-  (λ ha, Iff.mp h₂ (Iff.mp h₁ ha))
-  (λ hc, Iff.mpr h₁ (Iff.mpr h₂ hc))
+  (fun ha => Iff.mp h₂ (Iff.mp h₁ ha))
+  (fun hc => Iff.mpr h₁ (Iff.mpr h₂ hc))
 
 theorem Iff.symm (h : a ↔ b) : b ↔ a :=
 Iff.intro (Iff.right h) (Iff.left h)
@@ -823,14 +824,14 @@ theorem Eq.toIff {a b : Prop} (h : a = b) : a ↔ b :=
 Eq.recOn h Iff.rfl
 
 theorem neqOfNotIff {a b : Prop} : ¬(a ↔ b) → a ≠ b :=
-λ h₁ h₂,
+fun h₁ h₂ =>
 have a ↔ b, from Eq.subst h₂ (Iff.refl a),
 absurd this h₁
 
 theorem notIffNotOfIff (h₁ : a ↔ b) : ¬a ↔ ¬b :=
 Iff.intro
- (λ (hna : ¬ a) (hb : b), hna (Iff.right h₁ hb))
- (λ (hnb : ¬ b) (ha : a), hnb (Iff.left h₁ ha))
+ (fun (hna : ¬ a) (hb : b) => hna (Iff.right h₁ hb))
+ (fun (hnb : ¬ b) (ha : a) => hnb (Iff.left h₁ ha))
 
 theorem ofIffTrue (h : a ↔ True) : a :=
 Iff.mp (Iff.symm h) trivial
@@ -839,14 +840,14 @@ theorem notOfIffFalse : (a ↔ False) → ¬a := Iff.mp
 
 theorem iffTrueIntro (h : a) : a ↔ True :=
 Iff.intro
-  (λ hl, trivial)
-  (λ hr, h)
+  (fun hl => trivial)
+  (fun hr => h)
 
 theorem iffFalseIntro (h : ¬a) : a ↔ False :=
-Iff.intro h (False.rec (λ _, a))
+Iff.intro h (False.rec (fun _ => a))
 
 theorem notNotIntro (ha : a) : ¬¬a :=
-λ hna : ¬a, hna ha
+fun hna => hna ha
 
 theorem notTrue : (¬ True) ↔ False :=
 iffFalseIntro (notNotIntro trivial)
@@ -854,38 +855,38 @@ iffFalseIntro (notNotIntro trivial)
 /- or resolution rulses -/
 
 theorem resolveLeft {a b : Prop} (h : a ∨ b) (na : ¬ a) : b :=
-Or.elim h (λ ha, absurd ha na) id
+Or.elim h (fun ha => absurd ha na) id
 
 theorem negResolveLeft {a b : Prop} (h : ¬ a ∨ b) (ha : a) : b :=
-Or.elim h (λ na, absurd ha na) id
+Or.elim h (fun na => absurd ha na) id
 
 theorem resolveRight {a b : Prop} (h : a ∨ b) (nb : ¬ b) : a :=
-Or.elim h id (λ hb, absurd hb nb)
+Or.elim h id (fun hb => absurd hb nb)
 
 theorem negResolveRight {a b : Prop} (h : a ∨ ¬ b) (hb : b) : a :=
-Or.elim h id (λ nb, absurd hb nb)
+Or.elim h id (fun nb => absurd hb nb)
 
 /- Exists -/
 
 theorem Exists.elim {α : Sort u} {p : α → Prop} {b : Prop}
-   (h₁ : Exists (λ x, p x)) (h₂ : ∀ (a : α), p a → b) : b :=
+   (h₁ : Exists (fun x => p x)) (h₂ : ∀ (a : α), p a → b) : b :=
 Exists.rec h₂ h₁
 
 /- Decidable -/
 
 @[inlineIfReduce, nospecialize] def Decidable.decide (p : Prop) [h : Decidable p] : Bool :=
-Decidable.casesOn h (λ h₁, false) (λ h₂, true)
+Decidable.casesOn h (fun h₁ => false) (fun h₂ => true)
 
 export Decidable (isTrue isFalse decide)
 
 instance beqOfEq {α : Type u} [DecidableEq α] : HasBeq α :=
-⟨λ a b, decide (a = b)⟩
+⟨fun a b => decide (a = b)⟩
 
 theorem decideTrueEqTrue (h : Decidable True) : @decide True h = true :=
-Decidable.casesOn h (λ h, False.elim (Iff.mp notTrue h)) (λ _, rfl)
+Decidable.casesOn h (fun h => False.elim (Iff.mp notTrue h)) (fun _ => rfl)
 
 theorem decideFalseEqFalse (h : Decidable False) : @decide False h = false :=
-Decidable.casesOn h (λ h, rfl) (λ h, False.elim h)
+Decidable.casesOn h (fun h => rfl) (fun h => False.elim h)
 
 instance : Decidable True :=
 isTrue trivial
@@ -896,23 +897,23 @@ isFalse notFalse
 -- We use "dependent" if-then-else to be able to communicate the if-then-else condition
 -- to the branches
 @[macroInline] def dite (c : Prop) [h : Decidable c] {α : Sort u} : (c → α) → (¬ c → α) → α :=
-λ t e, Decidable.casesOn h e t
+fun t e => Decidable.casesOn h e t
 
 /- if-then-else -/
 
 @[macroInline] def ite (c : Prop) [h : Decidable c] {α : Sort u} (t e : α) : α :=
-Decidable.casesOn h (λ hnc, e) (λ hc, t)
+Decidable.casesOn h (fun hnc => e) (fun hc => t)
 
 namespace Decidable
 variables {p q : Prop}
 
 def recOnTrue [h : Decidable p] {h₁ : p → Sort u} {h₂ : ¬p → Sort u} (h₃ : p) (h₄ : h₁ h₃)
     : (Decidable.recOn h h₂ h₁ : Sort u) :=
-Decidable.casesOn h (λ h, False.rec _ (h h₃)) (λ h, h₄)
+Decidable.casesOn h (fun h => False.rec _ (h h₃)) (fun h => h₄)
 
 def recOnFalse [h : Decidable p] {h₁ : p → Sort u} {h₂ : ¬p → Sort u} (h₃ : ¬p) (h₄ : h₂ h₃)
     : (Decidable.recOn h h₂ h₁ : Sort u) :=
-Decidable.casesOn h (λ h, h₄) (λ h, False.rec _ (h₃ h))
+Decidable.casesOn h (fun h => h₄) (fun h => False.rec _ (h₃ h))
 
 @[macroInline] def byCases {q : Sort u} [s : Decidable p] (h1 : p → q) (h2 : ¬p → q) : q :=
 match s with
@@ -923,21 +924,21 @@ theorem em (p : Prop) [Decidable p] : p ∨ ¬p :=
 byCases Or.inl Or.inr
 
 theorem byContradiction [Decidable p] (h : ¬p → False) : p :=
-byCases id (λ np : ¬p, False.elim (h np))
+byCases id (fun np => False.elim (h np))
 
 theorem ofNotNot [Decidable p] : ¬ ¬ p → p :=
-λ hnn, byContradiction (λ hn, absurd hn hnn)
+fun hnn => byContradiction (fun hn => absurd hn hnn)
 
 theorem notNotIff (p) [Decidable p] : (¬ ¬ p) ↔ p :=
 Iff.intro ofNotNot notNotIntro
 
 theorem notAndIffOrNot (p q : Prop) [d₁ : Decidable p] [d₂ : Decidable q] : ¬ (p ∧ q) ↔ ¬ p ∨ ¬ q :=
 Iff.intro
-(λ h, match d₁, d₂ with
+(fun h => match d₁, d₂ with
       | isTrue h₁,  isTrue h₂  := absurd (And.intro h₁ h₂) h
       | _,           isFalse h₂ := Or.inr h₂
       | isFalse h₁, _           := Or.inl h₁)
-(λ h ⟨hp, hq⟩, Or.elim h (λ h, h hp) (λ h, h hq))
+(fun (h) ⟨hp, hq⟩ => Or.elim h (fun h => h hp) (fun h => h hq))
 
 end Decidable
 
@@ -957,51 +958,51 @@ variables {p q : Prop}
 @[macroInline] instance [Decidable p] [Decidable q] : Decidable (p ∧ q) :=
 if hp : p then
   if hq : q then isTrue ⟨hp, hq⟩
-  else isFalse (λ h : p ∧ q, hq (And.right h))
-else isFalse (λ h : p ∧ q, hp (And.left h))
+  else isFalse (fun h => hq (And.right h))
+else isFalse (fun h => hp (And.left h))
 
 @[macroInline] instance [Decidable p] [Decidable q] : Decidable (p ∨ q) :=
 if hp : p then isTrue (Or.inl hp) else
   if hq : q then isTrue (Or.inr hq) else
-    isFalse (λ h, Or.elim h hp hq)
+    isFalse (fun h => Or.elim h hp hq)
 
 instance [Decidable p] : Decidable (¬p) :=
 if hp : p then isFalse (absurd hp) else isTrue hp
 
 @[macroInline] instance implies.Decidable [Decidable p] [Decidable q] : Decidable (p → q) :=
 if hp : p then
-  if hq : q then isTrue (λ h, hq)
-  else isFalse (λ h : p → q, absurd (h hp) hq)
-else isTrue (λ h, absurd h hp)
+  if hq : q then isTrue (fun h => hq)
+  else isFalse (fun h => absurd (h hp) hq)
+else isTrue (fun h => absurd h hp)
 
 instance [Decidable p] [Decidable q] : Decidable (p ↔ q) :=
 if hp : p then
-  if hq : q then isTrue ⟨λ_, hq, λ_, hp⟩
-  else isFalse $ λh, hq (h.1 hp)
+  if hq : q then isTrue ⟨fun _ => hq, fun _ => hp⟩
+  else isFalse $ fun h => hq (h.1 hp)
 else
-  if hq : q then isFalse $ λh, hp (h.2 hq)
-  else isTrue $ ⟨λh, absurd h hp, λh, absurd h hq⟩
+  if hq : q then isFalse $ fun h => hp (h.2 hq)
+  else isTrue $ ⟨fun h => absurd h hp, fun h => absurd h hq⟩
 
 instance [Decidable p] [Decidable q] : Decidable (Xor p q) :=
 if hp : p then
-  if hq : q then isFalse (λ h, Or.elim h (λ ⟨_, h⟩, h hq : ¬(p ∧ ¬ q)) (λ ⟨_, h⟩, h hp : ¬(q ∧ ¬ p)))
+  if hq : q then isFalse (fun h => Or.elim h (fun ⟨_, h⟩ => h hq : ¬(p ∧ ¬ q)) (fun ⟨_, h⟩ => h hp : ¬(q ∧ ¬ p)))
   else isTrue $ Or.inl ⟨hp, hq⟩
 else
   if hq : q then isTrue $ Or.inr ⟨hq, hp⟩
-  else isFalse (λ h, Or.elim h (λ ⟨h, _⟩, hp h : ¬(p ∧ ¬ q)) (λ ⟨h, _⟩, hq h : ¬(q ∧ ¬ p)))
+  else isFalse (fun h => Or.elim h (fun ⟨h, _⟩ => hp h : ¬(p ∧ ¬ q)) (fun ⟨h, _⟩ => hq h : ¬(q ∧ ¬ p)))
 
 end
 
 @[inline] instance {α : Sort u} [DecidableEq α] (a b : α) : Decidable (a ≠ b) :=
 match decEq a b with
-| isTrue h := isFalse $ λ h', absurd h h'
+| isTrue h := isFalse $ fun h' => absurd h h'
 | isFalse h := isTrue h
 
 theorem Bool.falseNeTrue (h : false = true) : False :=
 Bool.noConfusion h
 
 instance : DecidableEq Bool :=
-{decEq := λ a b, match a, b with
+{decEq := fun a b => match a, b with
  | false, false := isTrue rfl
  | false, true  := isFalse Bool.falseNeTrue
  | true, false  := isFalse (Ne.symm Bool.falseNeTrue)
@@ -1020,7 +1021,7 @@ match h with
 | (isFalse hnc) := rfl
 
 -- Remark: dite and ite are "defally equal" when we ignore the proofs.
-theorem difEqIf (c : Prop) [h : Decidable c] {α : Sort u} (t : α) (e : α) : dite c (λ h, t) (λ h, e) = ite c t e :=
+theorem difEqIf (c : Prop) [h : Decidable c] {α : Sort u} (t : α) (e : α) : dite c (fun h => t) (fun h => e) = ite c t e :=
 match h with
 | (isTrue hc)   := rfl
 | (isFalse hnc) := rfl
@@ -1078,10 +1079,10 @@ instance Prop.Inhabited : Inhabited Prop :=
 ⟨True⟩
 
 instance Fun.Inhabited (α : Sort u) {β : Sort v} [h : Inhabited β] : Inhabited (α → β) :=
-Inhabited.casesOn h (λ b, ⟨λ a, b⟩)
+Inhabited.casesOn h (fun b => ⟨fun a => b⟩)
 
 instance Pi.Inhabited (α : Sort u) {β : α → Sort v} [Π x, Inhabited (β x)] : Inhabited (Π x, β x) :=
-⟨λ a, default (β a)⟩
+⟨fun a => default (β a)⟩
 
 instance : Inhabited Bool := ⟨false⟩
 
@@ -1102,7 +1103,7 @@ Nonempty.rec h₂ h₁
 instance nonemptyOfInhabited {α : Sort u} [Inhabited α] : Nonempty α :=
 ⟨default α⟩
 
-theorem nonemptyOfExists {α : Sort u} {p : α → Prop} : Exists (λ x, p x) → Nonempty α
+theorem nonemptyOfExists {α : Sort u} {p : α → Prop} : Exists (fun x => p x) → Nonempty α
 | ⟨w, h⟩ := ⟨w⟩
 
 /- Subsingleton -/
@@ -1111,22 +1112,22 @@ class inductive Subsingleton (α : Sort u) : Prop
 | intro (h : ∀ a b : α, a = b) : Subsingleton
 
 protected def Subsingleton.elim {α : Sort u} [h : Subsingleton α] : ∀ (a b : α), a = b :=
-Subsingleton.casesOn h (λ p, p)
+Subsingleton.casesOn h (fun p => p)
 
 protected def Subsingleton.helim {α β : Sort u} [h : Subsingleton α] (h : α = β) : ∀ (a : α) (b : β), a ≅ b :=
-Eq.recOn h (λ a b : α, heqOfEq (Subsingleton.elim a b))
+Eq.recOn h (fun a b => heqOfEq (Subsingleton.elim a b))
 
 instance subsingletonProp (p : Prop) : Subsingleton p :=
-⟨λ a b, proofIrrel a b⟩
+⟨fun a b => proofIrrel a b⟩
 
 instance (p : Prop) : Subsingleton (Decidable p) :=
-Subsingleton.intro (λ d₁,
+Subsingleton.intro (fun d₁ =>
   match d₁ with
-  | (isTrue t₁) := (λ d₂,
+  | (isTrue t₁) := (fun d₂ =>
     match d₂ with
     | (isTrue t₂) := Eq.recOn (proofIrrel t₁ t₂) rfl
     | (isFalse f₂) := absurd t₁ f₂)
-  | (isFalse f₁) := (λ d₂,
+  | (isFalse f₁) := (fun d₂ =>
     match d₂ with
     | (isTrue t₂) := absurd t₂ f₁
     | (isFalse f₂) := Eq.recOn (proofIrrel f₁ f₂) rfl))
@@ -1158,18 +1159,18 @@ def Irreflexive := ∀ x, ¬ r x x
 
 def AntiSymmetric := ∀ {x y}, r x y → r y x → x = y
 
-def emptyRelation := λ a₁ a₂ : α, False
+def emptyRelation := fun a₁ a₂ : α => False
 
 def Subrelation (q r : β → β → Prop) := ∀ {x y}, q x y → r x y
 
 def InvImage (f : α → β) : α → α → Prop :=
-λ a₁ a₂, r (f a₁) (f a₂)
+fun a₁ a₂ => r (f a₁) (f a₂)
 
 theorem InvImage.Transitive (f : α → β) (h : Transitive r) : Transitive (InvImage r f) :=
-λ (a₁ a₂ a₃ : α) (h₁ : InvImage r f a₁ a₂) (h₂ : InvImage r f a₂ a₃), h h₁ h₂
+fun (a₁ a₂ a₃ : α) (h₁ : InvImage r f a₁ a₂) (h₂ : InvImage r f a₂ a₃) => h h₁ h₂
 
 theorem InvImage.Irreflexive (f : α → β) (h : Irreflexive r) : Irreflexive (InvImage r f) :=
-λ (a : α) (h₁ : InvImage r f a a), h (f a) h₁
+fun (a : α) (h₁ : InvImage r f a a) => h (f a) h₁
 
 inductive TC {α : Sort u} (r : α → α → Prop) : α → α → Prop
 | base  : ∀ a b, r a b → TC a b
@@ -1180,7 +1181,7 @@ theorem TC.ndrec.{u1, u2} {α : Sort u} {r : α → α → Prop} {C : α → α
                 (m₁ : ∀ (a b : α), r a b → C a b)
                 (m₂ : ∀ (a b c : α), TC r a b → TC r b c → C a b → C b c → C a c)
                 {a b : α} (h : TC r a b) : C a b :=
-@TC.rec α r (λ a b _, C a b) m₁ m₂ a b h
+@TC.rec α r (fun a b _ => C a b) m₁ m₂ a b h
 
 @[elabAsEliminator]
 theorem TC.ndrecOn.{u1, u2} {α : Sort u} {r : α → α → Prop} {C : α → α → Prop}
@@ -1188,7 +1189,7 @@ theorem TC.ndrecOn.{u1, u2} {α : Sort u} {r : α → α → Prop} {C : α → 
                 (m₁ : ∀ (a b : α), r a b → C a b)
                 (m₂ : ∀ (a b c : α), TC r a b → TC r b c → C a b → C b c → C a c)
                 : C a b :=
-@TC.rec α r (λ a b _, C a b) m₁ m₂ a b h
+@TC.rec α r (fun a b _ => C a b) m₁ m₂ a b h
 
 end relation
 
@@ -1202,11 +1203,11 @@ def RightCommutative (h : β → α → β) := ∀ b a₁ a₂, h (h b a₁) a
 def LeftCommutative  (h : α → β → β) := ∀ a₁ a₂ b, h a₁ (h a₂ b) = h a₂ (h a₁ b)
 
 theorem leftComm : Commutative f → Associative f → LeftCommutative f :=
-λ hcomm hassoc, λ a b c,
+fun hcomm hassoc a b c =>
 ((Eq.symm (hassoc a b c)).trans (hcomm a b ▸ rfl : f (f a b) c = f (f b a) c)).trans (hassoc b a c)
 
 theorem rightComm : Commutative f → Associative f → RightCommutative f :=
-λ hcomm hassoc, λ a b c,
+fun hcomm hassoc a b c =>
 ((hassoc a b c).trans (hcomm b c ▸ rfl : f a (f b c) = f a (f c b))).trans (Eq.symm (hassoc a c b))
 
 end Binary
@@ -1214,7 +1215,7 @@ end Binary
 /- Subtype -/
 
 namespace Subtype
-def existsOfSubtype {α : Type u} {p : α → Prop} : { x // p x } → Exists (λ x, p x)
+def existsOfSubtype {α : Type u} {p : α → Prop} : { x // p x } → Exists (fun x => p x)
 | ⟨a, h⟩ := ⟨a, h⟩
 
 variables {α : Type u} {p : α → Prop}
@@ -1232,9 +1233,9 @@ instance {α : Type u} {p : α → Prop} {a : α} (h : p a) : Inhabited {x // p
 ⟨⟨a, h⟩⟩
 
 instance {α : Type u} {p : α → Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
-{decEq := λ ⟨a, h₁⟩ ⟨b, h₂⟩,
+{decEq := fun ⟨a, h₁⟩ ⟨b, h₂⟩ =>
   if h : a = b then isTrue (Subtype.eq h)
-  else isFalse (λ h', Subtype.noConfusion h' (λ h', absurd h' h))}
+  else isFalse (fun h' => Subtype.noConfusion h' (fun h' => absurd h' h))}
 end Subtype
 
 /- Sum -/
@@ -1251,14 +1252,14 @@ instance Sum.inhabitedRight [h : Inhabited β] : Inhabited (α ⊕ β) :=
 ⟨Sum.inr (default β)⟩
 
 instance {α : Type u} {β : Type v} [DecidableEq α] [DecidableEq β] : DecidableEq (α ⊕ β) :=
-{decEq := λ a b,
+{decEq := fun a b =>
  match a, b with
  | (Sum.inl a), (Sum.inl b) := if h : a = b then isTrue (h ▸ rfl)
-                               else isFalse (λ h', Sum.noConfusion h' (λ h', absurd h' h))
+                               else isFalse (fun h' => Sum.noConfusion h' (fun h' => absurd h' h))
  | (Sum.inr a), (Sum.inr b) := if h : a = b then isTrue (h ▸ rfl)
-                               else isFalse (λ h', Sum.noConfusion h' (λ h', absurd h' h))
- | (Sum.inr a), (Sum.inl b) := isFalse (λ h, Sum.noConfusion h)
- | (Sum.inl a), (Sum.inr b) := isFalse (λ h, Sum.noConfusion h)}
+                               else isFalse (fun h' => Sum.noConfusion h' (fun h' => absurd h' h))
+ | (Sum.inr a), (Sum.inl b) := isFalse (fun h => Sum.noConfusion h)
+ | (Sum.inl a), (Sum.inr b) := isFalse (fun h => Sum.noConfusion h)}
 end
 
 /- Product -/
@@ -1270,22 +1271,22 @@ instance [Inhabited α] [Inhabited β] : Inhabited (Prod α β) :=
 ⟨(default α, default β)⟩
 
 instance [DecidableEq α] [DecidableEq β] : DecidableEq (α × β) :=
-{decEq := λ ⟨a, b⟩ ⟨a', b'⟩,
+{decEq := fun ⟨a, b⟩ ⟨a', b'⟩ =>
   match (decEq a a') with
   | (isTrue e₁) :=
     (match (decEq b b') with
      | (isTrue e₂)  := isTrue (Eq.recOn e₁ (Eq.recOn e₂ rfl))
-     | (isFalse n₂) := isFalse (λ h, Prod.noConfusion h (λ e₁' e₂', absurd e₂' n₂)))
-  | (isFalse n₁) := isFalse (λ h, Prod.noConfusion h (λ e₁' e₂', absurd e₁' n₁))}
+     | (isFalse n₂) := isFalse (fun h => Prod.noConfusion h (fun e₁' e₂' => absurd e₂' n₂)))
+  | (isFalse n₁) := isFalse (fun h => Prod.noConfusion h (fun e₁' e₂' => absurd e₁' n₁))}
 
 instance [HasLess α] [HasLess β] : HasLess (α × β) :=
-⟨λ s t, s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)⟩
+⟨fun s t => s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)⟩
 
 instance prodHasDecidableLt
          [HasLess α] [HasLess β] [DecidableEq α] [DecidableEq β]
          [Π a b : α, Decidable (a < b)] [Π a b : β, Decidable (a < b)]
          : Π s t : α × β, Decidable (s < t) :=
-λ t s, Or.Decidable
+fun t s => Or.Decidable
 
 theorem Prod.ltDef [HasLess α] [HasLess β] (s t : α × β) : (s < t) = (s.1 < t.1 ∨ (s.1 = t.1 ∧ s.2 < t.2)) :=
 rfl
@@ -1300,13 +1301,13 @@ def Prod.map.{u₁, u₂, v₁, v₂} {α₁ : Type u₁} {α₂ : Type u₂} {
 -- notation `Σ` binders `, ` r:(scoped p, Sigma p) := r
 -- notation `Σ'` binders `, ` r:(scoped p, PSigma p) := r
 
-theorem exOfPsig {α : Type u} {p : α → Prop} : (PSigma (λ x, p x)) → Exists (λ x, p x)
+theorem exOfPsig {α : Type u} {p : α → Prop} : (PSigma (fun x => p x)) → Exists (fun x => p x)
 | ⟨x, hx⟩ := ⟨x, hx⟩
 
 section
 variables {α : Type u} {β : α → Type v}
 
-protected theorem Sigma.eq : ∀ {p₁ p₂ : Sigma (λ a : α, β a)} (h₁ : p₁.1 = p₂.1), (Eq.recOn h₁ p₁.2 : β p₂.1) = p₂.2 → p₁ = p₂
+protected theorem Sigma.eq : ∀ {p₁ p₂ : Sigma (fun a => β a)} (h₁ : p₁.1 = p₂.1), (Eq.recOn h₁ p₁.2 : β p₂.1) = p₂.2 → p₁ = p₂
 | ⟨a, b⟩ ⟨.(a), .(b)⟩ rfl rfl := rfl
 end
 
@@ -1332,7 +1333,7 @@ instance : Inhabited PUnit :=
 ⟨⟨⟩⟩
 
 instance : DecidableEq PUnit :=
-{decEq := λ a b, isTrue (punitEq a b)}
+{decEq := fun a b => isTrue (punitEq a b)}
 
 /- Setoid -/
 
@@ -1393,8 +1394,8 @@ lift f c q
 protected theorem inductionOn {α : Sort u} {r : α → α → Prop} {β : Quot r → Prop} (q : Quot r) (h : ∀ a, β (Quot.mk r a)) : β q :=
 ind h q
 
-theorem existsRep {α : Sort u} {r : α → α → Prop} (q : Quot r) : Exists (λ a : α, (Quot.mk r a) = q) :=
-Quot.inductionOn q (λ a, ⟨a, rfl⟩)
+theorem existsRep {α : Sort u} {r : α → α → Prop} (q : Quot r) : Exists (fun a => (Quot.mk r a) = q) :=
+Quot.inductionOn q (fun a => ⟨a, rfl⟩)
 
 section
 variable {α : Sort u}
@@ -1408,12 +1409,12 @@ protected def indep (f : Π a, β (Quot.mk r a)) (a : α) : PSigma β :=
 protected theorem indepCoherent (f : Π a, β (Quot.mk r a))
                      (h : ∀ (a b : α) (p : r a b), (Eq.rec (f a) (sound p) : β (Quot.mk r b)) = f b)
                      : ∀ a b, r a b → Quot.indep f a = Quot.indep f b  :=
-λ a b e, PSigma.eq (sound e) (h a b e)
+fun a b e => PSigma.eq (sound e) (h a b e)
 
 protected theorem liftIndepPr1
   (f : Π a, β (Quot.mk r a)) (h : ∀ (a b : α) (p : r a b), (Eq.rec (f a) (sound p) : β (Quot.mk r b)) = f b)
   (q : Quot r) : (lift (Quot.indep f) (Quot.indepCoherent f h) q).1 = q  :=
-Quot.ind (λ (a : α), Eq.refl (Quot.indep f a).1) q
+Quot.ind (fun (a : α) => Eq.refl (Quot.indep f a).1) q
 
 @[reducible, elabAsEliminator, inline]
 protected def rec
@@ -1429,13 +1430,13 @@ Quot.rec f h q
 @[reducible, elabAsEliminator, inline]
 protected def recOnSubsingleton
    [h : ∀ a, Subsingleton (β (Quot.mk r a))] (q : Quot r) (f : Π a, β (Quot.mk r a)) : β q :=
-Quot.rec f (λ a b h, Subsingleton.elim _ (f b)) q
+Quot.rec f (fun a b h => Subsingleton.elim _ (f b)) q
 
 @[reducible, elabAsEliminator, inline]
 protected def hrecOn
    (q : Quot r) (f : Π a, β (Quot.mk r a)) (c : ∀ (a b : α) (p : r a b), f a ≅ f b) : β q :=
 Quot.recOn q f $
-  λ a b p, eqOfHeq $
+  fun a b p => eqOfHeq $
     have p₁ : (Eq.rec (f a) (sound p) : β (Quot.mk r b)) ≅ f a, from eqRecHeq (sound p) (f a),
     Heq.trans p₁ (c a b p)
 
@@ -1472,7 +1473,7 @@ Quot.liftOn q f c
 protected theorem inductionOn {α : Sort u} [s : Setoid α] {β : Quotient s → Prop} (q : Quotient s) (h : ∀ a, β ⟦a⟧) : β q :=
 Quot.inductionOn q h
 
-theorem existsRep {α : Sort u} [s : Setoid α] (q : Quotient s) : Exists (λ a : α, ⟦a⟧ = q) :=
+theorem existsRep {α : Sort u} [s : Setoid α] (q : Quotient s) : Exists (fun a : α => ⟦a⟧ = q) :=
 Quot.existsRep q
 
 section
@@ -1512,14 +1513,14 @@ protected def lift₂
    (f : α → β → φ)(c : ∀ a₁ a₂ b₁ b₂, a₁ ≈ b₁ → a₂ ≈ b₂ → f a₁ a₂ = f b₁ b₂)
    (q₁ : Quotient s₁) (q₂ : Quotient s₂) : φ :=
 Quotient.lift
-  (λ (a₁ : α), Quotient.lift (f a₁) (λ (a b : β), c a₁ a a₁ b (Setoid.refl a₁)) q₂)
-  (λ (a b : α) (h : a ≈ b),
+  (fun (a₁ : α) => Quotient.lift (f a₁) (fun (a b : β) => c a₁ a a₁ b (Setoid.refl a₁)) q₂)
+  (fun (a b : α) (h : a ≈ b) =>
      @Quotient.ind β s₂
-       (λ (a1 : Quotient s₂),
-          (Quotient.lift (f a) (λ (a1 b : β), c a a1 a b (Setoid.refl a)) a1)
+       (fun (a1 : Quotient s₂) =>
+          (Quotient.lift (f a) (fun (a1 b : β) => c a a1 a b (Setoid.refl a)) a1)
           =
-          (Quotient.lift (f b) (λ (a b1 : β), c b a b b1 (Setoid.refl b)) a1))
-       (λ (a' : β), c a a' b a' h (Setoid.refl a'))
+          (Quotient.lift (f b) (fun (a b1 : β) => c b a b b1 (Setoid.refl b)) a1))
+       (fun (a' : β) => c a a' b a' h (Setoid.refl a'))
        q₂)
   q₁
 
@@ -1530,19 +1531,19 @@ Quotient.lift₂ f c q₁ q₂
 
 @[elabAsEliminator]
 protected theorem ind₂ {φ : Quotient s₁ → Quotient s₂ → Prop} (h : ∀ a b, φ ⟦a⟧ ⟦b⟧) (q₁ : Quotient s₁) (q₂ : Quotient s₂) : φ q₁ q₂ :=
-Quotient.ind (λ a₁, Quotient.ind (λ a₂, h a₁ a₂) q₂) q₁
+Quotient.ind (fun a₁ => Quotient.ind (fun a₂ => h a₁ a₂) q₂) q₁
 
 @[elabAsEliminator]
 protected theorem inductionOn₂
    {φ : Quotient s₁ → Quotient s₂ → Prop} (q₁ : Quotient s₁) (q₂ : Quotient s₂) (h : ∀ a b, φ ⟦a⟧ ⟦b⟧) : φ q₁ q₂ :=
-Quotient.ind (λ a₁, Quotient.ind (λ a₂, h a₁ a₂) q₂) q₁
+Quotient.ind (fun a₁ => Quotient.ind (fun a₂ => h a₁ a₂) q₂) q₁
 
 @[elabAsEliminator]
 protected theorem inductionOn₃
    [s₃ : Setoid φ]
    {δ : Quotient s₁ → Quotient s₂ → Quotient s₃ → Prop} (q₁ : Quotient s₁) (q₂ : Quotient s₂) (q₃ : Quotient s₃) (h : ∀ a b c, δ ⟦a⟧ ⟦b⟧ ⟦c⟧)
    : δ q₁ q₂ q₃ :=
-Quotient.ind (λ a₁, Quotient.ind (λ a₂, Quotient.ind (λ a₃, h a₁ a₂ a₃) q₃) q₂) q₁
+Quotient.ind (fun a₁ => Quotient.ind (fun a₂ => Quotient.ind (fun a₃ => h a₁ a₂ a₃) q₃) q₂) q₁
 end
 
 section Exact
@@ -1550,20 +1551,20 @@ variable   {α : Sort u}
 
 private def rel [s : Setoid α] (q₁ q₂ : Quotient s) : Prop :=
 Quotient.liftOn₂ q₁ q₂
-  (λ a₁ a₂, a₁ ≈ a₂)
-  (λ a₁ a₂ b₁ b₂ a₁b₁ a₂b₂,
+  (fun a₁ a₂ => a₁ ≈ a₂)
+  (fun a₁ a₂ b₁ b₂ a₁b₁ a₂b₂ =>
     propext (Iff.intro
-      (λ a₁a₂, Setoid.trans (Setoid.symm a₁b₁) (Setoid.trans a₁a₂ a₂b₂))
-      (λ b₁b₂, Setoid.trans a₁b₁ (Setoid.trans b₁b₂ (Setoid.symm a₂b₂)))))
+      (fun a₁a₂ => Setoid.trans (Setoid.symm a₁b₁) (Setoid.trans a₁a₂ a₂b₂))
+      (fun b₁b₂ => Setoid.trans a₁b₁ (Setoid.trans b₁b₂ (Setoid.symm a₂b₂)))))
 
 private theorem rel.refl [s : Setoid α] : ∀ q : Quotient s, rel q q :=
-λ q, Quot.inductionOn q (λ a, Setoid.refl a)
+fun q => Quot.inductionOn q (fun a => Setoid.refl a)
 
 private theorem eqImpRel [s : Setoid α] {q₁ q₂ : Quotient s} : q₁ = q₂ → rel q₁ q₂ :=
-λ h, Eq.ndrecOn h (rel.refl q₁)
+fun h => Eq.ndrecOn h (rel.refl q₁)
 
 theorem exact [s : Setoid α] {a b : α} : ⟦a⟧ = ⟦b⟧ → a ≈ b :=
-λ h, eqImpRel h
+fun h => eqImpRel h
 end Exact
 
 section
@@ -1575,8 +1576,8 @@ variables [s₁ : Setoid α] [s₂ : Setoid β]
 protected def recOnSubsingleton₂
    {φ : Quotient s₁ → Quotient s₂ → Sort uC} [h : ∀ a b, Subsingleton (φ ⟦a⟧ ⟦b⟧)]
    (q₁ : Quotient s₁) (q₂ : Quotient s₂) (f : Π a b, φ ⟦a⟧ ⟦b⟧) : φ q₁ q₂:=
-@Quotient.recOnSubsingleton _ s₁ (λ q, φ q q₂) (λ a, Quotient.ind (λ b, h a b) q₂) q₁
-  (λ a, Quotient.recOnSubsingleton q₂ (λ b, f a b))
+@Quotient.recOnSubsingleton _ s₁ (fun q => φ q q₂) (fun a => Quotient.ind (fun b => h a b) q₂) q₁
+  (fun a => Quotient.recOnSubsingleton q₂ (fun b => f a b))
 
 end
 end Quotient
@@ -1599,23 +1600,23 @@ Setoid.mk _ (EqvGen.isEquivalence r)
 
 theorem Quot.exact {a b : α} (H : Quot.mk r a = Quot.mk r b) : EqvGen r a b :=
 @Quotient.exact _ (EqvGen.Setoid r) a b (@congrArg _ _ _ _
-  (Quot.lift (@Quotient.mk _ (EqvGen.Setoid r)) (λx y h, Quot.sound (EqvGen.rel x y h))) H)
+  (Quot.lift (@Quotient.mk _ (EqvGen.Setoid r)) (fun x y h => Quot.sound (EqvGen.rel x y h))) H)
 
 theorem Quot.eqvGenSound {r : α → α → Prop} {a b : α} (H : EqvGen r a b) : Quot.mk r a = Quot.mk r b :=
 EqvGen.recOn H
-  (λ x y h, Quot.sound h)
-  (λ x, rfl)
-  (λ x y _ IH, Eq.symm IH)
-  (λ x y z _ _ IH₁ IH₂, Eq.trans IH₁ IH₂)
+  (fun x y h => Quot.sound h)
+  (fun x => rfl)
+  (fun x y _ IH => Eq.symm IH)
+  (fun x y z _ _ IH₁ IH₂ => Eq.trans IH₁ IH₂)
 end
 
 instance {α : Sort u} {s : Setoid α} [d : ∀ a b : α, Decidable (a ≈ b)] : DecidableEq (Quotient s) :=
-{decEq := λ q₁ q₂ : Quotient s,
+{decEq := fun (q₁ q₂ : Quotient s) =>
   Quotient.recOnSubsingleton₂ q₁ q₂
-    (λ a₁ a₂,
+    (fun a₁ a₂ =>
       match (d a₁ a₂) with
       | (isTrue h₁)  := isTrue (Quotient.sound h₁)
-      | (isFalse h₂) := isFalse (λ h, absurd (Quotient.exact h) h₂))}
+      | (isFalse h₂) := isFalse (fun h => absurd (Quotient.exact h) h₂))}
 
 /- Function extensionality -/
 
@@ -1624,13 +1625,14 @@ variables {α : Sort u} {β : α → Sort v}
 
 def Equiv (f₁ f₂ : Π x : α, β x) : Prop := ∀ x, f₁ x = f₂ x
 
-protected theorem Equiv.refl (f : Π x : α, β x) : Equiv f f := λ x, rfl
+protected theorem Equiv.refl (f : Π x : α, β x) : Equiv f f :=
+fun x => rfl
 
 protected theorem Equiv.symm {f₁ f₂ : Π x: α, β x} : Equiv f₁ f₂ → Equiv f₂ f₁ :=
-λ h x, Eq.symm (h x)
+fun h x => Eq.symm (h x)
 
 protected theorem Equiv.trans {f₁ f₂ f₃ : Π x: α, β x} : Equiv f₁ f₂ → Equiv f₂ f₃ → Equiv f₁ f₃ :=
-λ h₁ h₂ x, Eq.trans (h₁ x) (h₂ x)
+fun h₁ h₂ x => Eq.trans (h₁ x) (h₂ x)
 
 protected theorem Equiv.isEquivalence (α : Sort u) (β : α → Sort v) : Equivalence (@Function.Equiv α β) :=
 mkEquivalence (@Function.Equiv α β) (@Equiv.refl α β) (@Equiv.symm α β) (@Equiv.trans α β)
@@ -1645,10 +1647,10 @@ private def funSetoid (α : Sort u) (β : α → Sort v) : Setoid (Π x : α, β
 Setoid.mk (@Function.Equiv α β) (Function.Equiv.isEquivalence α β)
 
 private def extfunApp (f : Quotient $ funSetoid α β) : Π x : α, β x :=
-λ x,
+fun x =>
 Quot.liftOn f
-  (λ f : Π x : α, β x, f x)
-  (λ f₁ f₂ h, h x)
+  (fun (f : Π x : α, β x) => f x)
+  (fun f₁ f₂ h => h x)
 
 theorem funext {f₁ f₂ : Π x : α, β x} (h : ∀ x, f₁ x = f₂ x) : f₁ = f₂ :=
 show extfunApp ⟦f₁⟧ = extfunApp ⟦f₂⟧, from
@@ -1656,7 +1658,7 @@ congrArg extfunApp (sound h)
 end
 
 instance Pi.Subsingleton {α : Sort u} {β : α → Sort v} [∀ a, Subsingleton (β a)] : Subsingleton (Π a, β a) :=
-⟨λ f₁ f₂, funext (λ a, Subsingleton.elim (f₁ a) (f₂ a))⟩
+⟨fun f₁ f₂ => funext (fun a => Subsingleton.elim (f₁ a) (f₂ a))⟩
 
 /- General operations on functions -/
 namespace Function
@@ -1664,22 +1666,22 @@ universes u₁ u₂ u₃ u₄
 variables {α : Sort u₁} {β : Sort u₂} {φ : Sort u₃} {δ : Sort u₄} {ζ : Sort u₁}
 
 @[inline, reducible] def comp (f : β → φ) (g : α → β) : α → φ :=
-λ x, f (g x)
+fun x => f (g x)
 
 infixr  ` ∘ `      := Function.comp
 
 @[inline, reducible] def onFun (f : β → β → φ) (g : α → β) : α → α → φ :=
-λ x y, f (g x) (g y)
+fun x y => f (g x) (g y)
 
 @[inline, reducible] def combine (f : α → β → φ) (op : φ → δ → ζ) (g : α → β → δ)
   : α → β → ζ :=
-λ x y, op (f x y) (g x y)
+fun x y => op (f x y) (g x y)
 
 @[inline, reducible] def const (β : Sort u₂) (a : α) : β → α :=
-λ x, a
+fun x => a
 
 @[inline, reducible] def swap {φ : α → β → Sort u₃} (f : Π x y, φ x y) : Π y x, φ x y :=
-λ y x, f x y
+fun y x => f x y
 
 end Function
 
@@ -1690,86 +1692,86 @@ namespace Classical
 axiom choice {α : Sort u} : Nonempty α → α
 
 noncomputable def indefiniteDescription {α : Sort u} (p : α → Prop)
-  (h : Exists (λ x, p x)) : {x // p x} :=
+  (h : Exists (fun x => p x)) : {x // p x} :=
 choice $ let ⟨x, px⟩ := h; ⟨⟨x, px⟩⟩
 
-noncomputable def choose {α : Sort u} {p : α → Prop} (h : Exists (λ x, p x)) : α :=
+noncomputable def choose {α : Sort u} {p : α → Prop} (h : Exists (fun x => p x)) : α :=
 (indefiniteDescription p h).val
 
-theorem chooseSpec {α : Sort u} {p : α → Prop} (h : Exists (λ x, p x)) : p (choose h) :=
+theorem chooseSpec {α : Sort u} {p : α → Prop} (h : Exists (fun x => p x)) : p (choose h) :=
 (indefiniteDescription p h).property
 
 /- Diaconescu's theorem: excluded middle from choice, Function extensionality and propositional extensionality. -/
 theorem em (p : Prop) : p ∨ ¬p :=
 let U (x : Prop) : Prop := x = True ∨ p;
 let V (x : Prop) : Prop := x = False ∨ p;
-have exU : Exists (λ x, U x), from ⟨True, Or.inl rfl⟩,
-have exV : Exists (λ x, V x), from ⟨False, Or.inl rfl⟩,
+have exU : Exists (fun x => U x), from ⟨True, Or.inl rfl⟩,
+have exV : Exists (fun x => V x), from ⟨False, Or.inl rfl⟩,
 let u : Prop := choose exU;
 let v : Prop := choose exV;
 have uDef : U u, from chooseSpec exU,
 have vDef : V v, from chooseSpec exV,
 have notUvOrP : u ≠ v ∨ p, from
   Or.elim uDef
-    (λ hut : u = True,
+    (fun hut : u = True =>
       Or.elim vDef
-        (λ hvf : v = False,
+        (fun hvf : v = False =>
           have hne : u ≠ v, from hvf.symm ▸ hut.symm ▸ trueNeFalse,
           Or.inl hne)
         Or.inr)
     Or.inr,
 have pImpliesUv : p → u = v, from
-  λ hp : p,
+  fun hp : p =>
   have hpred : U = V, from
-    funext $ λ x : Prop,
+    funext $ fun x : Prop =>
       have hl : (x = True ∨ p) → (x = False ∨ p), from
-        λ a, Or.inr hp,
+        fun a => Or.inr hp,
       have hr : (x = False ∨ p) → (x = True ∨ p), from
-        λ a, Or.inr hp,
+        fun a => Or.inr hp,
       show (x = True ∨ p) = (x = False ∨ p), from
         propext (Iff.intro hl hr),
   have h₀ : ∀ exU exV, @choose _ U exU = @choose _ V exV, from
-    hpred ▸ λ exU exV, rfl,
+    hpred ▸ fun exU exV => rfl,
   show u = v, from h₀ _ _,
 Or.elim notUvOrP
-  (λ hne : u ≠ v, Or.inr (mt pImpliesUv hne))
+  (fun (hne : u ≠ v) => Or.inr (mt pImpliesUv hne))
   Or.inl
 
-theorem existsTrueOfNonempty {α : Sort u} : Nonempty α → Exists (λ x : α, True)
+theorem existsTrueOfNonempty {α : Sort u} : Nonempty α → Exists (fun x : α => True)
 | ⟨x⟩ := ⟨x, trivial⟩
 
 noncomputable def inhabitedOfNonempty {α : Sort u} (h : Nonempty α) : Inhabited α :=
 ⟨choice h⟩
 
-noncomputable def inhabitedOfExists {α : Sort u} {p : α → Prop} (h : Exists (λ x, p x)) :
+noncomputable def inhabitedOfExists {α : Sort u} {p : α → Prop} (h : Exists (fun x => p x)) :
   Inhabited α :=
-inhabitedOfNonempty (Exists.elim h (λ w hw, ⟨w⟩))
+inhabitedOfNonempty (Exists.elim h (fun w hw => ⟨w⟩))
 
 /- all propositions are Decidable -/
 noncomputable def propDecidable (a : Prop) : Decidable a :=
 choice $ Or.elim (em a)
-  (λ ha, ⟨isTrue ha⟩)
-  (λ hna, ⟨isFalse hna⟩)
+  (fun ha => ⟨isTrue ha⟩)
+  (fun hna => ⟨isFalse hna⟩)
 
 noncomputable def decidableInhabited (a : Prop) : Inhabited (Decidable a) :=
 ⟨propDecidable a⟩
 
 noncomputable def typeDecidableEq (α : Sort u) : DecidableEq α :=
-{decEq := λ x y, propDecidable (x = y)}
+{decEq := fun x y => propDecidable (x = y)}
 
 noncomputable def typeDecidable (α : Sort u) : PSum α (α → False) :=
 match (propDecidable (Nonempty α)) with
 | (isTrue hp)  := PSum.inl (@Inhabited.default _ (inhabitedOfNonempty hp))
-| (isFalse hn) := PSum.inr (λ a, absurd (Nonempty.intro a) hn)
+| (isFalse hn) := PSum.inr (fun a => absurd (Nonempty.intro a) hn)
 
 noncomputable def strongIndefiniteDescription {α : Sort u} (p : α → Prop)
-  (h : Nonempty α) : {x : α // Exists (λ y : α, p y) → p x} :=
-@dite (Exists (λ x : α, p x)) (propDecidable _) _
-  (λ hp : Exists (λ x : α, p x),
-    show {x : α // Exists (λ y : α, p y) → p x}, from
+  (h : Nonempty α) : {x : α // Exists (fun y : α => p y) → p x} :=
+@dite (Exists (fun x : α => p x)) (propDecidable _) _
+  (fun hp : Exists (fun x : α => p x) =>
+    show {x : α // Exists (fun y : α => p y) → p x}, from
     let xp := indefiniteDescription _ hp;
-    ⟨xp.val, λ h', xp.property⟩)
-  (λ hp, ⟨choice h, λ h, absurd h hp⟩)
+    ⟨xp.val, fun h' => xp.property⟩)
+  (fun hp => ⟨choice h, fun h => absurd h hp⟩)
 
 /- the Hilbert epsilon Function -/
 
@@ -1777,30 +1779,30 @@ noncomputable def epsilon {α : Sort u} [h : Nonempty α] (p : α → Prop) : α
 (strongIndefiniteDescription p h).val
 
 theorem epsilonSpecAux {α : Sort u} (h : Nonempty α) (p : α → Prop)
-  : Exists (λ y, p y) → p (@epsilon α h p) :=
+  : Exists (fun y => p y) → p (@epsilon α h p) :=
 (strongIndefiniteDescription p h).property
 
-theorem epsilonSpec {α : Sort u} {p : α → Prop} (hex : Exists (λ y, p y)) :
+theorem epsilonSpec {α : Sort u} {p : α → Prop} (hex : Exists (fun y => p y)) :
     p (@epsilon α (nonemptyOfExists hex) p) :=
 epsilonSpecAux (nonemptyOfExists hex) p hex
 
-theorem epsilonSingleton {α : Sort u} (x : α) : @epsilon α ⟨x⟩ (λ y, y = x) = x :=
-@epsilonSpec α (λ y, y = x) ⟨x, rfl⟩
+theorem epsilonSingleton {α : Sort u} (x : α) : @epsilon α ⟨x⟩ (fun y => y = x) = x :=
+@epsilonSpec α (fun y => y = x) ⟨x, rfl⟩
 
 /- the axiom of choice -/
 
-theorem axiomOfChoice {α : Sort u} {β : α → Sort v} {r : Π x, β x → Prop} (h : ∀ x, Exists (λ y, r x y)) :
-  Exists (λ (f : Π x, β x), ∀ x, r x (f x)) :=
-⟨_, λ x, chooseSpec (h x)⟩
+theorem axiomOfChoice {α : Sort u} {β : α → Sort v} {r : Π x, β x → Prop} (h : ∀ x, Exists (fun y => r x y)) :
+  Exists (fun (f : Π x, β x) => ∀ x, r x (f x)) :=
+⟨_, fun x => chooseSpec (h x)⟩
 
 theorem skolem {α : Sort u} {b : α → Sort v} {p : Π x, b x → Prop} :
-  (∀ x, Exists (λ y, p x y)) ↔ Exists (λ (f : Π x, b x), ∀ x, p x (f x)) :=
-⟨axiomOfChoice, λ ⟨f, hw⟩ x, ⟨f x, hw x⟩⟩
+  (∀ x, Exists (fun y => p x y)) ↔ Exists (fun (f : Π x, b x) => ∀ x, p x (f x)) :=
+⟨axiomOfChoice, fun ⟨f, hw⟩ (x) => ⟨f x, hw x⟩⟩
 
 theorem propComplete (a : Prop) : a = True ∨ a = False :=
 Or.elim (em a)
-  (λ t, Or.inl (eqTrueIntro t))
-  (λ f, Or.inr (eqFalseIntro f))
+  (fun t => Or.inl (eqTrueIntro t))
+  (fun f => Or.inr (eqFalseIntro f))
 
 -- this supercedes byCases in Decidable
 theorem byCases {p q : Prop} (hpq : p → q) (hnpq : ¬p → q) : q :=
diff --git a/library/init/data/array/basic.lean b/library/init/data/array/basic.lean
index 4f50a40a40..0b7dc2959b 100644
--- a/library/init/data/array/basic.lean
+++ b/library/init/data/array/basic.lean
@@ -30,19 +30,19 @@ variables {α : Type u} {β : Type v} {σ : Type w}
 @[extern cpp inline "lean::mk_empty_array(#2)"]
 def mkEmpty (c : @& Nat) : Array α :=
 { sz := 0,
-  data := λ ⟨x, h⟩, absurd h (Nat.notLtZero x) }
+  data := fun ⟨x, h⟩ => absurd h (Nat.notLtZero x) }
 
 @[extern cpp inline "lean::array_push(#2, #3)"]
 def push (a : Array α) (v : α) : Array α :=
 { sz   := Nat.succ a.sz,
-  data := λ ⟨j, h₁⟩,
+  data := fun ⟨j, h₁⟩ =>
     if h₂ : j = a.sz then v
     else a.data ⟨j, Nat.ltOfLeOfNe (Nat.leOfLtSucc h₁) h₂⟩ }
 
 @[extern cpp inline "lean::mk_array(#2, #3)"]
 def mkArray {α : Type u} (n : Nat) (v : α) : Array α :=
 { sz   := n,
-  data := λ _, v}
+  data := fun _ => v}
 
 theorem szMkArrayEq {α : Type u} (n : Nat) (v : α) : (mkArray n v).sz = n :=
 rfl
@@ -87,7 +87,7 @@ if h : i < a.size then some (a.fget ⟨i, h⟩) else none
 @[extern cpp inline "lean::array_fset(#2, #3, #4)"]
 def fset (a : Array α) (i : @& Fin a.size) (v : α) : Array α :=
 { sz   := a.sz,
-  data := λ j, if h : i = j then v else a.data j }
+  data := fun j => if h : i = j then v else a.data j }
 
 theorem szFSetEq (a : Array α) (i : Fin a.size) (v : α) : (fset a i v).size = a.size :=
 rfl
@@ -129,7 +129,7 @@ if h : i < a.size then fswapAt a ⟨i, h⟩ v else (v, a)
 @[extern cpp inline "lean::array_pop(#2)"]
 def pop (a : Array α) : Array α :=
 { sz   := Nat.pred a.size,
-  data := λ ⟨j, h⟩, a.fget ⟨j, Nat.ltOfLtOfLe h (Nat.predLe _)⟩ }
+  data := fun ⟨j, h⟩ => a.fget ⟨j, Nat.ltOfLtOfLe h (Nat.predLe _)⟩ }
 
 -- TODO(Leo): justify termination using wf-rec
 partial def shrink : Array α → Nat → Array α
@@ -150,10 +150,10 @@ variables {m : Type v → Type v} [Monad m]
 miterateAux a f 0 b
 
 @[inline] def mfoldl (f : β → α → m β) (b : β) (a : Array α) : m β :=
-miterate a b (λ _ b a, f a b)
+miterate a b (fun _ b a => f a b)
 
 @[inline] def mfoldlFrom (f : β → α → m β) (b : β) (a : Array α) (ini : Nat := 0) : m β :=
-miterateAux a (λ _ b a, f a b) ini b
+miterateAux a (fun _ b a => f a b) ini b
 
 -- TODO(Leo): justify termination using wf-rec
 @[specialize] partial def miterate₂Aux (a₁ : Array α) (a₂ : Array σ) (f : Π i : Fin a₁.size, α → σ → β → m β) : Nat → β → m β
@@ -170,7 +170,7 @@ miterateAux a (λ _ b a, f a b) ini b
 miterate₂Aux a₁ a₂ f 0 b
 
 @[inline] def mfoldl₂ (f : β → α → σ → m β) (b : β) (a₁ : Array α) (a₂ : Array σ): m β :=
-miterate₂ a₁ a₂ b (λ _ a₁ a₂ b, f b a₁ a₂)
+miterate₂ a₁ a₂ b (fun _ a₁ a₂ b => f b a₁ a₂)
 
 -- TODO(Leo): justify termination using wf-rec
 @[specialize] partial def mfindAux (a : Array α) (f : α → m (Option β)) : Nat → m (Option β)
@@ -195,7 +195,7 @@ Id.run $ miterateAux a f 0 b
 Id.run $ miterateAux a f i b
 
 @[inline] def foldl (f : β → α → β) (b : β) (a : Array α) : β :=
-iterate a b (λ _ a b, f b a)
+iterate a b (fun _ a b => f b a)
 
 @[inline] def foldlFrom (f : β → α → β) (b : β) (a : Array α) (ini : Nat := 0) : β :=
 Id.run $ mfoldlFrom f b a ini
@@ -204,7 +204,7 @@ Id.run $ mfoldlFrom f b a ini
 Id.run $ miterate₂Aux a₁ a₂ f 0 b
 
 @[inline] def foldl₂ (f : β → α → σ → β) (b : β) (a₁ : Array α) (a₂ : Array σ) : β :=
-iterate₂ a₁ a₂ b (λ _ a₁ a₂ b, f b a₁ a₂)
+iterate₂ a₁ a₂ b (fun _ a₁ a₂ b => f b a₁ a₂)
 
 @[inline] def find (a : Array α) (f : α → Option β) : Option β :=
 Id.run $ mfindAux a f 0
@@ -226,14 +226,14 @@ variables {m : Type → Type v} [Monad m]
 anyMAux a p 0
 
 @[inline] def allM (a : Array α) (p : α → m Bool) : m Bool :=
-not <$> anyM a (λ v, not <$> p v)
+not <$> anyM a (fun v => not <$> p v)
 end
 
 @[inline] def any (a : Array α) (p : α → Bool) : Bool :=
 Id.run $ anyM a p
 
 @[inline] def all (a : Array α) (p : α → Bool) : Bool :=
-!any a (λ v, !p v)
+!any a (fun v => !p v)
 
 @[specialize] private def revIterateAux (a : Array α) (f : Π i : Fin a.size, α → β → β) : Π (i : Nat), i ≤ a.size → β → β
 | 0     h b := b
@@ -245,7 +245,7 @@ Id.run $ anyM a p
 revIterateAux a f a.size (Nat.leRefl _) b
 
 @[inline] def revFoldl (a : Array α) (b : β) (f : α → β → β) : β :=
-revIterate a b (λ _, f)
+revIterate a b (fun _ => f)
 
 def toList (a : Array α) : List α :=
 a.revFoldl [] List.cons
@@ -271,16 +271,16 @@ variables {m : Type v → Type v} [Monad m]
      pure (unsafeCast a)
 
 @[inline] unsafe partial def ummap (f : α → m β) (as : Array α) : m (Array β) :=
-ummapAux (λ i a, f a) 0 as
+ummapAux (fun i a => f a) 0 as
 
 @[inline] unsafe partial def ummapIdx (f : Nat → α → m β) (as : Array α) : m (Array β) :=
 ummapAux f 0 as
 
 @[implementedBy Array.ummap] def mmap (f : α → m β) (as : Array α) : m (Array β) :=
-as.mfoldl (λ bs a, do b ← f a; pure (bs.push b)) (mkEmpty as.size)
+as.mfoldl (fun bs a => do b ← f a; pure (bs.push b)) (mkEmpty as.size)
 
 @[implementedBy Array.ummapIdx] def mmapIdx (f : Nat → α → m β) (as : Array α) : m (Array β) :=
-as.miterate (mkEmpty as.size) (λ i a bs, do b ← f i.val a; pure (bs.push b))
+as.miterate (mkEmpty as.size) (fun i a bs => do b ← f i.val a; pure (bs.push b))
 end
 
 @[inline] def modify [Inhabited α] (a : Array α) (i : Nat) (f : α → α) : Array α :=
@@ -331,7 +331,7 @@ if h : e ≤ a.size then extractAux a b e h r
 else r
 
 protected def append (a : Array α) (b : Array α) : Array α :=
-b.foldl (λ a v, a.push v) a
+b.foldl (fun a v => a.push v) a
 
 instance : HasAppend (Array α) := ⟨Array.append⟩
 
@@ -354,7 +354,7 @@ else
   false
 
 instance [HasBeq α] : HasBeq (Array α) :=
-⟨λ a b, isEqv a b HasBeq.beq⟩
+⟨fun a b => isEqv a b HasBeq.beq⟩
 
 -- TODO(Leo): justify termination using wf-rec, and use `fswap`
 partial def reverseAux : Array α → Nat → Array α
diff --git a/library/init/data/bytearray/basic.lean b/library/init/data/bytearray/basic.lean
index 38b8ac0ddd..b21ab72b1b 100644
--- a/library/init/data/bytearray/basic.lean
+++ b/library/init/data/bytearray/basic.lean
@@ -63,4 +63,4 @@ def List.toByteArray (bs : List UInt8) : ByteArray :=
 bs.toByteArrayAux ByteArray.empty
 
 instance : HasToString ByteArray :=
-⟨λ bs, bs.toList.toString⟩
+⟨fun bs => bs.toList.toString⟩
diff --git a/library/init/data/char/basic.lean b/library/init/data/char/basic.lean
index 06034cd01a..1029a3d707 100644
--- a/library/init/data/char/basic.lean
+++ b/library/init/data/char/basic.lean
@@ -14,7 +14,7 @@ structure Char :=
 (val : UInt32) (valid : isValidChar val)
 
 instance : HasSizeof Char :=
-⟨λ c, c.val.toNat⟩
+⟨fun c => c.val.toNat⟩
 
 namespace Char
 def utf8Size (c : Char) : UInt32 :=
@@ -57,13 +57,13 @@ theorem veqOfEq : ∀ {c d : Char}, c = d → c.val = d.val
 | _ _ rfl := rfl
 
 theorem neOfVne {c d : Char} (h : c.val ≠ d.val) : c ≠ d :=
-λ h', absurd (veqOfEq h') h
+fun h' => absurd (veqOfEq h') h
 
 theorem vneOfNe {c d : Char} (h : c ≠ d) : c.val ≠ d.val :=
-λ h', absurd (eqOfVeq h') h
+fun h' => absurd (eqOfVeq h') h
 
 instance : DecidableEq Char :=
-{decEq := λ i j, decidableOfDecidableOfIff
+{decEq := fun i j => decidableOfDecidableOfIff
   (decEq i.val j.val) ⟨Char.eqOfVeq, Char.veqOfEq⟩}
 
 instance : Inhabited Char :=
diff --git a/library/init/data/dlist.lean b/library/init/data/dlist.lean
index 653f50e5fc..65b8b3e228 100644
--- a/library/init/data/dlist.lean
+++ b/library/init/data/dlist.lean
@@ -21,10 +21,10 @@ variables {α : Type u}
 open List
 
 def ofList (l : List α) : DList α :=
-⟨append l, λ t, (appendNil l).symm ▸ rfl⟩
+⟨append l, fun t => (appendNil l).symm ▸ rfl⟩
 
 def empty : DList α :=
-⟨id, λ t, rfl⟩
+⟨id, fun t => rfl⟩
 
 instance : HasEmptyc (DList α) :=
 ⟨DList.empty⟩
@@ -33,22 +33,25 @@ def toList : DList α → List α
 | ⟨f, h⟩ := f []
 
 def singleton (a : α) : DList α :=
-⟨λ t, a :: t, λ t, rfl⟩
+⟨fun t => a :: t,
+ fun t => rfl⟩
 
 def cons : α → DList α → DList α
-| a ⟨f, h⟩ := ⟨λ t, a :: f t, λ t,
+| a ⟨f, h⟩ := ⟨fun t => a :: f t,
+               fun t =>
                show a :: f t = a :: f [] ++ t, from
                have h₁ : a :: f t = a :: (f nil ++ t), from h t ▸ rfl,
                have h₂ : a :: (f nil ++ t) = a :: f nil ++ t, from (consAppend _ _ _).symm,
                Eq.trans h₁ h₂⟩
 
 def append : DList α → DList α → DList α
-| ⟨f, h₁⟩ ⟨g, h₂⟩ := ⟨f ∘ g, λ t,
+| ⟨f, h₁⟩ ⟨g, h₂⟩ := ⟨f ∘ g, fun t =>
                       show f (g t) = (f (g [])) ++ t, from
                       (h₁ (g [])).symm ▸ (appendAssoc (f []) (g []) t).symm ▸ h₂ t ▸ h₁ (g t) ▸ rfl⟩
 
 def push : DList α → α → DList α
-| ⟨f, h⟩ a := ⟨λ t, f (a :: t), λ t, (h (a::t)).symm ▸ (h [a]).symm ▸ (appendAssoc (f []) [a] t).symm ▸ rfl⟩
+| ⟨f, h⟩ a := ⟨fun t => f (a :: t),
+               fun t => (h (a::t)).symm ▸ (h [a]).symm ▸ (appendAssoc (f []) [a] t).symm ▸ rfl⟩
 
 instance : HasAppend (DList α) :=
 ⟨DList.append⟩
diff --git a/library/init/data/fin/basic.lean b/library/init/data/fin/basic.lean
index f3e3dcb45c..5c2e569c7a 100644
--- a/library/init/data/fin/basic.lean
+++ b/library/init/data/fin/basic.lean
@@ -85,10 +85,10 @@ theorem veqOfEq : ∀ {i j : Fin n}, i = j → (val i) = (val j)
 | ⟨iv, ilt⟩ .(_) rfl := rfl
 
 theorem neOfVne {i j : Fin n} (h : val i ≠ val j) : i ≠ j :=
-λ h', absurd (veqOfEq h') h
+fun h' => absurd (veqOfEq h') h
 
 theorem vneOfNe {i j : Fin n} (h : i ≠ j) : val i ≠ val j :=
-λ h', absurd (eqOfVeq h') h
+fun h' => absurd (eqOfVeq h') h
 
 theorem modnLt : ∀ {m : Nat} (i : Fin n), m > 0 → (i %ₙ m).val < m
 | m ⟨a, h⟩ hp :=  Nat.ltOfLeOfLt (modLe _ _) (modLt _ hp)
@@ -98,5 +98,5 @@ end Fin
 open Fin
 
 instance (n : Nat) : DecidableEq (Fin n) :=
-{decEq := λ i j, decidableOfDecidableOfIff
+{decEq := fun i j => decidableOfDecidableOfIff
   (decEq i.val j.val) ⟨eqOfVeq, veqOfEq⟩}
diff --git a/library/init/data/hashmap/basic.lean b/library/init/data/hashmap/basic.lean
index aaf91eecb2..8fb94e0e40 100644
--- a/library/init/data/hashmap/basic.lean
+++ b/library/init/data/hashmap/basic.lean
@@ -43,7 +43,7 @@ let ⟨i, h⟩ := mkIdx data.property (hashFn a);
 data.update i (AssocList.cons a b (data.val.uget i h)) h
 
 @[inline] def mfoldBuckets {δ : Type w} {m : Type w → Type w} [Monad m] (data : HashMapBucket α β) (d : δ) (f : δ → α → β → m δ) : m δ :=
-data.val.mfoldl (λ d b, b.mfoldl f d) d
+data.val.mfoldl (fun d b => b.mfoldl f d) d
 
 @[inline] def foldBuckets {δ : Type w} (data : HashMapBucket α β) (d : δ) (f : δ → α → β → δ) : δ :=
 Id.run $ mfoldBuckets data d f
diff --git a/library/init/data/int/basic.lean b/library/init/data/int/basic.lean
index d7b7f1e859..cb047036fa 100644
--- a/library/init/data/int/basic.lean
+++ b/library/init/data/int/basic.lean
@@ -84,12 +84,12 @@ protected def decEq (a b : @& Int) : Decidable (a = b) :=
 match a, b with
  | ofNat a, ofNat b := match decEq a b with
    | isTrue h  := isTrue  $ h ▸ rfl
-   | isFalse h := isFalse $ λ h', Int.noConfusion h' (λ h', absurd h' h)
+   | isFalse h := isFalse $ fun h' => Int.noConfusion h' (fun h' => absurd h' h)
  | negSucc a, negSucc b := match decEq a b with
    | isTrue h  := isTrue  $ h ▸ rfl
-   | isFalse h := isFalse $ λ h', Int.noConfusion h' (λ h', absurd h' h)
- | ofNat a, negSucc b := isFalse $ λ h, Int.noConfusion h
- | negSucc a, ofNat b := isFalse $ λ h, Int.noConfusion h
+   | isFalse h := isFalse $ fun h' => Int.noConfusion h' (fun h' => absurd h' h)
+ | ofNat a, negSucc b := isFalse $ fun h => Int.noConfusion h
+ | negSucc a, ofNat b := isFalse $ fun h => Int.noConfusion h
 
 instance Int.DecidableEq : DecidableEq Int :=
 {decEq := Int.decEq}
@@ -98,7 +98,7 @@ instance Int.DecidableEq : DecidableEq Int :=
 private def decNonneg (m : @& Int) : Decidable (NonNeg m) :=
 match m with
 | ofNat m   := isTrue $ NonNeg.mk m
-| negSucc m := isFalse $ λ h, match h with end
+| negSucc m := isFalse $ fun h => match h with end
 
 @[extern cpp "lean::int_dec_le"]
 instance decLe (a b : @& Int) : Decidable (a ≤ b) :=
diff --git a/library/init/data/list/basic.lean b/library/init/data/list/basic.lean
index a67c6ded29..d737d221e4 100644
--- a/library/init/data/list/basic.lean
+++ b/library/init/data/list/basic.lean
@@ -18,15 +18,15 @@ namespace List
 
 protected def hasDecEq [DecidableEq α] : Π a b : List α, Decidable (a = b)
 | []      []      := isTrue rfl
-| (a::as) []      := isFalse (λ h, List.noConfusion h)
-| []      (b::bs) := isFalse (λ h, List.noConfusion h)
+| (a::as) []      := isFalse (fun h => List.noConfusion h)
+| []      (b::bs) := isFalse (fun h => List.noConfusion h)
 | (a::as) (b::bs) :=
   match decEq a b with
   | isTrue hab  :=
     match hasDecEq as bs with
     | isTrue habs  := isTrue (Eq.subst hab (Eq.subst habs rfl))
-    | isFalse nabs := isFalse (λ h, List.noConfusion h (λ _ habs, absurd habs nabs))
-  | isFalse nab := isFalse (λ h, List.noConfusion h (λ hab _, absurd hab nab))
+    | isFalse nabs := isFalse (fun h => List.noConfusion h (fun _ habs => absurd habs nabs))
+  | isFalse nab := isFalse (fun h => List.noConfusion h (fun hab _ => absurd hab nab))
 
 instance [DecidableEq α] : DecidableEq (List α) :=
 {decEq := List.hasDecEq}
@@ -36,7 +36,7 @@ def reverseAux : List α → List α → List α
 | (a::l) r := reverseAux l (a::r)
 
 def reverse : List α → List α :=
-λ l, reverseAux l []
+fun l => reverseAux l []
 
 protected def append (as bs : List α) : List α :=
 reverseAux as.reverse bs
@@ -62,7 +62,7 @@ theorem reverseAuxReverseAux : ∀ (as bs cs : List α), reverseAux (reverseAux
 | (a::as) bs cs :=
   Eq.trans
     (reverseAuxReverseAux as (a::bs) cs)
-    (congrArg (λ b, reverseAux bs b) (reverseAuxReverseAux as [a] cs).symm)
+    (congrArg (fun b => reverseAux bs b) (reverseAuxReverseAux as [a] cs).symm)
 
 theorem consAppend (a : α) (as bs : List α) : (a::as) ++ bs = a::(as ++ bs) :=
 reverseAuxReverseAux as [a] bs
@@ -71,9 +71,9 @@ theorem appendAssoc : ∀ (as bs cs : List α), (as ++ bs) ++ cs = as ++ (bs ++
 | []      bs cs := rfl
 | (a::as) bs cs :=
   show ((a::as) ++ bs) ++ cs = (a::as) ++ (bs ++ cs),      from
-  have h₁ : ((a::as) ++ bs) ++ cs = a::(as++bs) ++ cs,     from congrArg (λ ds, ds ++ cs) (consAppend a as bs),
+  have h₁ : ((a::as) ++ bs) ++ cs = a::(as++bs) ++ cs,     from congrArg (fun ds => ds ++ cs) (consAppend a as bs),
   have h₂ : a::(as++bs) ++ cs     = a::((as++bs) ++ cs),   from consAppend a (as++bs) cs,
-  have h₃ : a::((as++bs) ++ cs)   = a::(as ++ (bs ++ cs)), from congrArg (λ as, a::as) (appendAssoc as bs cs),
+  have h₃ : a::((as++bs) ++ cs)   = a::(as ++ (bs ++ cs)), from congrArg (fun as => a::as) (appendAssoc as bs cs),
   have h₄ : a::(as ++ (bs ++ cs)) = (a::as ++ (bs ++ cs)), from (consAppend a as (bs++cs)).symm,
   Eq.trans (Eq.trans (Eq.trans h₁ h₂) h₃) h₄
 
@@ -89,7 +89,7 @@ theorem notMem : ∀ {a b : α} {bs : List α}, a ≠ b → ¬ a ∈ bs → ¬ a
 | _ _ _ _ h₁ (Mem.inTail _ h₂) := absurd h₂ h₁
 
 instance decidableMem [DecidableEq α] (a : α) : ∀ (l : List α), Decidable (a ∈ l)
-| []      := isFalse (λ h, match h with end)
+| []      := isFalse (fun h => match h with end)
 | (b::bs) :=
   if h₁ : a = b then isTrue (h₁.symm ▸ Mem.eqHead b bs)
   else match decidableMem bs with
@@ -213,7 +213,7 @@ def lookup [HasBeq α] : α → List (α × β) → Option β
   | false := lookup a es
 
 def removeAll [HasBeq α] (xs ys : List α) : List α :=
-xs.filter (λ x, ys.notElem x)
+xs.filter (fun x => ys.notElem x)
 
 def drop : Nat → List α → List α
 | 0     a       := a
@@ -236,17 +236,17 @@ def take : Nat → List α → List α
 @[specialize] def foldr1 (f : α → α → α) : Π (xs : List α), xs ≠ [] → α
 | []               h := absurd rfl h
 | [a]              _ := a
-| (a :: as@(_::_)) _ := f a (foldr1 as (λ h, List.noConfusion h))
+| (a :: as@(_::_)) _ := f a (foldr1 as (fun h => List.noConfusion h))
 
 @[specialize] def foldr1Opt (f : α → α → α) : List α → Option α
 | []        := none
-| (a :: as) := some $ foldr1 f (a :: as) (λ h, List.noConfusion h)
+| (a :: as) := some $ foldr1 f (a :: as) (fun h => List.noConfusion h)
 
 @[inline] def any (l : List α) (p : α → Bool) : Bool :=
-foldr (λ a r, p a || r) false l
+foldr (fun a r => p a || r) false l
 
 @[inline] def all (l : List α) (p : α → Bool) : Bool :=
-foldr (λ a r, p a && r) true l
+foldr (fun a r => p a && r) true l
 
 def or  (bs : List Bool) : Bool := bs.any id
 
@@ -270,7 +270,7 @@ instance [DecidableEq α] : HasInsert α (List α) :=
 ⟨List.insert⟩
 
 def replicate (n : Nat) (a : α) : List α :=
-n.repeat (λ xs, a :: xs) []
+n.repeat (fun xs => a :: xs) []
 
 def rangeAux : Nat → List Nat → List Nat
 | 0     ns := ns
@@ -292,11 +292,11 @@ def enum : List α → List (Nat × α) := enumFrom 0
 def getLastOfNonNil : Π (as : List α), as ≠ [] → α
 | []         h := absurd rfl h
 | [a]        h := a
-| (a::b::as) h := getLastOfNonNil (b::as) (λ h, List.noConfusion h)
+| (a::b::as) h := getLastOfNonNil (b::as) (fun h => List.noConfusion h)
 
 def getLast [Inhabited α] : List α → α
 | []      := arbitrary α
-| (a::as) := getLastOfNonNil (a::as) (λ h, List.noConfusion h)
+| (a::as) := getLastOfNonNil (a::as) (fun h => List.noConfusion h)
 
 def init : List α → List α
 | []     := []
@@ -326,21 +326,21 @@ instance [HasLess α] : HasLess (List α) :=
 ⟨List.Less⟩
 
 instance hasDecidableLt [HasLess α] [h : DecidableRel HasLess.Less] : Π l₁ l₂ : List α, Decidable (l₁ < l₂)
-| []      []      := isFalse (λ h, match h with end)
+| []      []      := isFalse (fun h => match h with end)
 | []      (b::bs) := isTrue (Less.nil _ _)
-| (a::as) []      := isFalse (λ h, match h with end)
+| (a::as) []      := isFalse (fun h => match h with end)
 | (a::as) (b::bs) :=
   match h a b with
   | isTrue h₁  := isTrue (Less.head _ _ h₁)
   | isFalse h₁ :=
     match h b a with
-    | isTrue h₂  := isFalse (λ h, match h with
+    | isTrue h₂  := isFalse (fun h => match h with
        | Less.head _ _ h₁' := absurd h₁' h₁
        | Less.tail _ h₂' _ := absurd h₂ h₂')
     | isFalse h₂ :=
       match hasDecidableLt as bs with
       | isTrue h₃  := isTrue (Less.tail h₁ h₂ h₃)
-      | isFalse h₃ := isFalse (λ h, match h with
+      | isFalse h₃ := isFalse (fun h => match h with
          | Less.head _ _ h₁' := absurd h₁' h₁
          | Less.tail _ _ h₃' := absurd h₃' h₃)
 
@@ -351,7 +351,7 @@ instance [HasLess α] : HasLessEq (List α) :=
 ⟨List.LessEq⟩
 
 instance hasDecidableLe [HasLess α] [h : DecidableRel (HasLess.Less : α → α → Prop)] : Π l₁ l₂ : List α, Decidable (l₁ ≤ l₂) :=
-λ a b, Not.Decidable
+fun a b => Not.Decidable
 
 /--  `isPrefixOf l₁ l₂` returns `true` Iff `l₁` is a prefix of `l₂`. -/
 def isPrefixOf [HasBeq α] : List α → List α → Bool
diff --git a/library/init/data/nat/basic.lean b/library/init/data/nat/basic.lean
index fbe9a3cdc5..628f84b519 100644
--- a/library/init/data/nat/basic.lean
+++ b/library/init/data/nat/basic.lean
@@ -32,7 +32,7 @@ theorem neOfBeqEqFf : ∀ {n m : Nat}, beq n m = false → n ≠ m
 | (succ n) (succ m) h₁ h₂ :=
   have beq n m = false, from h₁,
   have n ≠ m, from neOfBeqEqFf this,
-  Nat.noConfusion h₂ (λ h₂, absurd h₂ this)
+  Nat.noConfusion h₂ (fun h₂ => absurd h₂ this)
 
 @[extern cpp "lean::nat_dec_eq"]
 protected def decEq (n m : @& Nat) : Decidable (n = m) :=
@@ -98,7 +98,7 @@ foldAux f n n a
 anyAux f n n
 
 @[inline] def all (f : Nat → Bool) (n : Nat) : Bool :=
-!any (λ i, !f i) n
+!any (fun i => !f i) n
 
 @[specialize] def repeatAux {α : Type u} (f : α → α) : Nat → α → α
 | 0         a := a
@@ -200,7 +200,7 @@ protected theorem leftDistrib : ∀ (n m k : Nat), n * (m + k) = n * m + n * k
   have h₁ : succ n * (m + k) = n * (m + k) + (m + k),              from succMul _ _,
   have h₂ : n * (m + k) + (m + k) = (n * m + n * k) + (m + k),     from leftDistrib n m k ▸ rfl,
   have h₃ : (n * m + n * k) + (m + k) = n * m + (n * k + (m + k)), from Nat.addAssoc _ _ _,
-  have h₄ : n * m + (n * k + (m + k)) = n * m + (m + (n * k + k)), from congrArg (λ x, n*m + x) (Nat.addLeftComm _ _ _),
+  have h₄ : n * m + (n * k + (m + k)) = n * m + (m + (n * k + k)), from congrArg (fun x => n*m + x) (Nat.addLeftComm _ _ _),
   have h₅ : n * m + (m + (n * k + k)) = (n * m + m) + (n * k + k), from (Nat.addAssoc _ _ _).symm,
   have h₆ : (n * m + m) + (n * k + k) = (n * m + m) + succ n * k,  from succMul n k ▸ rfl,
   have h₇ : (n * m + m) + succ n * k = succ n * m + succ n * k,    from succMul n m ▸ rfl,
@@ -289,8 +289,8 @@ protected theorem eqOrLtOfLe : ∀ {n m: Nat}, n ≤ m → n = m ∨ n < m
   have n ≤ m, from h,
   have n = m ∨ n < m, from eqOrLtOfLe this,
   Or.elim this
-   (λ h, Or.inl $ congrArg succ h)
-   (λ h, Or.inr $ succLtSucc h)
+   (fun h => Or.inl $ congrArg succ h)
+   (fun h => Or.inr $ succLtSucc h)
 
 theorem ltSuccOfLe {n m : Nat} : n ≤ m → n < succ m :=
 succLeSucc
@@ -301,10 +301,10 @@ rfl
 theorem succSubSuccEqSub (n m : Nat) : succ n - succ m = n - m :=
 Nat.recOn m
   (show succ n - succ zero = n - zero, from (Eq.refl (succ n - succ zero)))
-  (λ m, congrArg pred)
+  (fun m => congrArg pred)
 
 theorem notSuccLeSelf : ∀ n : Nat, ¬succ n ≤ n :=
-λ n, Nat.rec (notSuccLeZero 0) (λ a b c, b (leOfSuccLeSucc c)) n
+fun n => Nat.rec (notSuccLeZero 0) (fun a b c => b (leOfSuccLeSucc c)) n
 
 protected theorem ltIrrefl (n : Nat) : ¬n < n :=
 notSuccLeSelf n
@@ -328,7 +328,7 @@ theorem predLt : ∀ {n : Nat}, n ≠ 0 → pred n < n
 | (succ n) h := ltSuccOfLe (Nat.leRefl _)
 
 theorem subLe (n m : Nat) : n - m ≤ n :=
-Nat.recOn m (Nat.leRefl (n - 0)) (λ m, Nat.leTrans (predLe (n - m)))
+Nat.recOn m (Nat.leRefl (n - 0)) (fun m => Nat.leTrans (predLe (n - m)))
 
 theorem subLt : ∀ {n m : Nat}, 0 < n → 0 < m → n - m < n
 | 0     m     h1 h2 := absurd h1 (Nat.ltIrrefl 0)
@@ -391,7 +391,7 @@ protected theorem ltOrGe : ∀ (n m : Nat), n < m ∨ n ≥ m
 
 protected theorem leTotal (m n : Nat) : m ≤ n ∨ n ≤ m :=
 Or.elim (Nat.ltOrGe m n)
-  (λ h, Or.inl (Nat.leOfLt h))
+  (fun h => Or.inl (Nat.leOfLt h))
   Or.inr
 
 protected theorem ltOfLeAndNe {m n : Nat} (h1 : m ≤ n) : m ≠ n → m < n :=
@@ -414,8 +414,8 @@ h
 
 theorem ltOrEqOrLeSucc {m n : Nat} (h : m ≤ succ n) : m ≤ n ∨ m = succ n :=
 Decidable.byCases
-  (λ h' : m = succ n, Or.inr h')
-  (λ h' : m ≠ succ n,
+  (fun (h' : m = succ n) => Or.inr h')
+  (fun (h' : m ≠ succ n) =>
      have m < succ n, from Nat.ltOfLeAndNe h h',
      have succ m ≤ succ n, from succLeOfLt this,
      Or.inl (leOfSuccLeSucc this))
@@ -427,13 +427,13 @@ theorem leAddRight : ∀ (n k : Nat), n ≤ n + k
 theorem leAddLeft (n m : Nat): n ≤ m + n :=
 Nat.addComm n m ▸ leAddRight n m
 
-theorem le.dest : ∀ {n m : Nat}, n ≤ m → Exists (λ k, n + k = m)
+theorem le.dest : ∀ {n m : Nat}, n ≤ m → Exists (fun k => n + k = m)
 | zero     zero     h := ⟨0, rfl⟩
 | zero     (succ n) h := ⟨succ n, show 0 + succ n = succ n, from (Nat.addComm 0 (succ n)).symm ▸ rfl⟩
 | (succ n) zero     h := Bool.noConfusion h
 | (succ n) (succ m) h :=
   have n ≤ m, from h,
-  have Exists (λ k, n + k = m), from le.dest this,
+  have Exists (fun k => n + k = m), from le.dest this,
   match this with
   | ⟨k, h⟩ := ⟨k, show succ n + k = succ m, from ((succAdd n k).symm ▸ h ▸ rfl)⟩
 
@@ -441,19 +441,19 @@ theorem le.intro {n m k : Nat} (h : n + k = m) : n ≤ m :=
 h ▸ leAddRight n k
 
 protected theorem notLeOfGt {n m : Nat} (h : n > m) : ¬ n ≤ m :=
-λ h₁, Or.elim (Nat.ltOrGe n m)
-  (λ h₂, absurd (Nat.ltTrans h h₂) (Nat.ltIrrefl _))
-  (λ h₂, have Heq : n = m, from Nat.leAntisymm h₁ h₂, absurd (@Eq.subst _ _ _ _ Heq h) (Nat.ltIrrefl m))
+fun h₁ => Or.elim (Nat.ltOrGe n m)
+  (fun h₂ => absurd (Nat.ltTrans h h₂) (Nat.ltIrrefl _))
+  (fun h₂ => have Heq : n = m, from Nat.leAntisymm h₁ h₂, absurd (@Eq.subst _ _ _ _ Heq h) (Nat.ltIrrefl m))
 
 theorem gtOfNotLe {n m : Nat} (h : ¬ n ≤ m) : n > m :=
 Or.elim (Nat.ltOrGe m n)
-  (λ h₁, h₁)
-  (λ h₁, absurd h₁ h)
+  (fun h₁ => h₁)
+  (fun h₁ => absurd h₁ h)
 
 protected theorem ltOfLeOfNe {n m : Nat} (h₁ : n ≤ m) (h₂ : n ≠ m) : n < m :=
 Or.elim (Nat.ltOrGe n m)
-  (λ h₃, h₃)
-  (λ h₃, absurd (Nat.leAntisymm h₁ h₃) h₂)
+  (fun h₃ => h₃)
+  (fun h₃ => absurd (Nat.leAntisymm h₁ h₃) h₂)
 
 protected theorem addLeAddLeft {n m : Nat} (h : n ≤ m) (k : Nat) : k + n ≤ k + m :=
 match le.dest h with
@@ -466,7 +466,7 @@ protected theorem addLeAddRight {n m : Nat} (h : n ≤ m) (k : Nat) : n + k ≤
 have h₁ : n + k = k + n, from Nat.addComm _ _,
 have h₂ : k + n ≤ k + m, from Nat.addLeAddLeft h k,
 have h₃ : k + m = m + k, from Nat.addComm _ _,
-transRelLeft (λ a b, a ≤ b) (transRelRight (λ a b, a ≤ b) h₁ h₂) h₃
+transRelLeft (fun a b => a ≤ b) (transRelRight (fun a b => a ≤ b) h₁ h₂) h₃
 
 protected theorem addLtAddLeft {n m : Nat} (h : n < m) (k : Nat) : k + n < k + m :=
 ltOfSuccLe (addSucc k n ▸ Nat.addLeAddLeft (succLeOfLt h) k)
@@ -492,13 +492,13 @@ theorem natZeroEqZero : Nat.zero = 0 :=
 rfl
 
 protected theorem oneNeZero : 1 ≠ (0 : Nat) :=
-λ h, Nat.noConfusion h
+fun h => Nat.noConfusion h
 
 protected theorem zeroNeOne : 0 ≠ (1 : Nat) :=
-λ h, Nat.noConfusion h
+fun h => Nat.noConfusion h
 
 theorem succNeZero (n : Nat) : succ n ≠ 0 :=
-λ h, Nat.noConfusion h
+fun h => Nat.noConfusion h
 
 protected theorem bit0SuccEq (n : Nat) : bit0 (succ n) = succ (succ (bit0 n)) :=
 show succ (succ n + n) = succ (succ (n + n)), from
@@ -509,7 +509,7 @@ protected theorem zeroLtBit0 : ∀ {n : Nat}, n ≠ 0 → 0 < bit0 n
 | (succ n) h :=
   have h₁ : 0 < succ (succ (bit0 n)),             from zeroLtSucc _,
   have h₂ : succ (succ (bit0 n)) = bit0 (succ n), from (Nat.bit0SuccEq n).symm,
-  transRelLeft (λ a b, a < b) h₁ h₂
+  transRelLeft (fun a b => a < b) h₁ h₂
 
 protected theorem zeroLtBit1 (n : Nat) : 0 < bit1 n :=
 zeroLtSucc _
@@ -519,11 +519,11 @@ protected theorem bit0NeZero : ∀ {n : Nat}, n ≠ 0 → bit0 n ≠ 0
 | (n+1) h :=
   suffices (n+1) + (n+1) ≠ 0, from this,
   suffices succ ((n+1) + n) ≠ 0, from this,
-  λ h, Nat.noConfusion h
+  fun h => Nat.noConfusion h
 
 protected theorem bit1NeZero (n : Nat) : bit1 n ≠ 0 :=
 show succ (n + n) ≠ 0, from
-λ h, Nat.noConfusion h
+fun h => Nat.noConfusion h
 
 protected theorem bit1EqSuccBit0 (n : Nat) : bit1 n = succ (bit0 n) :=
 rfl
@@ -533,20 +533,20 @@ Eq.trans (Nat.bit1EqSuccBit0 (succ n)) (congrArg succ (Nat.bit0SuccEq n))
 
 protected theorem bit1NeOne : ∀ {n : Nat}, n ≠ 0 → bit1 n ≠ 1
 | 0     h h1 := absurd rfl h
-| (n+1) h h1 := Nat.noConfusion h1 (λ h2, absurd h2 (succNeZero _))
+| (n+1) h h1 := Nat.noConfusion h1 (fun h2 => absurd h2 (succNeZero _))
 
 protected theorem bit0NeOne : ∀ n : Nat, bit0 n ≠ 1
 | 0     h := absurd h (Ne.symm Nat.oneNeZero)
 | (n+1) h :=
   have h1 : succ (succ (n + n)) = 1, from succAdd n n ▸ h,
   Nat.noConfusion h1
-    (λ h2, absurd h2 (succNeZero (n + n)))
+    (fun h2 => absurd h2 (succNeZero (n + n)))
 
 protected theorem addSelfNeOne : ∀ (n : Nat), n + n ≠ 1
 | 0     h := Nat.noConfusion h
 | (n+1) h :=
   have h1 : succ (succ (n + n)) = 1, from succAdd n n ▸ h,
-  Nat.noConfusion h1 (λ h2, absurd h2 (Nat.succNeZero (n + n)))
+  Nat.noConfusion h1 (fun h2 => absurd h2 (Nat.succNeZero (n + n)))
 
 protected theorem bit1NeBit0 : ∀ (n m : Nat), bit1 n ≠ bit0 m
 | 0     m     h := absurd h (Ne.symm (Nat.addSelfNeOne m))
@@ -557,11 +557,11 @@ protected theorem bit1NeBit0 : ∀ (n m : Nat), bit1 n ≠ bit0 m
   have h1 : succ (succ (bit1 n)) = succ (succ (bit0 m)), from
     Nat.bit0SuccEq m ▸ Nat.bit1SuccEq n ▸ h,
   have h2 : bit1 n = bit0 m, from
-    Nat.noConfusion h1 (λ h2', Nat.noConfusion h2' (λ h2'', h2'')),
+    Nat.noConfusion h1 (fun h2' => Nat.noConfusion h2' (fun h2'' => h2'')),
   absurd h2 (bit1NeBit0 n m)
 
 protected theorem bit0NeBit1 : ∀ (n m : Nat), bit0 n ≠ bit1 m :=
-λ n m : Nat, Ne.symm (Nat.bit1NeBit0 m n)
+fun n m => Ne.symm (Nat.bit1NeBit0 m n)
 
 protected theorem bit0Inj : ∀ {n m : Nat}, bit0 n = bit0 m → n = m
 | 0     0     h := rfl
@@ -573,22 +573,22 @@ protected theorem bit0Inj : ∀ {n m : Nat}, bit0 n = bit0 m → n = m
   have succ (n + n) = succ (m + m), from this,
   have n + n = m + m, from Nat.noConfusion this id,
   have n = m, from bit0Inj this,
-  congrArg (λ a, a + 1) this
+  congrArg (fun a => a + 1) this
 
 protected theorem bit1Inj : ∀ {n m : Nat}, bit1 n = bit1 m → n = m :=
-λ n m h,
+fun n m h =>
 have succ (bit0 n) = succ (bit0 m), from Nat.bit1EqSuccBit0 n ▸ Nat.bit1EqSuccBit0 m ▸ h,
 have bit0 n = bit0 m, from Nat.noConfusion this id,
 Nat.bit0Inj this
 
 protected theorem bit0Ne {n m : Nat} : n ≠ m → bit0 n ≠ bit0 m :=
-λ h₁ h₂, absurd (Nat.bit0Inj h₂) h₁
+fun h₁ h₂ => absurd (Nat.bit0Inj h₂) h₁
 
 protected theorem bit1Ne {n m : Nat} : n ≠ m → bit1 n ≠ bit1 m :=
-λ h₁ h₂, absurd (Nat.bit1Inj h₂) h₁
+fun h₁ h₂ => absurd (Nat.bit1Inj h₂) h₁
 
 protected theorem zeroNeBit0 {n : Nat} : n ≠ 0 → 0 ≠ bit0 n :=
-λ h, Ne.symm (Nat.bit0NeZero h)
+fun h => Ne.symm (Nat.bit0NeZero h)
 
 protected theorem zeroNeBit1 (n : Nat) : 0 ≠ bit1 n :=
 Ne.symm (Nat.bit1NeZero n)
@@ -597,7 +597,7 @@ protected theorem oneNeBit0 (n : Nat) : 1 ≠ bit0 n :=
 Ne.symm (Nat.bit0NeOne n)
 
 protected theorem oneNeBit1 {n : Nat} : n ≠ 0 → 1 ≠ bit1 n :=
-λ h, Ne.symm (Nat.bit1NeOne h)
+fun h => Ne.symm (Nat.bit1NeOne h)
 
 protected theorem oneLtBit1 : ∀ {n : Nat}, n ≠ 0 → 1 < bit1 n
 | 0        h := absurd rfl h
@@ -682,10 +682,10 @@ theorem powLePowOfLeRight {n : Nat} (hx : n > 0) {i : Nat} : ∀ {j}, i ≤ j 
   this.symm ▸ Nat.leRefl _
 | (succ j) h :=
   Or.elim (ltOrEqOrLeSucc h)
-    (λ h, show n^i ≤ n^j * n, from
+    (fun h => show n^i ≤ n^j * n, from
           suffices n^i * 1 ≤ n^j * n, from Nat.mulOne (n^i) ▸ this,
           Nat.mulLeMul (powLePowOfLeRight h) hx)
-    (λ h, h.symm ▸ Nat.leRefl _)
+    (fun h => h.symm ▸ Nat.leRefl _)
 
 theorem posPowOfPos {n : Nat} (m : Nat) (h : 0 < n) : 0 < n^m :=
 powLePowOfLeRight h (Nat.zeroLe _)
@@ -706,6 +706,6 @@ Nat.foldAux f i.2 (i.2 - i.1) a
 Nat.anyAux f i.2 (i.2 - i.1)
 
 @[inline] def allI (f : Nat → Bool) (i : Nat × Nat) : Bool :=
-!Nat.anyAux (λ a, !f a) i.2 (i.2 - i.1)
+!Nat.anyAux (fun a => !f a) i.2 (i.2 - i.1)
 
 end Prod
diff --git a/library/init/data/nat/div.lean b/library/init/data/nat/div.lean
index d25eb045e0..ddea771616 100644
--- a/library/init/data/nat/div.lean
+++ b/library/init/data/nat/div.lean
@@ -8,7 +8,7 @@ import init.wf init.data.nat.basic
 namespace Nat
 
 private def divRecLemma {x y : Nat} : 0 < y ∧ y ≤ x → x - y < x :=
-λ h, And.rec (λ ypos ylex, subLt (Nat.ltOfLtOfLe ypos ylex) ypos) h
+fun h => And.rec (fun ypos ylex => subLt (Nat.ltOfLtOfLe ypos ylex) ypos) h
 
 private def div.F (x : Nat) (f : Π x₁, x₁ < x → Nat → Nat) (y : Nat) : Nat :=
 if h : 0 < y ∧ y ≤ x then f (x - y) (divRecLemma h) y + 1 else zero
@@ -69,39 +69,39 @@ div.inductionOn x y h₁ h₂
 
 theorem modZero (a : Nat) : a % 0 = a :=
 suffices (if 0 < 0 ∧ 0 ≤ a then (a - 0) % 0 else a) = a, from (modDef a 0).symm ▸ this,
-have h : ¬ (0 < 0 ∧ 0 ≤ a), from λ ⟨h₁, _⟩, absurd h₁ (Nat.ltIrrefl _),
+have h : ¬ (0 < 0 ∧ 0 ≤ a), from fun ⟨h₁, _⟩ => absurd h₁ (Nat.ltIrrefl _),
 ifNeg h
 
 theorem modEqOfLt {a b : Nat} (h : a < b) : a % b = a :=
 suffices (if 0 < b ∧ b ≤ a then (a - b) % b else a) = a, from (modDef a b).symm ▸ this,
-have h' : ¬(0 < b ∧ b ≤ a), from λ ⟨_, h₁⟩, absurd h₁ (Nat.notLeOfGt h),
+have h' : ¬(0 < b ∧ b ≤ a), from fun ⟨_, h₁⟩ => absurd h₁ (Nat.notLeOfGt h),
 ifNeg h'
 
 theorem modEqSubMod {a b : Nat} (h : a ≥ b) : a % b = (a - b) % b :=
 Or.elim (eqZeroOrPos b)
-  (λ h₁, h₁.symm ▸ (Nat.subZero a).symm ▸ rfl)
-  (λ h₁, (modDef a b).symm ▸ ifPos ⟨h₁, h⟩)
+  (fun h₁ => h₁.symm ▸ (Nat.subZero a).symm ▸ rfl)
+  (fun h₁ => (modDef a b).symm ▸ ifPos ⟨h₁, h⟩)
 
 theorem modLt (x : Nat) {y : Nat} : y > 0 → x % y < y :=
 mod.inductionOn x y
-  (λ x y ⟨_, h₁⟩ h₂ h₃,
+  (fun (x y) ⟨_, h₁⟩ (h₂ h₃) =>
    have ih  : (x - y) % y < y, from h₂ h₃,
    have Heq : x % y = (x - y) % y, from modEqSubMod h₁,
    Heq.symm ▸ ih)
-  (λ x y h₁ h₂,
+  (fun x y h₁ h₂ =>
     have h₁ : ¬ 0 < y ∨ ¬ y ≤ x, from Iff.mp (Decidable.notAndIffOrNot _ _) h₁,
     Or.elim h₁
-     (λ h₁, absurd h₂ h₁)
-     (λ h₁,
+     (fun h₁ => absurd h₂ h₁)
+     (fun h₁ =>
         have hgt : y > x, from gtOfNotLe h₁,
         have Heq : x % y = x, from modEqOfLt hgt,
         Heq.symm ▸ hgt))
 
 theorem modLe (x y : Nat) : x % y ≤ x :=
 Or.elim (Nat.ltOrGe x y)
-  (λ h₁ : x < y, (modEqOfLt h₁).symm ▸ Nat.leRefl _)
-  (λ h₁ : x ≥ y, Or.elim (eqZeroOrPos y)
-    (λ h₂ : y = 0, h₂.symm ▸ (Nat.modZero x).symm ▸ Nat.leRefl _)
-    (λ h₂ : y > 0, Nat.leTrans (Nat.leOfLt (Nat.modLt _ h₂)) h₁))
+  (fun (h₁ : x < y) => (modEqOfLt h₁).symm ▸ Nat.leRefl _)
+  (fun (h₁ : x ≥ y) => Or.elim (eqZeroOrPos y)
+    (fun (h₂ : y = 0) => h₂.symm ▸ (Nat.modZero x).symm ▸ Nat.leRefl _)
+    (fun (h₂ : y > 0) => Nat.leTrans (Nat.leOfLt (Nat.modLt _ h₂)) h₁))
 
 end Nat
diff --git a/library/init/data/option/basic.lean b/library/init/data/option/basic.lean
index 1a4c3a53af..a5336dce9e 100644
--- a/library/init/data/option/basic.lean
+++ b/library/init/data/option/basic.lean
@@ -43,7 +43,7 @@ def toMonad {m : Type → Type} [Monad m] [Alternative m] {A} : Option A → m A
 Option.bind o (some ∘ f)
 
 theorem mapId {α} : (Option.map id : Option α → Option α) = id :=
-funext (λo, match o with | none := rfl | some x := rfl)
+funext (fun o => match o with | none := rfl | some x := rfl)
 
 instance : Monad Option :=
 {pure := @some, bind := @Option.bind, map := @Option.map}
@@ -76,13 +76,13 @@ instance (α : Type u) : Inhabited (Option α) :=
 ⟨none⟩
 
 instance {α : Type u} [DecidableEq α] : DecidableEq (Option α) :=
-{decEq := λ a b, match a, b with
+{decEq := fun a b => match a, b with
  | none,      none      := isTrue rfl
- | none,      (some v₂) := isFalse (λ h, Option.noConfusion h)
- | (some v₁), none      := isFalse (λ h, Option.noConfusion h)
+ | none,      (some v₂) := isFalse (fun h => Option.noConfusion h)
+ | (some v₁), none      := isFalse (fun h => Option.noConfusion h)
  | (some v₁), (some v₂) :=
    match decEq v₁ v₂ with
    | (isTrue e)  := isTrue (congrArg (@some α) e)
-   | (isFalse n) := isFalse (λ h, Option.noConfusion h (λ e, absurd e n))}
+   | (isFalse n) := isFalse (fun h => Option.noConfusion h (fun e => absurd e n))}
 
 instance {α : Type u} [HasLess α] : HasLess (Option α) := ⟨Option.lt HasLess.Less⟩
diff --git a/library/init/data/ordering/basic.lean b/library/init/data/ordering/basic.lean
index 407cca7d1d..4c50dd3948 100644
--- a/library/init/data/ordering/basic.lean
+++ b/library/init/data/ordering/basic.lean
@@ -12,7 +12,7 @@ inductive Ordering
 | lt | Eq | gt
 
 instance : HasRepr Ordering :=
-⟨(λ s, match s with | Ordering.lt := "lt" | Ordering.Eq := "Eq" | Ordering.gt := "gt")⟩
+⟨(fun s => match s with | Ordering.lt := "lt" | Ordering.Eq := "Eq" | Ordering.gt := "gt")⟩
 
 namespace Ordering
 def swap : Ordering → Ordering
@@ -40,20 +40,20 @@ def cmp {α : Type u} [HasLess α] [DecidableRel (HasLess.Less : α → α → P
 cmpUsing HasLess.Less a b
 
 instance : DecidableEq Ordering :=
-{decEq := λ a b,
+{decEq := fun a b =>
   match a with
   | Ordering.lt :=
     match b with
     | Ordering.lt := isTrue rfl
-    | Ordering.Eq := isFalse (λ h, Ordering.noConfusion h)
-    | Ordering.gt := isFalse (λ h, Ordering.noConfusion h)
+    | Ordering.Eq := isFalse (fun h => Ordering.noConfusion h)
+    | Ordering.gt := isFalse (fun h => Ordering.noConfusion h)
   | Ordering.Eq :=
     match b with
-    | Ordering.lt := isFalse (λ h, Ordering.noConfusion h)
+    | Ordering.lt := isFalse (fun h => Ordering.noConfusion h)
     | Ordering.Eq := isTrue rfl
-    | Ordering.gt := isFalse (λ h, Ordering.noConfusion h)
+    | Ordering.gt := isFalse (fun h => Ordering.noConfusion h)
   | Ordering.gt :=
     match b with
-    | Ordering.lt := isFalse (λ h, Ordering.noConfusion h)
-    | Ordering.Eq := isFalse (λ h, Ordering.noConfusion h)
+    | Ordering.lt := isFalse (fun h => Ordering.noConfusion h)
+    | Ordering.Eq := isFalse (fun h => Ordering.noConfusion h)
     | Ordering.gt := isTrue rfl}
diff --git a/library/init/data/persistentarray/basic.lean b/library/init/data/persistentarray/basic.lean
index c72d33b279..e12e2f38af 100644
--- a/library/init/data/persistentarray/basic.lean
+++ b/library/init/data/persistentarray/basic.lean
@@ -59,7 +59,7 @@ partial def setAux : PersistentArrayNode α → USize → USize → α → Persi
   let j     := div2Shift i shift;
   let i     := mod2Shift i shift;
   let shift := shift - initShift;
-  node $ cs.modify j.toNat $ λ c, setAux c i shift a
+  node $ cs.modify j.toNat $ fun c => setAux c i shift a
 | (leaf cs) i _     a := leaf (cs.set i.toNat a)
 
 def set (t : PersistentArray α) (i : Nat) (a : α) : PersistentArray α :=
@@ -73,7 +73,7 @@ else
   let j     := div2Shift i shift;
   let i     := mod2Shift i shift;
   let shift := shift - initShift;
-  node $ cs.modify j.toNat $ λ c, modifyAux c i shift
+  node $ cs.modify j.toNat $ fun c => modifyAux c i shift
 | (leaf cs) i _     := leaf (cs.modify i.toNat f)
 
 @[specialize] def modify [Inhabited α] (t : PersistentArray α) (i : Nat) (f : α → α) : PersistentArray α :=
@@ -98,7 +98,7 @@ partial def insertNewLeaf : PersistentArrayNode α → USize → USize → Array
     let i     := mod2Shift i shift;
     let shift := shift - initShift;
     if j.toNat < cs.size then
-       node $ cs.modify j.toNat $ λ c, insertNewLeaf c i shift a
+       node $ cs.modify j.toNat $ fun c => insertNewLeaf c i shift a
     else
        node $ cs.push $ mkNewPath shift a
 | n _ _ _ := n -- unreachable
@@ -129,7 +129,7 @@ section
 variables {m : Type v → Type v} [Monad m]
 
 @[specialize] partial def mfoldlAux (f : β → α → m β) : PersistentArrayNode α → β → m β
-| (node cs) b := cs.mfoldl (λ b c, mfoldlAux c b) b
+| (node cs) b := cs.mfoldl (fun b c => mfoldlAux c b) b
 | (leaf vs) b := vs.mfoldl f b
 
 @[specialize] def mfoldl (f : β → α → m β) (b : β) (t : PersistentArray α) : m β :=
@@ -141,13 +141,13 @@ end
 Id.run (t.mfoldl f b)
 
 def toList (t : PersistentArray α) : List α :=
-(t.foldl (λ xs x, x :: xs) []).reverse
+(t.foldl (fun xs x => x :: xs) []).reverse
 
 section
 variables {m : Type v → Type v} [Monad m]
 
 @[specialize] partial def mmapAux (f : α → m β) : PersistentArrayNode α → m (PersistentArrayNode β)
-| (node cs) := node <$> cs.mmap (λ c, mmapAux c)
+| (node cs) := node <$> cs.mmap (fun c => mmapAux c)
 | (leaf vs) := leaf <$> vs.mmap f
 
 @[specialize] def mmap (f : α → m β) (t : PersistentArray α) : m (PersistentArray β) :=
@@ -166,7 +166,7 @@ structure Stats :=
 
 partial def collectStats : PersistentArrayNode α → Stats → Nat → Stats
 | (node cs) s d :=
-  cs.foldl (λ s c, collectStats c s (d+1))
+  cs.foldl (fun s c => collectStats c s (d+1))
     { numNodes := s.numNodes + 1,
       depth    := Nat.max d s.depth, .. s }
 | (leaf vs) s d := { numNodes := s.numNodes + 1, depth := Nat.max d s.depth, .. s }
diff --git a/library/init/data/random.lean b/library/init/data/random.lean
index 6dd8abe897..6bb3dc0946 100644
--- a/library/init/data/random.lean
+++ b/library/init/data/random.lean
@@ -34,7 +34,7 @@ structure StdGen :=
 def stdRange := (1, 2147483562)
 
 instance : HasRepr StdGen :=
-{ repr := λ ⟨s1, s2⟩, "⟨" ++ toString s1 ++ ", " ++ toString s2 ++ "⟩" }
+{ repr := fun ⟨s1, s2⟩ => "⟨" ++ toString s1 ++ ", " ++ toString s2 ++ "⟩" }
 
 def stdNext : StdGen → Nat × StdGen
 | ⟨s1, s2⟩ :=
@@ -58,7 +58,7 @@ def stdSplit : StdGen → StdGen × StdGen
   (leftG, rightG)
 
 instance : RandomGen StdGen :=
-{range  := λ _, stdRange,
+{range  := fun _ => stdRange,
  next   := stdNext,
  split  := stdSplit}
 
diff --git a/library/init/data/rbmap/basic.lean b/library/init/data/rbmap/basic.lean
index ba59ee648d..bf9144191b 100644
--- a/library/init/data/rbmap/basic.lean
+++ b/library/init/data/rbmap/basic.lean
@@ -24,12 +24,12 @@ def depth (f : Nat → Nat → Nat) : RBNode α β → Nat
 | leaf               := 0
 | (node _ l _ _ r)   := succ (f (depth l) (depth r))
 
-protected def min : RBNode α β → Option (Sigma (λ k : α, β k))
+protected def min : RBNode α β → Option (Sigma (fun k => β k))
 | leaf                  := none
 | (node _ leaf k v _)   := some ⟨k, v⟩
 | (node _ l k v _)      := min l
 
-protected def max : RBNode α β → Option (Sigma (λ k : α, β k))
+protected def max : RBNode α β → Option (Sigma (fun k => β k))
 | leaf                  := none
 | (node _ _ k v leaf)   := some ⟨k, v⟩
 | (node _ _ k v r)      := max r
@@ -174,14 +174,14 @@ end Erase
 section Membership
 variable (lt : α → α → Bool)
 
-@[specialize] def findCore : RBNode α β → Π k : α, Option (Sigma (λ k : α, β k))
+@[specialize] def findCore : RBNode α β → Π k : α, Option (Sigma (fun k => β k))
 | leaf               x := none
 | (node _ a ky vy b) x :=
    if lt x ky then findCore a x
    else if lt ky x then findCore b x
    else some ⟨ky, vy⟩
 
-@[specialize] def find {β : Type v} : RBNode α (λ _, β) → α → Option β
+@[specialize] def find {β : Type v} : RBNode α (fun _ => β) → α → Option β
 | leaf               x := none
 | (node _ a ky vy b) x :=
   if lt x ky then find a x
@@ -209,7 +209,7 @@ open RBNode
 /- TODO(Leo): define dRBMap -/
 
 def RBMap (α : Type u) (β : Type v) (lt : α → α → Bool) : Type (max u v) :=
-{t : RBNode α (λ _, β) // t.WellFormed lt }
+{t : RBNode α (fun _ => β) // t.WellFormed lt }
 
 @[inline] def mkRBMap (α : Type u) (β : Type v) (lt : α → α → Bool) : RBMap α β lt :=
 ⟨leaf, WellFormed.leafWff lt⟩
@@ -236,14 +236,14 @@ t.val.depth f
 | b ⟨t, _⟩ := t.mfold f b
 
 @[inline] def mfor {m : Type w → Type w'} [Monad m] (f : α → β → m σ) (t : RBMap α β lt) : m PUnit :=
-t.mfold (λ _ k v,  f k v *> pure ⟨⟩) ⟨⟩
+t.mfold (fun _ k v =>  f k v *> pure ⟨⟩) ⟨⟩
 
 @[inline] def isEmpty : RBMap α β lt → Bool
 | ⟨leaf, _⟩ := true
 | _         := false
 
 @[specialize] def toList : RBMap α β lt → List (α × β)
-| ⟨t, _⟩ := t.revFold (λ ps k v, (k, v)::ps) []
+| ⟨t, _⟩ := t.revFold (fun ps k v => (k, v)::ps) []
 
 @[inline] protected def min : RBMap α β lt → Option (α × β)
 | ⟨t, _⟩ :=
@@ -258,7 +258,7 @@ t.mfold (λ _ k v,  f k v *> pure ⟨⟩) ⟨⟩
   | none        := none
 
 instance [HasRepr α] [HasRepr β] : HasRepr (RBMap α β lt) :=
-⟨λ t, "rbmapOf " ++ repr t.toList⟩
+⟨fun t => "rbmapOf " ++ repr t.toList⟩
 
 @[inline] def insert : RBMap α β lt → α → β → RBMap α β lt
 | ⟨t, w⟩   k v := ⟨t.insert lt k v, WellFormed.insertWff w rfl⟩
@@ -270,7 +270,7 @@ instance [HasRepr α] [HasRepr β] : HasRepr (RBMap α β lt) :=
 | []          := mkRBMap _ _ _
 | (⟨k,v⟩::xs) := (ofList xs).insert k v
 
-@[inline] def findCore : RBMap α β lt → α → Option (Sigma (λ k : α, β))
+@[inline] def findCore : RBMap α β lt → α → Option (Sigma (fun (k : α) => β))
 | ⟨t, _⟩ x := t.findCore lt x
 
 @[inline] def find : RBMap α β lt → α → Option β
@@ -278,14 +278,14 @@ instance [HasRepr α] [HasRepr β] : HasRepr (RBMap α β lt) :=
 
 /-- (lowerBound k) retrieves the kv pair of the largest key smaller than or equal to `k`,
     if it exists. -/
-@[inline] def lowerBound : RBMap α β lt → α → Option (Sigma (λ k : α, β))
+@[inline] def lowerBound : RBMap α β lt → α → Option (Sigma (fun (k : α) => β))
 | ⟨t, _⟩ x := t.lowerBound lt x none
 
 @[inline] def contains (t : RBMap α β lt) (a : α) : Bool :=
 (t.find a).isSome
 
 @[inline] def fromList (l : List (α × β)) (lt : α → α → Bool) : RBMap α β lt :=
-l.foldl (λ r p, r.insert p.1 p.2) (mkRBMap α β lt)
+l.foldl (fun r p => r.insert p.1 p.2) (mkRBMap α β lt)
 
 @[inline] def all : RBMap α β lt → (α → β → Bool) → Bool
 | ⟨t, _⟩ p := t.all p
@@ -294,7 +294,7 @@ l.foldl (λ r p, r.insert p.1 p.2) (mkRBMap α β lt)
 | ⟨t, _⟩ p := t.any p
 
 def size (m : RBMap α β lt) : Nat :=
-m.fold (λ sz _ _, sz+1) 0
+m.fold (fun sz _ _ => sz+1) 0
 
 def maxDepth (t : RBMap α β lt) : Nat :=
 t.val.depth Nat.max
diff --git a/library/init/data/rbtree/basic.lean b/library/init/data/rbtree/basic.lean
index 50e9fc5061..431f8a7a09 100644
--- a/library/init/data/rbtree/basic.lean
+++ b/library/init/data/rbtree/basic.lean
@@ -23,22 +23,22 @@ variables {α : Type u} {β : Type v} {lt : α → α → Bool}
 RBMap.depth f t
 
 @[inline] def fold (f : β → α → β) (b : β) (t : RBTree α lt) : β :=
-RBMap.fold (λ r a _, f r a) b t
+RBMap.fold (fun r a _ => f r a) b t
 
 @[inline] def revFold (f : β → α → β) (b : β) (t : RBTree α lt) : β :=
-RBMap.revFold (λ r a _, f r a) b t
+RBMap.revFold (fun r a _ => f r a) b t
 
 @[inline] def mfold {m : Type v → Type w} [Monad m] (f : β → α → m β) (b : β) (t : RBTree α lt) : m β :=
-RBMap.mfold (λ r a _, f r a) b t
+RBMap.mfold (fun r a _ => f r a) b t
 
 @[inline] def mfor {m : Type v → Type w} [Monad m] (f : α → m β) (t : RBTree α lt) : m PUnit :=
-t.mfold (λ _ a, f a *> pure ⟨⟩) ⟨⟩
+t.mfold (fun _ a => f a *> pure ⟨⟩) ⟨⟩
 
 @[inline] def isEmpty (t : RBTree α lt) : Bool :=
 RBMap.isEmpty t
 
 @[specialize] def toList (t : RBTree α lt) : List α :=
-t.revFold (λ as a, a::as) []
+t.revFold (fun as a => a::as) []
 
 @[inline] protected def min (t : RBTree α lt) : Option α :=
 match RBMap.min t with
@@ -51,12 +51,12 @@ match RBMap.max t with
 | none        := none
 
 instance [HasRepr α] : HasRepr (RBTree α lt) :=
-⟨λ t, "rbtreeOf " ++ repr t.toList⟩
+⟨fun t => "rbtreeOf " ++ repr t.toList⟩
 
 @[inline] def insert (t : RBTree α lt) (a : α) : RBTree α lt :=
 RBMap.insert t a ()
 
-instance : HasInsert α (RBTree α lt) := ⟨λ a s, s.insert a⟩
+instance : HasInsert α (RBTree α lt) := ⟨fun a s => s.insert a⟩
 
 @[inline] def erase (t : RBTree α lt) (a : α) : RBTree α lt :=
 RBMap.erase t a
@@ -77,13 +77,13 @@ def fromList (l : List α) (lt : α → α → Bool) : RBTree α lt :=
 l.foldl insert (mkRBTree α lt)
 
 @[inline] def all (t : RBTree α lt) (p : α → Bool) : Bool :=
-RBMap.all t (λ a _, p a)
+RBMap.all t (fun a _ => p a)
 
 @[inline] def any (t : RBTree α lt) (p : α → Bool) : Bool :=
-RBMap.any t (λ a _, p a)
+RBMap.any t (fun a _ => p a)
 
 def subset (t₁ t₂ : RBTree α lt) : Bool :=
-t₁.all $ λ a, (t₂.find a).toBool
+t₁.all $ fun a => (t₂.find a).toBool
 
 def seteq (t₁ t₂ : RBTree α lt) : Bool :=
 subset t₁ t₂ && subset t₂ t₁
diff --git a/library/init/data/repr.lean b/library/init/data/repr.lean
index 7c1db01403..ed635bd29c 100644
--- a/library/init/data/repr.lean
+++ b/library/init/data/repr.lean
@@ -19,10 +19,10 @@ instance {α : Type u} [HasRepr α] : HasRepr (id α) :=
 inferInstanceAs (HasRepr α)
 
 instance : HasRepr Bool :=
-⟨λ b, cond b "true" "false"⟩
+⟨fun b => cond b "true" "false"⟩
 
 instance {p : Prop} : HasRepr (Decidable p) :=
-⟨λ b : Decidable p, @ite p b _ "true" "false"⟩
+⟨fun b => @ite p b _ "true" "false"⟩
 
 protected def List.reprAux {α : Type u} [HasRepr α] : Bool → List α → String
 | b     []      := ""
@@ -37,22 +37,22 @@ instance {α : Type u} [HasRepr α] : HasRepr (List α) :=
 ⟨List.repr⟩
 
 instance : HasRepr Unit :=
-⟨λ u, "()"⟩
+⟨fun u => "()"⟩
 
 instance {α : Type u} [HasRepr α] : HasRepr (Option α) :=
-⟨λ o, match o with | none := "none" | (some a) := "(some " ++ repr a ++ ")"⟩
+⟨fun o => match o with | none := "none" | (some a) := "(some " ++ repr a ++ ")"⟩
 
 instance {α : Type u} {β : Type v} [HasRepr α] [HasRepr β] : HasRepr (α ⊕ β) :=
-⟨λ s, match s with | (inl a) := "(inl " ++ repr a ++ ")" | (inr b) := "(inr " ++ repr b ++ ")"⟩
+⟨fun s => match s with | (inl a) := "(inl " ++ repr a ++ ")" | (inr b) := "(inr " ++ repr b ++ ")"⟩
 
 instance {α : Type u} {β : Type v} [HasRepr α] [HasRepr β] : HasRepr (α × β) :=
-⟨λ ⟨a, b⟩, "(" ++ repr a ++ ", " ++ repr b ++ ")"⟩
+⟨fun ⟨a, b⟩ => "(" ++ repr a ++ ", " ++ repr b ++ ")"⟩
 
 instance {α : Type u} {β : α → Type v} [HasRepr α] [s : ∀ x, HasRepr (β x)] : HasRepr (Sigma β) :=
-⟨λ ⟨a, b⟩, "⟨"  ++ repr a ++ ", " ++ repr b ++ "⟩"⟩
+⟨fun ⟨a, b⟩ => "⟨"  ++ repr a ++ ", " ++ repr b ++ "⟩"⟩
 
 instance {α : Type u} {p : α → Prop} [HasRepr α] : HasRepr (Subtype p) :=
-⟨λ s, repr (val s)⟩
+⟨fun s => repr (val s)⟩
 
 namespace Nat
 
@@ -112,7 +112,7 @@ else if  c.toNat <= 31 ∨ c = '\x7f' then "\\x" ++ charToHex c
 else String.singleton c
 
 instance : HasRepr Char :=
-⟨λ c, "'" ++ Char.quoteCore c ++ "'"⟩
+⟨fun c => "'" ++ Char.quoteCore c ++ "'"⟩
 
 def String.quoteAux : List Char → String
 | []      := ""
@@ -126,18 +126,18 @@ instance : HasRepr String :=
 ⟨String.quote⟩
 
 instance : HasRepr Substring :=
-⟨λ s, String.quote s.toString ++ ".toSubstring"⟩
+⟨fun s => String.quote s.toString ++ ".toSubstring"⟩
 
 instance : HasRepr String.Iterator :=
-⟨λ it, it.remainingToString.quote ++ ".mkIterator"⟩
+⟨fun it => it.remainingToString.quote ++ ".mkIterator"⟩
 
 instance (n : Nat) : HasRepr (Fin n) :=
-⟨λ f, repr (Fin.val f)⟩
+⟨fun f => repr (Fin.val f)⟩
 
-instance : HasRepr UInt16 := ⟨λ n, repr n.toNat⟩
-instance : HasRepr UInt32 := ⟨λ n, repr n.toNat⟩
-instance : HasRepr UInt64 := ⟨λ n, repr n.toNat⟩
-instance : HasRepr USize  := ⟨λ n, repr n.toNat⟩
+instance : HasRepr UInt16 := ⟨fun n => repr n.toNat⟩
+instance : HasRepr UInt32 := ⟨fun n => repr n.toNat⟩
+instance : HasRepr UInt64 := ⟨fun n => repr n.toNat⟩
+instance : HasRepr USize  := ⟨fun n => repr n.toNat⟩
 
 def Char.repr (c : Char) : String :=
 repr c
diff --git a/library/init/data/string/basic.lean b/library/init/data/string/basic.lean
index d1a4b41fcc..d2cd2a1905 100644
--- a/library/init/data/string/basic.lean
+++ b/library/init/data/string/basic.lean
@@ -23,7 +23,7 @@ def String.decEq (s₁ s₂ : @& String) : Decidable (s₁ = s₂) :=
 match s₁, s₂ with
 | ⟨s₁⟩, ⟨s₂⟩ :=
  if h : s₁ = s₂ then isTrue (congrArg _ h)
- else isFalse (λ h', String.noConfusion h' (λ h', absurd h' h))
+ else isFalse (fun h' => String.noConfusion h' (fun h' => absurd h' h))
 
 instance : DecidableEq String :=
 {decEq := String.decEq}
@@ -33,7 +33,7 @@ def List.asString (s : List Char) : String :=
 
 namespace String
 instance : HasLess String :=
-⟨λ s₁ s₂, s₁.data < s₂.data⟩
+⟨fun s₁ s₂ => s₁.data < s₂.data⟩
 
 @[extern cpp "lean::string_dec_lt"]
 instance decLt (s₁ s₂ : @& String) : Decidable (s₁ < s₂) :=
@@ -170,13 +170,13 @@ instance : HasAppend String :=
 def str : String → Char → String := push
 
 def pushn (s : String) (c : Char) (n : Nat) : String :=
-n.repeat (λ s, s.push c) s
+n.repeat (fun s => s.push c) s
 
 def isEmpty (s : String) : Bool :=
 s.bsize == 0
 
 def join (l : List String) : String :=
-l.foldl (λ r s, r ++ s) ""
+l.foldl (fun r s => r ++ s) ""
 
 def singleton (c : Char) : String :=
 "".push c
@@ -292,10 +292,10 @@ foldrAux f a s s.bsize 0
 anyAux s s.bsize p 0
 
 @[inline] def all (s : String) (p : Char → Bool) : Bool :=
-!s.any (λ c, !p c)
+!s.any (fun c => !p c)
 
 def contains (s : String) (c : Char) : Bool :=
-s.any (λ a, a == c)
+s.any (fun a => a == c)
 
 @[specialize] partial def mapAux (f : Char → Char) : Pos → String → String
 | i s :=
@@ -309,10 +309,10 @@ s.any (λ a, a == c)
 mapAux f 0 s
 
 def toNat (s : String) : Nat :=
-s.foldl (λ n c, n*10 + (c.toNat - '0'.toNat)) 0
+s.foldl (fun n c => n*10 + (c.toNat - '0'.toNat)) 0
 
 def isNat (s : String) : Bool :=
-s.all $ λ c, c.isDigit
+s.all $ fun c => c.isDigit
 
 partial def isPrefixOfAux (p s : String) : Pos → Bool
 | i :=
@@ -409,10 +409,10 @@ match s with
 | ⟨s, b, e⟩ := String.anyAux s e p b
 
 @[inline] def all (s : Substring) (p : Char → Bool) : Bool :=
-!s.any (λ c, !p c)
+!s.any (fun c => !p c)
 
 def contains (s : Substring) (c : Char) : Bool :=
-s.any (λ a, a == c)
+s.any (fun a => a == c)
 
 @[specialize] partial def takeWhileAux (s : String) (stopPos : String.Pos) (p : Char → Bool) : String.Pos → String.Pos
 | i :=
@@ -462,10 +462,10 @@ s.dropRightWhile Char.isWhitespace
   ⟨s, b, e⟩
 
 def toNat (s : Substring) : Nat :=
-s.foldl (λ n c, n*10 + (c.toNat - '0'.toNat)) 0
+s.foldl (fun n c => n*10 + (c.toNat - '0'.toNat)) 0
 
 def isNat (s : Substring) : Bool :=
-s.all $ λ c, c.isDigit
+s.all $ fun c => c.isDigit
 
 end Substring
 
diff --git a/library/init/data/tostring.lean b/library/init/data/tostring.lean
index d42583a181..1d50163b46 100644
--- a/library/init/data/tostring.lean
+++ b/library/init/data/tostring.lean
@@ -19,20 +19,20 @@ instance {α : Type u} [HasToString α] : HasToString (id α) :=
 inferInstanceAs (HasToString α)
 
 instance : HasToString String :=
-⟨λ s, s⟩
+⟨fun s => s⟩
 
 instance : HasToString Substring :=
-⟨λ s, s.toString⟩
+⟨fun s => s.toString⟩
 
 instance : HasToString String.Iterator :=
-⟨λ it, it.remainingToString⟩
+⟨fun it => it.remainingToString⟩
 
 instance : HasToString Bool :=
-⟨λ b, cond b "true" "false"⟩
+⟨fun b => cond b "true" "false"⟩
 
 instance {p : Prop} : HasToString (Decidable p) :=
 -- Remark: type class inference will not consider local instance `b` in the new Elaborator
-⟨λ b : Decidable p, @ite p b _ "true" "false"⟩
+⟨fun b => @ite p b _ "true" "false"⟩
 
 protected def List.toStringAux {α : Type u} [HasToString α] : Bool → List α → String
 | b     []      := ""
@@ -47,43 +47,43 @@ instance {α : Type u} [HasToString α] : HasToString (List α) :=
 ⟨List.toString⟩
 
 instance : HasToString Unit :=
-⟨λ u, "()"⟩
+⟨fun u => "()"⟩
 
 instance : HasToString Nat :=
-⟨λ n, repr n⟩
+⟨fun n => repr n⟩
 
 instance : HasToString Char :=
-⟨λ c, c.toString⟩
+⟨fun c => c.toString⟩
 
 instance (n : Nat) : HasToString (Fin n) :=
-⟨λ f, toString (Fin.val f)⟩
+⟨fun f => toString (Fin.val f)⟩
 
 instance : HasToString UInt8 :=
-⟨λ n, toString n.toNat⟩
+⟨fun n => toString n.toNat⟩
 
 instance : HasToString UInt16 :=
-⟨λ n, toString n.toNat⟩
+⟨fun n => toString n.toNat⟩
 
 instance : HasToString UInt32 :=
-⟨λ n, toString n.toNat⟩
+⟨fun n => toString n.toNat⟩
 
 instance : HasToString UInt64 :=
-⟨λ n, toString n.toNat⟩
+⟨fun n => toString n.toNat⟩
 
 instance : HasToString USize :=
-⟨λ n, toString n.toNat⟩
+⟨fun n => toString n.toNat⟩
 
 instance {α : Type u} [HasToString α] : HasToString (Option α) :=
-⟨λ o, match o with | none := "none" | (some a) := "(some " ++ toString a ++ ")"⟩
+⟨fun o => match o with | none := "none" | (some a) := "(some " ++ toString a ++ ")"⟩
 
 instance {α : Type u} {β : Type v} [HasToString α] [HasToString β] : HasToString (α ⊕ β) :=
-⟨λ s, match s with | (inl a) := "(inl " ++ toString a ++ ")" | (inr b) := "(inr " ++ toString b ++ ")"⟩
+⟨fun s => match s with | (inl a) := "(inl " ++ toString a ++ ")" | (inr b) := "(inr " ++ toString b ++ ")"⟩
 
 instance {α : Type u} {β : Type v} [HasToString α] [HasToString β] : HasToString (α × β) :=
-⟨λ ⟨a, b⟩, "(" ++ toString a ++ ", " ++ toString b ++ ")"⟩
+⟨fun ⟨a, b⟩ => "(" ++ toString a ++ ", " ++ toString b ++ ")"⟩
 
 instance {α : Type u} {β : α → Type v} [HasToString α] [s : ∀ x, HasToString (β x)] : HasToString (Sigma β) :=
-⟨λ ⟨a, b⟩, "⟨"  ++ toString a ++ ", " ++ toString b ++ "⟩"⟩
+⟨fun ⟨a, b⟩ => "⟨"  ++ toString a ++ ", " ++ toString b ++ "⟩"⟩
 
 instance {α : Type u} {p : α → Prop} [HasToString α] : HasToString (Subtype p) :=
-⟨λ s, toString (val s)⟩
+⟨fun s => toString (val s)⟩
diff --git a/library/init/data/uint.lean b/library/init/data/uint.lean
index b4201143b1..7780591a48 100644
--- a/library/init/data/uint.lean
+++ b/library/init/data/uint.lean
@@ -49,17 +49,17 @@ instance : Inhabited UInt8   := ⟨0⟩
 
 @[extern cpp inline "#1 == #2"]
 def UInt8.decEq (a b : UInt8) : Decidable (a = b) :=
-UInt8.casesOn a $ λ n, UInt8.casesOn b $ λ m,
-  if h : n = m then isTrue (h ▸ rfl) else isFalse (λ h', UInt8.noConfusion h' (λ h', absurd h' h))
+UInt8.casesOn a $ fun n => UInt8.casesOn b $ fun m =>
+  if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt8.noConfusion h' (fun h' => absurd h' h))
 
 @[extern cpp inline "#1 < #2"]
 def UInt8.decLt (a b : UInt8) : Decidable (a < b) :=
-UInt8.casesOn a $ λ n, UInt8.casesOn b $ λ m,
+UInt8.casesOn a $ fun n => UInt8.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n < m))
 
 @[extern cpp inline "#1 <= #2"]
 def UInt8.decLe (a b : UInt8) : Decidable (a ≤ b) :=
-UInt8.casesOn a $ λ n, UInt8.casesOn b $ λ m,
+UInt8.casesOn a $ fun n => UInt8.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n <= m))
 
 instance : DecidableEq UInt8 := {decEq := UInt8.decEq}
@@ -107,17 +107,17 @@ instance : Inhabited UInt16   := ⟨0⟩
 
 @[extern cpp inline "#1 == #2"]
 def UInt16.decEq (a b : UInt16) : Decidable (a = b) :=
-UInt16.casesOn a $ λ n, UInt16.casesOn b $ λ m,
-  if h : n = m then isTrue (h ▸ rfl) else isFalse (λ h', UInt16.noConfusion h' (λ h', absurd h' h))
+UInt16.casesOn a $ fun n => UInt16.casesOn b $ fun m =>
+  if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt16.noConfusion h' (fun h' => absurd h' h))
 
 @[extern cpp inline "#1 < #2"]
 def UInt16.decLt (a b : UInt16) : Decidable (a < b) :=
-UInt16.casesOn a $ λ n, UInt16.casesOn b $ λ m,
+UInt16.casesOn a $ fun n => UInt16.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n < m))
 
 @[extern cpp inline "#1 <= #2"]
 def UInt16.decLe (a b : UInt16) : Decidable (a ≤ b) :=
-UInt16.casesOn a $ λ n, UInt16.casesOn b $ λ m,
+UInt16.casesOn a $ fun n => UInt16.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n <= m))
 
 instance : DecidableEq UInt16 := {decEq := UInt16.decEq}
@@ -165,17 +165,17 @@ instance : Inhabited UInt32   := ⟨0⟩
 
 @[extern cpp inline "#1 == #2"]
 def UInt32.decEq (a b : UInt32) : Decidable (a = b) :=
-UInt32.casesOn a $ λ n, UInt32.casesOn b $ λ m,
-  if h : n = m then isTrue (h ▸ rfl) else isFalse (λ h', UInt32.noConfusion h' (λ h', absurd h' h))
+UInt32.casesOn a $ fun n => UInt32.casesOn b $ fun m =>
+  if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt32.noConfusion h' (fun h' => absurd h' h))
 
 @[extern cpp inline "#1 < #2"]
 def UInt32.decLt (a b : UInt32) : Decidable (a < b) :=
-UInt32.casesOn a $ λ n, UInt32.casesOn b $ λ m,
+UInt32.casesOn a $ fun n => UInt32.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n < m))
 
 @[extern cpp inline "#1 <= #2"]
 def UInt32.decLe (a b : UInt32) : Decidable (a ≤ b) :=
-UInt32.casesOn a $ λ n, UInt32.casesOn b $ λ m,
+UInt32.casesOn a $ fun n => UInt32.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n <= m))
 
 instance : DecidableEq UInt32 := {decEq := UInt32.decEq}
@@ -223,17 +223,17 @@ instance : Inhabited UInt64   := ⟨0⟩
 
 @[extern cpp inline "#1 == #2"]
 def UInt64.decEq (a b : UInt64) : Decidable (a = b) :=
-UInt64.casesOn a $ λ n, UInt64.casesOn b $ λ m,
-  if h : n = m then isTrue (h ▸ rfl) else isFalse (λ h', UInt64.noConfusion h' (λ h', absurd h' h))
+UInt64.casesOn a $ fun n => UInt64.casesOn b $ fun m =>
+  if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => UInt64.noConfusion h' (fun h' => absurd h' h))
 
 @[extern cpp inline "#1 < #2"]
 def UInt64.decLt (a b : UInt64) : Decidable (a < b) :=
-UInt64.casesOn a $ λ n, UInt64.casesOn b $ λ m,
+UInt64.casesOn a $ fun n => UInt64.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n < m))
 
 @[extern cpp inline "#1 <= #2"]
 def UInt64.decLe (a b : UInt64) : Decidable (a ≤ b) :=
-UInt64.casesOn a $ λ n, UInt64.casesOn b $ λ m,
+UInt64.casesOn a $ fun n => UInt64.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n <= m))
 
 instance : DecidableEq UInt64 := {decEq := UInt64.decEq}
@@ -290,17 +290,17 @@ instance : Inhabited USize   := ⟨0⟩
 
 @[extern cpp inline "#1 == #2"]
 def USize.decEq (a b : USize) : Decidable (a = b) :=
-USize.casesOn a $ λ n, USize.casesOn b $ λ m,
-  if h : n = m then isTrue (h ▸ rfl) else isFalse (λ h', USize.noConfusion h' (λ h', absurd h' h))
+USize.casesOn a $ fun n => USize.casesOn b $ fun m =>
+  if h : n = m then isTrue (h ▸ rfl) else isFalse (fun h' => USize.noConfusion h' (fun h' => absurd h' h))
 
 @[extern cpp inline "#1 < #2"]
 def USize.decLt (a b : USize) : Decidable (a < b) :=
-USize.casesOn a $ λ n, USize.casesOn b $ λ m,
+USize.casesOn a $ fun n => USize.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n < m))
 
 @[extern cpp inline "#1 <= #2"]
 def USize.decLe (a b : USize) : Decidable (a ≤ b) :=
-USize.casesOn a $ λ n, USize.casesOn b $ λ m,
+USize.casesOn a $ fun n => USize.casesOn b $ fun m =>
   inferInstanceAs (Decidable (n <= m))
 
 instance : DecidableEq USize := {decEq := USize.decEq}
diff --git a/library/init/fix.lean b/library/init/fix.lean
index 0599738219..f488bcc1b2 100644
--- a/library/init/fix.lean
+++ b/library/init/fix.lean
@@ -19,10 +19,10 @@ bfix1 base rec usizeSz
 fixCore1 base rec
 
 @[inline] def fix1 {α β : Type u} [Inhabited β] (rec : (α → β) → α → β) : α → β :=
-fixCore1 (λ _, default β) rec
+fixCore1 (fun _ => default β) rec
 
 @[inline] def fix {α β : Type u} [Inhabited β] (rec : (α → β) → α → β) : α → β :=
-fixCore1 (λ _, default β) rec
+fixCore1 (fun _ => default β) rec
 
 def bfix2 {α₁ α₂ β : Type u} (base : α₁ → α₂ → β) (rec : (α₁ → α₂ → β) → α₁ → α₂ → β) : Nat → α₁ → α₂ → β
 | 0     a₁ a₂ := base a₁ a₂
@@ -33,7 +33,7 @@ def fixCore2 {α₁ α₂ β : Type u} (base : α₁ → α₂ → β) (rec : (
 bfix2 base rec usizeSz
 
 @[inline] def fix2 {α₁ α₂ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → β) → α₁ → α₂ → β) : α₁ → α₂ → β :=
-fixCore2 (λ _ _, default β) rec
+fixCore2 (fun _ _ => default β) rec
 
 def bfix3 {α₁ α₂ α₃ β : Type u} (base : α₁ → α₂ → α₃ → β) (rec : (α₁ → α₂ → α₃ → β) → α₁ → α₂ → α₃ → β) : Nat → α₁ → α₂ → α₃ → β
 | 0     a₁ a₂ a₃ := base a₁ a₂ a₃
@@ -44,7 +44,7 @@ def fixCore3 {α₁ α₂ α₃ β : Type u} (base : α₁ → α₂ → α₃ 
 bfix3 base rec usizeSz
 
 @[inline] def fix3 {α₁ α₂ α₃ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → β) → α₁ → α₂ → α₃ → β) : α₁ → α₂ → α₃ → β :=
-fixCore3 (λ _ _ _, default β) rec
+fixCore3 (fun _ _ _ => default β) rec
 
 def bfix4 {α₁ α₂ α₃ α₄ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → β) (rec : (α₁ → α₂ → α₃ → α₄ → β) → α₁ → α₂ → α₃ → α₄ → β) : Nat → α₁ → α₂ → α₃ → α₄ → β
 | 0     a₁ a₂ a₃ a₄ := base a₁ a₂ a₃ a₄
@@ -55,7 +55,7 @@ def fixCore4 {α₁ α₂ α₃ α₄ β : Type u} (base : α₁ → α₂ → 
 bfix4 base rec usizeSz
 
 @[inline] def fix4 {α₁ α₂ α₃ α₄ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → α₄ → β) → α₁ → α₂ → α₃ → α₄ → β) : α₁ → α₂ → α₃ → α₄ → β :=
-fixCore4 (λ _ _ _ _, default β) rec
+fixCore4 (fun _ _ _ _ => default β) rec
 
 def bfix5 {α₁ α₂ α₃ α₄ α₅ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → α₅ → β) (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → β) : Nat → α₁ → α₂ → α₃ → α₄ → α₅ → β
 | 0     a₁ a₂ a₃ a₄ a₅ := base a₁ a₂ a₃ a₄ a₅
@@ -66,7 +66,7 @@ def fixCore5 {α₁ α₂ α₃ α₄ α₅ β : Type u} (base : α₁ → α₂
 bfix5 base rec usizeSz
 
 @[inline] def fix5 {α₁ α₂ α₃ α₄ α₅ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → β) : α₁ → α₂ → α₃ → α₄ → α₅ → β :=
-fixCore5 (λ _ _ _ _ _, default β) rec
+fixCore5 (fun _ _ _ _ _ => default β) rec
 
 def bfix6 {α₁ α₂ α₃ α₄ α₅ α₆ β : Type u} (base : α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) : Nat → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β
 | 0     a₁ a₂ a₃ a₄ a₅ a₆ := base a₁ a₂ a₃ a₄ a₅ a₆
@@ -77,4 +77,4 @@ def fixCore6 {α₁ α₂ α₃ α₄ α₅ α₆ β : Type u} (base : α₁ →
 bfix6 base rec usizeSz
 
 @[inline] def fix6 {α₁ α₂ α₃ α₄ α₅ α₆ β : Type u} [Inhabited β] (rec : (α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) → α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β) : α₁ → α₂ → α₃ → α₄ → α₅ → α₆ → β :=
-fixCore6 (λ _ _ _ _ _ _, default β) rec
+fixCore6 (fun _ _ _ _ _ _ => default β) rec
diff --git a/library/init/io.lean b/library/init/io.lean
index 07cdde2418..81f2502842 100644
--- a/library/init/io.lean
+++ b/library/init/io.lean
@@ -153,7 +153,7 @@ do b ← h.read 1,
 -- h.putStr s *> h.putStr "\n"
 
 def handle.readToEnd (h : handle) : m String :=
-Prim.liftIO $ Prim.iterate "" $ λ r, do
+Prim.liftIO $ Prim.iterate "" $ fun r => do
   done ← h.isEof;
   if done
   then pure (Sum.inr r) -- stop
@@ -256,11 +256,11 @@ class HasEval (α : Type u) :=
 (eval : α → IO Unit)
 
 instance HasRepr.HasEval {α : Type u} [HasRepr α] : HasEval α :=
-⟨λ a, IO.println (repr a)⟩
+⟨fun a => IO.println (repr a)⟩
 
 instance IO.HasEval {α : Type} [HasEval α] : HasEval (IO α) :=
-⟨λ x, do a ← x; HasEval.eval a⟩
+⟨fun x => do a ← x; HasEval.eval a⟩
 
 -- special case: do not print `()`
 instance IOUnit.HasEval : HasEval (IO Unit) :=
-⟨λ x, x⟩
+⟨fun x => x⟩
diff --git a/library/init/lean/attributes.lean b/library/init/lean/attributes.lean
index 5aee30a245..9ccc1e60b0 100644
--- a/library/init/lean/attributes.lean
+++ b/library/init/lean/attributes.lean
@@ -29,8 +29,8 @@ end ScopeManagerState
 def regScopeManagerExtension : IO (SimplePersistentEnvExtension Name ScopeManagerState) :=
 registerSimplePersistentEnvExtension {
   name            := `scopes,
-  addImportedFn   := λ as, mkStateFromImportedEntries ScopeManagerState.saveNamespace {} as,
-  addEntryFn      := λ s n, { allNamespaces := s.allNamespaces.insert n, .. s },
+  addImportedFn   := fun as => mkStateFromImportedEntries ScopeManagerState.saveNamespace {} as,
+  addEntryFn      := fun s n => { allNamespaces := s.allNamespaces.insert n, .. s },
 }
 
 @[init regScopeManagerExtension]
@@ -76,7 +76,7 @@ def toValidNamespace (env : Environment) (n : Name) : Option Name :=
 let s := scopeManagerExt.getState env;
 if s.allNamespaces.contains n then some n
 else s.namespaces.foldl
-  (λ r ns, match r with
+  (fun r ns => match r with
     | some _ := r
     | none   :=
       let c := ns ++ n;
@@ -95,7 +95,7 @@ def pushScopeCore (env : Environment) (header : Name) (isNamespace : Bool) : Env
 let ns    := env.getNamespace;
 let newNs := if isNamespace then ns ++ header else ns;
 let env   := env.registerNamespaceAux newNs;
-let env   := scopeManagerExt.modifyState env $ λ s,
+let env   := scopeManagerExt.modifyState env $ fun s =>
   { headers     := header :: s.headers,
     namespaces  := newNs :: s.namespaces,
     isNamespace := isNamespace :: s.isNamespace,
@@ -104,7 +104,7 @@ env
 
 def popScopeCore (env : Environment) : Environment :=
 if env.getNamespaces.isEmpty then env
-else scopeManagerExt.modifyState env $ λ s,
+else scopeManagerExt.modifyState env $ fun s =>
   { headers     := s.headers.tail,
     namespaces  := s.namespaces.tail,
     isNamespace := s.isNamespace.tail,
@@ -129,7 +129,7 @@ structure AttributeImpl :=
 (applicationTime := AttributeApplicationTime.afterTypeChecking)
 
 instance AttributeImpl.inhabited : Inhabited AttributeImpl :=
-⟨{ name := default _, descr := default _, add := λ env _ _ _, pure env }⟩
+⟨{ name := default _, descr := default _, add := fun env _ _ _ => pure env }⟩
 
 def mkAttributeMapRef : IO (IO.Ref (HashMap Name AttributeImpl)) :=
 IO.mkRef {}
@@ -149,8 +149,8 @@ do m ← attributeMapRef.get;
    when (m.contains attr.name) $ throw (IO.userError ("invalid attribute declaration, '" ++ toString attr.name ++ "' has already been used"));
    initializing ← IO.initializing;
    unless initializing $ throw (IO.userError ("failed to register attribute, attributes can only be registered during initialization"));
-   attributeMapRef.modify (λ m, m.insert attr.name attr);
-   attributeArrayRef.modify (λ attrs, attrs.push attr)
+   attributeMapRef.modify (fun m => m.insert attr.name attr);
+   attributeArrayRef.modify (fun attrs => attrs.push attr)
 
 /- Return true iff `n` is the name of a registered attribute. -/
 @[export lean.is_attribute_core]
@@ -159,7 +159,7 @@ do m ← attributeMapRef.get; pure (m.contains n)
 
 /- Return the name of all registered attributes. -/
 def getAttributeNames : IO (List Name) :=
-do m ← attributeMapRef.get; pure $ m.fold (λ r n _, n::r) []
+do m ← attributeMapRef.get; pure $ m.fold (fun r n _ => n::r) []
 
 def getAttributeImpl (attrName : Name) : IO AttributeImpl :=
 do m ← attributeMapRef.get;
@@ -218,7 +218,7 @@ do attr ← getAttributeImpl attrName;
 @[export lean.activate_scoped_attributes_core]
 def activateScopedAttributes (env : Environment) (scope : Name) : IO Environment :=
 do attrs ← attributeArrayRef.get;
-   attrs.mfoldl (λ env attr, attr.activateScoped env scope) env
+   attrs.mfoldl (fun env attr => attr.activateScoped env scope) env
 
 /- We use this function to implement commands `namespace foo` and `section foo`.
    It activates scoped attributes in the new resulting namespace. -/
@@ -227,14 +227,14 @@ def pushScope (env : Environment) (header : Name) (isNamespace : Bool) : IO Envi
 do let env := env.pushScopeCore header isNamespace;
    let ns  := env.getNamespace;
    attrs ← attributeArrayRef.get;
-   attrs.mfoldl (λ env attr, do env ← attr.pushScope env; if isNamespace then attr.activateScoped env ns else pure env) env
+   attrs.mfoldl (fun env attr => do env ← attr.pushScope env; if isNamespace then attr.activateScoped env ns else pure env) env
 
 /- We use this function to implement commands `end foo` for closing namespaces and sections. -/
 @[export lean.pop_scope_core]
 def popScope (env : Environment) : IO Environment :=
 do let env := env.popScopeCore;
    attrs ← attributeArrayRef.get;
-   attrs.mfoldl (λ env attr, attr.popScope env) env
+   attrs.mfoldl (fun env attr => attr.popScope env) env
 
 end Environment
 
@@ -250,21 +250,21 @@ structure TagAttribute :=
 (attr : AttributeImpl)
 (ext  : PersistentEnvExtension Name NameSet)
 
-def registerTagAttribute (name : Name) (descr : String) (validate : Environment → Name → Except String Unit := λ _ _, Except.ok ()) : IO TagAttribute :=
+def registerTagAttribute (name : Name) (descr : String) (validate : Environment → Name → Except String Unit := fun _ _ => Except.ok ()) : IO TagAttribute :=
 do
 ext : PersistentEnvExtension Name NameSet ← registerPersistentEnvExtension {
   name            := name,
-  addImportedFn   := λ _, {},
-  addEntryFn      := λ (s : NameSet) n, s.insert n,
-  exportEntriesFn := λ es,
-    let r : Array Name := es.fold (λ a e, a.push e) Array.empty;
+  addImportedFn   := fun _ => {},
+  addEntryFn      := fun (s : NameSet) n => s.insert n,
+  exportEntriesFn := fun es =>
+    let r : Array Name := es.fold (fun a e => a.push e) Array.empty;
     r.qsort Name.quickLt,
-  statsFn         := λ s, "tag attribute" ++ Format.line ++ "number of local entries: " ++ format s.size
+  statsFn         := fun s => "tag attribute" ++ Format.line ++ "number of local entries: " ++ format s.size
 };
 let attrImpl : AttributeImpl := {
   name  := name,
   descr := descr,
-  add   := λ env decl args persistent, do
+  add   := fun env decl args persistent => do
     unless args.isMissing $ throw (IO.userError ("invalid attribute '" ++ toString name ++ "', unexpected argument"));
     unless persistent $ throw (IO.userError ("invalid attribute '" ++ toString name ++ "', must be persistent"));
     unless (env.getModuleIdxFor decl).isNone $
@@ -299,21 +299,21 @@ structure ParametricAttribute (α : Type) :=
 
 def registerParametricAttribute {α : Type} [Inhabited α] (name : Name) (descr : String)
        (getParam : Environment → Name → Syntax → Except String α)
-       (afterSet : Environment → Name → α → Except String Environment := λ env _ _, Except.ok env) : IO (ParametricAttribute α) :=
+       (afterSet : Environment → Name → α → Except String Environment := fun env _ _ => Except.ok env) : IO (ParametricAttribute α) :=
 do
 ext : PersistentEnvExtension (Name × α) (NameMap α) ← registerPersistentEnvExtension {
   name            := name,
-  addImportedFn   := λ _, {},
-  addEntryFn      := λ (s : NameMap α) (p : Name × α), s.insert p.1 p.2,
-  exportEntriesFn := λ m,
-    let r : Array (Name × α) := m.fold (λ a n p, a.push (n, p)) Array.empty;
-    r.qsort (λ a b, Name.quickLt a.1 b.1),
-  statsFn         := λ s, "parametric attribute" ++ Format.line ++ "number of local entries: " ++ format s.size
+  addImportedFn   := fun _ => {},
+  addEntryFn      := fun (s : NameMap α) (p : Name × α) => s.insert p.1 p.2,
+  exportEntriesFn := fun m =>
+    let r : Array (Name × α) := m.fold (fun a n p => a.push (n, p)) Array.empty;
+    r.qsort (fun a b => Name.quickLt a.1 b.1),
+  statsFn         := fun s => "parametric attribute" ++ Format.line ++ "number of local entries: " ++ format s.size
 };
 let attrImpl : AttributeImpl := {
   name  := name,
   descr := descr,
-  add   := λ env decl args persistent, do
+  add   := fun env decl args persistent => do
     unless persistent $ throw (IO.userError ("invalid attribute '" ++ toString name ++ "', must be persistent"));
     unless (env.getModuleIdxFor decl).isNone $
       throw (IO.userError ("invalid attribute '" ++ toString name ++ "', declaration is in an imported module"));
@@ -335,7 +335,7 @@ instance {α : Type} : Inhabited (ParametricAttribute α) := ⟨{attr := default
 def getParam {α : Type} [Inhabited α] (attr : ParametricAttribute α) (env : Environment) (decl : Name) : Option α :=
 match env.getModuleIdxFor decl with
 | some modIdx :=
-  match (attr.ext.getModuleEntries env modIdx).binSearch (decl, default _) (λ a b, Name.quickLt a.1 b.1) with
+  match (attr.ext.getModuleEntries env modIdx).binSearch (decl, default _) (fun a b => Name.quickLt a.1 b.1) with
   | some (_, val) := some val
   | none          := none
 | none        := (attr.ext.getState env).find decl
@@ -358,21 +358,21 @@ structure EnumAttributes (α : Type) :=
 (attrs : List AttributeImpl)
 (ext   : PersistentEnvExtension (Name × α) (NameMap α))
 
-def registerEnumAttributes {α : Type} [Inhabited α] (extName : Name) (attrDescrs : List (Name × String × α)) (validate : Environment → Name → α → Except String Unit := λ _ _ _, Except.ok ()) : IO (EnumAttributes α) :=
+def registerEnumAttributes {α : Type} [Inhabited α] (extName : Name) (attrDescrs : List (Name × String × α)) (validate : Environment → Name → α → Except String Unit := fun _ _ _ => Except.ok ()) : IO (EnumAttributes α) :=
 do
 ext : PersistentEnvExtension (Name × α) (NameMap α) ← registerPersistentEnvExtension {
   name            := extName,
-  addImportedFn   := λ _, {},
-  addEntryFn      := λ (s : NameMap α) (p : Name × α), s.insert p.1 p.2,
-  exportEntriesFn := λ m,
-    let r : Array (Name × α) := m.fold (λ a n p, a.push (n, p)) Array.empty;
-    r.qsort (λ a b, Name.quickLt a.1 b.1),
-  statsFn         := λ s, "enumeration attribute extension" ++ Format.line ++ "number of local entries: " ++ format s.size
+  addImportedFn   := fun _ => {},
+  addEntryFn      := fun (s : NameMap α) (p : Name × α) => s.insert p.1 p.2,
+  exportEntriesFn := fun m =>
+    let r : Array (Name × α) := m.fold (fun a n p => a.push (n, p)) Array.empty;
+    r.qsort (fun a b => Name.quickLt a.1 b.1),
+  statsFn         := fun s => "enumeration attribute extension" ++ Format.line ++ "number of local entries: " ++ format s.size
 };
-let attrs := attrDescrs.map $ λ ⟨name, descr, val⟩, { AttributeImpl .
+let attrs := attrDescrs.map $ fun ⟨name, descr, val⟩ => { AttributeImpl .
   name  := name,
   descr := descr,
-  add   := λ env decl args persistent, do
+  add   := fun env decl args persistent => do
     unless persistent $ throw (IO.userError ("invalid attribute '" ++ toString name ++ "', must be persistent"));
     unless (env.getModuleIdxFor decl).isNone $
       throw (IO.userError ("invalid attribute '" ++ toString name ++ "', declaration is in an imported module"));
@@ -390,7 +390,7 @@ instance {α : Type} : Inhabited (EnumAttributes α) := ⟨{attrs := [], ext :=
 def getValue {α : Type} [Inhabited α] (attr : EnumAttributes α) (env : Environment) (decl : Name) : Option α :=
 match env.getModuleIdxFor decl with
 | some modIdx :=
-  match (attr.ext.getModuleEntries env modIdx).binSearch (decl, default _) (λ a b, Name.quickLt a.1 b.1) with
+  match (attr.ext.getModuleEntries env modIdx).binSearch (decl, default _) (fun a b => Name.quickLt a.1 b.1) with
   | some (_, val) := some val
   | none          := none
 | none        := (attr.ext.getState env).find decl
diff --git a/library/init/lean/class.lean b/library/init/lean/class.lean
index 04f86a0b91..20d3f83963 100644
--- a/library/init/lean/class.lean
+++ b/library/init/lean/class.lean
@@ -53,7 +53,7 @@ def mkClassExtension : IO (SimplePersistentEnvExtension ClassEntry ClassState) :
 registerSimplePersistentEnvExtension {
   name          := `classExt,
   addEntryFn    := ClassState.addEntry,
-  addImportedFn := λ es, (mkStateFromImportedEntries ClassState.addEntry {} es).switch
+  addImportedFn := fun es => (mkStateFromImportedEntries ClassState.addEntry {} es).switch
 }
 
 @[init mkClassExtension]
@@ -124,7 +124,7 @@ match env.find instName with
 registerAttribute {
   name  := `class,
   descr := "type class",
-  add   := λ env decl args persistent, do
+  add   := fun env decl args persistent => do
     unless args.isMissing $ throw (IO.userError ("invalid attribute 'class', unexpected argument"));
     unless persistent $ throw (IO.userError ("invalid attribute 'class', must be persistent"));
     IO.ofExcept (addClass env decl)
@@ -134,7 +134,7 @@ registerAttribute {
 registerAttribute {
   name  := `instance,
   descr := "type class instance",
-  add   := λ env decl args persistent, do
+  add   := fun env decl args persistent => do
     unless args.isMissing $ throw (IO.userError ("invalid attribute 'instance', unexpected argument"));
     unless persistent $ throw (IO.userError ("invalid attribute 'instance', must be persistent"));
     IO.ofExcept (addInstance env decl)
diff --git a/library/init/lean/compiler/closedtermcache.lean b/library/init/lean/compiler/closedtermcache.lean
index 81925e50db..e458505375 100644
--- a/library/init/lean/compiler/closedtermcache.lean
+++ b/library/init/lean/compiler/closedtermcache.lean
@@ -13,10 +13,10 @@ abbrev ClosedTermCache := SMap Expr Name Expr.quickLt
 def mkClosedTermCacheExtension : IO (SimplePersistentEnvExtension (Expr × Name) ClosedTermCache) :=
 registerSimplePersistentEnvExtension {
   name       := `closedTermCache,
-  addImportedFn := λ as,
-    let cache : ClosedTermCache := mkStateFromImportedEntries (λ s (p : Expr × Name), s.insert p.1 p.2) {} as;
+  addImportedFn := fun as =>
+    let cache : ClosedTermCache := mkStateFromImportedEntries (fun s (p : Expr × Name) => s.insert p.1 p.2) {} as;
     cache.switch,
-  addEntryFn := λ s ⟨e, n⟩, s.insert e n
+  addEntryFn := fun s ⟨e, n⟩ => s.insert e n
 }
 
 @[init mkClosedTermCacheExtension]
diff --git a/library/init/lean/compiler/constfolding.lean b/library/init/lean/compiler/constfolding.lean
index 22e6df41e3..3224d60c30 100644
--- a/library/init/lean/compiler/constfolding.lean
+++ b/library/init/lean/compiler/constfolding.lean
@@ -30,10 +30,10 @@ def numScalarTypes : List NumScalarTypeInfo :=
  {id := `USize, nbits := System.platform.nbits}]
 
 def isOfNat (fn : Name) : Bool :=
-numScalarTypes.any (λ info, info.ofNatFn = fn)
+numScalarTypes.any (fun info => info.ofNatFn = fn)
 
 def isToNat (fn : Name) : Bool :=
-numScalarTypes.any (λ info, info.toNatFn = fn)
+numScalarTypes.any (fun info => info.toNatFn = fn)
 
 def getInfoFromFn (fn : Name) : List NumScalarTypeInfo → Option NumScalarTypeInfo
 | []            := none
@@ -63,18 +63,18 @@ do n₁   ← getNumLit a₁;
    info ← getInfoFromVal a₁;
    pure $ mkUIntLit info (fn info beforeErasure n₁ n₂)
 
-def foldUIntAdd := foldBinUInt $ λ _ _, HasAdd.add
-def foldUIntMul := foldBinUInt $ λ _ _, HasMul.mul
-def foldUIntDiv := foldBinUInt $ λ _ _, HasDiv.div
-def foldUIntMod := foldBinUInt $ λ _ _, HasMod.mod
-def foldUIntSub := foldBinUInt $ λ info _ a b, (a + (info.size - b))
+def foldUIntAdd := foldBinUInt $ fun _ _ => HasAdd.add
+def foldUIntMul := foldBinUInt $ fun _ _ => HasMul.mul
+def foldUIntDiv := foldBinUInt $ fun _ _ => HasDiv.div
+def foldUIntMod := foldBinUInt $ fun _ _ => HasMod.mod
+def foldUIntSub := foldBinUInt $ fun info _ a b => (a + (info.size - b))
 
 def preUIntBinFoldFns : List (Name × BinFoldFn) :=
 [(`add, foldUIntAdd), (`mul, foldUIntMul), (`div, foldUIntDiv),
  (`mod, foldUIntMod), (`sub, foldUIntSub)]
 
 def uintBinFoldFns : List (Name × BinFoldFn) :=
-numScalarTypes.foldl (λ r info, r ++ (preUIntBinFoldFns.map (λ ⟨suffix, fn⟩, (info.id ++ suffix, fn)))) []
+numScalarTypes.foldl (fun r info => r ++ (preUIntBinFoldFns.map (fun ⟨suffix, fn⟩ => (info.id ++ suffix, fn)))) []
 
 def foldNatBinOp (fn : Nat → Nat → Nat) (a₁ a₂ : Expr) : Option Expr :=
 do n₁   ← getNumLit a₁;
@@ -109,9 +109,9 @@ do n₁   ← getNumLit a₁;
    n₂   ← getNumLit a₂;
    pure $ toDecidableExpr beforeErasure (mkPred a₁ a₂) (fn n₁ n₂)
 
-def foldNatDecEq := foldNatBinPred mkNatEq (λ a b, a = b)
-def foldNatDecLt := foldNatBinPred mkNatLt (λ a b, a < b)
-def foldNatDecLe := foldNatBinPred mkNatLe (λ a b, a ≤ b)
+def foldNatDecEq := foldNatBinPred mkNatEq (fun a b => a = b)
+def foldNatDecLt := foldNatBinPred mkNatLt (fun a b => a < b)
+def foldNatDecLe := foldNatBinPred mkNatLe (fun a b => a ≤ b)
 
 def natFoldFns : List (Name × BinFoldFn) :=
 [(`Nat.add, foldNatAdd),
@@ -171,7 +171,7 @@ do n ← getNumLit a;
    pure $ Expr.lit (Literal.natVal n)
 
 def uintFoldToNatFns : List (Name × UnFoldFn) :=
-numScalarTypes.foldl (λ r info, (info.toNatFn, foldToNat) :: r) []
+numScalarTypes.foldl (fun r info => (info.toNatFn, foldToNat) :: r) []
 
 def unFoldFns : List (Name × UnFoldFn) :=
 [(`Nat.succ, foldNatSucc),
diff --git a/library/init/lean/compiler/exportattr.lean b/library/init/lean/compiler/exportattr.lean
index f69173035e..79d60dac3e 100644
--- a/library/init/lean/compiler/exportattr.lean
+++ b/library/init/lean/compiler/exportattr.lean
@@ -10,7 +10,7 @@ namespace Lean
 
 private def isValidCppId (id : String) : Bool :=
 let first := id.get 0;
-first.isAlpha  && (id.toSubstring.drop 1).all (λ c, c.isAlpha || c.isDigit || c == '_')
+first.isAlpha  && (id.toSubstring.drop 1).all (fun c => c.isAlpha || c.isDigit || c == '_')
 
 private def isValidCppName : Name → Bool
 | (Name.mkString Name.anonymous s) := isValidCppId s
@@ -18,7 +18,7 @@ private def isValidCppName : Name → Bool
 | _ := false
 
 def mkExportAttr : IO (ParametricAttribute Name) :=
-registerParametricAttribute `export "name to be used by code generators" $ λ _ _ stx,
+registerParametricAttribute `export "name to be used by code generators" $ fun _ _ stx =>
   match attrParamSyntaxToIdentifier stx with
   | some exportName :=
     if isValidCppName exportName then Except.ok exportName
diff --git a/library/init/lean/compiler/externattr.lean b/library/init/lean/compiler/externattr.lean
index a0ba80f65a..2e12b6dba1 100644
--- a/library/init/lean/compiler/externattr.lean
+++ b/library/init/lean/compiler/externattr.lean
@@ -82,8 +82,8 @@ constant addExtern (env : Environment) (n : Name) : ExceptT String Id Environmen
 
 def mkExternAttr : IO (ParametricAttribute ExternAttrData) :=
 registerParametricAttribute `extern "builtin and foreign functions"
-  (λ _ _, syntaxToExternAttrData)
-  (λ env declName _,
+  (fun _ _ => syntaxToExternAttrData)
+  (fun env declName _ =>
     if env.isProjectionFn declName || env.isConstructor declName then
       addExtern env declName
     else
diff --git a/library/init/lean/compiler/implementedbyattr.lean b/library/init/lean/compiler/implementedbyattr.lean
index 0e5c38e0b6..17df597e50 100644
--- a/library/init/lean/compiler/implementedbyattr.lean
+++ b/library/init/lean/compiler/implementedbyattr.lean
@@ -10,7 +10,7 @@ namespace Lean
 namespace Compiler
 
 def mkImplementedByAttr : IO (ParametricAttribute Name) :=
-registerParametricAttribute `implementedBy "name of the Lean (probably unsafe) function that implements opaque constant" $ λ env declName stx,
+registerParametricAttribute `implementedBy "name of the Lean (probably unsafe) function that implements opaque constant" $ fun env declName stx =>
   match env.find declName with
   | none := Except.error "unknown declaration"
   | some decl :=
diff --git a/library/init/lean/compiler/initattr.lean b/library/init/lean/compiler/initattr.lean
index f32601d51c..9da6e6cc5e 100644
--- a/library/init/lean/compiler/initattr.lean
+++ b/library/init/lean/compiler/initattr.lean
@@ -23,7 +23,7 @@ match getIOTypeArg type with
 | _ := false
 
 def mkInitAttr : IO (ParametricAttribute Name) :=
-registerParametricAttribute `init "initialization procedure for global references" $ λ env declName stx,
+registerParametricAttribute `init "initialization procedure for global references" $ fun env declName stx =>
   match env.find declName with
   | none := Except.error "unknown declaration"
   | some decl :=
diff --git a/library/init/lean/compiler/inlineattrs.lean b/library/init/lean/compiler/inlineattrs.lean
index cd8b869a31..3c0f28f046 100644
--- a/library/init/lean/compiler/inlineattrs.lean
+++ b/library/init/lean/compiler/inlineattrs.lean
@@ -34,7 +34,7 @@ registerEnumAttributes `inlineAttrs
    (`inlineIfReduce, "mark definition to be inlined when resultant term after reduction is not a `cases_on` application", InlineAttributeKind.inlineIfReduce),
    (`noinline, "mark definition to never be inlined", InlineAttributeKind.noinline),
    (`macroInline, "mark definition to always be inlined before ANF conversion", InlineAttributeKind.macroInline)]
-  (λ env declName _, checkIsDefinition env declName)
+  (fun env declName _ => checkIsDefinition env declName)
 
 @[init mkInlineAttrs]
 constant inlineAttrs : EnumAttributes InlineAttributeKind := default _
diff --git a/library/init/lean/compiler/ir/basic.lean b/library/init/lean/compiler/ir/basic.lean
index fdf2077657..da705f1402 100644
--- a/library/init/lean/compiler/ir/basic.lean
+++ b/library/init/lean/compiler/ir/basic.lean
@@ -33,17 +33,17 @@ structure JoinPointId :=
 abbrev Index.lt (a b : Index) : Bool := a < b
 
 namespace VarId
-instance : HasBeq VarId := ⟨λ a b, a.idx == b.idx⟩
-instance : HasToString VarId := ⟨λ a, "x_" ++ toString a.idx⟩
-instance : HasFormat VarId := ⟨λ a, toString a⟩
-instance : Hashable VarId := ⟨λ a, hash a.idx⟩
+instance : HasBeq VarId := ⟨fun a b => a.idx == b.idx⟩
+instance : HasToString VarId := ⟨fun a => "x_" ++ toString a.idx⟩
+instance : HasFormat VarId := ⟨fun a => toString a⟩
+instance : Hashable VarId := ⟨fun a => hash a.idx⟩
 end VarId
 
 namespace JoinPointId
-instance : HasBeq JoinPointId := ⟨λ a b, a.idx == b.idx⟩
-instance : HasToString JoinPointId := ⟨λ a, "block_" ++ toString a.idx⟩
-instance : HasFormat JoinPointId := ⟨λ a, toString a⟩
-instance : Hashable JoinPointId := ⟨λ a, hash a.idx⟩
+instance : HasBeq JoinPointId := ⟨fun a b => a.idx == b.idx⟩
+instance : HasToString JoinPointId := ⟨fun a => "block_" ++ toString a.idx⟩
+instance : HasFormat JoinPointId := ⟨fun a => toString a⟩
+instance : Hashable JoinPointId := ⟨fun a => hash a.idx⟩
 end JoinPointId
 
 abbrev MData := KVMap
@@ -347,12 +347,12 @@ def reshape (bs : Array FnBody) (term : FnBody) : FnBody :=
 reshapeAux bs bs.size term
 
 @[inline] def modifyJPs (bs : Array FnBody) (f : FnBody → FnBody) : Array FnBody :=
-bs.map $ λ b, match b with
+bs.map $ fun b => match b with
   | FnBody.jdecl j xs v k := FnBody.jdecl j xs (f v) k
   | other                 := other
 
 @[inline] def mmodifyJPs {m : Type → Type} [Monad m] (bs : Array FnBody) (f : FnBody → m FnBody) : m (Array FnBody) :=
-bs.mmap $ λ b, match b with
+bs.mmap $ fun b => match b with
   | FnBody.jdecl j xs v k := do v ← f v; pure $ FnBody.jdecl j xs v k
   | other                 := pure other
 
@@ -468,7 +468,7 @@ def Arg.alphaEqv (ρ : IndexRenaming) : Arg → Arg → Bool
 instance Arg.hasAeqv : HasAlphaEqv Arg := ⟨Arg.alphaEqv⟩
 
 def args.alphaEqv (ρ : IndexRenaming) (args₁ args₂ : Array Arg) : Bool :=
-Array.isEqv args₁ args₂ (λ a b, aeqv ρ a b)
+Array.isEqv args₁ args₂ (fun a b => aeqv ρ a b)
 
 instance args.hasAeqv : HasAlphaEqv (Array Arg) := ⟨args.alphaEqv⟩
 
@@ -500,7 +500,7 @@ else none
 
 def addParamsRename (ρ : IndexRenaming) (ps₁ ps₂ : Array Param) : Option IndexRenaming :=
 if ps₁.size != ps₂.size then none
-else Array.foldl₂ (λ ρ p₁ p₂, do ρ ← ρ; addParamRename ρ p₁ p₂) (some ρ) ps₁ ps₂
+else Array.foldl₂ (fun ρ p₁ p₂ => do ρ ← ρ; addParamRename ρ p₁ p₂) (some ρ) ps₁ ps₂
 
 partial def FnBody.alphaEqv : IndexRenaming → FnBody → FnBody → Bool
 | ρ (FnBody.vdecl x₁ t₁ v₁ b₁)      (FnBody.vdecl x₂ t₂ v₂ b₂)        := t₁ == t₂ && aeqv ρ v₁ v₂ && FnBody.alphaEqv (addVarRename ρ x₁.idx x₂.idx) b₁ b₂
@@ -516,7 +516,7 @@ partial def FnBody.alphaEqv : IndexRenaming → FnBody → FnBody → Bool
 | ρ (FnBody.dec x₁ n₁ c₁ b₁)        (FnBody.dec x₂ n₂ c₂ b₂)          := aeqv ρ x₁ x₂ && n₁ == n₂ && c₁ == c₂ && FnBody.alphaEqv ρ b₁ b₂
 | ρ (FnBody.del x₁ b₁)              (FnBody.del x₂ b₂)                := aeqv ρ x₁ x₂ && FnBody.alphaEqv ρ b₁ b₂
 | ρ (FnBody.mdata m₁ b₁)            (FnBody.mdata m₂ b₂)              := m₁ == m₂ && FnBody.alphaEqv ρ b₁ b₂
-| ρ (FnBody.case n₁ x₁ alts₁)       (FnBody.case n₂ x₂ alts₂)         := n₁ == n₂ && aeqv ρ x₁ x₂ && Array.isEqv alts₁ alts₂ (λ alt₁ alt₂,
+| ρ (FnBody.case n₁ x₁ alts₁)       (FnBody.case n₂ x₂ alts₂)         := n₁ == n₂ && aeqv ρ x₁ x₂ && Array.isEqv alts₁ alts₂ (fun alt₁ alt₂ =>
    match alt₁, alt₂ with
    | Alt.ctor i₁ b₁, Alt.ctor i₂ b₂ := i₁ == i₂ && FnBody.alphaEqv ρ b₁ b₂
    | Alt.default b₁, Alt.default b₂ := FnBody.alphaEqv ρ b₁ b₂
@@ -531,7 +531,7 @@ FnBody.alphaEqv ∅  b₁ b₂
 
 instance FnBody.HasBeq : HasBeq FnBody := ⟨FnBody.beq⟩
 
-abbrev VarIdSet := RBTree VarId (λ x y, x.idx < y.idx)
+abbrev VarIdSet := RBTree VarId (fun x y => x.idx < y.idx)
 namespace VarIdSet
 instance : Inhabited VarIdSet := ⟨{}⟩
 end VarIdSet
diff --git a/library/init/lean/compiler/ir/borrow.lean b/library/init/lean/compiler/ir/borrow.lean
index 73efeeeded..7fc3fb0461 100644
--- a/library/init/lean/compiler/ir/borrow.lean
+++ b/library/init/lean/compiler/ir/borrow.lean
@@ -40,7 +40,7 @@ end Key
 abbrev ParamMap := HashMap Key (Array Param)
 
 def ParamMap.fmt (map : ParamMap) : Format :=
-let fmts := map.fold (λ fmt k ps,
+let fmts := map.fold (fun fmt k ps =>
   let k := match k with
     | Key.decl n  := format n
     | Key.jp n id := format n ++ ":" ++ format id;
@@ -49,13 +49,13 @@ let fmts := map.fold (λ fmt k ps,
 "{" ++ (Format.nest 1 fmts) ++ "}"
 
 instance : HasFormat ParamMap := ⟨ParamMap.fmt⟩
-instance : HasToString ParamMap := ⟨λ m, Format.pretty (format m)⟩
+instance : HasToString ParamMap := ⟨fun m => Format.pretty (format m)⟩
 
 namespace InitParamMap
 
 /- Mark parameters that take a reference as borrow -/
 def initBorrow (ps : Array Param) : Array Param :=
-ps.map $ λ p, { borrow := p.ty.isObj, .. p }
+ps.map $ fun p => { borrow := p.ty.isObj, .. p }
 
 /- We do perform borrow inference for constants marked as `export`.
    Reason: we current write wrappers in C++ for using exported functions.
@@ -70,7 +70,7 @@ if exported then ps else initBorrow ps
 
 partial def visitFnBody (fnid : FunId) : FnBody → State ParamMap Unit
 | (FnBody.jdecl j xs v b) := do
-  modify $ λ m, m.insert (Key.jp fnid j) (initBorrow xs);
+  modify $ fun m => m.insert (Key.jp fnid j) (initBorrow xs);
   visitFnBody v;
   visitFnBody b
 | e :=
@@ -79,10 +79,10 @@ partial def visitFnBody (fnid : FunId) : FnBody → State ParamMap Unit
     visitFnBody b
 
 def visitDecls (env : Environment) (decls : Array Decl) : State ParamMap Unit :=
-decls.mfor $ λ decl, match decl with
+decls.mfor $ fun decl => match decl with
   | Decl.fdecl f xs _ b := do
     let exported := isExport env f;
-    modify $ λ m, m.insert (Key.decl f) (initBorrowIfNotExported exported xs);
+    modify $ fun m => m.insert (Key.decl f) (initBorrowIfNotExported exported xs);
     visitFnBody f b
   | _ := pure ()
 end InitParamMap
@@ -109,7 +109,7 @@ partial def visitFnBody : FnBody → FunId → ParamMap → FnBody
     instr.setBody b
 
 def visitDecls (decls : Array Decl) (map : ParamMap) : Array Decl :=
-decls.map $ λ decl, match decl with
+decls.map $ fun decl => match decl with
   | Decl.fdecl f xs ty b :=
     let b := visitFnBody b f map;
     match map.find (Key.decl f) with
@@ -120,7 +120,7 @@ decls.map $ λ decl, match decl with
 end ApplyParamMap
 
 def applyParamMap (decls : Array Decl) (map : ParamMap) : Array Decl :=
--- dbgTrace ("applyParamMap " ++ toString map) $ λ _,
+-- dbgTrace ("applyParamMap " ++ toString map) $ fun _ =>
 ApplyParamMap.visitDecls decls map
 
 structure BorrowInfCtx :=
@@ -139,11 +139,11 @@ structure BorrowInfState :=
 abbrev M := ReaderT BorrowInfCtx (State BorrowInfState)
 
 def markModifiedParamMap : M Unit :=
-modify $ λ s, { modifiedParamMap := true, .. s }
+modify $ fun s => { modifiedParamMap := true, .. s }
 
 def ownVar (x : VarId) : M Unit :=
--- dbgTrace ("ownVar " ++ toString x) $ λ _,
-modify $ λ s,
+-- dbgTrace ("ownVar " ++ toString x) $ fun _ =>
+modify $ fun s =>
   if s.owned.contains x.idx then s
   else { owned := s.owned.insert x.idx, modifiedOwned := true, .. s }
 
@@ -165,12 +165,12 @@ do
 s ← get;
 match s.map.find k with
 | some ps := do
-  ps ← ps.mmap $ λ (p : Param),
+  ps ← ps.mmap $ fun (p : Param) =>
    if p.borrow && s.owned.contains p.x.idx then do
      markModifiedParamMap; pure { borrow := false, .. p }
    else
      pure p;
-  modify $ λ s, { map := s.map.insert k ps, .. s }
+  modify $ fun s => { map := s.map.insert k ps, .. s }
 | none    := pure ()
 
 def getParamInfo (k : Key) : M (Array Param) :=
@@ -189,7 +189,7 @@ match s.map.find k with
 
 /- For each ps[i], if ps[i] is owned, then mark xs[i] as owned. -/
 def ownArgsUsingParams (xs : Array Arg) (ps : Array Param) : M Unit :=
-xs.size.mfor $ λ i, do
+xs.size.mfor $ fun i => do
   let x := xs.get i;
   let p := ps.get i;
   unless p.borrow $ ownArg x
@@ -200,7 +200,7 @@ xs.size.mfor $ λ i, do
    we would have to insert a `dec xs[i]` after `f xs` and consequently
    "break" the tail call. -/
 def ownParamsUsingArgs (xs : Array Arg) (ps : Array Param) : M Unit :=
-xs.size.mfor $ λ i, do
+xs.size.mfor $ fun i => do
   let x := xs.get i;
   let p := ps.get i;
   match x with
@@ -220,7 +220,7 @@ xs.size.mfor $ λ i, do
 def ownArgsIfParam (xs : Array Arg) : M Unit :=
 do
 ctx ← read;
-xs.mfor $ λ x,
+xs.mfor $ fun x =>
   match x with
   | Arg.var x := when (ctx.paramSet.contains x.idx) $ ownVar x
   | _ := pure ()
@@ -231,7 +231,7 @@ def collectExpr (z : VarId) : Expr → M Unit
 | (Expr.ctor _ xs)      := ownVar z *> ownArgsIfParam xs
 | (Expr.proj _ x)       := mwhen (isOwned z) $ ownVar x
 | (Expr.fap g xs)       := do ps ← getParamInfo (Key.decl g);
-  -- dbgTrace ("collectExpr: " ++ toString g ++ " " ++ toString (formatParams ps)) $ λ _,
+  -- dbgTrace ("collectExpr: " ++ toString g ++ " " ++ toString (formatParams ps)) $ fun _ =>
   ownVar z *> ownArgsUsingParams xs ps
 | (Expr.ap x ys)        := ownVar z *> ownVar x *> ownArgs ys
 | (Expr.pap _ xs)       := ownVar z *> ownArgs xs
@@ -242,17 +242,17 @@ do ctx ← read;
 match v, b with
 | (Expr.fap g ys), (FnBody.ret (Arg.var z)) :=
   when (ctx.currFn == g && x == z) $ do
-    -- dbgTrace ("preserveTailCall " ++ toString b) $ λ _, do
+    -- dbgTrace ("preserveTailCall " ++ toString b) $ fun _ => do
     ps ← getParamInfo (Key.decl g);
     ownParamsUsingArgs ys ps
 | _, _ := pure ()
 
 def updateParamSet (ctx : BorrowInfCtx) (ps : Array Param) : BorrowInfCtx :=
-{ paramSet := ps.foldl (λ s p, s.insert p.x.idx) ctx.paramSet, .. ctx }
+{ paramSet := ps.foldl (fun s p => s.insert p.x.idx) ctx.paramSet, .. ctx }
 
 partial def collectFnBody : FnBody → M Unit
 | (FnBody.jdecl j ys v b) := do
-  adaptReader (λ ctx, updateParamSet ctx ys) (collectFnBody v);
+  adaptReader (fun ctx => updateParamSet ctx ys) (collectFnBody v);
   ctx ← read;
   updateParamMap (Key.jp ctx.currFn j);
   collectFnBody b
@@ -262,12 +262,12 @@ partial def collectFnBody : FnBody → M Unit
   ps ← getParamInfo (Key.jp ctx.currFn j);
   ownArgsUsingParams ys ps; -- for making sure the join point can reuse
   ownParamsUsingArgs ys ps  -- for making sure the tail call is preserved
-| (FnBody.case _ _ alts) := alts.mfor $ λ alt, collectFnBody alt.body
+| (FnBody.case _ _ alts) := alts.mfor $ fun alt => collectFnBody alt.body
 | e                      := unless (e.isTerminal) $ collectFnBody e.body
 
 @[specialize] partial def whileModifingOwnedAux (x : M Unit) : Unit → M Unit
 | _ := do
-  modify $ λ s, { modifiedOwned := false, .. s };
+  modify $ fun s => { modifiedOwned := false, .. s };
   x;
   s ← get;
   if s.modifiedOwned then whileModifingOwnedAux ()
@@ -279,17 +279,17 @@ whileModifingOwnedAux x ()
 
 partial def collectDecl : Decl → M Unit
 | (Decl.fdecl f ys _ b) :=
-  adaptReader (λ ctx, let ctx := updateParamSet ctx ys; { currFn := f, .. ctx }) $ do
-   modify $ λ s : BorrowInfState, { owned := {}, .. s };
+  adaptReader (fun ctx => let ctx := updateParamSet ctx ys; { currFn := f, .. ctx }) $ do
+   modify $ fun s : BorrowInfState => { owned := {}, .. s };
    whileModifingOwned (collectFnBody b);
    updateParamMap (Key.decl f)
 | _ := pure ()
 
 @[specialize] partial def whileModifingParamMapAux (x : M Unit) : Unit → M Unit
 | _ := do
-  modify $ λ s, { modifiedParamMap := false, .. s };
+  modify $ fun s => { modifiedParamMap := false, .. s };
   s ← get;
-  -- dbgTrace (toString s.map) $ λ _, do
+  -- dbgTrace (toString s.map) $ fun _ => do
   x;
   s ← get;
   if s.modifiedParamMap then whileModifingParamMapAux ()
diff --git a/library/init/lean/compiler/ir/boxing.lean b/library/init/lean/compiler/ir/boxing.lean
index 011f5d3d35..cf96ffcb73 100644
--- a/library/init/lean/compiler/ir/boxing.lean
+++ b/library/init/lean/compiler/ir/boxing.lean
@@ -36,19 +36,19 @@ abbrev N := State Nat
 
 private def mkFresh : N VarId :=
 do idx ← get;
-   modify (λ n, n + 1);
+   modify (fun n => n + 1);
    pure {idx := idx }
 
 def requiresBoxedVersion (env : Environment) (decl : Decl) : Bool :=
 let ps := decl.params;
-ps.size > 0 && (decl.resultType.isScalar || ps.any (λ p, p.ty.isScalar || p.borrow) || isExtern env decl.name)
+ps.size > 0 && (decl.resultType.isScalar || ps.any (fun p => p.ty.isScalar || p.borrow) || isExtern env decl.name)
 
 def mkBoxedVersionAux (decl : Decl) : N Decl :=
 do
 let ps := decl.params;
-qs ← ps.mmap (λ _, do x ← mkFresh; pure { Param . x := x, ty := IRType.object, borrow := false });
+qs ← ps.mmap (fun _ => do x ← mkFresh; pure { Param . x := x, ty := IRType.object, borrow := false });
 (newVDecls, xs) ← qs.size.mfold
-  (λ i (r : Array FnBody × Array Arg),
+  (fun i (r : Array FnBody × Array Arg) =>
      let (newVDecls, xs) := r;
      let p := ps.get i;
      let q := qs.get i;
@@ -74,7 +74,7 @@ def mkBoxedVersion (decl : Decl) : Decl :=
 
 def addBoxedVersions (env : Environment) (decls : Array Decl) : Array Decl :=
 let boxedDecls := decls.foldl
-  (λ (newDecls : Array Decl) decl, if requiresBoxedVersion env decl then newDecls.push (mkBoxedVersion decl) else newDecls)
+  (fun (newDecls : Array Decl) decl => if requiresBoxedVersion env decl then newDecls.push (mkBoxedVersion decl) else newDecls)
   Array.empty;
 decls ++ boxedDecls
 
@@ -90,7 +90,7 @@ else
 def getScrutineeType (alts : Array Alt) : IRType :=
 let isScalar :=
    alts.size > 1 && -- Recall that we encode Unit and PUnit using `object`.
-   alts.all (λ alt, match alt with
+   alts.all (fun alt => match alt with
     | Alt.ctor c _  := c.isScalar
     | Alt.default _ := false);
 match isScalar with
@@ -111,7 +111,7 @@ structure BoxingContext :=
 abbrev M := ReaderT BoxingContext (StateT Index Id)
 
 def mkFresh : M VarId :=
-do idx ← getModify (λ n, n + 1);
+do idx ← getModify (fun n => n + 1);
    pure { idx := idx }
 
 def getEnv : M Environment := BoxingContext.env <$> read
@@ -135,13 +135,13 @@ do ctx ← read;
    | none      := pure (default _) -- unreachable if well-formed
 
 @[inline] def withParams {α : Type} (xs : Array Param) (k : M α) : M α :=
-adaptReader (λ ctx : BoxingContext, { localCtx := ctx.localCtx.addParams xs, .. ctx }) k
+adaptReader (fun ctx : BoxingContext => { localCtx := ctx.localCtx.addParams xs, .. ctx }) k
 
 @[inline] def withVDecl {α : Type} (x : VarId) (ty : IRType) (v : Expr) (k : M α) : M α :=
-adaptReader (λ ctx : BoxingContext, { localCtx := ctx.localCtx.addLocal x ty v, .. ctx }) k
+adaptReader (fun ctx : BoxingContext => { localCtx := ctx.localCtx.addLocal x ty v, .. ctx }) k
 
 @[inline] def withJDecl {α : Type} (j : JoinPointId) (xs : Array Param) (v : FnBody) (k : M α) : M α :=
-adaptReader (λ ctx : BoxingContext, { localCtx := ctx.localCtx.addJP j xs v, .. ctx }) k
+adaptReader (fun ctx : BoxingContext => { localCtx := ctx.localCtx.addJP j xs v, .. ctx }) k
 
 /- Auxiliary function used by castVarIfNeeded.
    It is used when the expected type does not match `xType`.
@@ -159,11 +159,11 @@ do xType ← getVarType x;
 
 @[inline] def castArgIfNeeded (x : Arg) (expected : IRType) (k : Arg → M FnBody) : M FnBody :=
 match x with
-| Arg.var x := castVarIfNeeded x expected (λ x, k (Arg.var x))
+| Arg.var x := castVarIfNeeded x expected (fun x => k (Arg.var x))
 | _         := k x
 
 @[specialize] def castArgsIfNeededAux (xs : Array Arg) (typeFromIdx : Nat → IRType) : M (Array Arg × Array FnBody) :=
-xs.miterate (Array.empty, Array.empty) $ λ i (x : Arg) (r : Array Arg × Array FnBody),
+xs.miterate (Array.empty, Array.empty) $ fun i (x : Arg) (r : Array Arg × Array FnBody) =>
   let expected := typeFromIdx i.val;
   let (xs, bs) := r;
   match x with
@@ -178,12 +178,12 @@ xs.miterate (Array.empty, Array.empty) $ λ i (x : Arg) (r : Array Arg × Array
       pure (xs.push (Arg.var y), bs.push b)
 
 @[inline] def castArgsIfNeeded (xs : Array Arg) (ps : Array Param) (k : Array Arg → M FnBody) : M FnBody :=
-do (ys, bs) ← castArgsIfNeededAux xs (λ i, (ps.get i).ty);
+do (ys, bs) ← castArgsIfNeededAux xs (fun i => (ps.get i).ty);
    b ← k ys;
    pure (reshape bs b)
 
 @[inline] def boxArgsIfNeeded (xs : Array Arg) (k : Array Arg → M FnBody) : M FnBody :=
-do (ys, bs) ← castArgsIfNeededAux xs (λ _, IRType.object);
+do (ys, bs) ← castArgsIfNeededAux xs (fun _ => IRType.object);
    b ← k ys;
    pure (reshape bs b)
 
@@ -206,20 +206,20 @@ match e with
   if c.isScalar && ty.isScalar then
     pure $ FnBody.vdecl x ty (Expr.lit (LitVal.num c.cidx)) b
   else
-    boxArgsIfNeeded ys $ λ ys, pure $ FnBody.vdecl x ty (Expr.ctor c ys) b
+    boxArgsIfNeeded ys $ fun ys => pure $ FnBody.vdecl x ty (Expr.ctor c ys) b
 | Expr.reuse w c u ys :=
-  boxArgsIfNeeded ys $ λ ys, pure $ FnBody.vdecl x ty (Expr.reuse w c u ys) b
+  boxArgsIfNeeded ys $ fun ys => pure $ FnBody.vdecl x ty (Expr.reuse w c u ys) b
 | Expr.fap f ys := do
   decl ← getDecl f;
-  castArgsIfNeeded ys decl.params $ λ ys,
+  castArgsIfNeeded ys decl.params $ fun ys =>
   castResultIfNeeded x ty (Expr.fap f ys) decl.resultType b
 | Expr.pap f ys := do
   env ← getEnv;
   decl ← getDecl f;
   let f := if requiresBoxedVersion env decl then mkBoxedName f else f;
-  boxArgsIfNeeded ys $ λ ys, pure $ FnBody.vdecl x ty (Expr.pap f ys) b
+  boxArgsIfNeeded ys $ fun ys => pure $ FnBody.vdecl x ty (Expr.pap f ys) b
 | Expr.ap f ys :=
-  boxArgsIfNeeded ys $ λ ys,
+  boxArgsIfNeeded ys $ fun ys =>
   unboxResultIfNeeded x ty (Expr.ap f ys) b
 | other :=
   pure $ FnBody.vdecl x ty e b
@@ -234,31 +234,31 @@ partial def visitFnBody : FnBody → M FnBody
   pure $ FnBody.jdecl j xs v b
 | (FnBody.uset x i y b)      := do
   b ← visitFnBody b;
-  castVarIfNeeded y IRType.usize $ λ y,
+  castVarIfNeeded y IRType.usize $ fun y =>
     pure $ FnBody.uset x i y b
 | (FnBody.sset x i o y ty b) := do
   b ← visitFnBody b;
-  castVarIfNeeded y ty $ λ y,
+  castVarIfNeeded y ty $ fun y =>
     pure $ FnBody.sset x i o y ty b
 | (FnBody.mdata d b)         :=
   FnBody.mdata d <$> visitFnBody b
 | (FnBody.case tid x alts)   := do
   let expected := getScrutineeType alts;
-  alts ← alts.mmap $ λ alt, alt.mmodifyBody visitFnBody;
-  castVarIfNeeded x expected $ λ x,
+  alts ← alts.mmap $ fun alt => alt.mmodifyBody visitFnBody;
+  castVarIfNeeded x expected $ fun x =>
     pure $ FnBody.case tid x alts
 | (FnBody.ret x)             := do
   expected ← getResultType;
-  castArgIfNeeded x expected (λ x, pure $ FnBody.ret x)
+  castArgIfNeeded x expected (fun x => pure $ FnBody.ret x)
 | (FnBody.jmp j ys)          := do
   ps ← getJPParams j;
-  castArgsIfNeeded ys ps (λ ys, pure $ FnBody.jmp j ys)
+  castArgsIfNeeded ys ps (fun ys => pure $ FnBody.jmp j ys)
 | other                      :=
   pure other
 
 def run (env : Environment) (decls : Array Decl) : Array Decl :=
 let ctx : BoxingContext := { decls := decls, env := env };
-let decls := decls.map (λ decl, match decl with
+let decls := decls.map (fun decl => match decl with
   | Decl.fdecl f xs t b :=
     let nextIdx := decl.maxIndex + 1;
     let b := (withParams xs (visitFnBody b) { resultType := t, .. ctx }).run' nextIdx;
diff --git a/library/init/lean/compiler/ir/checker.lean b/library/init/lean/compiler/ir/checker.lean
index 9ae95a1442..85e8869f83 100644
--- a/library/init/lean/compiler/ir/checker.lean
+++ b/library/init/lean/compiler/ir/checker.lean
@@ -76,34 +76,34 @@ def checkExpr (ty : IRType) : Expr → M Unit
 | (Expr.ctor c ys)          := when c.isRef (checkObjType ty) *> checkArgs ys
 | (Expr.reset _ x)          := checkObjVar x *> checkObjType ty
 | (Expr.reuse x i u ys)     := checkObjVar x *> checkArgs ys *> checkObjType ty
-| (Expr.box xty x)          := checkObjType ty *> checkScalarVar x *> checkVarType x (λ t, t == xty)
+| (Expr.box xty x)          := checkObjType ty *> checkScalarVar x *> checkVarType x (fun t => t == xty)
 | (Expr.unbox x)            := checkScalarType ty *> checkObjVar x
 | (Expr.proj _ x)           := checkObjVar x *> checkObjType ty
-| (Expr.uproj _ x)          := checkObjVar x *> checkType ty (λ t, t == IRType.usize)
+| (Expr.uproj _ x)          := checkObjVar x *> checkType ty (fun t => t == IRType.usize)
 | (Expr.sproj _ _ x)        := checkObjVar x *> checkScalarType ty
-| (Expr.isShared x)         := checkObjVar x *> checkType ty (λ t, t == IRType.uint8)
-| (Expr.isTaggedPtr x)      := checkObjVar x *> checkType ty (λ t, t == IRType.uint8)
+| (Expr.isShared x)         := checkObjVar x *> checkType ty (fun t => t == IRType.uint8)
+| (Expr.isTaggedPtr x)      := checkObjVar x *> checkType ty (fun t => t == IRType.uint8)
 | (Expr.lit (LitVal.str _)) := checkObjType ty
 | (Expr.lit _)              := pure ()
 
 @[inline] def withParams (ps : Array Param) (k : M Unit) : M Unit :=
 do ctx ← read;
-   localCtx ← ps.mfoldl (λ (ctx : LocalContext) p, do
+   localCtx ← ps.mfoldl (fun (ctx : LocalContext) p => do
       when (ctx.contains p.x.idx) $ throw ("invalid parameter declaration, shadowing is not allowed");
       pure $ ctx.addParam p) ctx.localCtx;
-   adaptReader (λ _, { localCtx := localCtx, .. ctx }) k
+   adaptReader (fun _ => { localCtx := localCtx, .. ctx }) k
 
 partial def checkFnBody : FnBody → M Unit
 | (FnBody.vdecl x t v b)    := do
   checkExpr t v;
   ctx ← read;
   when (ctx.localCtx.contains x.idx) $ throw ("invalid variable declaration, shadowing is not allowed");
-  adaptReader (λ ctx : Context, { localCtx := ctx.localCtx.addLocal x t v, .. ctx }) (checkFnBody b)
+  adaptReader (fun (ctx : Context) => { localCtx := ctx.localCtx.addLocal x t v, .. ctx }) (checkFnBody b)
 | (FnBody.jdecl j ys v b) := do
   withParams ys (checkFnBody v);
   ctx ← read;
   when (ctx.localCtx.contains j.idx) $ throw ("invalid join point declaration, shadowing is not allowed");
-  adaptReader (λ ctx : Context, { localCtx := ctx.localCtx.addJP j ys v, .. ctx }) (checkFnBody b)
+  adaptReader (fun (ctx : Context) => { localCtx := ctx.localCtx.addJP j ys v, .. ctx }) (checkFnBody b)
 | (FnBody.set x _ y b)      := checkVar x *> checkArg y *> checkFnBody b
 | (FnBody.uset x _ y b)     := checkVar x *> checkVar y *> checkFnBody b
 | (FnBody.sset x _ _ y _ b) := checkVar x *> checkVar y *> checkFnBody b
@@ -114,7 +114,7 @@ partial def checkFnBody : FnBody → M Unit
 | (FnBody.mdata _ b)        := checkFnBody b
 | (FnBody.jmp j ys)         := checkJP j *> checkArgs ys
 | (FnBody.ret x)            := checkArg x
-| (FnBody.case _ x alts)    := checkVar x *> alts.mfor (λ alt, checkFnBody alt.body)
+| (FnBody.case _ x alts)    := checkVar x *> alts.mfor (fun alt => checkFnBody alt.body)
 | (FnBody.unreachable)      := pure ()
 
 def checkDecl : Decl → M Unit
diff --git a/library/init/lean/compiler/ir/compilerm.lean b/library/init/lean/compiler/ir/compilerm.lean
index 7b33c54103..cab6a8c383 100644
--- a/library/init/lean/compiler/ir/compilerm.lean
+++ b/library/init/lean/compiler/ir/compilerm.lean
@@ -18,7 +18,7 @@ inductive LogEntry
 
 namespace LogEntry
 protected def fmt : LogEntry → Format
-| (step cls decls) := Format.bracket "[" (format cls) "]" ++ decls.foldl (λ fmt decl, fmt ++ Format.line ++ format decl) Format.nil
+| (step cls decls) := Format.bracket "[" (format cls) "]" ++ decls.foldl (fun fmt decl => fmt ++ Format.line ++ format decl) Format.nil
 | (message msg)    := msg
 
 instance : HasFormat LogEntry := ⟨LogEntry.fmt⟩
@@ -27,7 +27,7 @@ end LogEntry
 abbrev Log := Array LogEntry
 
 def Log.format (log : Log) : Format :=
-log.foldl (λ fmt entry, fmt ++ Format.line ++ format entry) Format.nil
+log.foldl (fun fmt entry => fmt ++ Format.line ++ format entry) Format.nil
 
 @[export lean.ir.log_to_string_core]
 def Log.toString (log : Log) : String :=
@@ -39,7 +39,7 @@ structure CompilerState :=
 abbrev CompilerM := ReaderT Options (EState String CompilerState)
 
 def log (entry : LogEntry) : CompilerM Unit :=
-modify $ λ s, { log := s.log.push entry, .. s }
+modify $ fun s => { log := s.log.push entry, .. s }
 
 def tracePrefixOptionName := `trace.compiler.ir
 
@@ -66,7 +66,7 @@ logMessageIfAux (tracePrefixOptionName ++ cls) a
 logMessageIfAux tracePrefixOptionName a
 
 @[inline] def modifyEnv (f : Environment → Environment) : CompilerM Unit :=
-modify $ λ s, { env := f s.env, .. s }
+modify $ fun s => { env := f s.env, .. s }
 
 abbrev DeclMap := SMap Name Decl Name.quickLt
 
@@ -75,16 +75,16 @@ abbrev DeclMap := SMap Name Decl Name.quickLt
 private def mkEntryArray (decls : List Decl) : Array Decl :=
 /- Remove duplicates by adding decls into a map -/
 let map : HashMap Name Decl := {};
-let map := decls.foldl (λ (map : HashMap Name Decl) decl, map.insert decl.name decl) map;
-map.fold (λ a k v, a.push v) Array.empty
+let map := decls.foldl (fun (map : HashMap Name Decl) decl => map.insert decl.name decl) map;
+map.fold (fun a k v => a.push v) Array.empty
 
 def mkDeclMapExtension : IO (SimplePersistentEnvExtension Decl DeclMap) :=
 registerSimplePersistentEnvExtension {
   name       := `IRDecls,
-  addImportedFn := λ as,
-     let m : DeclMap := mkStateFromImportedEntries (λ s (d : Decl), s.insert d.name d) {} as;
+  addImportedFn := fun as =>
+     let m : DeclMap := mkStateFromImportedEntries (fun s (d : Decl) => s.insert d.name d) {} as;
      m.switch,
-  addEntryFn := λ s d, s.insert d.name d,
+  addEntryFn := fun s d => s.insert d.name d,
   toArrayFn  := mkEntryArray
 }
 
@@ -117,13 +117,13 @@ def getEnv : CompilerM Environment :=
 do s ← get; pure s.env
 
 def addDecl (decl : Decl) : CompilerM Unit :=
-modifyEnv (λ env, declMapExt.addEntry env decl)
+modifyEnv (fun env => declMapExt.addEntry env decl)
 
 def addDecls (decls : Array Decl) : CompilerM Unit :=
 decls.mfor addDecl
 
 def findEnvDecl' (env : Environment) (n : Name) (decls : Array Decl) : Option Decl :=
-match decls.find (λ decl, if decl.name == n then some decl else none) with
+match decls.find (fun decl => if decl.name == n then some decl else none) with
 | some decl := some decl
 | none      := (declMapExt.getState env).find n
 
@@ -131,7 +131,7 @@ def findDecl' (n : Name) (decls : Array Decl) : CompilerM (Option Decl) :=
 do s ← get; pure $ findEnvDecl' s.env n decls
 
 def containsDecl' (n : Name) (decls : Array Decl) : CompilerM Bool :=
-if decls.any (λ decl, decl.name == n) then pure true
+if decls.any (fun decl => decl.name == n) then pure true
 else do
   s ← get;
   pure $ (declMapExt.getState s.env).contains n
diff --git a/library/init/lean/compiler/ir/elimdead.lean b/library/init/lean/compiler/ir/elimdead.lean
index 6351c48d43..5411bea880 100644
--- a/library/init/lean/compiler/ir/elimdead.lean
+++ b/library/init/lean/compiler/ir/elimdead.lean
@@ -37,7 +37,7 @@ partial def FnBody.elimDead : FnBody → FnBody
   let bs         := modifyJPs bs FnBody.elimDead;
   let term       := match term with
     | FnBody.case tid x alts :=
-      let alts := alts.map $ λ alt, alt.modifyBody FnBody.elimDead;
+      let alts := alts.map $ fun alt => alt.modifyBody FnBody.elimDead;
       FnBody.case tid x alts
     | other := other;
   reshapeWithoutDead bs term
diff --git a/library/init/lean/compiler/ir/emitcpp.lean b/library/init/lean/compiler/ir/emitcpp.lean
index 4bd9fda67f..e1fdfd761a 100644
--- a/library/init/lean/compiler/ir/emitcpp.lean
+++ b/library/init/lean/compiler/ir/emitcpp.lean
@@ -41,13 +41,13 @@ do env ← getEnv;
    | none   := throw ("unknown declaration '" ++ toString n ++ "'")
 
 @[inline] def emit {α : Type} [HasToString α] (a : α) : M Unit :=
-modify (λ out, out ++ toString a)
+modify (fun out => out ++ toString a)
 
 @[inline] def emitLn {α : Type} [HasToString α] (a : α) : M Unit :=
 emit a *> emit "\n"
 
 def emitLns {α : Type} [HasToString α] (as : List α) : M Unit :=
-as.mfor $ λ a, emitLn a
+as.mfor $ fun a => emitLn a
 
 def argToCppString (x : Arg) : String :=
 match x with
@@ -132,7 +132,7 @@ when (ps.isEmpty && addExternForConsts) (emit "extern ");
 emit (toCppType decl.resultType ++ " " ++ cppBaseName);
 unless (ps.isEmpty) $ do {
   emit "(";
-  ps.size.mfor $ λ i, do {
+  ps.size.mfor $ fun i => do {
     when (i > 0) (emit ", ");
     emit (toCppType (ps.get i).ty)
   };
@@ -165,10 +165,10 @@ def emitFnDecls : M Unit :=
 do
 env ← getEnv;
 let decls := getDecls env;
-let modDecls  : NameSet := decls.foldl (λ s d, s.insert d.name) {};
-let usedDecls : NameSet := decls.foldl (λ s d, collectUsedDecls env d (s.insert d.name)) {};
+let modDecls  : NameSet := decls.foldl (fun s d => s.insert d.name) {};
+let usedDecls : NameSet := decls.foldl (fun s d => collectUsedDecls env d (s.insert d.name)) {};
 let usedDecls := usedDecls.toList;
-usedDecls.mfor $ λ n, do
+usedDecls.mfor $ fun n => do
   decl ← getDecl n;
   match getExternNameFor env `cpp decl.name with
   | some cppName := emitExternDeclAux decl cppName
@@ -222,7 +222,7 @@ match d with
 def hasMainFn : M Bool :=
 do env ← getEnv;
    let decls := getDecls env;
-   pure $ decls.any (λ d, d.name == `main)
+   pure $ decls.any (fun d => d.name == `main)
 
 def emitMainFnIfNeeded : M Unit :=
 mwhen hasMainFn emitMainFn
@@ -234,7 +234,7 @@ modName ← getModName;
 emitLn "// Lean compiler output";
 emitLn ("// Module: " ++ toString modName);
 emit "// Imports:";
-env.imports.mfor $ λ m, emit (" " ++ toString m);
+env.imports.mfor $ fun m => emit (" " ++ toString m);
 emitLn "";
 emitLn "#include \"runtime/object.h\"";
 emitLn "#include \"runtime/apply.h\"";
@@ -271,7 +271,7 @@ def declareVar (x : VarId) (t : IRType) : M Unit :=
 do emit (toCppType t); emit " "; emit x; emit "; "
 
 def declareParams (ps : Array Param) : M Unit :=
-ps.mfor $ λ p, declareVar p.x p.ty
+ps.mfor $ fun p => declareVar p.x p.ty
 
 partial def declareVars : FnBody → Bool → M Bool
 | e@(FnBody.vdecl x t _ b)  d := do
@@ -310,7 +310,7 @@ match isIf alts with
 | _ := do
   emit "switch ("; emitTag x; emitLn ") {";
   let alts := ensureHasDefault alts;
-  alts.mfor $ λ alt, match alt with
+  alts.mfor $ fun alt => match alt with
     | Alt.ctor c b  := emit "case " *> emit c.cidx *> emitLn ":" *> emitBody b
     | Alt.default b := emitLn "default: " *> emitBody b;
   emitLn "}"
@@ -355,7 +355,7 @@ def emitJmp (j : JoinPointId) (xs : Array Arg) : M Unit :=
 do
   ps ← getJPParams j;
   unless (xs.size == ps.size) (throw "invalid goto");
-  xs.size.mfor $ λ i, do {
+  xs.size.mfor $ fun i => do {
     let p := ps.get i;
     let x := xs.get i;
     emit p.x; emit " = "; emitArg x; emitLn ";"
@@ -366,7 +366,7 @@ def emitLhs (z : VarId) : M Unit :=
 do emit z; emit " = "
 
 def emitArgs (ys : Array Arg) : M Unit :=
-ys.size.mfor $ λ i, do
+ys.size.mfor $ fun i => do
   when (i > 0) (emit ", ");
   emitArg (ys.get i)
 
@@ -381,7 +381,7 @@ emit "lean::alloc_cnstr("; emit c.cidx; emit ", "; emit c.size; emit ", ";
 emitCtorScalarSize c.usize c.ssize; emitLn ");"
 
 def emitCtorSetArgs (z : VarId) (ys : Array Arg) : M Unit :=
-ys.size.mfor $ λ i, do
+ys.size.mfor $ fun i => do
   emit "lean::cnstr_set("; emit z; emit ", "; emit i; emit ", "; emitArg (ys.get i); emitLn ");"
 
 def emitCtor (z : VarId) (c : CtorInfo) (ys : Array Arg) : M Unit :=
@@ -395,7 +395,7 @@ else do
 def emitReset (z : VarId) (n : Nat) (x : VarId) : M Unit :=
 do
 emit "if (lean::is_exclusive("; emit x; emitLn ")) {";
-n.mfor $ λ i, do {
+n.mfor $ fun i => do {
   emit " lean::cnstr_release("; emit x; emit ", "; emit i; emitLn ");"
 };
 emit " "; emitLhs z; emit x; emitLn ";";
@@ -442,7 +442,7 @@ do
 decl ← getDecl f;
 let arity := decl.params.size;
 emitLhs z; emit "lean::alloc_closure(reinterpret_cast<void*>("; emitCppName f; emit "), "; emit arity; emit ", "; emit ys.size; emitLn ");";
-ys.size.mfor $ λ i, do {
+ys.size.mfor $ fun i => do {
    let y := ys.get i;
    emit "lean::closure_set("; emit z; emit ", "; emit i; emit ", "; emitArg y; emitLn ");"
 }
@@ -488,7 +488,7 @@ String.singleton c.digitChar
 def quoteString (s : String) : String :=
 let q := "\"";
 let q := s.foldl
-  (λ q c, q ++
+  (fun q c => q ++
     if c == '\n' then "\\n"
     else if c == '\n' then "\\t"
     else if c == '\\' then "\\\\"
@@ -560,9 +560,9 @@ That is, we have
 -/
 def overwriteParam (ps : Array Param) (ys : Array Arg) : Bool :=
 let n := ps.size;
-n.any $ λ i,
+n.any $ fun i =>
   let p := ps.get i;
-  (i+1, n).anyI $ λ j, paramEqArg p (ys.get j)
+  (i+1, n).anyI $ fun j => paramEqArg p (ys.get j)
 
 def emitTailCall (v : Expr) : M Unit :=
 match v with
@@ -572,21 +572,21 @@ match v with
   unless (ps.size == ys.size) (throw "invalid tail call");
   if overwriteParam ps ys then do {
     emitLn "{";
-    ps.size.mfor $ λ i, do {
+    ps.size.mfor $ fun i => do {
       let p := ps.get i;
       let y := ys.get i;
       unless (paramEqArg p y) $ do {
         emit (toCppType p.ty); emit " _tmp_"; emit i; emit " = "; emitArg y; emitLn ";"
       }
     };
-    ps.size.mfor $ λ i, do {
+    ps.size.mfor $ fun i => do {
       let p := ps.get i;
       let y := ys.get i;
       unless (paramEqArg p y) (do emit p.x; emit " = _tmp_"; emit i; emitLn ";")
     };
     emitLn "}"
   } else do {
-    ys.size.mfor $ λ i, do {
+    ys.size.mfor $ fun i => do {
       let p := ps.get i;
       let y := ys.get i;
       unless (paramEqArg p y) (do emit p.x; emit " = "; emitArg y; emitLn ";")
@@ -629,7 +629,7 @@ def emitDeclAux (d : Decl) : M Unit :=
 do
 env ← getEnv;
 let (vMap, jpMap) := mkVarJPMaps d;
-adaptReader (λ ctx : Context, { varMap := vMap, jpMap := jpMap, .. ctx }) $ do
+adaptReader (fun ctx : Context => { varMap := vMap, jpMap := jpMap, .. ctx }) $ do
 unless (hasInitAttr env d.name) $
   match d with
   | Decl.fdecl f xs t b := do
@@ -639,7 +639,7 @@ unless (hasInitAttr env d.name) $
     if xs.size > 0 then do {
       emit baseName;
       emit "(";
-      xs.size.mfor $ λ i, do {
+      xs.size.mfor $ fun i => do {
         when (i > 0) (emit ", ");
         let x := xs.get i;
         emit (toCppType x.ty); emit " "; emit(x.x)
@@ -650,7 +650,7 @@ unless (hasInitAttr env d.name) $
     };
     emitLn " {";
     emitLn "_start:";
-    adaptReader (λ ctx : Context, { mainFn := f, mainParams := xs, .. ctx }) (emitFnBody b);
+    adaptReader (fun ctx : Context => { mainFn := f, mainParams := xs, .. ctx }) (emitFnBody b);
     emitLn "}";
     closeNamespacesFor f
   | _ := pure ()
@@ -659,7 +659,7 @@ def emitDecl (d : Decl) : M Unit :=
 let d := d.normalizeIds;
 catch
   (emitDeclAux d)
-  (λ err, throw (err ++ "\ncompiling:\n" ++ toString d))
+  (fun err => throw (err ++ "\ncompiling:\n" ++ toString d))
 
 def emitFns : M Unit :=
 do
@@ -717,7 +717,7 @@ def emitInitFn : M Unit :=
 do
 env ← getEnv;
 modName ← getModName;
-env.imports.mfor $ λ m, emitLn ("obj* initialize_" ++ m.mangle "" ++ "(obj*);");
+env.imports.mfor $ fun m => emitLn ("obj* initialize_" ++ m.mangle "" ++ "(obj*);");
 emitLns [
     "static bool _G_initialized = false;",
     "obj* initialize_" ++ modName.mangle "" ++ "(obj* w) {",
@@ -725,7 +725,7 @@ emitLns [
     "_G_initialized = true;",
     "if (io_result_is_error(w)) return w;"
 ];
-env.imports.mfor $ λ m, emitLns [
+env.imports.mfor $ fun m => emitLns [
   "w = initialize_" ++ m.mangle "" ++ "(w);",
   "if (io_result_is_error(w)) return w;"
 ];
diff --git a/library/init/lean/compiler/ir/emitutil.lean b/library/init/lean/compiler/ir/emitutil.lean
index 07891d5472..89f06a85d3 100644
--- a/library/init/lean/compiler/ir/emitutil.lean
+++ b/library/init/lean/compiler/ir/emitutil.lean
@@ -33,7 +33,7 @@ partial def visitFnBody : FnBody → M Bool
        if s.contains f then
          visitFnBody b
        else do
-         modify (λ s, s.insert f);
+         modify (fun s => s.insert f);
          env ← read;
          match findEnvDecl env f with
          | some (Decl.fdecl _ _ _ fbody) := visitFnBody fbody <||> visitFnBody b
@@ -44,7 +44,7 @@ partial def visitFnBody : FnBody → M Bool
   | Expr.pap f _ := checkFn f
   | other        := visitFnBody b
 | (FnBody.jdecl _ _ v b) := visitFnBody v <||> visitFnBody b
-| (FnBody.case _ _ alts) := alts.anyM $ λ alt, visitFnBody alt.body
+| (FnBody.case _ _ alts) := alts.anyM $ fun alt => visitFnBody alt.body
 | e :=
   if e.isTerminal then pure false
   else visitFnBody e.body
@@ -61,7 +61,7 @@ namespace CollectUsedDecls
 abbrev M := ReaderT Environment (State NameSet)
 
 @[inline] def collect (f : FunId) : M Unit :=
-modify (λ s, s.insert f)
+modify (fun s => s.insert f)
 
 partial def collectFnBody : FnBody → M Unit
 | (FnBody.vdecl _ _ v b) :=
@@ -70,7 +70,7 @@ partial def collectFnBody : FnBody → M Unit
   | Expr.pap f _ := collect f *> collectFnBody b
   | other        := collectFnBody b
 | (FnBody.jdecl _ _ v b) := collectFnBody v *> collectFnBody b
-| (FnBody.case _ _ alts) := alts.mfor $ λ alt, collectFnBody alt.body
+| (FnBody.case _ _ alts) := alts.mfor $ fun alt => collectFnBody alt.body
 | e := unless e.isTerminal $ collectFnBody e.body
 
 def collectInitDecl (fn : Name) : M Unit :=
@@ -96,7 +96,7 @@ abbrev Collector := (VarTypeMap × JPParamsMap) → (VarTypeMap × JPParamsMap)
 @[inline] def collectVar (x : VarId) (t : IRType) : Collector
 | (vs, js) := (vs.insert x t, js)
 def collectParams (ps : Array Param) : Collector :=
-λ s, ps.foldl (λ s p, collectVar p.x p.ty s) s
+fun s => ps.foldl (fun s p => collectVar p.x p.ty s) s
 @[inline] def collectJP (j : JoinPointId) (xs : Array Param) : Collector
 | (vs, js) := (vs, js.insert j xs)
 
@@ -104,7 +104,7 @@ def collectParams (ps : Array Param) : Collector :=
 partial def collectFnBody : FnBody → Collector
 | (FnBody.vdecl x t _ b)  := collectVar x t ∘ collectFnBody b
 | (FnBody.jdecl j xs v b) := collectJP j xs ∘ collectParams xs ∘ collectFnBody v ∘ collectFnBody b
-| (FnBody.case _ _ alts)  := λ s, alts.foldl (λ s alt, collectFnBody alt.body s) s
+| (FnBody.case _ _ alts)  := fun s => alts.foldl (fun s alt => collectFnBody alt.body s) s
 | e                       := if e.isTerminal then id else collectFnBody e.body
 
 def collectDecl : Decl → Collector
diff --git a/library/init/lean/compiler/ir/expandresetreuse.lean b/library/init/lean/compiler/ir/expandresetreuse.lean
index 3603e25490..a043785c72 100644
--- a/library/init/lean/compiler/ir/expandresetreuse.lean
+++ b/library/init/lean/compiler/ir/expandresetreuse.lean
@@ -18,7 +18,7 @@ abbrev ProjMap  := HashMap VarId Expr
 namespace CollectProjMap
 abbrev Collector := ProjMap → ProjMap
 @[inline] def collectVDecl (x : VarId) (v : Expr) : Collector :=
-λ m, match v with
+fun m => match v with
  | Expr.proj _ _    := m.insert x v
  | Expr.sproj _ _ _ := m.insert x v
  | Expr.uproj _ _   := m.insert x v
@@ -27,7 +27,7 @@ abbrev Collector := ProjMap → ProjMap
 partial def collectFnBody : FnBody → Collector
 | (FnBody.vdecl x _ v b)  := collectVDecl x v ∘ collectFnBody b
 | (FnBody.jdecl _ _ v b)  := collectFnBody v ∘ collectFnBody b
-| (FnBody.case _ _ alts)  := λ s, alts.foldl (λ s alt, collectFnBody alt.body s) s
+| (FnBody.case _ _ alts)  := fun s => alts.foldl (fun s alt => collectFnBody alt.body s) s
 | e                       := if e.isTerminal then id else collectFnBody e.body
 end CollectProjMap
 
@@ -49,7 +49,7 @@ partial def consumed (x : VarId) : FnBody → Bool
   | Expr.reuse y _ _ _   := x == y || consumed b
   | _                    := consumed b
 | (FnBody.dec y _ _ b)   := x == y || consumed b
-| (FnBody.case _ _ alts) := alts.all $ λ alt, consumed alt.body
+| (FnBody.case _ _ alts) := alts.all $ fun alt => consumed alt.body
 | e := !e.isTerminal && consumed e.body
 
 abbrev Mask := Array (Option VarId)
@@ -105,7 +105,7 @@ partial def reuseToCtor (x : VarId) : FnBody → FnBody
   | _ :=
     FnBody.vdecl z t v (reuseToCtor b)
 | (FnBody.case tid y alts) :=
-  let alts := alts.map $ λ alt, alt.modifyBody reuseToCtor;
+  let alts := alts.map $ fun alt => alt.modifyBody reuseToCtor;
   FnBody.case tid y alts
 | e :=
   if e.isTerminal then e
@@ -130,18 +130,18 @@ def mkSlowPath (x y : VarId) (mask : Mask) (b : FnBody) : FnBody :=
 let b := reuseToCtor x b;
 let b := FnBody.dec y 1 true b;
 mask.foldl
-  (λ b m, match m with
+  (fun b m => match m with
     | some z := FnBody.inc z 1 true b
     | none   := b)
   b
 
 abbrev M := ReaderT Context (State Nat)
 def mkFresh : M VarId :=
-do idx ← get; modify (λ n, n + 1); pure { idx := idx }
+do idx ← get; modify (fun n => n + 1); pure { idx := idx }
 
 def releaseUnreadFields (y : VarId) (mask : Mask) (b : FnBody) : M FnBody :=
 mask.size.mfold
-  (λ i b,
+  (fun i b =>
     match mask.get i with
     | some _ := pure b -- code took ownership of this field
     | none   := do
@@ -151,7 +151,7 @@ mask.size.mfold
 
 def setFields (y : VarId) (zs : Array Arg) (b : FnBody) : FnBody :=
 zs.size.fold
-  (λ i b, FnBody.set y i (zs.get i) b)
+  (fun i b => FnBody.set y i (zs.get i) b)
   b
 
 /- Given `set x[i] := y`, return true iff `y := proj[i] x` -/
@@ -187,7 +187,7 @@ partial def removeSelfSet (ctx : Context) : FnBody → FnBody
   if isSelfSSet ctx x n i y then removeSelfSet b
   else FnBody.sset x n i y t (removeSelfSet b)
 | (FnBody.case tid y alts) :=
-  let alts := alts.map $ λ alt, alt.modifyBody removeSelfSet;
+  let alts := alts.map $ fun alt => alt.modifyBody removeSelfSet;
   FnBody.case tid y alts
 | e :=
   if e.isTerminal then e
@@ -210,7 +210,7 @@ partial def reuseToSet (ctx : Context) (x y : VarId) : FnBody → FnBody
     else FnBody.vdecl z t v (reuseToSet b)
   | _ := FnBody.vdecl z t v (reuseToSet b)
 | (FnBody.case tid y alts) :=
-  let alts := alts.map $ λ alt, alt.modifyBody reuseToSet;
+  let alts := alts.map $ fun alt => alt.modifyBody reuseToSet;
   FnBody.case tid y alts
 | e :=
   if e.isTerminal then e
@@ -268,7 +268,7 @@ partial def searchAndExpand : FnBody → Array FnBody → M FnBody
   v ← searchAndExpand v Array.empty;
   searchAndExpand b (push bs (FnBody.jdecl j xs v FnBody.nil))
 | (FnBody.case tid x alts) bs := do
-  alts ← alts.mmap $ λ alt, alt.mmodifyBody $ λ b, searchAndExpand b Array.empty;
+  alts ← alts.mmap $ fun alt => alt.mmodifyBody $ fun b => searchAndExpand b Array.empty;
   pure $ reshape bs (FnBody.case tid x alts)
 | b bs :=
   if b.isTerminal then pure $ reshape bs b
diff --git a/library/init/lean/compiler/ir/format.lean b/library/init/lean/compiler/ir/format.lean
index c2d549c17a..a2f6341afd 100644
--- a/library/init/lean/compiler/ir/format.lean
+++ b/library/init/lean/compiler/ir/format.lean
@@ -16,7 +16,7 @@ private def formatArg : Arg → Format
 instance argHasFormat : HasFormat Arg := ⟨formatArg⟩
 
 private def formatArray {α : Type} [HasFormat α] (args : Array α) : Format :=
-args.foldl (λ r a, r ++ " " ++ format a) Format.nil
+args.foldl (fun r a => r ++ " " ++ format a) Format.nil
 
 private def formatLitVal : LitVal → Format
 | (LitVal.num v) := format v
@@ -50,7 +50,7 @@ private def formatExpr : Expr → Format
 | (Expr.isTaggedPtr x)   := "isTaggedPtr " ++ format x
 
 instance exprHasFormat   : HasFormat Expr := ⟨formatExpr⟩
-instance exprHasToString : HasToString Expr := ⟨λ e, Format.pretty (format e)⟩
+instance exprHasToString : HasToString Expr := ⟨fun e => Format.pretty (format e)⟩
 
 private def formatIRType : IRType → Format
 | IRType.float      := "float"
@@ -88,13 +88,13 @@ partial def formatFnBody (indent : Nat := 2) : FnBody → Format
 | (FnBody.dec x n c b)       := "dec" ++ (if n != 1 then Format.sbracket (format n) else "") ++ " " ++ format x ++ ";" ++ Format.line ++ formatFnBody b
 | (FnBody.del x b)           := "del " ++ format x ++ ";" ++ Format.line ++ formatFnBody b
 | (FnBody.mdata d b)         := "mdata " ++ format d ++ ";" ++ Format.line ++ formatFnBody b
-| (FnBody.case tid x cs)     := "case " ++ format x ++ " of" ++ cs.foldl (λ r c, r ++ Format.line ++ formatAlt formatFnBody indent c) Format.nil
+| (FnBody.case tid x cs)     := "case " ++ format x ++ " of" ++ cs.foldl (fun r c => r ++ Format.line ++ formatAlt formatFnBody indent c) Format.nil
 | (FnBody.jmp j ys)          := "jmp " ++ format j ++ formatArray ys
 | (FnBody.ret x)             := "ret " ++ format x
 | FnBody.unreachable         := "⊥"
 
 instance fnBodyHasFormat : HasFormat FnBody := ⟨formatFnBody⟩
-instance fnBodyHasToString : HasToString FnBody := ⟨λ b, (format b).pretty⟩
+instance fnBodyHasToString : HasToString FnBody := ⟨fun b => (format b).pretty⟩
 
 def formatDecl (indent : Nat := 2) : Decl → Format
 | (Decl.fdecl f xs ty b)  := "def " ++ format f ++ formatParams xs ++ format " : " ++ format ty ++ " :=" ++ Format.nest indent (Format.line ++ formatFnBody indent b)
diff --git a/library/init/lean/compiler/ir/freevars.lean b/library/init/lean/compiler/ir/freevars.lean
index da9ac60f72..803327e665 100644
--- a/library/init/lean/compiler/ir/freevars.lean
+++ b/library/init/lean/compiler/ir/freevars.lean
@@ -21,7 +21,7 @@ namespace MaxIndex
 abbrev Collector := Index → Index
 
 @[inline] private def skip : Collector := id
-@[inline] private def collect (x : Index) : Collector := λ y, if x > y then x else y
+@[inline] private def collect (x : Index) : Collector := fun y => if x > y then x else y
 @[inline] private def collectVar (x : VarId) : Collector := collect x.idx
 @[inline] private def collectJP (j : JoinPointId) : Collector := collect j.idx
 @[inline] private def seq (k₁ k₂ : Collector) : Collector := k₂ ∘ k₁
@@ -32,7 +32,7 @@ private def collectArg : Arg → Collector
 | irrelevant  := skip
 
 @[specialize] private def collectArray {α : Type} (as : Array α) (f : α → Collector) : Collector :=
-λ m, as.foldl (λ m a, f a m) m
+fun m => as.foldl (fun m a => f a m) m
 
 private def collectArgs (as : Array Arg) : Collector := collectArray as collectArg
 private def collectParam (p : Param) : Collector := collectVar p.x
@@ -55,7 +55,7 @@ private def collectExpr : Expr → Collector
 | (Expr.isTaggedPtr x)   := collectVar x
 
 private def collectAlts (f : FnBody → Collector) (alts : Array Alt) : Collector :=
-collectArray alts $ λ alt, f alt.body
+collectArray alts $ fun alt => f alt.body
 
 partial def collectFnBody : FnBody → Collector
 | (FnBody.vdecl x _ v b)    := collectExpr v >> collectFnBody b
@@ -92,10 +92,10 @@ namespace FreeIndices
 abbrev Collector := IndexSet → IndexSet → IndexSet
 
 @[inline] private def skip : Collector :=
-λ bv fv, fv
+fun bv fv => fv
 
 @[inline] private def collectIndex (x : Index) : Collector :=
-λ bv fv, if bv.contains x then fv else fv.insert x
+fun bv fv => if bv.contains x then fv else fv.insert x
 
 @[inline] private def collectVar (x : VarId) : Collector :=
 collectIndex x.idx
@@ -104,7 +104,7 @@ collectIndex x.idx
 collectIndex x.idx
 
 @[inline] private def withIndex (x : Index) : Collector → Collector :=
-λ k bv fv, k (bv.insert x) fv
+fun k bv fv => k (bv.insert x) fv
 
 @[inline] private def withVar (x : VarId) : Collector → Collector :=
 withIndex x.idx
@@ -113,13 +113,13 @@ withIndex x.idx
 withIndex x.idx
 
 def insertParams (s : IndexSet) (ys : Array Param) : IndexSet :=
-ys.foldl (λ s p, s.insert p.x.idx) s
+ys.foldl (fun s p => s.insert p.x.idx) s
 
 @[inline] private def withParams (ys : Array Param) : Collector → Collector :=
-λ k bv fv, k (insertParams bv ys) fv
+fun k bv fv => k (insertParams bv ys) fv
 
 @[inline] private def seq : Collector → Collector → Collector :=
-λ k₁ k₂ bv fv, k₂ bv (k₁ bv fv)
+fun k₁ k₂ bv fv => k₂ bv (k₁ bv fv)
 
 instance : HasAndthen Collector := ⟨seq⟩
 
@@ -128,7 +128,7 @@ private def collectArg : Arg → Collector
 | irrelevant  := skip
 
 @[specialize] private def collectArray {α : Type} (as : Array α) (f : α → Collector) : Collector :=
-λ bv fv, as.foldl (λ fv a, f a bv fv) fv
+fun bv fv => as.foldl (fun fv a => f a bv fv) fv
 
 private def collectArgs (as : Array Arg) : Collector :=
 collectArray as collectArg
@@ -150,7 +150,7 @@ private def collectExpr : Expr → Collector
 | (Expr.isTaggedPtr x)   := collectVar x
 
 private def collectAlts (f : FnBody → Collector) (alts : Array Alt) : Collector :=
-collectArray alts $ λ alt, f alt.body
+collectArray alts $ fun alt => f alt.body
 
 partial def collectFnBody : FnBody → Collector
 | (FnBody.vdecl x _ v b)    := collectExpr v >> withVar x (collectFnBody b)
@@ -192,7 +192,7 @@ def visitArgs (w : Index) (xs : Array Arg) : Bool :=
 xs.any (visitArg w)
 
 def visitParams (w : Index) (ps : Array Param) : Bool :=
-ps.any (λ p, w == p.x.idx)
+ps.any (fun p => w == p.x.idx)
 
 def visitExpr (w : Index) : Expr → Bool
 | (Expr.ctor _ ys)       := visitArgs w ys
@@ -223,7 +223,7 @@ partial def visitFnBody (w : Index) : FnBody → Bool
 | (FnBody.mdata _ b)        := visitFnBody b
 | (FnBody.jmp j ys)         := visitJP w j || visitArgs w ys
 | (FnBody.ret x)            := visitArg w x
-| (FnBody.case _ x alts)    := visitVar w x || alts.any (λ alt, visitFnBody alt.body)
+| (FnBody.case _ x alts)    := visitVar w x || alts.any (fun alt => visitFnBody alt.body)
 | (FnBody.unreachable)      := false
 
 end HasIndex
diff --git a/library/init/lean/compiler/ir/livevars.lean b/library/init/lean/compiler/ir/livevars.lean
index 61759848ba..06245c6cb6 100644
--- a/library/init/lean/compiler/ir/livevars.lean
+++ b/library/init/lean/compiler/ir/livevars.lean
@@ -69,7 +69,7 @@ partial def visitFnBody (w : Index) : FnBody → M Bool
       pure false
   }
 | (FnBody.ret x)            := visitArg w x
-| (FnBody.case _ x alts)    := visitVar w x <||> alts.anyM (λ alt, visitFnBody alt.body)
+| (FnBody.case _ x alts)    := visitVar w x <||> alts.anyM (fun alt => visitFnBody alt.body)
 | (FnBody.unreachable)      := pure false
 
 end IsLive
@@ -84,7 +84,7 @@ def FnBody.hasLiveVar (b : FnBody) (ctx : LocalContext) (x : VarId) : Bool :=
 (IsLive.visitFnBody x.idx b).run' ctx
 
 abbrev LiveVarSet   := VarIdSet
-abbrev JPLiveVarMap := RBMap JoinPointId LiveVarSet (λ j₁ j₂, j₁.idx < j₂.idx)
+abbrev JPLiveVarMap := RBMap JoinPointId LiveVarSet (fun j₁ j₂ => j₁.idx < j₂.idx)
 
 instance LiveVarSet.inhabited : Inhabited LiveVarSet := ⟨{}⟩
 
@@ -92,25 +92,25 @@ namespace LiveVars
 
 abbrev Collector := LiveVarSet → LiveVarSet
 
-@[inline] private def skip : Collector := λ s, s
-@[inline] private def collectVar (x : VarId) : Collector := λ s, s.insert x
+@[inline] private def skip : Collector := fun s => s
+@[inline] private def collectVar (x : VarId) : Collector := fun s => s.insert x
 private def collectArg : Arg → Collector
 | (Arg.var x) := collectVar x
 | irrelevant  := skip
 @[specialize] private def collectArray {α : Type} (as : Array α) (f : α → Collector) : Collector :=
-λ s, as.foldl (λ s a, f a s) s
+fun s => as.foldl (fun s a => f a s) s
 private def collectArgs (as : Array Arg) : Collector :=
 collectArray as collectArg
 private def accumulate (s' : LiveVarSet) : Collector :=
-λ s, s'.fold (λ s x, s.insert x) s
+fun s => s'.fold (fun s x => s.insert x) s
 private def collectJP (m : JPLiveVarMap) (j : JoinPointId) : Collector :=
 match m.find j with
 | some xs := accumulate xs
 | none    := skip -- unreachable for well-formed code
 private def bindVar (x : VarId) : Collector :=
-λ s, s.erase x
+fun s => s.erase x
 private def bindParams (ps : Array Param) : Collector :=
-λ s, ps.foldl (λ s p, s.erase p.x) s
+fun s => ps.foldl (fun s p => s.erase p.x) s
 
 def collectExpr : Expr → Collector
 | (Expr.ctor _ ys)       := collectArgs ys
@@ -143,7 +143,7 @@ partial def collectFnBody : FnBody → JPLiveVarMap → Collector
 | (FnBody.del x b)          m := collectVar x ∘ collectFnBody b m
 | (FnBody.mdata _ b)        m := collectFnBody b m
 | (FnBody.ret x)            m := collectArg x
-| (FnBody.case _ x alts)    m := collectVar x ∘ collectArray alts (λ alt, collectFnBody alt.body m)
+| (FnBody.case _ x alts)    m := collectVar x ∘ collectArray alts (fun alt => collectFnBody alt.body m)
 | (FnBody.unreachable)      m := skip
 | (FnBody.jmp j xs)         m := collectJP m j ∘ collectArgs xs
 
diff --git a/library/init/lean/compiler/ir/normids.lean b/library/init/lean/compiler/ir/normids.lean
index 834969d1de..70553c4efa 100644
--- a/library/init/lean/compiler/ir/normids.lean
+++ b/library/init/lean/compiler/ir/normids.lean
@@ -17,15 +17,15 @@ abbrev M := StateT IndexSet Id
 def checkId (id : Index) : M Bool :=
 do found ← get;
    if found.contains id then pure false
-   else modify (λ s, s.insert id) *> pure true
+   else modify (fun s => s.insert id) *> pure true
 
 def checkParams (ps : Array Param) : M Bool :=
-ps.allM $ λ p, checkId p.x.idx
+ps.allM $ fun p => checkId p.x.idx
 
 partial def checkFnBody : FnBody → M Bool
 | (FnBody.vdecl x _ _ b)  := checkId x.idx <&&> checkFnBody b
 | (FnBody.jdecl j ys _ b) := checkId j.idx <&&> checkParams ys <&&> checkFnBody b
-| (FnBody.case _ _ alts)  := alts.allM $ λ alt, checkFnBody alt.body
+| (FnBody.case _ _ alts)  := alts.allM $ fun alt => checkFnBody alt.body
 | b                       := if b.isTerminal then pure true else checkFnBody b.body
 
 partial def checkDecl : Decl → M Bool
@@ -43,7 +43,7 @@ namespace NormalizeIds
 abbrev M := ReaderT IndexRenaming Id
 
 def normIndex (x : Index) : M Index :=
-λ m, match m.find x with
+fun m => match m.find x with
 | some y := y
 | none   := x
 
@@ -58,7 +58,7 @@ def normArg : Arg → M Arg
 | other       := pure other
 
 def normArgs (as : Array Arg) : M (Array Arg) :=
-λ m, as.map $ λ a, normArg a m
+fun m => as.map $ fun a => normArg a m
 
 def normExpr : Expr → M Expr
 | (Expr.ctor c ys)      m := Expr.ctor c (normArgs ys m)
@@ -79,29 +79,29 @@ def normExpr : Expr → M Expr
 abbrev N := ReaderT IndexRenaming (State Nat)
 
 @[inline] def withVar {α : Type} (x : VarId) (k : VarId → N α) : N α :=
-λ m, do
-  n ← getModify (λ n, n + 1);
+fun m => do
+  n ← getModify (fun n => n + 1);
   k { idx := n } (m.insert x.idx n)
 
 @[inline] def withJP {α : Type} (x : JoinPointId) (k : JoinPointId → N α) : N α :=
-λ m, do
-  n ← getModify (λ n, n + 1);
+fun m => do
+  n ← getModify (fun n => n + 1);
   k { idx := n } (m.insert x.idx n)
 
 @[inline] def withParams {α : Type} (ps : Array Param) (k : Array Param → N α) : N α :=
-λ m, do
-  m ← ps.mfoldl (λ (m : IndexRenaming) p, do n ← getModify (λ n, n + 1); pure $ m.insert p.x.idx n) m;
-  let ps := ps.map $ λ p, { x := normVar p.x m, .. p };
+fun m => do
+  m ← ps.mfoldl (fun (m : IndexRenaming) p => do n ← getModify (fun n => n + 1); pure $ m.insert p.x.idx n) m;
+  let ps := ps.map $ fun p => { x := normVar p.x m, .. p };
   k ps m
 
 instance MtoN {α} : HasCoe (M α) (N α) :=
-⟨λ x m, pure $ x m⟩
+⟨fun x m => pure $ x m⟩
 
 partial def normFnBody : FnBody → N FnBody
-| (FnBody.vdecl x t v b)     := do v ← normExpr v; withVar x $ λ x, FnBody.vdecl x t v <$> normFnBody b
+| (FnBody.vdecl x t v b)     := do v ← normExpr v; withVar x $ fun x => FnBody.vdecl x t v <$> normFnBody b
 | (FnBody.jdecl j ys v b)    := do
-  (ys, v) ← withParams ys $ λ ys, do { v ← normFnBody v; pure (ys, v) };
-  withJP j $ λ j, FnBody.jdecl j ys v <$> normFnBody b
+  (ys, v) ← withParams ys $ fun ys => do { v ← normFnBody v; pure (ys, v) };
+  withJP j $ fun j => FnBody.jdecl j ys v <$> normFnBody b
 | (FnBody.set x i y b)       := do x ← normVar x; y ← normArg y; FnBody.set x i y <$> normFnBody b
 | (FnBody.uset x i y b)      := do x ← normVar x; y ← normVar y; FnBody.uset x i y <$> normFnBody b
 | (FnBody.sset x i o y t b)  := do x ← normVar x; y ← normVar y; FnBody.sset x i o y t <$> normFnBody b
@@ -112,14 +112,14 @@ partial def normFnBody : FnBody → N FnBody
 | (FnBody.mdata d b)         := FnBody.mdata d <$> normFnBody b
 | (FnBody.case tid x alts)   := do
   x ← normVar x;
-  alts ← alts.mmap $ λ alt, alt.mmodifyBody normFnBody;
+  alts ← alts.mmap $ fun alt => alt.mmodifyBody normFnBody;
   pure $ FnBody.case tid x alts
 | (FnBody.jmp j ys)         := FnBody.jmp <$> normJP j <*> normArgs ys
 | (FnBody.ret x)            := FnBody.ret <$> normArg x
 | FnBody.unreachable        := pure FnBody.unreachable
 
 def normDecl : Decl → N Decl
-| (Decl.fdecl f xs t b) := withParams xs $ λ xs, Decl.fdecl f xs t <$> normFnBody b
+| (Decl.fdecl f xs t b) := withParams xs $ fun xs => Decl.fdecl f xs t <$> normFnBody b
 | other                 := pure other
 
 end NormalizeIds
@@ -166,7 +166,7 @@ as.map (mapArg f)
 | (FnBody.dec x n c b)       := FnBody.dec (f x) n c (mapFnBody b)
 | (FnBody.del x b)           := FnBody.del (f x) (mapFnBody b)
 | (FnBody.mdata d b)         := FnBody.mdata d (mapFnBody b)
-| (FnBody.case tid x alts)   := FnBody.case tid (f x) (alts.map (λ alt, alt.modifyBody mapFnBody))
+| (FnBody.case tid x alts)   := FnBody.case tid (f x) (alts.map (fun alt => alt.modifyBody mapFnBody))
 | (FnBody.jmp j ys)          := FnBody.jmp j (mapArgs f ys)
 | (FnBody.ret x)             := FnBody.ret (mapArg f x)
 | FnBody.unreachable         := FnBody.unreachable
@@ -178,7 +178,7 @@ MapVars.mapFnBody f b
 
 /- Replace `x` with `y` in `b`. This function assumes `b` does not shadow `x` -/
 def FnBody.replaceVar (x y : VarId) (b : FnBody) : FnBody :=
-b.mapVars $ λ z, if x == z then y else z
+b.mapVars $ fun z => if x == z then y else z
 
 end IR
 end Lean
diff --git a/library/init/lean/compiler/ir/pushproj.lean b/library/init/lean/compiler/ir/pushproj.lean
index d9c98cc73f..5dfa7d778d 100644
--- a/library/init/lean/compiler/ir/pushproj.lean
+++ b/library/init/lean/compiler/ir/pushproj.lean
@@ -20,10 +20,10 @@ partial def pushProjs : Array FnBody → Array Alt → Array IndexSet → Array
     let skip (_ : Unit) := pushProjs bs alts altsF (ctx.push b) (b.collectFreeIndices ctxF);
     let push (x : VarId) (t : IRType) (v : Expr) :=
         if !ctxF.contains x.idx then
-          let alts := alts.mapIdx $ λ i alt, alt.modifyBody $ λ b',
+          let alts := alts.mapIdx $ fun i alt => alt.modifyBody $ fun b' =>
              if (altsF.get i).contains x.idx then b.setBody b'
              else b';
-          let altsF  := altsF.map $ λ s, if s.contains x.idx then b.collectFreeIndices s else s;
+          let altsF  := altsF.map $ fun s => if s.contains x.idx then b.collectFreeIndices s else s;
           pushProjs bs alts altsF ctx ctxF
         else
           skip ();
@@ -44,9 +44,9 @@ partial def FnBody.pushProj : FnBody → FnBody
   let bs         := modifyJPs bs FnBody.pushProj;
   match term with
   | FnBody.case tid x alts :=
-    let altsF      := alts.map $ λ alt, alt.body.freeIndices;
+    let altsF      := alts.map $ fun alt => alt.body.freeIndices;
     let (bs, alts) := pushProjs bs alts altsF Array.empty {x.idx};
-    let alts       := alts.map $ λ alt, alt.modifyBody FnBody.pushProj;
+    let alts       := alts.map $ fun alt => alt.modifyBody FnBody.pushProj;
     let term       := FnBody.case tid x alts;
     reshape bs term
   | other := reshape bs term
diff --git a/library/init/lean/compiler/ir/rc.lean b/library/init/lean/compiler/ir/rc.lean
index 1c0666a0cf..3fb053a2fb 100644
--- a/library/init/lean/compiler/ir/rc.lean
+++ b/library/init/lean/compiler/ir/rc.lean
@@ -21,7 +21,7 @@ structure VarInfo :=
 (persistent : Bool := false) -- true if the variable is statically known to be marked a Persistent at runtime
 (consume    : Bool := false) -- true if the variable RC must be "consumed"
 
-abbrev VarMap := RBMap VarId VarInfo (λ x y, x.idx < y.idx)
+abbrev VarMap := RBMap VarId VarInfo (fun x y => x.idx < y.idx)
 
 structure Context :=
 (env            : Environment)
@@ -70,26 +70,26 @@ else let m := ctx.varMap;
 
 private def addDecForAlt (ctx : Context) (caseLiveVars altLiveVars : LiveVarSet) (b : FnBody) : FnBody :=
 caseLiveVars.fold
-  (λ b x, if !altLiveVars.contains x && mustConsume ctx x then addDec x b else b)
+  (fun b x => if !altLiveVars.contains x && mustConsume ctx x then addDec x b else b)
   b
 
 /- `isFirstOcc xs x i = true` if `xs[i]` is the first occurrence of `xs[i]` in `xs` -/
 private def isFirstOcc (xs : Array Arg) (i : Nat) : Bool :=
 let x := xs.get i;
-i.all $ λ j, xs.get j != x
+i.all $ fun j => xs.get j != x
 
 /- Return true if `x` also occurs in `ys` in a position that is not consumed.
    That is, it is also passed as a borrow reference. -/
 @[specialize]
 private def isBorrowParamAux (x : VarId) (ys : Array Arg) (consumeParamPred : Nat → Bool) : Bool :=
-ys.size.any $ λ i,
+ys.size.any $ fun i =>
   let y := ys.get i;
   match y with
   | Arg.irrelevant := false
   | Arg.var y      := x == y && !consumeParamPred i
 
 private def isBorrowParam (x : VarId) (ys : Array Arg) (ps : Array Param) : Bool :=
-isBorrowParamAux x ys (λ i, !(ps.get i).borrow)
+isBorrowParamAux x ys (fun i => !(ps.get i).borrow)
 
 /-
 Return `n`, the number of times `x` is consumed.
@@ -99,7 +99,7 @@ Return `n`, the number of times `x` is consumed.
 @[specialize]
 private def getNumConsumptions (x : VarId) (ys : Array Arg) (consumeParamPred : Nat → Bool) : Nat :=
 ys.size.fold
-  (λ i n,
+  (fun i n =>
     let y := ys.get i;
     match y with
     | Arg.irrelevant := n
@@ -109,7 +109,7 @@ ys.size.fold
 @[specialize]
 private def addIncBeforeAux (ctx : Context) (xs : Array Arg) (consumeParamPred : Nat → Bool) (b : FnBody) (liveVarsAfter : LiveVarSet) : FnBody :=
 xs.size.fold
-  (λ i b,
+  (fun i b =>
     let x := xs.get i;
     match x with
     | Arg.irrelevant := b
@@ -126,17 +126,17 @@ xs.size.fold
           else numConsuptions - 1;
         -- dbgTrace ("addInc " ++ toString x ++ " nconsumptions: " ++ toString numConsuptions ++ " incs: " ++ toString numIncs
         --         ++ " consume: " ++ toString info.consume ++ " live: " ++ toString (liveVarsAfter.contains x)
-        --         ++ " borrowParam : " ++ toString (isBorrowParamAux x xs consumeParamPred)) $ λ _,
+        --         ++ " borrowParam : " ++ toString (isBorrowParamAux x xs consumeParamPred)) $ fun _ =>
         addInc x b numIncs)
   b
 
 private def addIncBefore (ctx : Context) (xs : Array Arg) (ps : Array Param) (b : FnBody) (liveVarsAfter : LiveVarSet) : FnBody :=
-addIncBeforeAux ctx xs (λ i, !(ps.get i).borrow) b liveVarsAfter
+addIncBeforeAux ctx xs (fun i => !(ps.get i).borrow) b liveVarsAfter
 
 /- See `addIncBeforeAux`/`addIncBefore` for the procedure that inserts `inc` operations before an application.  -/
 private def addDecAfterFullApp (ctx : Context) (xs : Array Arg) (ps : Array Param) (b : FnBody) (bLiveVars : LiveVarSet) : FnBody :=
 xs.size.fold
-  (λ i b,
+  (fun i b =>
     match xs.get i with
     | Arg.irrelevant := b
     | Arg.var x      :=
@@ -150,13 +150,13 @@ xs.size.fold
   b
 
 private def addIncBeforeConsumeAll (ctx : Context) (xs : Array Arg) (b : FnBody) (liveVarsAfter : LiveVarSet) : FnBody :=
-addIncBeforeAux ctx xs (λ i, true) b liveVarsAfter
+addIncBeforeAux ctx xs (fun i => true) b liveVarsAfter
 
 /- Add `dec` instructions for parameters that are references, are not alive in `b`, and are not borrow.
    That is, we must make sure these parameters are consumed. -/
 private def addDecForDeadParams (ps : Array Param) (b : FnBody) (bLiveVars : LiveVarSet) : FnBody :=
 ps.foldl
-  (λ b p, if !p.borrow && p.ty.isObj && !bLiveVars.contains p.x then addDec p.x b else b)
+  (fun b p => if !p.borrow && p.ty.isObj && !bLiveVars.contains p.x then addDec p.x b else b)
   b
 
 private def isPersistent : Expr → Bool
@@ -189,7 +189,7 @@ private def addDecIfNeeded (ctx : Context) (x : VarId) (b : FnBody) (bLiveVars :
 if mustConsume ctx x && !bLiveVars.contains x then addDec x b else b
 
 private def processVDecl (ctx : Context) (z : VarId) (t : IRType) (v : Expr) (b : FnBody) (bLiveVars : LiveVarSet) : FnBody × LiveVarSet :=
--- dbgTrace ("processVDecl " ++ toString z ++ " " ++ toString (format v)) $ λ _,
+-- dbgTrace ("processVDecl " ++ toString z ++ " " ++ toString (format v)) $ fun _ =>
 let b := match v with
   | (Expr.ctor _ ys)       := addIncBeforeConsumeAll ctx ys (FnBody.vdecl z t v b) bLiveVars
   | (Expr.reuse _ _ _ ys)  := addIncBeforeConsumeAll ctx ys (FnBody.vdecl z t v b) bLiveVars
@@ -200,7 +200,7 @@ let b := match v with
   | (Expr.uproj _ x)       := FnBody.vdecl z t v (addDecIfNeeded ctx x b bLiveVars)
   | (Expr.sproj _ _ x)     := FnBody.vdecl z t v (addDecIfNeeded ctx x b bLiveVars)
   | (Expr.fap f ys)        :=
-    -- dbgTrace ("processVDecl " ++ toString v) $ λ _,
+    -- dbgTrace ("processVDecl " ++ toString v) $ fun _ =>
     let ps := (getDecl ctx f).params;
     let b  := addDecAfterFullApp ctx ys ps b bLiveVars;
     let b  := FnBody.vdecl z t v b;
@@ -216,7 +216,7 @@ let liveVars := liveVars.erase z;
 (b, liveVars)
 
 def updateVarInfoWithParams (ctx : Context) (ps : Array Param) : Context :=
-let m := ps.foldl (λ (m : VarMap) p, m.insert p.x { ref := p.ty.isObj, consume := !p.borrow }) ctx.varMap;
+let m := ps.foldl (fun (m : VarMap) p => m.insert p.x { ref := p.ty.isObj, consume := !p.borrow }) ctx.varMap;
 { varMap := m, .. ctx }
 
 partial def visitFnBody : FnBody → Context → (FnBody × LiveVarSet)
@@ -245,7 +245,7 @@ partial def visitFnBody : FnBody → Context → (FnBody × LiveVarSet)
   (FnBody.mdata m b, s)
 | b@(FnBody.case tid x alts) ctx :=
   let caseLiveVars := collectLiveVars b ctx.jpLiveVarMap;
-  let alts         := alts.map $ λ alt, match alt with
+  let alts         := alts.map $ fun alt => match alt with
     | Alt.ctor c b  :=
       let ctx              := updateRefUsingCtorInfo ctx x c;
       let (b, altLiveVars) := visitFnBody b ctx;
diff --git a/library/init/lean/compiler/ir/resetreuse.lean b/library/init/lean/compiler/ir/resetreuse.lean
index aabd44b2a7..0964e01b69 100644
--- a/library/init/lean/compiler/ir/resetreuse.lean
+++ b/library/init/lean/compiler/ir/resetreuse.lean
@@ -48,7 +48,7 @@ private partial def S (w : VarId) (c : CtorInfo) : FnBody → FnBody
   let v' := S v;
   if v == v' then FnBody.jdecl j ys v (S b)
   else FnBody.jdecl j ys v' b
-| (FnBody.case tid x alts)  := FnBody.case tid x $ alts.map $ λ alt, alt.modifyBody S
+| (FnBody.case tid x alts)  := FnBody.case tid x $ alts.map $ fun alt => alt.modifyBody S
 | b :=
   if b.isTerminal then b
   else let
@@ -59,7 +59,7 @@ private partial def S (w : VarId) (c : CtorInfo) : FnBody → FnBody
 abbrev M := ReaderT LocalContext (StateT Index Id)
 
 private def mkFresh : M VarId :=
-do idx ← getModify (λ n, n + 1);
+do idx ← getModify (fun n => n + 1);
    pure { idx := idx }
 
 private def tryS (x : VarId) (c : CtorInfo) (b : FnBody) : M FnBody :=
@@ -73,7 +73,7 @@ private def Dfinalize (x : VarId) (c : CtorInfo) : FnBody × Bool → M FnBody
 | (b, false) := tryS x c b
 
 private def argsContainsVar (ys : Array Arg) (x : VarId) : Bool :=
-ys.any $ λ arg, match arg with
+ys.any $ fun arg => match arg with
   | Arg.var y := x == y
   | _         := false
 
@@ -93,11 +93,11 @@ private partial def Dmain (x : VarId) (c : CtorInfo) : FnBody → M (FnBody × B
   ctx ← read;
   if e.hasLiveVar ctx x then do
     /- If `x` is live in `e`, we recursively process each branch. -/
-    alts ← alts.mmap $ λ alt, alt.mmodifyBody (λ b, Dmain b >>= Dfinalize x c);
+    alts ← alts.mmap $ fun alt => alt.mmodifyBody (fun b => Dmain b >>= Dfinalize x c);
     pure (FnBody.case tid y alts, true)
   else pure (e, false)
 | (FnBody.jdecl j ys v b) := do
-  (b, _) ← adaptReader (λ ctx : LocalContext, ctx.addJP j ys v) (Dmain b);
+  (b, _) ← adaptReader (fun ctx : LocalContext => ctx.addJP j ys v) (Dmain b);
   (v, found) ← Dmain v;
   /- If `found == true`, then `Dmain b` must also have returned `(b, true)` since
      we assume the IR does not have dead join points. So, if `x` is live in `j`,
@@ -129,7 +129,7 @@ Dmain x c b >>= Dfinalize x c
 
 partial def R : FnBody → M FnBody
 | (FnBody.case tid x alts) := do
-    alts ← alts.mmap $ λ alt, do {
+    alts ← alts.mmap $ fun alt => do {
       alt ← alt.mmodifyBody R;
       match alt with
       | Alt.ctor c b :=
@@ -140,7 +140,7 @@ partial def R : FnBody → M FnBody
     pure $ FnBody.case tid x alts
 | (FnBody.jdecl j ys v b) := do
   v ← R v;
-  b ← adaptReader (λ ctx : LocalContext, ctx.addJP j ys v) (R b);
+  b ← adaptReader (fun (ctx : LocalContext) => ctx.addJP j ys v) (R b);
   pure $ FnBody.jdecl j ys v b
 | e := do
   if e.isTerminal then pure e
diff --git a/library/init/lean/compiler/ir/simpcase.lean b/library/init/lean/compiler/ir/simpcase.lean
index 467e8972af..d3505bbae7 100644
--- a/library/init/lean/compiler/ir/simpcase.lean
+++ b/library/init/lean/compiler/ir/simpcase.lean
@@ -20,11 +20,11 @@ else
 
 private def getOccsOf (alts : Array Alt) (i : Nat) : Nat :=
 let aBody := (alts.get i).body;
-alts.iterateFrom 1 (i + 1) $ λ _ a' n,
+alts.iterateFrom 1 (i + 1) $ fun _ a' n =>
   if a'.body == aBody then n+1 else n
 
 private def maxOccs (alts : Array Alt) : Alt × Nat :=
-alts.iterateFrom (alts.get 0, getOccsOf alts 0) 1 $ λ i a p,
+alts.iterateFrom (alts.get 0, getOccsOf alts 0) 1 $ fun i a p =>
   let noccs := getOccsOf alts i.val;
   if noccs > p.2 then (alts.fget i, noccs) else p
 
@@ -34,11 +34,11 @@ else
   let (max, noccs) := maxOccs alts;
   if noccs == 1 then alts
   else
-    let alts := alts.filter $ (λ alt, alt.body != max.body);
+    let alts := alts.filter $ (fun alt => alt.body != max.body);
     alts.push (Alt.default max.body)
 
 private def mkSimpCase (tid : Name) (x : VarId) (alts : Array Alt) : FnBody :=
-let alts := alts.filter (λ alt, alt.body != FnBody.unreachable);
+let alts := alts.filter (fun alt => alt.body != FnBody.unreachable);
 let alts := addDefault alts;
 if alts.size == 0 then
   FnBody.unreachable
@@ -53,7 +53,7 @@ partial def FnBody.simpCase : FnBody → FnBody
   let bs         := modifyJPs bs FnBody.simpCase;
   match term with
   | FnBody.case tid x alts :=
-    let alts := alts.map $ λ alt, alt.modifyBody FnBody.simpCase;
+    let alts := alts.map $ fun alt => alt.modifyBody FnBody.simpCase;
     reshape bs (mkSimpCase tid x alts)
   | other := reshape bs term
 
diff --git a/library/init/lean/compiler/specialize.lean b/library/init/lean/compiler/specialize.lean
index 8e4693bc9f..ebbbfdce2f 100644
--- a/library/init/lean/compiler/specialize.lean
+++ b/library/init/lean/compiler/specialize.lean
@@ -30,7 +30,7 @@ def mkSpecializeAttrs : IO (EnumAttributes SpecializeAttributeKind) :=
 registerEnumAttributes `specializeAttrs
   [(`specialize, "mark definition to always be inlined", SpecializeAttributeKind.specialize),
    (`nospecialize, "mark definition to never be inlined", SpecializeAttributeKind.nospecialize) ]
-  (λ env declName _, checkIsDefinition env declName)
+  (fun env declName _ => checkIsDefinition env declName)
 
 @[init mkSpecializeAttrs]
 constant specializeAttrs : EnumAttributes SpecializeAttributeKind := default _
@@ -84,7 +84,7 @@ def mkSpecExtension : IO (SimplePersistentEnvExtension SpecEntry SpecState) :=
 registerSimplePersistentEnvExtension {
   name          := `specialize,
   addEntryFn    := SpecState.addEntry,
-  addImportedFn := λ es, (mkStateFromImportedEntries SpecState.addEntry {} es).switch
+  addImportedFn := fun es => (mkStateFromImportedEntries SpecState.addEntry {} es).switch
 }
 
 @[init mkSpecExtension]
diff --git a/library/init/lean/compiler/util.lean b/library/init/lean/compiler/util.lean
index 408502a654..e7cb50b129 100644
--- a/library/init/lean/compiler/util.lean
+++ b/library/init/lean/compiler/util.lean
@@ -23,7 +23,7 @@ structure AtMostOnceData :=
 def Visitor := AtMostOnceData → AtMostOnceData
 
 @[inline] def seq (f g : Visitor) : Visitor :=
-λ d, match f d with
+fun d => match f d with
 | ⟨found, false⟩ := ⟨found, false⟩
 | other          := g other
 
@@ -73,7 +73,7 @@ def isEagerLambdaLiftingName : Name → Bool
 @[export lean.get_decl_names_for_code_gen_core]
 private def getDeclNamesForCodeGen : Declaration → List Name
 | (Declaration.defnDecl { name := n, .. })   := [n]
-| (Declaration.mutualDefnDecl defs)          := defs.map $ λ d, d.name
+| (Declaration.mutualDefnDecl defs)          := defs.map $ fun d => d.name
 | _                                          := []
 
 def checkIsDefinition (env : Environment) (n : Name) : Except String Unit :=
diff --git a/library/init/lean/environment.lean b/library/init/lean/environment.lean
index 6e9811672f..c188f3251c 100644
--- a/library/init/lean/environment.lean
+++ b/library/init/lean/environment.lean
@@ -118,7 +118,7 @@ let s : EnvExtensionState := env.extensions.get ext.idx;
 constant getState {σ : Type} (ext : EnvExtension σ) (env : Environment) : σ := ext.initial
 
 @[inline] unsafe def modifyStateUnsafe {σ : Type} (ext : EnvExtension σ) (env : Environment) (f : σ → σ) : Environment :=
-{ extensions := env.extensions.modify ext.idx $ λ s,
+{ extensions := env.extensions.modify ext.idx $ fun s =>
     let s : σ := (@unsafeCast _ _ ⟨ext.initial⟩ s);
     let s : σ := f s;
     unsafeCast s,
@@ -148,7 +148,7 @@ let ext : EnvExtension σ := {
    idx     := idx,
    initial := initState
 };
-envExtensionsRef.modify (λ exts, exts.push (unsafeCast ext));
+envExtensionsRef.modify (fun exts => exts.push (unsafeCast ext));
 pure ext
 
 /- Environment extensions can only be registered during initialization.
@@ -159,7 +159,7 @@ pure ext
 constant registerEnvExtension {σ : Type} (initState : σ) : IO (EnvExtension σ) := default _
 
 private def mkInitialExtensionStates : IO (Array EnvExtensionState) :=
-do exts ← envExtensionsRef.get; pure $ exts.map $ λ ext, ext.initial
+do exts ← envExtensionsRef.get; pure $ exts.map $ fun ext => ext.initial
 
 @[export lean.mk_empty_environment_core]
 def mkEmptyEnvironment (trustLevel : UInt32 := 0) : IO Environment :=
@@ -200,10 +200,10 @@ instance PersistentEnvExtensionState.inhabited {α σ} [Inhabited σ] : Inhabite
 instance PersistentEnvExtension.inhabited {α σ} [Inhabited σ] : Inhabited (PersistentEnvExtension α σ) :=
 ⟨{ toEnvExtension := { idx := 0, initial := default _ },
    name := default _,
-   addImportedFn := λ _, default _,
-   addEntryFn := λ s _, s,
-   exportEntriesFn := λ _, Array.empty,
-   statsFn := λ _, Format.nil }⟩
+   addImportedFn := fun _ => default _,
+   addEntryFn := fun s _ => s,
+   exportEntriesFn := fun _ => Array.empty,
+   statsFn := fun _ => Format.nil }⟩
 
 namespace PersistentEnvExtension
 
@@ -211,7 +211,7 @@ def getModuleEntries {α σ : Type} (ext : PersistentEnvExtension α σ) (env :
 (ext.toEnvExtension.getState env).importedEntries.get m
 
 def addEntry {α σ : Type} (ext : PersistentEnvExtension α σ) (env : Environment) (a : α) : Environment :=
-ext.toEnvExtension.modifyState env $ λ s,
+ext.toEnvExtension.modifyState env $ fun s =>
   let state   := ext.addEntryFn s.state a;
   { state := state, .. s }
 
@@ -219,10 +219,10 @@ def getState {α σ : Type} (ext : PersistentEnvExtension α σ) (env : Environm
 (ext.toEnvExtension.getState env).state
 
 def setState {α σ : Type} (ext : PersistentEnvExtension α σ) (env : Environment) (s : σ) : Environment :=
-ext.toEnvExtension.modifyState env $ λ ps, { state := s, .. ps }
+ext.toEnvExtension.modifyState env $ fun ps => { state := s, .. ps }
 
 def modifyState {α σ : Type} (ext : PersistentEnvExtension α σ) (env : Environment) (f : σ → σ) : Environment :=
-ext.toEnvExtension.modifyState env $ λ ps, { state := f (ps.state), .. ps }
+ext.toEnvExtension.modifyState env $ fun ps => { state := f (ps.state), .. ps }
 
 end PersistentEnvExtension
 
@@ -237,7 +237,7 @@ structure PersistentEnvExtensionDescr (α σ : Type) :=
 (addImportedFn   : Array (Array α) → σ)
 (addEntryFn      : σ → α → σ)
 (exportEntriesFn : σ → Array α)
-(statsFn         : σ → Format := λ _, Format.nil)
+(statsFn         : σ → Format := fun _ => Format.nil)
 
 unsafe def registerPersistentEnvExtensionUnsafe {α σ : Type} (descr : PersistentEnvExtensionDescr α σ) : IO (PersistentEnvExtension α σ) :=
 do
@@ -245,7 +245,7 @@ let s : PersistentEnvExtensionState α σ := {
   importedEntries := Array.empty,
   state           := descr.addImportedFn Array.empty };
 pExts ← persistentEnvExtensionsRef.get;
-when (pExts.any (λ ext, ext.name == descr.name)) $ throw (IO.userError ("invalid environment extension, '" ++ toString descr.name ++ "' has already been used"));
+when (pExts.any (fun ext => ext.name == descr.name)) $ throw (IO.userError ("invalid environment extension, '" ++ toString descr.name ++ "' has already been used"));
 ext ← registerEnvExtension s;
 let pExt : PersistentEnvExtension α σ := {
   toEnvExtension  := ext,
@@ -255,7 +255,7 @@ let pExt : PersistentEnvExtension α σ := {
   exportEntriesFn := descr.exportEntriesFn,
   statsFn         := descr.statsFn
 };
-persistentEnvExtensionsRef.modify (λ pExts, pExts.push (unsafeCast pExt));
+persistentEnvExtensionsRef.modify (fun pExts => pExts.push (unsafeCast pExt));
 pure pExt
 
 @[implementedBy registerPersistentEnvExtensionUnsafe]
@@ -266,22 +266,22 @@ constant registerPersistentEnvExtension {α σ : Type} (descr : PersistentEnvExt
 def SimplePersistentEnvExtension (α σ : Type) := PersistentEnvExtension α (List α × σ)
 
 @[specialize] def mkStateFromImportedEntries {α σ : Type} (addEntryFn : σ → α → σ) (initState : σ) (as : Array (Array α)) : σ :=
-as.foldl (λ r es, es.foldl (λ r e, addEntryFn r e) r) initState
+as.foldl (fun r es => es.foldl (fun r e => addEntryFn r e) r) initState
 
 structure SimplePersistentEnvExtensionDescr (α σ : Type) :=
 (name          : Name)
 (addEntryFn    : σ → α → σ)
 (addImportedFn : Array (Array α) → σ)
-(toArrayFn     : List α → Array α := λ es, es.toArray)
+(toArrayFn     : List α → Array α := fun es => es.toArray)
 
 def registerSimplePersistentEnvExtension {α σ : Type} (descr : SimplePersistentEnvExtensionDescr α σ) : IO (SimplePersistentEnvExtension α σ) :=
 registerPersistentEnvExtension {
   name := descr.name,
-  addImportedFn := λ as, ([], descr.addImportedFn as),
-  addEntryFn := λ s e, match s with
+  addImportedFn := fun as => ([], descr.addImportedFn as),
+  addEntryFn := fun s e => match s with
     | (entries, s) := (e::entries, descr.addEntryFn s e),
-  exportEntriesFn := λ s, descr.toArrayFn s.1.reverse,
-  statsFn := λ s, format "number of local entries: " ++ format s.1.length
+  exportEntriesFn := fun s => descr.toArrayFn s.1.reverse,
+  statsFn := fun s => format "number of local entries: " ++ format s.1.length
 }
 
 namespace SimplePersistentEnvExtension
@@ -296,10 +296,10 @@ def getState {α σ : Type} (ext : SimplePersistentEnvExtension α σ) (env : En
 (PersistentEnvExtension.getState ext env).2
 
 def setState {α σ : Type} (ext : SimplePersistentEnvExtension α σ) (env : Environment) (s : σ) : Environment :=
-PersistentEnvExtension.modifyState ext env (λ ⟨entries, _⟩, (entries, s))
+PersistentEnvExtension.modifyState ext env (fun ⟨entries, _⟩ => (entries, s))
 
 def modifyState {α σ : Type} (ext : SimplePersistentEnvExtension α σ) (env : Environment) (f : σ → σ) : Environment :=
-PersistentEnvExtension.modifyState ext env (λ ⟨entries, s⟩, (entries, f s))
+PersistentEnvExtension.modifyState ext env (fun ⟨entries, s⟩ => (entries, f s))
 
 end SimplePersistentEnvExtension
 
@@ -343,7 +343,7 @@ constant modListExtension : EnvExtension (List Modification) := default _
 /- The C++ code uses this function to store the given modification object into the environment. -/
 @[export lean.environment_add_modification_core]
 def addModification (env : Environment) (mod : Modification) : Environment :=
-modListExtension.modifyState env $ λ mods, mod :: mods
+modListExtension.modifyState env $ fun mods => mod :: mods
 
 /- mkModuleData invokes this function to convert a list of modification objects into
    a serialized byte array. -/
@@ -373,7 +373,7 @@ def mkModuleData (env : Environment) : IO ModuleData :=
 do
 pExts ← persistentEnvExtensionsRef.get;
 let entries : Array (Name × Array EnvExtensionEntry) := pExts.size.fold
-  (λ i result,
+  (fun i result =>
     let state  := (pExts.get i).getState env;
     let exportEntriesFn := (pExts.get i).exportEntriesFn;
     let extName    := (pExts.get i).name;
@@ -382,7 +382,7 @@ let entries : Array (Name × Array EnvExtensionEntry) := pExts.size.fold
 bytes ← serializeModifications (modListExtension.getState env);
 pure {
 imports    := env.header.imports,
-constants  := env.constants.foldStage2 (λ cs _ c, cs.push c) Array.empty,
+constants  := env.constants.foldStage2 (fun cs _ c => cs.push c) Array.empty,
 entries    := entries,
 serialized := bytes
 }
@@ -418,29 +418,29 @@ private partial def getEntriesFor (mod : ModuleData) (extId : Name) : Nat → Ar
 private def setImportedEntries (env : Environment) (mods : Array ModuleData) : IO Environment :=
 do
 pExtDescrs ← persistentEnvExtensionsRef.get;
-pure $ mods.iterate env $ λ _ mod env,
-  pExtDescrs.iterate env $ λ _ extDescr env,
+pure $ mods.iterate env $ fun _ mod env =>
+  pExtDescrs.iterate env $ fun _ extDescr env =>
     let entries := getEntriesFor mod extDescr.name 0;
-    extDescr.toEnvExtension.modifyState env $ λ s,
+    extDescr.toEnvExtension.modifyState env $ fun s =>
       { importedEntries := s.importedEntries.push entries,
         .. s }
 
 private def finalizePersistentExtensions (env : Environment) : IO Environment :=
 do
 pExtDescrs ← persistentEnvExtensionsRef.get;
-pure $ pExtDescrs.iterate env $ λ _ extDescr env,
-  extDescr.toEnvExtension.modifyState env $ λ s,
+pure $ pExtDescrs.iterate env $ fun _ extDescr env =>
+  extDescr.toEnvExtension.modifyState env $ fun s =>
     { state := extDescr.addImportedFn s.importedEntries, .. s }
 
 @[export lean.import_modules_core]
 def importModules (modNames : List Name) (trustLevel : UInt32 := 0) : IO Environment :=
 do
 (_, mods) ← importModulesAux modNames ({}, Array.empty);
-let const2ModIdx := mods.iterate {} $ λ modIdx (mod : ModuleData) (m : HashMap Name ModuleIdx),
-  mod.constants.iterate m $ λ _ cinfo m,
+let const2ModIdx := mods.iterate {} $ fun (modIdx) (mod : ModuleData) (m : HashMap Name ModuleIdx) =>
+  mod.constants.iterate m $ fun _ cinfo m =>
     m.insert cinfo.name modIdx.val;
-constants ← mods.miterate SMap.empty $ λ _ (mod : ModuleData) (cs : ConstMap),
-  mod.constants.miterate cs $ λ _ cinfo cs, do {
+constants ← mods.miterate SMap.empty $ fun _ (mod : ModuleData) (cs : ConstMap) =>
+  mod.constants.miterate cs $ fun _ cinfo cs => do {
     when (cs.contains cinfo.name) $ throw (IO.userError ("import failed, environment already contains '" ++ toString cinfo.name ++ "'"));
     pure $ cs.insert cinfo.name cinfo
   };
@@ -458,7 +458,7 @@ let env : Environment := {
 };
 env ← setImportedEntries env mods;
 env ← finalizePersistentExtensions env;
-env ← mods.miterate env $ λ _ mod env, performModifications env mod.serialized;
+env ← mods.miterate env $ fun _ mod env => performModifications env mod.serialized;
 pure env
 
 namespace Environment
@@ -477,12 +477,12 @@ IO.println ("number of buckets for imported consts: " ++ toString env.constants.
 IO.println ("map depth for local consts:            " ++ toString env.constants.maxDepth);
 IO.println ("trust level:                           " ++ toString env.header.trustLevel);
 IO.println ("number of extensions:                  " ++ toString env.extensions.size);
-pExtDescrs.mfor $ λ extDescr, do {
+pExtDescrs.mfor $ fun extDescr => do {
   IO.println ("extension '" ++ toString extDescr.name ++ "'");
   let s := extDescr.toEnvExtension.getState env;
   let fmt := extDescr.statsFn s.state;
   unless fmt.isNil (IO.println ("  " ++ toString (Format.nest 2 (extDescr.statsFn s.state))));
-  IO.println ("  number of imported entries: " ++ toString (s.importedEntries.foldl (λ sum es, sum + es.size) 0));
+  IO.println ("  number of imported entries: " ++ toString (s.importedEntries.foldl (fun sum es => sum + es.size) 0));
   pure ()
 };
 pure ()
diff --git a/library/init/lean/evalconst.lean b/library/init/lean/evalconst.lean
index ea221c0c05..2375df627c 100644
--- a/library/init/lean/evalconst.lean
+++ b/library/init/lean/evalconst.lean
@@ -26,14 +26,14 @@ unsafe constant getConstTable : IO (Array (Name × NonScalar)) := default _
    See `src/init/init.cpp` -/
 @[export lean.sort_const_table_core]
 unsafe def sortConstTable : IO Unit :=
-modifyConstTable (λ cs, cs.qsort (λ e₁ e₂, Name.quickLt e₁.1 e₂.1))
+modifyConstTable (fun cs => cs.qsort (fun e₁ e₂ => Name.quickLt e₁.1 e₂.1))
 
 /- We make this primitive as `unsafe` because it uses `unsafeCast`, and
    the program may crash if the type provided by the user is incorrect.
    It also assumes there are no threads trying to update the table concurrently. -/
 unsafe def evalConst (α : Type) [Inhabited α] (c : Name) : IO α :=
 do cs ← getConstTable;
-   match cs.binSearch (c, default _) (λ e₁ e₂, Name.quickLt e₁.1 e₂.1) with
+   match cs.binSearch (c, default _) (fun e₁ e₂ => Name.quickLt e₁.1 e₂.1) with
    | some (_, v) := pure (unsafeCast v)
    | none        := throw (IO.userError ("unknow constant '" ++ toString c ++ "'"))
 
diff --git a/library/init/lean/format.lean b/library/init/lean/format.lean
index ed1604d204..dd41cd6cbd 100644
--- a/library/init/lean/format.lean
+++ b/library/init/lean/format.lean
@@ -159,17 +159,17 @@ instance listHasFormat {α : Type u} [HasFormat α] : HasFormat (List α) :=
 ⟨List.format⟩
 
 instance prodHasFormat {α : Type u} {β : Type v} [HasFormat α] [HasFormat β] : HasFormat (Prod α β) :=
-⟨λ ⟨a, b⟩, paren $ format a ++ "," ++ line ++ format b⟩
+⟨fun ⟨a, b⟩ => paren $ format a ++ "," ++ line ++ format b⟩
 
 def Format.joinArraySep {α : Type u} [HasFormat α] (a : Array α) (sep : Format) : Format :=
-a.iterate nil (λ i a r, if i.val > 0 then r ++ sep ++ format a else r ++ format a)
+a.iterate nil (fun i a r => if i.val > 0 then r ++ sep ++ format a else r ++ format a)
 
-instance natHasFormat : HasFormat Nat       := ⟨λ n, toString n⟩
-instance uint16HasFormat : HasFormat UInt16 := ⟨λ n, toString n⟩
-instance uint32HasFormat : HasFormat UInt32 := ⟨λ n, toString n⟩
-instance uint64HasFormat : HasFormat UInt64 := ⟨λ n, toString n⟩
-instance usizeHasFormat : HasFormat USize   := ⟨λ n, toString n⟩
-instance nameHasFormat : HasFormat Name     := ⟨λ n, n.toString⟩
+instance natHasFormat : HasFormat Nat       := ⟨fun n => toString n⟩
+instance uint16HasFormat : HasFormat UInt16 := ⟨fun n => toString n⟩
+instance uint32HasFormat : HasFormat UInt32 := ⟨fun n => toString n⟩
+instance uint64HasFormat : HasFormat UInt64 := ⟨fun n => toString n⟩
+instance usizeHasFormat : HasFormat USize   := ⟨fun n => toString n⟩
+instance nameHasFormat : HasFormat Name     := ⟨fun n => n.toString⟩
 
 protected def Format.repr : Format → Format
 | nil := "Format.nil"
diff --git a/library/init/lean/kvmap.lean b/library/init/lean/kvmap.lean
index bd4e138b26..d71791aaf8 100644
--- a/library/init/lean/kvmap.lean
+++ b/library/init/lean/kvmap.lean
@@ -119,19 +119,19 @@ export isKVMapVal (set)
 isKVMapVal.get m k defVal
 
 instance boolVal : isKVMapVal Bool :=
-{ defVal := false, set := setBool, get := λ k n v, getBool k n v }
+{ defVal := false, set := setBool, get := fun k n v => getBool k n v }
 
 instance natVal : isKVMapVal Nat :=
-{ defVal := 0, set := setNat, get := λ k n v, getNat k n v }
+{ defVal := 0, set := setNat, get := fun k n v => getNat k n v }
 
 instance intVal : isKVMapVal Int :=
-{ defVal := 0, set := setInt, get := λ k n v, getInt k n v }
+{ defVal := 0, set := setInt, get := fun k n v => getInt k n v }
 
 instance nameVal : isKVMapVal Name :=
-{ defVal := Name.anonymous, set := setName, get := λ k n v, getName k n v }
+{ defVal := Name.anonymous, set := setName, get := fun k n v => getName k n v }
 
 instance stringVal : isKVMapVal String :=
-{ defVal := "", set := setString, get := λ k n v, getString k n v }
+{ defVal := "", set := setString, get := fun k n v => getString k n v }
 
 end KVMap
 end Lean
diff --git a/library/init/lean/level.lean b/library/init/lean/level.lean
index f47e73cabe..c2f213f0d1 100644
--- a/library/init/lean/level.lean
+++ b/library/init/lean/level.lean
@@ -111,8 +111,8 @@ partial def Result.format : Result → Bool → Format
 | (Result.offset f (k+1)) r :=
   let f' := Result.format f false;
   parenIfFalse (f' ++ "+" ++ fmt (k+1)) r
-| (Result.maxNode fs)    r := parenIfFalse (Format.group $ "max"  ++ formatLst (λ r, Result.format r false) fs) r
-| (Result.imaxNode fs)   r := parenIfFalse (Format.group $ "imax" ++ formatLst (λ r, Result.format r false) fs) r
+| (Result.maxNode fs)    r := parenIfFalse (Format.group $ "max"  ++ formatLst (fun r => Result.format r false) fs) r
+| (Result.imaxNode fs)   r := parenIfFalse (Format.group $ "imax" ++ formatLst (fun r => Result.format r false) fs) r
 
 def Level.toResult : Level → Result
 | Level.zero         := Result.num 0
diff --git a/library/init/lean/message.lean b/library/init/lean/message.lean
index 91c60eee85..b1bdbab9e1 100644
--- a/library/init/lean/message.lean
+++ b/library/init/lean/message.lean
@@ -56,7 +56,7 @@ instance : HasAppend MessageLog :=
 ⟨MessageLog.append⟩
 
 def hasErrors (log : MessageLog) : Bool :=
-log.revList.any $ λ m, match m.severity with
+log.revList.any $ fun m => match m.severity with
 | MessageSeverity.error := true
 | _                     := false
 
diff --git a/library/init/lean/modifiers.lean b/library/init/lean/modifiers.lean
index 6ebf2de085..03e8b9a5e3 100644
--- a/library/init/lean/modifiers.lean
+++ b/library/init/lean/modifiers.lean
@@ -11,9 +11,9 @@ namespace Lean
 def mkProtectedExtension : IO (SimplePersistentEnvExtension Name NameSet) :=
 registerSimplePersistentEnvExtension {
   name          := `protected,
-  addImportedFn := λ as, {},
-  addEntryFn    := λ s n, s.insert n,
-  toArrayFn     := λ es, es.toArray.qsort Name.quickLt
+  addImportedFn := fun as => {},
+  addEntryFn    := fun s n => s.insert n,
+  toArrayFn     := fun es => es.toArray.qsort Name.quickLt
 }
 
 @[init mkProtectedExtension]
diff --git a/library/init/lean/name.lean b/library/init/lean/name.lean
index 52363c40bf..6175b11014 100644
--- a/library/init/lean/name.lean
+++ b/library/init/lean/name.lean
@@ -63,20 +63,20 @@ protected def decEq : Π (a b : @& Name), Decidable (a = b)
   if h₁ : s₁ = s₂ then
     match decEq p₁ p₂ with
     | isTrue h₂  := isTrue $ h₁ ▸ h₂ ▸ rfl
-    | isFalse h₂ := isFalse $ λ h, Name.noConfusion h $ λ hp hs, absurd hp h₂
-  else isFalse $ λ h, Name.noConfusion h $ λ hp hs, absurd hs h₁
+    | isFalse h₂ := isFalse $ fun h => Name.noConfusion h $ fun hp hs => absurd hp h₂
+  else isFalse $ fun h => Name.noConfusion h $ fun hp hs => absurd hs h₁
 | (mkNumeral p₁ n₁) (mkNumeral p₂ n₂) :=
   if h₁ : n₁ = n₂ then
     match decEq p₁ p₂ with
     | isTrue h₂  := isTrue $ h₁ ▸ h₂ ▸ rfl
-    | isFalse h₂ := isFalse $ λ h, Name.noConfusion h $ λ hp hs, absurd hp h₂
-  else isFalse $ λ h, Name.noConfusion h $ λ hp hs, absurd hs h₁
-| anonymous         (mkString _ _)    := isFalse $ λ h, Name.noConfusion h
-| anonymous         (mkNumeral _ _)   := isFalse $ λ h, Name.noConfusion h
-| (mkString _ _)    anonymous         := isFalse $ λ h, Name.noConfusion h
-| (mkString _ _)    (mkNumeral _ _)   := isFalse $ λ h, Name.noConfusion h
-| (mkNumeral _ _)   anonymous         := isFalse $ λ h, Name.noConfusion h
-| (mkNumeral _ _)   (mkString _ _)    := isFalse $ λ h, Name.noConfusion h
+    | isFalse h₂ := isFalse $ fun h => Name.noConfusion h $ fun hp hs => absurd hp h₂
+  else isFalse $ fun h => Name.noConfusion h $ fun hp hs => absurd hs h₁
+| anonymous         (mkString _ _)    := isFalse $ fun h => Name.noConfusion h
+| anonymous         (mkNumeral _ _)   := isFalse $ fun h => Name.noConfusion h
+| (mkString _ _)    anonymous         := isFalse $ fun h => Name.noConfusion h
+| (mkString _ _)    (mkNumeral _ _)   := isFalse $ fun h => Name.noConfusion h
+| (mkNumeral _ _)   anonymous         := isFalse $ fun h => Name.noConfusion h
+| (mkNumeral _ _)   (mkString _ _)    := isFalse $ fun h => Name.noConfusion h
 
 instance : DecidableEq Name :=
 {decEq := Name.decEq}
@@ -125,10 +125,10 @@ else quickLtCore n₁ n₂
 
 /- Alternative HasLt instance. -/
 @[inline] protected def hasLtQuick : HasLess Name :=
-⟨λ a b, Name.quickLt a b = true⟩
+⟨fun a b => Name.quickLt a b = true⟩
 
 @[inline] instance : DecidableRel (@HasLess.Less Name Name.hasLtQuick) :=
-inferInstanceAs (DecidableRel (λ a b, Name.quickLt a b = true))
+inferInstanceAs (DecidableRel (fun a b => Name.quickLt a b = true))
 
 def toStringWithSep (sep : String) : Name → String
 | anonymous               := "[anonymous]"
@@ -159,16 +159,16 @@ def isInternal : Name → Bool
 | _ := false
 
 theorem mkStringNeMkStringOfNePrefix {p₁ : Name} (s₁ : String) {p₂ : Name} (s₂ : String) : p₁ ≠ p₂ → mkString p₁ s₁ ≠ mkString p₂ s₂ :=
-λ h₁ h₂, Name.noConfusion h₂ (λ h _, absurd h h₁)
+fun h₁ h₂ => Name.noConfusion h₂ (fun h _ => absurd h h₁)
 
 theorem mkStringNeMkStringOfNeString (p₁ : Name) {s₁ : String} (p₂ : Name) {s₂ : String} : s₁ ≠ s₂ → mkString p₁ s₁ ≠ mkString p₂ s₂ :=
-λ h₁ h₂, Name.noConfusion h₂ (λ _ h, absurd h h₁)
+fun h₁ h₂ => Name.noConfusion h₂ (fun _ h => absurd h h₁)
 
 theorem mkNumeralNeMkNumeralOfNePrefix {p₁ : Name} (n₁ : Nat) {p₂ : Name} (n₂ : Nat) : p₁ ≠ p₂ → mkNumeral p₁ n₁ ≠ mkNumeral p₂ n₂ :=
-λ h₁ h₂, Name.noConfusion h₂ (λ h _, absurd h h₁)
+fun h₁ h₂ => Name.noConfusion h₂ (fun h _ => absurd h h₁)
 
 theorem mkNumeralNeMkNumeralOfNeNumeral (p₁ : Name) {n₁ : Nat} (p₂ : Name) {n₂ : Nat} : n₁ ≠ n₂ → mkNumeral p₁ n₁ ≠ mkNumeral p₂ n₂ :=
-λ h₁ h₂, Name.noConfusion h₂ (λ _ h, absurd h h₁)
+fun h₁ h₂ => Name.noConfusion h₂ (fun _ h => absurd h h₁)
 
 end Name
 
@@ -212,4 +212,4 @@ open Lean
 
 def String.toName (s : String) : Name :=
 let ps := s.split ".";
-ps.foldl (λ n p, Name.mkString n p.trim) Name.anonymous
+ps.foldl (fun n p => Name.mkString n p.trim) Name.anonymous
diff --git a/library/init/lean/parser/level.lean b/library/init/lean/parser/level.lean
index a4c9085e1a..a2ba6bd67a 100644
--- a/library/init/lean/parser/level.lean
+++ b/library/init/lean/parser/level.lean
@@ -16,7 +16,7 @@ constant builtinLevelParsingTable : IO.Ref ParsingTables := default _
 registerBuiltinParserAttribute `builtinLevelParser `Lean.Parser.builtinLevelParsingTable
 
 def levelParser {k : ParserKind} (rbp : Nat := 0) : Parser k :=
-{ fn := λ _, runBuiltinParser "universe level" builtinLevelParsingTable rbp }
+{ fn := fun _ => runBuiltinParser "universe level" builtinLevelParsingTable rbp }
 
 namespace Level
 
diff --git a/library/init/lean/parser/parser.lean b/library/init/lean/parser/parser.lean
index 2aeb4fd0c5..f009d58a25 100644
--- a/library/init/lean/parser/parser.lean
+++ b/library/init/lean/parser/parser.lean
@@ -139,7 +139,7 @@ def BasicParserFn := ParserContext → ParserState → ParserState
 
 def ParserFn (k : ParserKind) := ParserArg k → BasicParserFn
 
-instance ParserFn.inhabited (k : ParserKind) : Inhabited (ParserFn k) := ⟨λ _ _, id⟩
+instance ParserFn.inhabited (k : ParserKind) : Inhabited (ParserFn k) := ⟨fun _ _ => id⟩
 
 inductive FirstTokens
 | epsilon : FirstTokens
@@ -168,7 +168,7 @@ instance : HasToString FirstTokens := ⟨toStr⟩
 end FirstTokens
 
 structure ParserInfo :=
-(updateTokens : Trie TokenConfig → ExceptT String Id (Trie TokenConfig) := λ tks, pure tks)
+(updateTokens : Trie TokenConfig → ExceptT String Id (Trie TokenConfig) := fun tks => pure tks)
 (firstTokens  : FirstTokens := FirstTokens.unknown)
 
 structure Parser (k : ParserKind := leading) :=
@@ -176,7 +176,7 @@ structure Parser (k : ParserKind := leading) :=
 (fn   : ParserFn k)
 
 instance Parser.inhabited {k : ParserKind} : Inhabited (Parser k) :=
-⟨{ fn := λ _ _ s, s }⟩
+⟨{ fn := fun _ _ s => s }⟩
 
 abbrev TrailingParser := Parser trailing
 
@@ -184,14 +184,14 @@ abbrev TrailingParser := Parser trailing
 { firstTokens := FirstTokens.epsilon }
 
 @[inline] def pushLeadingFn : ParserFn trailing :=
-λ a c s, s.pushSyntax a
+fun a c s => s.pushSyntax a
 
 @[inline] def pushLeading : TrailingParser :=
 { info := epsilonInfo,
   fn   := pushLeadingFn }
 
 @[inline] def checkLeadingFn (p : Syntax → Bool) : ParserFn trailing :=
-λ a c s,
+fun a c s =>
   if p a then s
   else s.mkError "invalid leading token"
 
@@ -200,15 +200,15 @@ abbrev TrailingParser := Parser trailing
   fn   := checkLeadingFn p }
 
 @[inline] def andthenAux (p q : BasicParserFn) : BasicParserFn :=
-λ c s,
+fun c s =>
   let s := p c s;
   if s.hasError then s else q c s
 
 @[inline] def andthenFn {k : ParserKind} (p q : ParserFn k) : ParserFn k :=
-λ a c s, andthenAux (p a) (q a) c s
+fun a c s => andthenAux (p a) (q a) c s
 
 @[noinline] def andthenInfo (p q : ParserInfo) : ParserInfo :=
-{ updateTokens := λ tks, q.updateTokens tks >>= p.updateTokens,
+{ updateTokens := fun tks => q.updateTokens tks >>= p.updateTokens,
   firstTokens  := p.firstTokens.seq q.firstTokens }
 
 @[inline] def andthen {k : ParserKind} (p q : Parser k) : Parser k :=
@@ -246,7 +246,7 @@ node n p
   if s.hasError && s.pos == iniPos then q a c (s.restore iniSz iniPos) else s
 
 @[noinline] def orelseInfo (p q : ParserInfo) : ParserInfo :=
-{ updateTokens := λ tks, q.updateTokens tks >>= p.updateTokens,
+{ updateTokens := fun tks => q.updateTokens tks >>= p.updateTokens,
   firstTokens  := p.firstTokens.merge q.firstTokens }
 
 @[inline] def orelse {k : ParserKind} (p q : Parser k) : Parser k :=
@@ -272,7 +272,7 @@ instance hashOrelse {k : ParserKind} : HasOrelse (Parser k) :=
   fn   := tryFn p.fn }
 
 @[inline] def optionalFn {k : ParserKind} (p : ParserFn k) : ParserFn k :=
-λ a c s,
+fun a c s =>
   let iniSz  := s.stackSize;
   let iniPos := s.pos;
   let s      := p a c s;
@@ -293,7 +293,7 @@ instance hashOrelse {k : ParserKind} : HasOrelse (Parser k) :=
   else manyAux a c s
 
 @[inline] def manyFn {k : ParserKind} (p : ParserFn k) : ParserFn k :=
-λ a c s,
+fun a c s =>
   let iniSz  := s.stackSize;
   let s := manyAux p a c s;
   s.mkNode nullKind iniSz
@@ -303,7 +303,7 @@ instance hashOrelse {k : ParserKind} : HasOrelse (Parser k) :=
   fn   := manyFn p.fn }
 
 @[inline] def many1Fn {k : ParserKind} (p : ParserFn k) : ParserFn k :=
-λ a c s,
+fun a c s =>
   let iniSz  := s.stackSize;
   let s := andthenFn p (manyAux p) a c s;
   s.mkNode nullKind iniSz
@@ -346,10 +346,10 @@ instance hashOrelse {k : ParserKind} : HasOrelse (Parser k) :=
   sepByFnAux p sep allowTrailingSep iniSz false a c s
 
 @[noinline] def sepByInfo (p sep : ParserInfo) : ParserInfo :=
-{ updateTokens := λ tks, p.updateTokens tks >>= sep.updateTokens }
+{ updateTokens := fun tks => p.updateTokens tks >>= sep.updateTokens }
 
 @[noinline] def sepBy1Info (p sep : ParserInfo) : ParserInfo :=
-{ updateTokens := λ tks, p.updateTokens tks >>= sep.updateTokens,
+{ updateTokens := fun tks => p.updateTokens tks >>= sep.updateTokens,
   firstTokens  := p.firstTokens }
 
 @[inline] def sepBy {k : ParserKind} (p sep : Parser k) (allowTrailingSep : Bool := false) : Parser k :=
@@ -375,7 +375,7 @@ instance hashOrelse {k : ParserKind} : HasOrelse (Parser k) :=
   else takeUntilFn c (s.next c.input i)
 
 @[specialize] def takeWhileFn (p : Char → Bool) : BasicParserFn :=
-takeUntilFn (λ c, !p c)
+takeUntilFn (fun c => !p c)
 
 @[inline] def takeWhile1Fn (p : Char → Bool) (errorMsg : String) : BasicParserFn :=
 andthenAux (satisfyFn p errorMsg) (takeWhileFn p)
@@ -417,7 +417,7 @@ partial def whitespace : BasicParserFn
     else if curr == '-' then
       let i    := input.next i;
       let curr := input.get i;
-      if curr == '-' then andthenAux (takeUntilFn (λ c, c = '\n')) whitespace c (s.next input i)
+      if curr == '-' then andthenAux (takeUntilFn (fun c => c = '\n')) whitespace c (s.next input i)
       else s
     else if curr == '/' then
       let i    := input.next i;
@@ -486,7 +486,7 @@ def quotedCharFn : BasicParserFn
 
 /-- Push `(Syntax.node tk <new-atom>)` into syntax stack -/
 def mkNodeToken (n : SyntaxNodeKind) (startPos : Nat) : BasicParserFn :=
-λ c s,
+fun c s =>
 let input     := c.input;
 let stopPos   := s.pos;
 let leading   := mkEmptySubstringAt input startPos;
@@ -511,8 +511,8 @@ partial def strLitFnAux (startPos : Nat) : BasicParserFn
     else strLitFnAux c s
 
 def decimalNumberFn (startPos : Nat) : BasicParserFn :=
-λ c s,
-  let s     := takeWhileFn (λ c, c.isDigit) c s;
+fun c s =>
+  let s     := takeWhileFn (fun c => c.isDigit) c s;
   let input := c.input;
   let i     := s.pos;
   let curr  := input.get i;
@@ -522,28 +522,28 @@ def decimalNumberFn (startPos : Nat) : BasicParserFn :=
       let i    := input.next i;
       let curr := input.get i;
       if curr.isDigit then
-        takeWhileFn (λ c, c.isDigit) c (s.setPos i)
+        takeWhileFn (fun c => c.isDigit) c (s.setPos i)
       else s
     else s;
   mkNodeToken numLitKind startPos c s
 
 def binNumberFn (startPos : Nat) : BasicParserFn :=
-λ c s,
-  let s := takeWhile1Fn (λ c, c == '0' || c == '1') "expected binary number" c s;
+fun c s =>
+  let s := takeWhile1Fn (fun c => c == '0' || c == '1') "expected binary number" c s;
   mkNodeToken numLitKind startPos c s
 
 def octalNumberFn (startPos : Nat) : BasicParserFn :=
-λ c s,
-  let s := takeWhile1Fn (λ c, '0' ≤ c && c ≤ '7') "expected octal number" c s;
+fun c s =>
+  let s := takeWhile1Fn (fun c => '0' ≤ c && c ≤ '7') "expected octal number" c s;
   mkNodeToken numLitKind startPos c s
 
 def hexNumberFn (startPos : Nat) : BasicParserFn :=
-λ c s,
-  let s := takeWhile1Fn (λ c, ('0' ≤ c && c ≤ '9') || ('a' ≤ c && c ≤ 'f') || ('A' ≤ c && c ≤ 'F')) "expected hexadecimal number" c s;
+fun c s =>
+  let s := takeWhile1Fn (fun c => ('0' ≤ c && c ≤ '9') || ('a' ≤ c && c ≤ 'f') || ('A' ≤ c && c ≤ 'F')) "expected hexadecimal number" c s;
   mkNodeToken numLitKind startPos c s
 
 def numberFnAux : BasicParserFn :=
-λ c s,
+fun c s =>
   let input    := c.input;
   let startPos := s.pos;
   if input.atEnd startPos then s.mkEOIError
@@ -588,7 +588,7 @@ match tk with
   tk.val.bsize ≥ idStopPos - idStopPos
 
 def mkTokenAndFixPos (startPos : Nat) (tk : Option TokenConfig) : BasicParserFn :=
-λ c s,
+fun c s =>
 match tk with
 | none    := s.mkErrorAt "token expected" startPos
 | some tk :=
@@ -604,7 +604,7 @@ match tk with
   s.pushSyntax atom
 
 def mkIdResult (startPos : Nat) (tk : Option TokenConfig) (val : Name) : BasicParserFn :=
-λ c s,
+fun c s =>
 let stopPos              := s.pos;
 if isToken startPos stopPos tk then
   mkTokenAndFixPos startPos tk c s
@@ -673,7 +673,7 @@ match s with
 | other := other
 
 def tokenFn : BasicParserFn :=
-λ c s,
+fun c s =>
   let input := c.input;
   let i     := s.pos;
   if input.atEnd i then s.mkEOIError
@@ -696,7 +696,7 @@ else
   (s.restore iniSz iniPos, some stx)
 
 @[inline] def satisfySymbolFn (p : String → Bool) (errorMsg : String) : BasicParserFn :=
-λ c s,
+fun c s =>
   let startPos := s.pos;
   let s        := tokenFn c s;
   if s.hasError then
@@ -707,7 +707,7 @@ else
     | _                 := s.mkErrorAt errorMsg startPos
 
 def symbolFnAux (sym : String) (errorMsg : String) : BasicParserFn :=
-satisfySymbolFn (λ s, s == sym) errorMsg
+satisfySymbolFn (fun s => s == sym) errorMsg
 
 def insertToken (sym : String) (lbp : Option Nat) (tks : Trie TokenConfig) : ExceptT String Id (Trie TokenConfig) :=
 match tks.find sym, lbp with
@@ -723,7 +723,7 @@ def symbolInfo (sym : String) (lbp : Option Nat) : ParserInfo :=
   firstTokens  := FirstTokens.tokens [ { val := sym, lbp := lbp } ] }
 
 @[inline] def symbolFn {k : ParserKind} (sym : String) : ParserFn k :=
-λ _, symbolFnAux sym ("expected '" ++ sym ++ "'")
+fun _ => symbolFnAux sym ("expected '" ++ sym ++ "'")
 
 @[inline] def symbol {k : ParserKind} (sym : String) (lbp : Option Nat := none) : Parser k :=
 let sym := sym.trim;
@@ -731,14 +731,14 @@ let sym := sym.trim;
   fn   := symbolFn sym }
 
 def unicodeSymbolFnAux (sym asciiSym : String) (errorMsg : String) : BasicParserFn :=
-satisfySymbolFn (λ s, s == sym || s == asciiSym) errorMsg
+satisfySymbolFn (fun s => s == sym || s == asciiSym) errorMsg
 
 def unicodeSymbolInfo (sym asciiSym : String) (lbp : Option Nat) : ParserInfo :=
-{ updateTokens := λ tks, insertToken sym lbp tks >>= insertToken asciiSym lbp,
+{ updateTokens := fun tks => insertToken sym lbp tks >>= insertToken asciiSym lbp,
   firstTokens  := FirstTokens.tokens [ { val := sym, lbp := lbp }, { val := asciiSym, lbp := lbp } ] }
 
 @[inline] def unicodeSymbolFn {k : ParserKind} (sym asciiSym : String) : ParserFn k :=
-λ _, unicodeSymbolFnAux sym asciiSym ("expected '" ++ sym ++ "' or '" ++ asciiSym ++ "'")
+fun _ => unicodeSymbolFnAux sym asciiSym ("expected '" ++ sym ++ "' or '" ++ asciiSym ++ "'")
 
 @[inline] def unicodeSymbol {k : ParserKind} (sym asciiSym : String) (lbp : Option Nat := none) : Parser k :=
 { info := unicodeSymbolInfo sym asciiSym lbp,
@@ -748,7 +748,7 @@ def mkAtomicInfo (k : String) : ParserInfo :=
 { firstTokens := FirstTokens.tokens [ { val := k } ] }
 
 def numLitFn {k : ParserKind} : ParserFn k :=
-λ _ c s,
+fun _ c s =>
   let s := tokenFn c s;
   if s.hasError || !(s.stxStack.back.isOfKind numLitKind) then s.mkError "expected numeral" else s
 
@@ -757,7 +757,7 @@ def numLitFn {k : ParserKind} : ParserFn k :=
   info := mkAtomicInfo "numLit" }
 
 def strLitFn {k : ParserKind} : ParserFn k :=
-λ _ c s,
+fun _ c s =>
 let s := tokenFn c s;
 if s.hasError || !(s.stxStack.back.isOfKind strLitKind) then s.mkError "expected string literal" else s
 
@@ -766,7 +766,7 @@ if s.hasError || !(s.stxStack.back.isOfKind strLitKind) then s.mkError "expected
   info := mkAtomicInfo "strLit" }
 
 def identFn {k : ParserKind} : ParserFn k :=
-λ _ c s,
+fun _ c s =>
 let s := tokenFn c s;
 if s.hasError || !(s.stxStack.back.isIdent) then
   s.mkError "expected identifier"
@@ -821,7 +821,7 @@ s.keepLatest startStackSize
 end ParserState
 
 def longestMatchStep {k : ParserKind} (startSize : Nat) (startPos : String.Pos) (p : ParserFn k) : ParserFn k :=
-λ a c s,
+fun a c s =>
 let prevErrorMsg  := s.errorMsg;
 let prevStopPos   := s.pos;
 let prevSize      := s.stackSize;
@@ -845,21 +845,21 @@ def longestMatchMkResult (startSize : Nat) (s : ParserState) : ParserState :=
 if !s.hasError && s.stackSize > startSize + 1 then s.mkNode choiceKind startSize else s
 
 def longestMatchFnAux {k : ParserKind} (startSize : Nat) (startPos : String.Pos) : List (Parser k) → ParserFn k
-| []      := λ _ _ s, longestMatchMkResult startSize s
-| (p::ps) := λ a c s,
+| []      := fun _ _ s => longestMatchMkResult startSize s
+| (p::ps) := fun a c s =>
    let s := longestMatchStep startSize startPos p.fn a c s;
    longestMatchFnAux ps a c s
 
 def longestMatchFn₁ {k : ParserKind} (p : ParserFn k) : ParserFn k :=
-λ a c s,
+fun a c s =>
 let startSize := s.stackSize;
 let s := p a c s;
 if s.hasError then s else s.mkLongestNodeAlt startSize
 
 def longestMatchFn {k : ParserKind} : List (Parser k) → ParserFn k
-| []      := λ _ _ s, s.mkError "longestMatch: empty list"
+| []      := fun _ _ s => s.mkError "longestMatch: empty list"
 | [p]     := longestMatchFn₁ p.fn
-| (p::ps) := λ a c s,
+| (p::ps) := fun a c s =>
   let startSize := s.stackSize;
   let startPos  := s.pos;
   let s         := p.fn a c s;
@@ -925,7 +925,7 @@ if s.stackSize == iniSz + 1 then s
 else s.mkNode nullKind iniSz -- throw error instead?
 
 def leadingParser (kind : String) (tables : ParsingTables) : ParserFn leading :=
-λ a c s,
+fun a c s =>
   let iniSz   := s.stackSize;
   let (s, ps) := indexed tables.leadingTable c s;
   if ps.isEmpty then
@@ -953,7 +953,7 @@ partial def trailingLoop (kind : String) (tables : ParsingTables) (rbp : Nat) (c
         trailingLoop left s
 
 def prattParser (kind : String) (tables : ParsingTables) : ParserFn leading :=
-λ rbp c s,
+fun rbp c s =>
   let c := { tokens := tables.tokens, .. c };
   let s := leadingParser kind tables rbp c s;
   if s.hasError then s
@@ -995,7 +995,7 @@ do tables ← tablesRef.get;
    tables ← updateTokens tables p.info;
    match p.info.firstTokens with
    | FirstTokens.tokens tks :=
-     let tables := tks.foldl (λ (tables : ParsingTables) tk, { leadingTable := tables.leadingTable.insert (mkSimpleName tk.val) p, .. tables }) tables;
+     let tables := tks.foldl (fun (tables : ParsingTables) tk => { leadingTable := tables.leadingTable.insert (mkSimpleName tk.val) p, .. tables }) tables;
      tablesRef.set tables
    | _ :=
      throw (IO.userError ("invalid builtin parser '" ++ toString declName ++ "', initial token is not statically known"))
@@ -1006,7 +1006,7 @@ do tables ← tablesRef.get;
    tables ← updateTokens tables p.info;
    match p.info.firstTokens with
    | FirstTokens.tokens tks :=
-     let tables := tks.foldl (λ (tables : ParsingTables) tk, { trailingTable := tables.trailingTable.insert (mkSimpleName tk.val) p, .. tables }) tables;
+     let tables := tks.foldl (fun (tables : ParsingTables) tk => { trailingTable := tables.trailingTable.insert (mkSimpleName tk.val) p, .. tables }) tables;
      tablesRef.set tables
    | _ :=
      let tables := { trailingParsers := p :: tables.trailingParsers, .. tables };
@@ -1034,7 +1034,7 @@ def registerBuiltinParserAttribute (attrName : Name) (refDeclName : Name) : IO U
 registerAttribute {
  name  := attrName,
  descr := "Builtin parser",
- add   := λ env declName args persistent, do {
+ add   := fun env declName args persistent => do {
    unless args.isMissing $ throw (IO.userError ("invalid attribute '" ++ toString attrName ++ "', unexpected argument"));
    unless persistent $ throw (IO.userError ("invalid attribute '" ++ toString attrName ++ "', must be persistent"));
    match env.find declName with
@@ -1058,7 +1058,7 @@ constant builtinCommandParsingTable : IO.Ref ParsingTables := default _
 registerBuiltinParserAttribute `builtinCommandParser `Lean.Parser.builtinCommandParsingTable
 
 @[noinline] unsafe def runBuiltinParserUnsafe (kind : String) (ref : IO.Ref ParsingTables) : ParserFn leading :=
-λ a c s,
+fun a c s =>
 match unsafeIO (do tables ← ref.get; pure $ prattParser kind tables a c s) with
 | some s := s
 | none   := s.mkError "failed to access builtin reference"
@@ -1067,7 +1067,7 @@ match unsafeIO (do tables ← ref.get; pure $ prattParser kind tables a c s) wit
 constant runBuiltinParser (kind : String) (ref : IO.Ref ParsingTables) : ParserFn leading := default _
 
 def commandParser (rbp : Nat := 0) : Parser :=
-{ fn := λ _, runBuiltinParser "command" builtinCommandParsingTable rbp }
+{ fn := fun _ => runBuiltinParser "command" builtinCommandParsingTable rbp }
 
 /- TODO(Leo): delete -/
 @[init mkBuiltinParsingTablesRef]
@@ -1076,7 +1076,7 @@ constant builtinTestParsingTable : IO.Ref ParsingTables := default _
 registerBuiltinParserAttribute `builtinTestParser `Lean.Parser.builtinTestParsingTable
 
 def testParser (rbp : Nat := 0) : Parser :=
-{ fn := λ _, runBuiltinParser "testExpr" builtinTestParsingTable rbp }
+{ fn := fun _ => runBuiltinParser "testExpr" builtinTestParsingTable rbp }
 
 end Parser
 end Lean
diff --git a/library/init/lean/parser/term.lean b/library/init/lean/parser/term.lean
index dc89759ca3..084e1f0620 100644
--- a/library/init/lean/parser/term.lean
+++ b/library/init/lean/parser/term.lean
@@ -17,7 +17,7 @@ constant builtinTermParsingTable : IO.Ref ParsingTables := default _
 registerBuiltinParserAttribute `builtinTermParser `Lean.Parser.builtinTermParsingTable
 
 def termParser {k : ParserKind} (rbp : Nat := 0) : Parser k :=
-{ fn := λ _, runBuiltinParser "term" builtinTermParsingTable rbp }
+{ fn := fun _ => runBuiltinParser "term" builtinTermParsingTable rbp }
 
 namespace Term
 
diff --git a/library/init/lean/parser/trie.lean b/library/init/lean/parser/trie.lean
index c68e72b682..79fdcf85c9 100644
--- a/library/init/lean/parser/trie.lean
+++ b/library/init/lean/parser/trie.lean
@@ -13,7 +13,7 @@ namespace Lean
 namespace Parser
 
 inductive Trie (α : Type)
-| Node : Option α → RBNode Char (λ _, Trie) → Trie
+| Node : Option α → RBNode Char (fun _ => Trie) → Trie
 
 namespace Trie
 variables {α : Type}
@@ -85,11 +85,11 @@ def matchPrefix (s : String) (t : Trie α) (i : String.Pos) : String.Pos × Opti
 matchPrefixAux s t i (i, none)
 
 private partial def toStringAux {α : Type} : Trie α → List Format
-| (Trie.Node val map) := map.fold (λ Fs c t,
+| (Trie.Node val map) := map.fold (fun Fs c t =>
   format (repr c) :: (Format.group $ Format.nest 2 $ flip Format.joinSep Format.line $ toStringAux t) :: Fs) []
 
 instance {α : Type} : HasToString (Trie α) :=
-⟨λ t, (flip Format.joinSep Format.line $ toStringAux t).pretty⟩
+⟨fun t => (flip Format.joinSep Format.line $ toStringAux t).pretty⟩
 end Trie
 
 end Parser
diff --git a/library/init/lean/position.lean b/library/init/lean/position.lean
index d4be3e991c..f8a9336a92 100644
--- a/library/init/lean/position.lean
+++ b/library/init/lean/position.lean
@@ -14,17 +14,17 @@ structure Position :=
 
 namespace Position
 instance : DecidableEq Position :=
-{decEq := λ ⟨l₁, c₁⟩ ⟨l₂, c₂⟩,
+{decEq := fun ⟨l₁, c₁⟩ ⟨l₂, c₂⟩ =>
   if h₁ : l₁ = l₂ then
   if h₂ : c₁ = c₂ then isTrue (Eq.recOn h₁ (Eq.recOn h₂ rfl))
-  else isFalse (λ contra, Position.noConfusion contra (λ e₁ e₂, absurd e₂ h₂))
-  else isFalse (λ contra, Position.noConfusion contra (λ e₁ e₂, absurd e₁ h₁))}
+  else isFalse (fun contra => Position.noConfusion contra (fun e₁ e₂ => absurd e₂ h₂))
+  else isFalse (fun contra => Position.noConfusion contra (fun e₁ e₂ => absurd e₁ h₁))}
 
 protected def lt : Position → Position → Bool
 | ⟨l₁, c₁⟩ ⟨l₂, c₂⟩ := (l₁, c₁) < (l₂, c₂)
 
 instance : HasFormat Position :=
-⟨λ ⟨l, c⟩, "⟨" ++ fmt l ++ ", " ++ fmt c ++ "⟩"⟩
+⟨fun ⟨l, c⟩ => "⟨" ++ fmt l ++ ", " ++ fmt c ++ "⟩"⟩
 
 instance : Inhabited Position := ⟨⟨1, 0⟩⟩
 end Position
diff --git a/library/init/lean/projfns.lean b/library/init/lean/projfns.lean
index 8a4852ea7b..1e122879ee 100644
--- a/library/init/lean/projfns.lean
+++ b/library/init/lean/projfns.lean
@@ -22,9 +22,9 @@ instance ProjectionFunctionInfo.inhabited : Inhabited ProjectionFunctionInfo :=
 def mkProjectionFnInfoExtension : IO (SimplePersistentEnvExtension (Name × ProjectionFunctionInfo) (NameMap ProjectionFunctionInfo)) :=
 registerSimplePersistentEnvExtension {
   name          := `projinfo,
-  addImportedFn := λ as, {},
-  addEntryFn    := λ s p, s.insert p.1 p.2,
-  toArrayFn     := λ es, es.toArray.qsort (λ a b, Name.quickLt a.1 b.1)
+  addImportedFn := fun as => {},
+  addEntryFn    := fun s p => s.insert p.1 p.2,
+  toArrayFn     := fun es => es.toArray.qsort (fun a b => Name.quickLt a.1 b.1)
 }
 
 @[init mkProjectionFnInfoExtension]
@@ -40,14 +40,14 @@ namespace Environment
 def getProjectionFnInfo (env : Environment) (projName : Name) : Option ProjectionFunctionInfo :=
 match env.getModuleIdxFor projName with
 | some modIdx :=
-  match (projectionFnInfoExt.getModuleEntries env modIdx).binSearch (projName, default _) (λ a b, Name.quickLt a.1 b.1) with
+  match (projectionFnInfoExt.getModuleEntries env modIdx).binSearch (projName, default _) (fun a b => Name.quickLt a.1 b.1) with
   | some e := some e.2
   | none   := none
 | none        := (projectionFnInfoExt.getState env).find projName
 
 def isProjectionFn (env : Environment) (n : Name) : Bool :=
 match env.getModuleIdxFor n with
-| some modIdx := (projectionFnInfoExt.getModuleEntries env modIdx).binSearchContains (n, default _) (λ a b, Name.quickLt a.1 b.1)
+| some modIdx := (projectionFnInfoExt.getModuleEntries env modIdx).binSearchContains (n, default _) (fun a b => Name.quickLt a.1 b.1)
 | none        := (projectionFnInfoExt.getState env).contains n
 
 end Environment
diff --git a/library/init/lean/syntax.lean b/library/init/lean/syntax.lean
index b97982ef65..e1b4e53c6b 100644
--- a/library/init/lean/syntax.lean
+++ b/library/init/lean/syntax.lean
@@ -149,7 +149,7 @@ private def updateLeadingAux : Syntax → State String.Pos (Option Syntax)
     Note that, the `SourceInfo.trailing` fields are correct.
     The implementation of this Function relies on this property. -/
 def updateLeading : Syntax → Syntax :=
-λ stx, Prod.fst <$> (mreplace updateLeadingAux stx).run 0
+fun stx => Prod.fst <$> (mreplace updateLeadingAux stx).run 0
 
 partial def updateTrailing (trailing : Substring) : Syntax → Syntax
 | (Syntax.atom (some info) val)                     := Syntax.atom (some (info.updateTrailing trailing)) val
@@ -185,8 +185,8 @@ partial def reprint : Syntax → Option String
     if args.size == 0 then failure
     else do
       s ← reprint (args.get 0);
-      args.mfoldlFrom (λ s stx, do s' ← reprint stx; guard (s == s'); pure s) s 1
-  else args.mfoldl (λ r stx, do s ← reprint stx; pure $ r ++ s) ""
+      args.mfoldlFrom (fun s stx => do s' ← reprint stx; guard (s == s'); pure s) s 1
+  else args.mfoldl (fun r stx => do s ← reprint stx; pure $ r ++ s) ""
 | missing := ""
 
 open Lean.Format
diff --git a/library/init/lean/toexpr.lean b/library/init/lean/toexpr.lean
index 2f7c1f1344..10d385194a 100644
--- a/library/init/lean/toexpr.lean
+++ b/library/init/lean/toexpr.lean
@@ -16,9 +16,9 @@ export ToExpr (toExpr)
 
 instance exprToExpr : ToExpr Expr := ⟨id⟩
 
-instance natToExpr : ToExpr Nat := ⟨λ n, Expr.lit (Literal.natVal n)⟩
+instance natToExpr : ToExpr Nat := ⟨fun n => Expr.lit (Literal.natVal n)⟩
 
-instance strToExpr : ToExpr String := ⟨λ s, Expr.lit (Literal.strVal s)⟩
+instance strToExpr : ToExpr String := ⟨fun s => Expr.lit (Literal.strVal s)⟩
 
 def nameToExprAux : Name → Expr
 | Name.anonymous       := mkConst `Lean.Name.anonymous
diff --git a/library/init/lean/trace.lean b/library/init/lean/trace.lean
index 67fc9136bb..9c52249d6c 100644
--- a/library/init/lean/trace.lean
+++ b/library/init/lean/trace.lean
@@ -21,7 +21,7 @@ inductive Trace
 
 partial def Trace.pp : Trace → Format
 | (Trace.mk (Message.fromFormat fmt) subtraces) :=
-fmt ++ Format.nest 2 (Format.join $ subtraces.map (λ t, Format.line ++ t.pp))
+fmt ++ Format.nest 2 (Format.join $ subtraces.map (fun t => Format.line ++ t.pp))
 
 namespace Trace
 
@@ -47,16 +47,16 @@ def Trace {m} [Monad m] [MonadTracer m] (cls : Name) (msg : Message) : m Unit :=
 traceCtx cls msg (pure () : m Unit)
 
 instance (m) [Monad m] : MonadTracer (TraceT m) :=
-{ traceRoot := λ α pos cls msg ctx, do {
+{ traceRoot := fun α pos cls msg ctx => do {
     st ← get;
     if st.opts.getBool cls = true then do {
-      modify $ λ st, {curPos := pos, curTraces := [], ..st};
+      modify $ fun st => {curPos := pos, curTraces := [], ..st};
       a ← ctx.get;
-      modify $ λ (st : TraceState), {roots := st.roots.insert pos ⟨msg, st.curTraces⟩, ..st};
+      modify $ fun (st : TraceState) => {roots := st.roots.insert pos ⟨msg, st.curTraces⟩, ..st};
       pure a
     } else ctx.get
   },
-  traceCtx := λ α cls msg ctx, do {
+  traceCtx := fun α cls msg ctx => do {
     st ← get;
     -- tracing enabled?
     some _ ← pure st.curPos | ctx.get;
@@ -64,13 +64,13 @@ instance (m) [Monad m] : MonadTracer (TraceT m) :=
     if st.opts.getBool cls = true then do {
       set {curTraces := [], ..st};
       a ← ctx.get;
-      modify $ λ (st' : TraceState), {curTraces := st.curTraces ++ [⟨msg, st'.curTraces⟩], ..st'};
+      modify $ fun (st' : TraceState) => {curTraces := st.curTraces ++ [⟨msg, st'.curTraces⟩], ..st'};
       pure a
     } else
       -- disable tracing inside 'ctx'
       adaptState'
-        (λ _, {curPos := none, ..st})
-        (λ st', {curPos := st.curPos, ..st'})
+        (fun _ => {curPos := none, ..st})
+        (fun st' => {curPos := st.curPos, ..st'})
         ctx.get
   }
 }
diff --git a/library/init/wf.lean b/library/init/wf.lean
index fd0dc6067d..5b7d17961c 100644
--- a/library/init/wf.lean
+++ b/library/init/wf.lean
@@ -17,20 +17,20 @@ inductive Acc {α : Sort u} (r : α → α → Prop) : α → Prop
 def Acc.ndrec.{u1, u2} {α : Sort u2} {r : α → α → Prop} {C : α → Sort u1}
     (m : Π (x : α) (h : ∀ (y : α), r y x → Acc r y), (Π (y : α) (a : r y x), C y) → C x)
     {a : α} (n : Acc r a) : C a :=
-@Acc.rec α r (λ α _, C α) m a n
+@Acc.rec α r (fun α _ => C α) m a n
 
 @[elabAsEliminator, inline, reducible]
 def Acc.ndrecOn.{u1, u2} {α : Sort u2} {r : α → α → Prop} {C : α → Sort u1}
     {a : α} (n : Acc r a)
     (m : Π (x : α) (h : ∀ (y : α), r y x → Acc r y), (Π (y : α) (a : r y x), C y) → C x)
     : C a :=
-@Acc.rec α r (λ α _, C α) m a n
+@Acc.rec α r (fun α _ => C α) m a n
 
 namespace Acc
 variables {α : Sort u} {r : α → α → Prop}
 
 def inv {x y : α} (h₁ : Acc r x) (h₂ : r y x) : Acc r y :=
-Acc.recOn h₁ (λ x₁ ac₁ ih h₂, ac₁ y h₂) h₂
+Acc.recOn h₁ (fun x₁ ac₁ ih h₂ => ac₁ y h₂) h₂
 
 end Acc
 
@@ -42,13 +42,13 @@ class HasWellFounded (α : Sort u) : Type u :=
 
 namespace WellFounded
 def apply {α : Sort u} {r : α → α → Prop} (wf : WellFounded r) : ∀ a, Acc r a :=
-λ a, WellFounded.recOn wf (λ p, p) a
+fun a => WellFounded.recOn wf (fun p => p) a
 
 section
 variables {α : Sort u} {r : α → α → Prop} (hwf : WellFounded r)
 
 theorem recursion {C : α → Sort v} (a : α) (h : Π x, (Π y, r y x → C y) → C x) : C a :=
-Acc.recOn (apply hwf a) (λ x₁ ac₁ ih, h x₁ ih)
+Acc.recOn (apply hwf a) (fun x₁ ac₁ ih => h x₁ ih)
 
 theorem induction {C : α → Prop} (a : α) (h : ∀ x, (∀ y, r y x → C y) → C x) : C a :=
 recursion hwf a h
@@ -57,11 +57,11 @@ variable {C : α → Sort v}
 variable F : Π x, (Π y, r y x → C y) → C x
 
 def fixF (x : α) (a : Acc r x) : C x :=
-Acc.recOn a (λ x₁ ac₁ ih, F x₁ ih)
+Acc.recOn a (fun x₁ ac₁ ih => F x₁ ih)
 
 theorem fixFEq (x : α) (acx : Acc r x) :
-  fixF F x acx = F x (λ (y : α) (p : r y x), fixF F y (Acc.inv acx p)) :=
-Acc.rec (λ x r ih, rfl) acx
+  fixF F x acx = F x (fun (y : α) (p : r y x) => fixF F y (Acc.inv acx p)) :=
+Acc.rec (fun x r ih => rfl) acx
 end
 
 variables {α : Sort u} {C : α → Sort v} {r : α → α → Prop}
@@ -72,7 +72,7 @@ fixF F x (apply hwf x)
 
 -- Well-founded fixpoint satisfies fixpoint equation
 theorem fixEq (hwf : WellFounded r) (F : Π x, (Π y, r y x → C y) → C x) (x : α) :
-  fix hwf F x = F x (λ y h, fix hwf F y) :=
+  fix hwf F x = F x (fun y h => fix hwf F y) :=
 fixFEq F x (apply hwf x)
 end WellFounded
 
@@ -80,19 +80,19 @@ open WellFounded
 
 -- Empty relation is well-founded
 def emptyWf {α : Sort u} : WellFounded (@emptyRelation α) :=
-WellFounded.intro (λ (a : α),
-  Acc.intro a (λ (b : α) (lt : False), False.rec _ lt))
+WellFounded.intro (fun (a : α) =>
+  Acc.intro a (fun (b : α) (lt : False) => False.rec _ lt))
 
 -- Subrelation of a well-founded relation is well-founded
 namespace Subrelation
 variables {α : Sort u} {r q : α → α → Prop}
 
 def accessible {a : α} (h₁ : Subrelation q r) (ac : Acc r a) : Acc q a :=
-Acc.recOn ac $ λ x ax ih,
-  Acc.intro x $ λ (y : α) (lt : q y x), ih y (h₁ lt)
+Acc.recOn ac $ fun x ax ih =>
+  Acc.intro x $ fun (y : α) (lt : q y x) => ih y (h₁ lt)
 
 def wf (h₁ : Subrelation q r) (h₂ : WellFounded r) : WellFounded q :=
-⟨λ a, accessible @h₁ (apply h₂ a)⟩
+⟨fun a => accessible @h₁ (apply h₂ a)⟩
 end Subrelation
 
 -- The inverse image of a well-founded relation is well-founded
@@ -100,15 +100,15 @@ namespace InvImage
 variables {α : Sort u} {β : Sort v} {r : β → β → Prop}
 
 private def accAux (f : α → β) {b : β} (ac : Acc r b) : ∀ (x : α), f x = b → Acc (InvImage r f) x :=
-Acc.ndrecOn ac $ λ x acx ih z e,
-  Acc.intro z  $ λ y lt,
-    Eq.ndrecOn e (λ acx ih, ih (f y) lt y rfl) acx ih
+Acc.ndrecOn ac $ fun x acx ih z e =>
+  Acc.intro z  $ fun y lt =>
+    Eq.ndrecOn e (fun acx ih => ih (f y) lt y rfl) acx ih
 
 def accessible {a : α} (f : α → β) (ac : Acc r (f a)) : Acc (InvImage r f) a :=
 accAux f ac a rfl
 
 def wf (f : α → β) (h : WellFounded r) : WellFounded (InvImage r f) :=
-⟨λ a, accessible f (apply h (f a))⟩
+⟨fun a => accessible f (apply h (f a))⟩
 end InvImage
 
 -- The transitive closure of a well-founded relation is well-founded
@@ -116,27 +116,27 @@ namespace TC
 variables {α : Sort u} {r : α → α → Prop}
 
 def accessible {z : α} (ac : Acc r z) : Acc (TC r) z :=
-Acc.ndrecOn ac $ λ x acx ih,
-  Acc.intro x $ λ y rel,
+Acc.ndrecOn ac $ fun x acx ih =>
+  Acc.intro x $ fun y rel =>
     TC.ndrecOn rel
-      (λ a b rab acx ih, ih a rab)
-      (λ a b c rab rbc ih₁ ih₂ acx ih, Acc.inv (ih₂ acx ih) rab)
+      (fun a b rab acx ih => ih a rab)
+      (fun a b c rab rbc ih₁ ih₂ acx ih => Acc.inv (ih₂ acx ih) rab)
       acx ih
 
 def wf (h : WellFounded r) : WellFounded (TC r) :=
-⟨λ a, accessible (apply h a)⟩
+⟨fun a => accessible (apply h a)⟩
 end TC
 
 -- less-than is well-founded
 def Nat.ltWf : WellFounded Nat.lt :=
 ⟨Nat.rec
-  (Acc.intro 0 (λ n h, absurd h (Nat.notLtZero n)))
-  (λ n ih, Acc.intro (Nat.succ n) $ λ m h,
+  (Acc.intro 0 (fun n h => absurd h (Nat.notLtZero n)))
+  (fun n ih => Acc.intro (Nat.succ n) $ fun m h =>
      Or.elim (Nat.eqOrLtOfLe (Nat.leOfSuccLeSucc h))
-        (λ e, Eq.substr e ih) (Acc.inv ih))⟩
+        (fun e => Eq.substr e ih) (Acc.inv ih))⟩
 
 def measure {α : Sort u} : (α → Nat) → α → α → Prop :=
-InvImage (λ a b, a < b)
+InvImage (fun a b => a < b)
 
 def measureWf {α : Sort u} (f : α → Nat) : WellFounded (measure f) :=
 InvImage.wf f Nat.ltWf
@@ -173,23 +173,23 @@ variables {α : Type u} {β : Type v}
 variables {ra  : α → α → Prop} {rb  : β → β → Prop}
 
 def lexAccessible {a} (aca : Acc ra a) (acb : ∀ b, Acc rb b): ∀ b, Acc (Lex ra rb) (a, b) :=
-Acc.ndrecOn aca $ λ xa aca iha b,
-  Acc.ndrecOn (acb b) $ λ xb acb ihb,
-    Acc.intro (xa, xb)  $ λ p lt,
+Acc.ndrecOn aca $ fun xa aca iha b =>
+  Acc.ndrecOn (acb b) $ fun xb acb ihb =>
+    Acc.intro (xa, xb)  $ fun p lt =>
       have aux : xa = xa → xb = xb → Acc (Lex ra rb) p, from
-        @Prod.Lex.recOn α β ra rb (λ p₁ p₂ _, fst p₂ = xa → snd p₂ = xb → Acc (Lex ra rb) p₁)
+        @Prod.Lex.recOn α β ra rb (fun p₁ p₂ _ => fst p₂ = xa → snd p₂ = xb → Acc (Lex ra rb) p₁)
                          p (xa, xb) lt
-          (λ a₁ b₁ a₂ b₂ h (Eq₂ : a₂ = xa) (Eq₃ : b₂ = xb), iha a₁ (Eq.recOn Eq₂ h) b₁)
-          (λ a b₁ b₂ h (Eq₂ : a = xa) (Eq₃ : b₂ = xb), Eq.recOn Eq₂.symm (ihb b₁ (Eq.recOn Eq₃ h))),
+          (fun (a₁ b₁ a₂ b₂ h) (Eq₂ : a₂ = xa) (Eq₃ : b₂ = xb) => iha a₁ (Eq.recOn Eq₂ h) b₁)
+          (fun (a b₁ b₂ h) (Eq₂ : a = xa) (Eq₃ : b₂ = xb) => Eq.recOn Eq₂.symm (ihb b₁ (Eq.recOn Eq₃ h))),
       aux rfl rfl
 
 -- The lexicographical order of well founded relations is well-founded
 def lexWf (ha : WellFounded ra) (hb : WellFounded rb) : WellFounded (Lex ra rb) :=
-⟨λ p, casesOn p $ λ a b, lexAccessible (apply ha a) (WellFounded.apply hb) b⟩
+⟨fun p => casesOn p $ fun a b => lexAccessible (apply ha a) (WellFounded.apply hb) b⟩
 
 -- relational product is a Subrelation of the Lex
 def rprodSubLex : ∀ a b, Rprod ra rb a b → Lex ra rb a b :=
-@Prod.Rprod.rec _ _ ra rb (λ a b _, Lex ra rb a b) (λ a₁ b₁ a₂ b₂ h₁ h₂, Lex.left rb b₁ b₂ h₁)
+@Prod.Rprod.rec _ _ ra rb (fun a b _ => Lex ra rb a b) (fun a₁ b₁ a₂ b₂ h₁ h₂ => Lex.left rb b₁ b₂ h₁)
 
 -- The relational product of well founded relations is well-founded
 def rprodWf (ha : WellFounded ra) (hb : WellFounded rb) : WellFounded (Rprod ra rb) :=
@@ -218,51 +218,51 @@ variables {α : Sort u} {β : α → Sort v}
 variables {r  : α → α → Prop} {s : Π a : α, β a → β a → Prop}
 
 def lexAccessible {a} (aca : Acc r a) (acb : ∀ a, WellFounded (s a)) : ∀ (b : β a), Acc (Lex r s) ⟨a, b⟩ :=
-Acc.ndrecOn aca $ λ xa aca (iha : ∀ y, r y xa → ∀ b : β y, Acc (Lex r s) ⟨y, b⟩) (b : β xa),
-  Acc.ndrecOn (WellFounded.apply (acb xa) b) $ λ xb acb (ihb : ∀ (y : β xa), s xa y xb → Acc (Lex r s) ⟨xa, y⟩),
-     Acc.intro ⟨xa, xb⟩ $ λ p (lt : Lex r s p ⟨xa, xb⟩),
+Acc.ndrecOn aca $ fun (xa aca) (iha : ∀ y, r y xa → ∀ b : β y, Acc (Lex r s) ⟨y, b⟩) (b : β xa) =>
+  Acc.ndrecOn (WellFounded.apply (acb xa) b) $ fun xb acb (ihb : ∀ (y : β xa), s xa y xb → Acc (Lex r s) ⟨xa, y⟩) =>
+     Acc.intro ⟨xa, xb⟩ $ fun (p) (lt : Lex r s p ⟨xa, xb⟩) =>
         have aux : xa = xa → xb ≅ xb → Acc (Lex r s) p, from
-          @PSigma.Lex.recOn α β r s (λ p₁ p₂ _, p₂.1 = xa → p₂.2 ≅ xb → Acc (Lex r s) p₁)
+          @PSigma.Lex.recOn α β r s (fun p₁ p₂ _ => p₂.1 = xa → p₂.2 ≅ xb → Acc (Lex r s) p₁)
                             p ⟨xa, xb⟩ lt
-            (λ (a₁ : α) (b₁ : β a₁) (a₂ : α) (b₂ : β a₂) (h : r a₁ a₂) (Eq₂ : a₂ = xa) (Eq₃ : b₂ ≅ xb),
+            (fun (a₁ : α) (b₁ : β a₁) (a₂ : α) (b₂ : β a₂) (h : r a₁ a₂) (Eq₂ : a₂ = xa) (Eq₃ : b₂ ≅ xb) =>
               have aux : (∀ (y : α), r y xa → ∀ (b : β y), Acc (Lex r s) ⟨y, b⟩) →
                          r a₁ a₂ → ∀ (b₁ : β a₁), Acc (Lex r s) ⟨a₁, b₁⟩,
-              from Eq.subst Eq₂ (λ iha h b₁, iha a₁ h b₁),
+              from Eq.subst Eq₂ (fun iha h b₁ => iha a₁ h b₁),
               aux iha h b₁)
-            (λ (a : α) (b₁ b₂ : β a) (h : s a b₁ b₂) (Eq₂ : a = xa) (Eq₃ : b₂ ≅ xb),
+            (fun (a : α) (b₁ b₂ : β a) (h : s a b₁ b₂) (Eq₂ : a = xa) (Eq₃ : b₂ ≅ xb) =>
               have aux : ∀ (xb : β xa), (∀ (y : β xa), s xa y xb → Acc (s xa) y) →
                            (∀ (y : β xa), s xa y xb → Acc (Lex r s) ⟨xa, y⟩) →
                            Lex r s p ⟨xa, xb⟩ → ∀ (b₁ : β a), s a b₁ b₂ → b₂ ≅ xb → Acc (Lex r s) ⟨a, b₁⟩,
-              from Eq.subst Eq₂ $ λ xb acb ihb lt b₁ h Eq₃,
+              from Eq.subst Eq₂ $ fun xb acb ihb lt b₁ h Eq₃ =>
                 have newEq₃ : b₂ = xb, from eqOfHeq Eq₃,
                 have aux : (∀ (y : β a), s a y xb → Acc (Lex r s) ⟨a, y⟩) →
                            ∀ (b₁ : β a), s a b₁ b₂ → Acc (Lex r s) ⟨a, b₁⟩,
-                from Eq.subst newEq₃ (λ ihb b₁ h, ihb b₁ h),
+                from Eq.subst newEq₃ (fun ihb b₁ h => ihb b₁ h),
                 aux ihb b₁ h,
               aux xb acb ihb lt b₁ h Eq₃),
         aux rfl (Heq.refl xb)
 
 -- The lexicographical order of well founded relations is well-founded
 def lexWf (ha : WellFounded r) (hb : ∀ x, WellFounded (s x)) : WellFounded (Lex r s) :=
-WellFounded.intro $ λ ⟨a, b⟩, lexAccessible (WellFounded.apply ha a) hb b
+WellFounded.intro $ fun ⟨a, b⟩ => lexAccessible (WellFounded.apply ha a) hb b
 end
 
 section
 variables {α : Sort u} {β : Sort v}
 
 def lexNdep (r : α → α → Prop) (s : β → β → Prop) :=
-Lex r (λ a : α, s)
+Lex r (fun a => s)
 
 def lexNdepWf {r  : α → α → Prop} {s : β → β → Prop} (ha : WellFounded r) (hb : WellFounded s)
                 : WellFounded (lexNdep r s) :=
-WellFounded.intro $ λ ⟨a, b⟩, lexAccessible (WellFounded.apply ha a) (λ x, hb) b
+WellFounded.intro $ fun ⟨a, b⟩ => lexAccessible (WellFounded.apply ha a) (fun x => hb) b
 end
 
 section
 variables {α : Sort u} {β : Sort v}
 
 -- Reverse lexicographical order based on r and s
-inductive RevLex (r  : α → α → Prop) (s  : β → β → Prop) : @PSigma α (λ a, β) → @PSigma α (λ a, β) → Prop
+inductive RevLex (r  : α → α → Prop) (s  : β → β → Prop) : @PSigma α (fun a => β) → @PSigma α (fun a => β) → Prop
 | left  : ∀ {a₁ a₂ : α} (b : β), r a₁ a₂ → RevLex ⟨a₁, b⟩ ⟨a₂, b⟩
 | right : ∀ (a₁ : α) {b₁ : β} (a₂ : α) {b₂ : β}, s b₁ b₂ → RevLex ⟨a₁, b₁⟩ ⟨a₂, b₂⟩
 end
@@ -273,29 +273,29 @@ variables {α : Sort u} {β : Sort v}
 variables {r  : α → α → Prop} {s : β → β → Prop}
 
 def revLexAccessible {b} (acb : Acc s b) (aca : ∀ a, Acc r a): ∀ a, Acc (RevLex r s) ⟨a, b⟩ :=
-Acc.recOn acb $ λ xb acb (ihb : ∀ y, s y xb → ∀ a, Acc (RevLex r s) ⟨a, y⟩) a,
-  Acc.recOn (aca a) $ λ xa aca (iha : ∀ y, r y xa → Acc (RevLex r s) (mk y xb)),
-    Acc.intro ⟨xa, xb⟩ $ λ p (lt : RevLex r s p ⟨xa, xb⟩),
+Acc.recOn acb $ fun (xb acb) (ihb : ∀ y, s y xb → ∀ a, Acc (RevLex r s) ⟨a, y⟩) (a) =>
+  Acc.recOn (aca a) $ fun (xa aca) (iha : ∀ y, r y xa → Acc (RevLex r s) (mk y xb)) =>
+    Acc.intro ⟨xa, xb⟩ $ fun (p) (lt : RevLex r s p ⟨xa, xb⟩) =>
       have aux : xa = xa → xb = xb → Acc (RevLex r s) p, from
-        @RevLex.recOn α β r s (λ p₁ p₂ _, fst p₂ = xa → snd p₂ = xb → Acc (RevLex r s) p₁)
+        @RevLex.recOn α β r s (fun p₁ p₂ _ => fst p₂ = xa → snd p₂ = xb → Acc (RevLex r s) p₁)
                             p ⟨xa, xb⟩ lt
-          (λ a₁ a₂ b (h : r a₁ a₂) (Eq₂ : a₂ = xa) (Eq₃ : b = xb),
+          (fun (a₁ a₂ b) (h : r a₁ a₂) (Eq₂ : a₂ = xa) (Eq₃ : b = xb) =>
              show Acc (RevLex r s) ⟨a₁, b⟩, from
              have r₁ : r a₁ xa, from Eq.recOn Eq₂ h,
              have aux : Acc (RevLex r s) ⟨a₁, xb⟩, from iha a₁ r₁,
              Eq.recOn (Eq.symm Eq₃) aux)
-          (λ a₁ b₁ a₂ b₂ (h : s b₁ b₂) (Eq₂ : a₂ = xa) (Eq₃ : b₂ = xb),
+          (fun (a₁ b₁ a₂ b₂) (h : s b₁ b₂) (Eq₂ : a₂ = xa) (Eq₃ : b₂ = xb) =>
             show Acc (RevLex r s) (mk a₁ b₁), from
             have s₁ : s b₁ xb, from Eq.recOn Eq₃ h,
             ihb b₁ s₁ a₁),
       aux rfl rfl
 
 def revLexWf (ha : WellFounded r) (hb : WellFounded s) : WellFounded (RevLex r s) :=
-WellFounded.intro $ λ ⟨a, b⟩, revLexAccessible (apply hb b) (WellFounded.apply ha) a
+WellFounded.intro $ fun ⟨a, b⟩ => revLexAccessible (apply hb b) (WellFounded.apply ha) a
 end
 
 section
-def skipLeft (α : Type u) {β : Type v} (s : β → β → Prop) : @PSigma α (λ a, β) → @PSigma α (λ a, β) → Prop :=
+def skipLeft (α : Type u) {β : Type v} (s : β → β → Prop) : @PSigma α (fun a => β) → @PSigma α (fun a => β) → Prop :=
 RevLex emptyRelation s
 
 def skipLeftWf (α : Type u) {β : Type v} {s : β → β → Prop} (hb : WellFounded s) : WellFounded (skipLeft α s) :=
@@ -306,6 +306,6 @@ RevLex.right _ _ _ h
 end
 
 instance HasWellFounded {α : Type u} {β : α → Type v} [s₁ : HasWellFounded α] [s₂ : ∀ a, HasWellFounded (β a)] : HasWellFounded (PSigma β) :=
-{r := Lex s₁.r (λ a, (s₂ a).r), wf := lexWf s₁.wf (λ a, (s₂ a).wf)}
+{r := Lex s₁.r (fun a => (s₂ a).r), wf := lexWf s₁.wf (fun a => (s₂ a).wf)}
 
 end PSigma
diff --git a/src/frontends/lean/brackets.cpp b/src/frontends/lean/brackets.cpp
index 8d8221b50f..0f46cfa1a4 100644
--- a/src/frontends/lean/brackets.cpp
+++ b/src/frontends/lean/brackets.cpp
@@ -162,7 +162,7 @@ expr parse_curly_bracket(parser & p, unsigned, expr const *, pos_info const & po
         } else if (p.curr_is_token(get_period_tk())) {
             p.next();
             return parse_qualified_structure_instance(p, id, id_pos);
-        } else if (p.curr_is_token(get_assign_tk()) || p.curr_is_token(get_fieldarrow_tk())) {
+        } else if (p.curr_is_token(get_assign_tk())) {
             return parse_structure_instance(p, id);
         } else if (p.curr_is_token(get_membership_tk()) || p.curr_is_token(get_in_tk())) {
             p.next();
diff --git a/src/frontends/lean/builtin_exprs.cpp b/src/frontends/lean/builtin_exprs.cpp
index aff3579b5b..18c98c33fc 100644
--- a/src/frontends/lean/builtin_exprs.cpp
+++ b/src/frontends/lean/builtin_exprs.cpp
@@ -653,13 +653,13 @@ static expr parse_lambda_binder(parser & p, pos_info const & pos) {
         p.add_local(local);
     parser::local_scope scope2(p, new_env);
     expr body;
-    if (p.curr_is_token(get_comma_tk())) {
+    if (/* p.curr_is_token(get_comma_tk()) || */ p.curr_is_token(get_darrow_tk())) {
         p.next();
         body = p.parse_expr();
     } else if (p.curr_is_token(get_langle_tk())) {
         body = parse_lambda_core(p, pos);
     } else {
-        p.maybe_throw_error({"invalid lambda expression, ',' or '⟨' expected", p.pos()});
+        p.maybe_throw_error({"invalid lambda expression, ',', '=>' or '⟨' expected", p.pos()});
         body = p.parse_expr();
     }
     return p.rec_save_pos(Fun(locals, body, p), pos);
@@ -677,7 +677,7 @@ static expr parse_lambda_constructor(parser & p, pos_info const & ini_pos) {
     for (expr const & local : locals)
         p.add_local(local);
     expr body;
-    if (p.curr_is_token(get_comma_tk())) {
+    if (/* p.curr_is_token(get_comma_tk()) || */ p.curr_is_token(get_darrow_tk())) {
         p.next();
         body = p.parse_expr();
     } else {
diff --git a/src/frontends/lean/decl_attributes.cpp b/src/frontends/lean/decl_attributes.cpp
index f7b728ef36..e509cb8801 100644
--- a/src/frontends/lean/decl_attributes.cpp
+++ b/src/frontends/lean/decl_attributes.cpp
@@ -170,7 +170,7 @@ void decl_attributes::parse_compact(parser & p) {
     parse_core(p, true);
 }
 
-void decl_attributes::set_attribute(environment const & env, name const & attr_name) {
+void decl_attributes::set_attribute(environment const & /* env */, name const & attr_name) {
     if (is_new_attribute(attr_name)) {
         // Temporary Hack... ignore attr_data_ptr
         syntax args(box(0));
@@ -192,7 +192,7 @@ bool decl_attributes::has_attribute(list<new_entry> const & entries, name const
     return false;
 }
 
-bool decl_attributes::has_attribute(environment const & env, name const & attr_name) const {
+bool decl_attributes::has_attribute(environment const & /* env */, name const & attr_name) const {
     if (is_new_attribute(attr_name)) {
         return has_attribute(m_after_tc_entries, attr_name) || has_attribute(m_after_comp_entries, attr_name);
     } else {
@@ -218,7 +218,7 @@ environment decl_attributes::apply_new_entries(environment env, list<new_entry>
     return env;
 }
 
-environment decl_attributes::apply_after_tc(environment env, io_state const & ios, name const & d) const {
+environment decl_attributes::apply_after_tc(environment env, io_state const & /* ios */, name const & d) const {
     return apply_new_entries(env, m_after_tc_entries, d);
 }
 
diff --git a/src/frontends/lean/token_table.cpp b/src/frontends/lean/token_table.cpp
index 4a5a612862..0958251daa 100644
--- a/src/frontends/lean/token_table.cpp
+++ b/src/frontends/lean/token_table.cpp
@@ -90,7 +90,7 @@ void init_token_table(token_table & t) {
          {"Type", g_max_prec}, {"Type*", g_max_prec}, {"Sort", g_max_prec}, {"Sort*", g_max_prec},
          {"(:", g_max_prec}, {":)", 0}, {".(", g_max_prec}, {"._", g_max_prec},
          {"⟨", g_max_prec}, {"⟩", 0}, {"^", 0},
-         {"//", 0}, {"|", 0}, {"with", 0}, {"without", 0}, {"..", 0}, {"...", 0}, {",", 0},
+         {"//", 0}, {"|", 0}, {"with", 0}, {"without", 0}, {"..", 0}, {"...", 0}, {",", 0}, {"=>", 0},
          {".", 0}, {":", 0}, {"!", 0}, {":=", 0}, {"--", 0}, {"#", g_max_prec},
          {"/-", 0}, {"/--", 0}, {"/-!", 0}, {"begin", g_max_prec}, {"using", 0},
          {"@@", g_max_prec}, {"@", g_max_prec}, {"@&", g_max_prec},
@@ -136,6 +136,7 @@ void init_token_table(token_table & t) {
     }
     t = add_token(t, "→", "->", get_arrow_prec());
     t = add_token(t, "←", "<-", 0);
+    t = add_token(t, "⇒", "=>", 0);
 
     auto it4 = cmd_aliases;
     while (it4->first) {
diff --git a/src/frontends/lean/tokens.cpp b/src/frontends/lean/tokens.cpp
index 6a017c802a..151799aa7b 100644
--- a/src/frontends/lean/tokens.cpp
+++ b/src/frontends/lean/tokens.cpp
@@ -7,7 +7,6 @@ static name const * g_aliases_tk = nullptr;
 static name const * g_period_tk = nullptr;
 static name const * g_backtick_tk = nullptr;
 static name const * g_dslash_tk = nullptr;
-static name const * g_fieldarrow_tk = nullptr;
 static name const * g_placeholder_tk = nullptr;
 static name const * g_colon_tk = nullptr;
 static name const * g_semicolon_tk = nullptr;
@@ -67,6 +66,7 @@ static name const * g_classes_tk = nullptr;
 static name const * g_attributes_tk = nullptr;
 static name const * g_arrow_tk = nullptr;
 static name const * g_larrow_tk = nullptr;
+static name const * g_darrow_tk = nullptr;
 static name const * g_hiding_tk = nullptr;
 static name const * g_example_tk = nullptr;
 static name const * g_exposing_tk = nullptr;
@@ -134,7 +134,6 @@ void initialize_tokens() {
     g_period_tk = new name{"."};
     g_backtick_tk = new name{"`"};
     g_dslash_tk = new name{"//"};
-    g_fieldarrow_tk = new name{"~>"};
     g_placeholder_tk = new name{"_"};
     g_colon_tk = new name{":"};
     g_semicolon_tk = new name{";"};
@@ -194,6 +193,7 @@ void initialize_tokens() {
     g_attributes_tk = new name{"attributes"};
     g_arrow_tk = new name{"->"};
     g_larrow_tk = new name{"<-"};
+    g_darrow_tk = new name{"=>"};
     g_hiding_tk = new name{"hiding"};
     g_example_tk = new name{"example"};
     g_exposing_tk = new name{"exposing"};
@@ -262,7 +262,6 @@ void finalize_tokens() {
     delete g_period_tk;
     delete g_backtick_tk;
     delete g_dslash_tk;
-    delete g_fieldarrow_tk;
     delete g_placeholder_tk;
     delete g_colon_tk;
     delete g_semicolon_tk;
@@ -322,6 +321,7 @@ void finalize_tokens() {
     delete g_attributes_tk;
     delete g_arrow_tk;
     delete g_larrow_tk;
+    delete g_darrow_tk;
     delete g_hiding_tk;
     delete g_example_tk;
     delete g_exposing_tk;
@@ -389,7 +389,6 @@ name const & get_aliases_tk() { return *g_aliases_tk; }
 name const & get_period_tk() { return *g_period_tk; }
 name const & get_backtick_tk() { return *g_backtick_tk; }
 name const & get_dslash_tk() { return *g_dslash_tk; }
-name const & get_fieldarrow_tk() { return *g_fieldarrow_tk; }
 name const & get_placeholder_tk() { return *g_placeholder_tk; }
 name const & get_colon_tk() { return *g_colon_tk; }
 name const & get_semicolon_tk() { return *g_semicolon_tk; }
@@ -449,6 +448,7 @@ name const & get_classes_tk() { return *g_classes_tk; }
 name const & get_attributes_tk() { return *g_attributes_tk; }
 name const & get_arrow_tk() { return *g_arrow_tk; }
 name const & get_larrow_tk() { return *g_larrow_tk; }
+name const & get_darrow_tk() { return *g_darrow_tk; }
 name const & get_hiding_tk() { return *g_hiding_tk; }
 name const & get_example_tk() { return *g_example_tk; }
 name const & get_exposing_tk() { return *g_exposing_tk; }
diff --git a/src/frontends/lean/tokens.h b/src/frontends/lean/tokens.h
index c5b340f9e3..95a28c87b9 100644
--- a/src/frontends/lean/tokens.h
+++ b/src/frontends/lean/tokens.h
@@ -9,7 +9,6 @@ name const & get_aliases_tk();
 name const & get_period_tk();
 name const & get_backtick_tk();
 name const & get_dslash_tk();
-name const & get_fieldarrow_tk();
 name const & get_placeholder_tk();
 name const & get_colon_tk();
 name const & get_semicolon_tk();
@@ -69,6 +68,7 @@ name const & get_classes_tk();
 name const & get_attributes_tk();
 name const & get_arrow_tk();
 name const & get_larrow_tk();
+name const & get_darrow_tk();
 name const & get_hiding_tk();
 name const & get_example_tk();
 name const & get_exposing_tk();
diff --git a/src/frontends/lean/tokens.txt b/src/frontends/lean/tokens.txt
index fba2d6779c..f753c0165a 100644
--- a/src/frontends/lean/tokens.txt
+++ b/src/frontends/lean/tokens.txt
@@ -2,7 +2,6 @@ aliases      aliases
 period       .
 backtick     `
 dslash       //
-fieldarrow   ~>
 placeholder  _
 colon        :
 semicolon    ;
@@ -62,6 +61,7 @@ classes      classes
 attributes   attributes
 arrow        ->
 larrow       <-
+darrow       =>
 hiding       hiding
 example      example
 exposing     exposing
diff --git a/tests/compiler/array_test.lean b/tests/compiler/array_test.lean
index c5a5f9a99a..921e0dc80c 100644
--- a/tests/compiler/array_test.lean
+++ b/tests/compiler/array_test.lean
@@ -12,7 +12,7 @@ do
  IO.println (toString a.sz);
  let a := foo a;
  IO.println (toString a);
- let a := a.map (+10);
+ let a := a.map (fun a => a + 10);
  IO.println (toString a);
  IO.println (toString a.sz);
  let a1 := a.pop;
@@ -21,7 +21,7 @@ do
  IO.println (toString a2);
  let a2 := a.pop;
  IO.println a2;
- IO.println $ (([1, 2, 3, 4].toArray).map (+2)).map toString;
+ IO.println $ (([1, 2, 3, 4].toArray).map (fun a => a + 2)).map toString;
  IO.println $ ([1, 2, 3, 4].toArray.extract 1 3);
  IO.println $ ([1, 2, 3, 4].toArray.extract 0 100);
  IO.println $ ([1, 2, 3, 4].toArray.extract 1 1);
@@ -29,10 +29,10 @@ do
  IO.println [1,2,3,4].toArray.reverse;
  IO.println ([] : List Nat).toArray.reverse;
  IO.println [1,2,3].toArray.reverse;
- IO.println $ [1,2,3,4].toArray.filter (λ a, a % 2 == 0);
- IO.println $ [1,2,3,4,5].toArray.filter (λ a, a % 2 == 0);
- IO.println $ [1,2,3,4,5].toArray.filter (λ a, a % 2 == 1);
- IO.println $ [1,2,3,4].toArray.filter (>2);
- IO.println $ [1,2,3,4].toArray.filter (>10);
- IO.println $ [1,2,3,4].toArray.filter (>0);
+ IO.println $ [1,2,3,4].toArray.filter (fun a => a % 2 == 0);
+ IO.println $ [1,2,3,4,5].toArray.filter (fun a =>  a % 2 == 0);
+ IO.println $ [1,2,3,4,5].toArray.filter (fun a => a % 2 == 1);
+ IO.println $ [1,2,3,4].toArray.filter (fun a => a > 2);
+ IO.println $ [1,2,3,4].toArray.filter (fun a => a > 10);
+ IO.println $ [1,2,3,4].toArray.filter (fun a => a > 0);
  pure 0
diff --git a/tests/compiler/array_test2.lean b/tests/compiler/array_test2.lean
index 1814af3b50..de5ff83c34 100644
--- a/tests/compiler/array_test2.lean
+++ b/tests/compiler/array_test2.lean
@@ -7,9 +7,9 @@ let a1 := [2, 3, 5].toArray in
 let a2 := [4, 7, 9].toArray in
 let a3 := [4, 7, 8].toArray in
 do
- check (Array.isEqv a1 a2 (λ v w, v % 2 == w % 2));
- check (!Array.isEqv a1 a3 (λ v w, v % 2 == w % 2));
+ check (Array.isEqv a1 a2 (fun v w => v % 2 == w % 2));
+ check (!Array.isEqv a1 a3 (fun v w => v % 2 == w % 2));
  check (a1 ++ a2 == [2, 3, 5, 4, 7, 9].toArray);
- check (a1.any (>4));
- check (!a1.any (>10));
- check (a1.all (<10))
+ check (a1.any (fun a => a > 4));
+ check (!a1.any (fun a => a >10));
+ check (a1.all (fun a => a < 10))
diff --git a/tests/compiler/lazylist.lean b/tests/compiler/lazylist.lean
index 29dd85a98a..a8921c5e83 100644
--- a/tests/compiler/lazylist.lean
+++ b/tests/compiler/lazylist.lean
@@ -84,7 +84,7 @@ instance isMonad : Monad LazyList :=
 { pure := @LazyList.pure, bind := @LazyList.bind, map := @LazyList.map }
 
 instance : Alternative LazyList :=
-{ failure := λ _, nil,
+{ failure := fun _ => nil,
   orelse  := @LazyList.append,
   .. LazyList.isMonad }
 
@@ -108,7 +108,7 @@ partial def filter (p : α → Bool) : LazyList α → LazyList α
 end LazyList
 
 def fib : LazyList Nat :=
-LazyList.iterate₂ (+) 0 1
+LazyList.iterate₂ Nat.add 0 1
 
 def iota (i : Nat := 0) : LazyList Nat :=
 LazyList.iterate Nat.succ i
@@ -123,5 +123,5 @@ def main : IO Unit :=
 do let n := 40;
    IO.println $ tst.isEmpty;
    IO.println $ tst.head;
-   IO.println $ (fib.interleave (iota.map (+100))).approx n;
-   IO.println $ (((iota.map (+10)).filter (λ v, v % 2 == 0)).approx n)
+   IO.println $ (fib.interleave (iota.map (fun a => a + 100))).approx n;
+   IO.println $ (((iota.map (fun a => a + 10)).filter (fun v => v % 2 == 0)).approx n)
diff --git a/tests/compiler/map_big.lean b/tests/compiler/map_big.lean
index 4fc10b1645..50070aec83 100644
--- a/tests/compiler/map_big.lean
+++ b/tests/compiler/map_big.lean
@@ -1,6 +1,6 @@
 def f2 (n : Nat) (xs : List Nat) : List (List Nat) :=
 let ys := List.replicate n 0 in
-xs.map (λ x, x :: ys)
+xs.map (fun x => x :: ys)
 
 def main : IO UInt32 :=
 let n := 100000 in
diff --git a/tests/compiler/rbmap.lean b/tests/compiler/rbmap.lean
index 02313fbc5d..727a8df358 100644
--- a/tests/compiler/rbmap.lean
+++ b/tests/compiler/rbmap.lean
@@ -2,13 +2,13 @@ def check (b : Bool) : IO Unit :=
 unless b $ IO.println "ERROR"
 
 def sz {α β : Type} {lt : α → α → Bool} (m : RBMap α β lt) : Nat :=
-m.fold (λ sz _ _, sz+1) 0
+m.fold (fun sz _ _ => sz+1) 0
 
 def depth {α β : Type} {lt : α → α → Bool} (m : RBMap α β lt) : Nat :=
 m.depth Nat.max
 
 def tst1 : IO Unit :=
-do let Map := RBMap String Nat (λ a b, a < b);
+do let Map := RBMap String Nat (fun a b => a < b);
    let m : Map := {};
    let m := m.insert "hello" 0;
    let m := m.insert "world" 1;
@@ -20,20 +20,20 @@ do let Map := RBMap String Nat (λ a b, a < b);
    pure ()
 
 def tst2 : IO Unit :=
-do let Map := RBMap Nat Nat (λ a b, a < b);
+do let Map := RBMap Nat Nat (fun a b => a < b);
    let m : Map := {};
    let n : Nat := 10000;
-   let m := n.fold (λ i (m : Map), m.insert i (i*10)) m;
-   check (m.all (λ k v, v == k*10));
+   let m := n.fold (fun i (m : Map) => m.insert i (i*10)) m;
+   check (m.all (fun k v => v == k*10));
    check (sz m == n);
    IO.println (">> " ++ toString (depth m) ++ ", " ++ toString (sz m));
-   let m := (n/2).fold (λ i (m : Map), m.erase (2*i)) m;
-   check (m.all (λ k v, v == k*10));
+   let m := (n/2).fold (fun i (m : Map) => m.erase (2*i)) m;
+   check (m.all (fun k v => v == k*10));
    check (sz m == n / 2);
    IO.println (">> " ++ toString (depth m) ++ ", " ++ toString (sz m));
    pure ()
 
-abbrev Map := RBMap Nat Nat (λ a b, a < b)
+abbrev Map := RBMap Nat Nat (fun a b => a < b)
 
 def mkRandMap (max : Nat) : Nat → Map → Array (Nat × Nat) → IO (Map × Array (Nat × Nat))
 | 0     m a := pure (m, a)
@@ -51,11 +51,11 @@ def tst3 (seed : Nat) (n : Nat) (max : Nat) : IO Unit :=
 do IO.setRandSeed seed;
    (m, a) ← mkRandMap max n {} Array.empty;
    check (sz m == a.size);
-   check (a.all (λ ⟨k, v⟩, m.find k == some v));
+   check (a.all (fun ⟨k, v⟩ => m.find k == some v));
    IO.println ("tst3 size: " ++ toString a.size);
-   let m := a.iterate m (λ i ⟨k, v⟩ m, if i.val % 2 == 0 then m.erase k else m);
+   let m := a.iterate m (fun i ⟨k, v⟩ m => if i.val % 2 == 0 then m.erase k else m);
    check (sz m == a.size / 2);
-   a.miterate () (λ i ⟨k, v⟩ _, when (i.val % 2 == 1) (check (m.find k == some v)));
+   a.miterate () (fun i ⟨k, v⟩ _ => when (i.val % 2 == 1) (check (m.find k == some v)));
    IO.println ("tst3 after, depth: " ++ toString (depth m) ++ ", size: " ++ toString (sz m));
    pure ()
 
diff --git a/tests/compiler/t4.lean b/tests/compiler/t4.lean
index 56fcb64614..10785ed045 100644
--- a/tests/compiler/t4.lean
+++ b/tests/compiler/t4.lean
@@ -38,7 +38,7 @@ partial def addAux : Expr → Expr → Expr
 | f         g               := Add f g
 
 def add (a b : Expr) : Expr :=
--- dbgTrace (">> add (" ++ toString a ++ ", " ++ toString b ++ ")") $ λ _,
+-- dbgTrace (">> add (" ++ toString a ++ ", " ++ toString b ++ ")") $ fun _ =>
 addAux a b
 
 -- set_option trace.compiler.borrowed_inference true
@@ -56,7 +56,7 @@ partial def mulAux : Expr → Expr → Expr
 | f         g               := Mul f g
 
 def mul (a b : Expr) : Expr :=
--- dbgTrace (">> mul (" ++ toString a ++ ", " ++ toString b ++ ")") $ λ _,
+-- dbgTrace (">> mul (" ++ toString a ++ ", " ++ toString b ++ ")") $ fun _ =>
 mulAux a b
 
 def pow : Expr → Expr → Expr
@@ -75,7 +75,7 @@ def d (x : String) : Expr → Expr
 | (Var y)   := if x = y then Val 1 else Val 0
 | (Add f g) := add (d f) (d g)
 | (Mul f g) :=
-  -- dbgTrace (">> d (" ++ toString f ++ ", " ++ toString g ++ ")") $ λ _,
+  -- dbgTrace (">> d (" ++ toString f ++ ", " ++ toString g ++ ")") $ fun _ =>
   add (mul f (d g)) (mul g (d f))
 | (Pow f g) := mul (pow f g) (add (mul (mul g (d f)) (pow f (Val (-1)))) (mul (ln f) (d g)))
 | (Ln f)    := mul (d f) (pow f (Val (-1)))
diff --git a/tests/compiler/thunk.lean b/tests/compiler/thunk.lean
index 600e28c94f..98d38f2e8e 100644
--- a/tests/compiler/thunk.lean
+++ b/tests/compiler/thunk.lean
@@ -1,9 +1,9 @@
 def compute (v : Nat) : Thunk Nat :=
-⟨λ _, let xs := List.replicate 100000 v in xs.foldl (+) 0⟩
+⟨fun _ => let xs := List.replicate 100000 v in xs.foldl Nat.add 0⟩
 
 @[noinline]
 def test (t : Thunk Nat) (n : Nat) : Nat :=
-n.repeat (λ r, t.get + r) 0
+n.repeat (fun r => t.get + r) 0
 
 def main (xs : List String) : IO UInt32 :=
 IO.println (toString (test (compute 1) 100000)) *>
diff --git a/tests/lean/repr_issue.lean b/tests/lean/repr_issue.lean
index 549a22c395..5651e61f14 100644
--- a/tests/lean/repr_issue.lean
+++ b/tests/lean/repr_issue.lean
@@ -1,7 +1,7 @@
 def foo {m} [Monad m] [MonadExcept String m] [MonadState (Array Nat) m] : m Nat :=
-catch (do modify $ λ a : Array Nat, a.set 0 33;
+catch (do modify $ fun (a : Array Nat) => a.set 0 33;
           throw "error")
-      (λ _, do a ← get; pure $ a.get 0)
+      (fun _ => do a ← get; pure $ a.get 0)
 
 def ex₁ : StateT (Array Nat) (ExceptT String Id) Nat :=
 foo
diff --git a/tests/lean/run/1968.lean b/tests/lean/run/1968.lean
index 8c9e716308..ee111ca82b 100644
--- a/tests/lean/run/1968.lean
+++ b/tests/lean/run/1968.lean
@@ -29,7 +29,7 @@ open value
 -- #eval value.op (op.mul 32) [[[ const 32, const 32 ]]]
 
 -- This also works
--- instance bvHasMul (w : Nat) : HasMul (value (bv w)) := ⟨λx y, value.op (op.mul w) [[[x, y]]]⟩
+-- instance bvHasMul (w : Nat) : HasMul (value (bv w)) := ⟨fun x y => w value.op (op.mul w) [[[x, y]]]⟩
 -- #eval const 32 * const 32
 
 -- This works
diff --git a/tests/lean/run/array1.lean b/tests/lean/run/array1.lean
index 97995386d9..652065af44 100644
--- a/tests/lean/run/array1.lean
+++ b/tests/lean/run/array1.lean
@@ -1,15 +1,15 @@
 #check @Array.mk
 
-def v : Array Nat := @Array.mk Nat 10 (λ ⟨i, _⟩, i)
+def v : Array Nat := @Array.mk Nat 10 (fun ⟨i, _⟩ => i)
 
 def w : Array Nat :=
 (mkArray 9 1).push 3
 
 def f : Fin w.sz → Nat :=
-Array.casesOn w (λ _ f, f)
+Array.casesOn w (fun _ f => f)
 
 def arraySum (a : Array Nat) : Nat :=
-a.foldl (+) 0
+a.foldl Nat.add 0
 
 #exit
 
diff --git a/tests/lean/run/coroutine.lean b/tests/lean/run/coroutine.lean
index 68cdb1a286..55cd1c4a02 100644
--- a/tests/lean/run/coroutine.lean
+++ b/tests/lean/run/coroutine.lean
@@ -30,21 +30,21 @@ export coroutineResultCore (done yielded)
 | (mk k) a := k a
 
 @[inline] protected def pure (b : β) : coroutine α δ β :=
-mk $ λ _, done b
+mk $ fun _ => done b
 
 /-- Read the input argument passed to the coroutine.
     Remark: should we use a different Name? I added an instance [MonadReader] later. -/
 @[inline] protected def read : coroutine α δ α :=
-mk $ λ a, done a
+mk $ fun a => done a
 
 /-- Run nested coroutine with transformed input argument. Like `ReaderT.adapt`, but
     cannot change the input Type. -/
 @[inline] protected def adapt (f : α → α) (c : coroutine α δ β) : coroutine α δ β :=
-mk $ λ a, c.resume (f a)
+mk $ fun a => c.resume (f a)
 
 /-- Return the control to the invoker with Result `d` -/
 @[inline] protected def yield (d : δ) : coroutine α δ PUnit :=
-mk $ λ a : α, yielded d (coroutine.pure ⟨⟩)
+mk $ fun a => yielded d (coroutine.pure ⟨⟩)
 
 /-
 TODO(Leo): following relations have been commented because Lean4 is currently
@@ -58,8 +58,8 @@ theorem directSubcoroutineWf : WellFounded (@directSubcoroutine α δ β) :=
 begin
   Constructor, intro c,
   apply @coroutine.ind _ _ _
-          (λ c, Acc directSubcoroutine c)
-          (λ r, ∀ (d : δ) (c : coroutine α δ β), r = yielded d c → Acc directSubcoroutine c),
+          (fun c => Acc directSubcoroutine c)
+          (fun r => ∀ (d : δ) (c : coroutine α δ β), r = yielded d c → Acc directSubcoroutine c),
   { intros k ih, dsimp at ih, Constructor, intros c' h, cases h, apply ih hA hD, assumption },
   { intros, contradiction },
   { intros d c ih d₁ c₁ Heq, injection Heq, subst c, assumption }
@@ -76,12 +76,12 @@ Tc.wf directSubcoroutineWf
 -- Local instances for proving termination by well founded relation
 
 def bindWfInst : HasWellFounded (Σ' a : coroutine α δ β, (β → coroutine α δ γ)) :=
-{ r  := Psigma.Lex directSubcoroutine (λ _, emptyRelation),
-  wf := Psigma.lexWf directSubcoroutineWf (λ _, emptyWf) }
+{ r  := Psigma.Lex directSubcoroutine (fun _ => emptyRelation),
+  wf := Psigma.lexWf directSubcoroutineWf (fun _ => emptyWf) }
 
 def pipeWfInst : HasWellFounded (Σ' a : coroutine α δ β, coroutine δ γ β) :=
-{ r  := Psigma.Lex directSubcoroutine (λ _, emptyRelation),
-  wf := Psigma.lexWf directSubcoroutineWf (λ _, emptyWf) }
+{ r  := Psigma.Lex directSubcoroutine (fun _ => emptyRelation),
+  wf := Psigma.lexWf directSubcoroutineWf (fun _ => emptyWf) }
 
 local attribute [instance] wfInst₁ wfInst₂
 
@@ -92,7 +92,7 @@ open wellFoundedTactics
 /- TODO: remove `unsafe` keyword after we restore well-founded recursion -/
 
 @[inlineIfReduce] protected unsafe def bind : coroutine α δ β → (β → coroutine α δ γ) → coroutine α δ γ
-| (mk k) f := mk $ λ a,
+| (mk k) f := mk $ fun a =>
     match k a, rfl : ∀ (n : _), n = k a → _ with
     | done b, _      := coroutine.resume (f b) a
     | yielded d c, h :=
@@ -101,7 +101,7 @@ open wellFoundedTactics
 --  usingWellFounded { decTac := unfoldWfRel >> processLex (tactic.assumption) }
 
 unsafe def pipe : coroutine α δ β → coroutine δ γ β → coroutine α γ β
-| (mk k₁) (mk k₂) := mk $ λ a,
+| (mk k₁) (mk k₂) := mk $ fun a =>
   match k₁ a, rfl : ∀ (n : _), n = k₁ a → _ with
   | done b, h        := done b
   | yielded d k₁', h :=
@@ -120,7 +120,7 @@ private unsafe def finishAux (f : δ → α) : coroutine α δ β → α → Lis
 
 /-- Run a coroutine to completion, feeding back yielded items after transforming them with `f`. -/
 unsafe def finish (f : δ → α) : coroutine α δ β → α → List δ × β :=
-λ k a, finishAux f k a []
+fun k a => finishAux f k a []
 
 unsafe instance : Monad (coroutine α δ) :=
 { pure := @coroutine.pure _ _,
@@ -140,7 +140,7 @@ instance (α : Type u) (δ : Type v) : monadCoroutine α δ (coroutine α δ) :=
 
 instance monadCoroutineTrans (α : Type u) (δ : Type v) (m : Type w → Type r) (n : Type w → Type s)
                                [HasMonadLift m n] [monadCoroutine α δ m] : monadCoroutine α δ n :=
-{ yield := λ d, monadLift (monadCoroutine.yield d : m _) }
+{ yield := fun d => monadLift (monadCoroutine.yield d : m _) }
 
 export monadCoroutine (yield)
 
diff --git a/tests/lean/run/ext_eff.lean b/tests/lean/run/ext_eff.lean
index 95c0802e9d..3dec31292f 100644
--- a/tests/lean/run/ext_eff.lean
+++ b/tests/lean/run/ext_eff.lean
@@ -67,40 +67,40 @@ inductive eff (effs : List effect) (α : Type)
 
 def eff.bind {α β : Type} {effs : List effect} : eff effs α → (α → eff effs β) → eff effs β
 | (eff.pure a) f := f a
-| (@eff.impure _ _ β u k) f := eff.impure u (λ b, eff.bind (k b) f)
+| (@eff.impure _ _ β u k) f := eff.impure u (fun b => eff.bind (k b) f)
 
 instance (effs) : Monad (eff effs) :=
-{ pure := λ α, eff.pure,
-  bind := λ α β, eff.bind }
+{ pure := fun α => eff.pure,
+  bind := fun α β => eff.bind }
 
 @[inline] def eff.send {e : effect} {effs α} [member e effs] : e α → eff effs α :=
-λ x, eff.impure (union.inj x) pure
+fun x => eff.impure (union.inj x) pure
 
 @[inline] def eff.sendM {e : effect} {effs α} [Monad e] [lastMember e effs] : e α → eff effs α :=
-λ x, eff.impure (union.inj x) pure
+fun x => eff.impure (union.inj x) pure
 
 @[inline] def eff.handleRelay {e : effect} {effs α β} (ret : β → eff effs α)
   (h : ∀ {β}, e β → (β → eff effs α) → eff effs α) : eff (e :: effs) β → eff effs α
 | (eff.pure a) := ret a
 | (@eff.impure _ _ β u k) := match u.decomp with
-  | Sum.inl e := h e (λ b, eff.handleRelay (k b))
-  | Sum.inr u := eff.impure u (λ b, eff.handleRelay (k b))
+  | Sum.inl e := h e (fun b => eff.handleRelay (k b))
+  | Sum.inr u := eff.impure u (fun b => eff.handleRelay (k b))
 
 
 @[inline] def eff.handleRelayΣ {e : effect} {effs α β} {σ : Type} (ret : σ → β → eff effs α)
   (h : ∀ {β}, σ → e β → (σ → β → eff effs α) → eff effs α) : σ → eff (e :: effs) β → eff effs α
 | st (eff.pure a) := ret st a
 | st (@eff.impure _ _ β u k) := match u.decomp with
-  | Sum.inl e := h st e (λ st b, eff.handleRelayΣ st (k b))
-  | Sum.inr u := eff.impure u (λ b, eff.handleRelayΣ st (k b))
+  | Sum.inl e := h st e (fun st b => eff.handleRelayΣ st (k b))
+  | Sum.inr u := eff.impure u (fun b => eff.handleRelayΣ st (k b))
 
 
 @[inline] def eff.interpose (e : effect) {effs α β} [member e effs] (ret : β → eff effs α)
   (h : ∀ {β}, e β → (β → eff effs α) → eff effs α) : eff effs β → eff effs α
 | (eff.pure a) := ret a
 | (@eff.impure _ _ β u k) := match u.prj e with
-  | some e := h e (λ b, eff.interpose (k b))
-  | none   := eff.impure u (λ b, eff.interpose (k b))
+  | some e := h e (fun b => eff.interpose (k b))
+  | none   := eff.impure u (fun b => eff.interpose (k b))
 
 
 inductive Reader (ρ : Type) : Type → Type
@@ -110,7 +110,7 @@ inductive Reader (ρ : Type) : Type → Type
 instance {ρ effs} [member (Reader ρ) effs] : MonadReader ρ (eff effs) := ⟨eff.read⟩
 
 @[inline] def Reader.run {ρ effs α} (env : ρ) : eff (Reader ρ :: effs) α → eff effs α :=
-eff.handleRelay pure (λ β x k, by cases x; exact k env)
+eff.handleRelay pure (fun β x k => by cases x; exact k env)
 
 
 inductive State (σ : Type) : Type → Type
@@ -120,13 +120,13 @@ inductive State (σ : Type) : Type → Type
 @[inline] def eff.get {σ effs} [member (State σ) effs] : eff effs σ := eff.send State.get
 @[inline] def eff.put {σ effs} [member (State σ) effs] (s : σ) : eff effs Unit := eff.send (State.put s)
 instance {σ effs} [member (State σ) effs] : MonadState σ (eff effs) :=
-⟨λ α x, do st ← eff.get;
+⟨fun α x => do st ← eff.get;
            let ⟨a, s'⟩ := x.run st;
            eff.put s';
            pure a⟩
 
 @[inline] def State.run {σ effs α} (st : σ) : eff (State σ :: effs) α → eff effs (α × σ) :=
-eff.handleRelayΣ (λ st a, pure (a, st)) (λ β st x k, begin
+eff.handleRelayΣ (fun st a => pure (a, st)) (fun β st x k => begin
   cases x,
   case State.get { exact k st st },
   case State.put : st' { exact k st' () }
@@ -137,12 +137,12 @@ inductive Exception (ε α : Type) : Type
 
 @[inline] def eff.throw {ε α effs} [member (Exception ε) effs] (ex : ε) : eff effs α := eff.send (Exception.throw ex)
 @[inline] def eff.catch {ε α effs} [member (Exception ε) effs] (x : eff effs α) (handle : ε → eff effs α) : eff effs α :=
-x.interpose (Exception ε) pure (λ β x k, match x with Exception.throw e := handle e)
+x.interpose (Exception ε) pure (fun β x k => match x with Exception.throw e := handle e)
 instance {ε effs} [member (Exception ε) effs] : MonadExcept ε (eff effs) :=
-⟨λ α, eff.throw, λ α, eff.catch⟩
+⟨fun α => eff.throw, fun α => eff.catch⟩
 
 @[inline] def Exception.run {ε effs α} : eff (Exception ε :: effs) α → eff effs (Except ε α) :=
-eff.handleRelay (pure ∘ Except.ok) (λ β x k, match x with Exception.throw e := pure (Except.error e))
+eff.handleRelay (pure ∘ Except.ok) (fun β x k => match x with Exception.throw e := pure (Except.error e))
 
 
 def eff.run {α : Type} : eff [] α → α
@@ -151,25 +151,25 @@ def eff.run {α : Type} : eff [] α → α
 def eff.runM {α : Type} {m} [Monad m] : eff [m] α → m α
 | (eff.pure a) := pure a
 | (eff.impure u k) := match u.decomp with
-  | Sum.inl m := m >>= λ a, eff.runM (k a)
+  | Sum.inl m := m >>= fun a => eff.runM (k a)
 
 instance (m effs) [member m effs] : HasMonadLift m (eff effs) :=
-⟨λ α, eff.send⟩
+⟨fun α => eff.send⟩
 
 section examples
 
 -- from http://okmij.org/ftp/Haskell/extensible/EffDynCatch.hs
 
 @[inline] def IO.try {α} : IO α → IO (Except IO.error α) :=
-λ x, IO.catch (Except.ok <$> x) (pure ∘ Except.error)
+fun x => IO.catch (Except.ok <$> x) (pure ∘ Except.error)
 
 instance : HasRepr IO.error :=
-⟨λ e, match e with
+⟨fun e => match e with
       | IO.error.sys n := "IO.error.sys " ++ repr n
       | IO.error.other s := "IO.error.other " ++ repr s⟩
 
 @[inline] def eff.catchIO {effs α} [member IO effs] (x : eff effs α) (catch : IO.error → eff effs α) : eff effs α :=
-x.interpose IO pure (λ β x k, do ex ← monadLift x.try;
+x.interpose IO pure (fun β x k => do ex ← monadLift x.try;
                                  match ex with
                                  | Except.ok b := k b
                                  | Except.error e := catch e)
@@ -184,11 +184,11 @@ eff.catchIO (Except.ok <$> x) (pure ∘ Except.error)
 
 -- handle IO exceptions before State
 def test1 :=
-  let tf : Bool → eff [IO] _ := λ (x : Bool), Reader.run x $ State.run ([] : List String) $ eff.tryIo $
-  do modify (λ xs, "begin"::xs);
+  let tf : Bool → eff [IO] _ := fun (x : Bool) => Reader.run x $ State.run ([] : List String) $ eff.tryIo $
+  do modify (fun xs => "begin"::xs);
      x ← read;
      r ← monadLift $ exfn x;
-     modify (λ xs, "end"::xs);
+     modify (fun xs => "end"::xs);
      pure r in
   do repr <$> eff.runM (tf tt) >>= IO.println;
      repr <$> eff.runM (tf ff) >>= IO.println
@@ -197,11 +197,11 @@ def test1 :=
 
 -- handle IO exceptions after State
 def test2 :=
-  let tf : Bool → eff [IO] _ := λ (x : Bool), Reader.run x $ eff.tryIo $ State.run ([] : List String) $
-  do modify (λ xs, "begin"::xs);
+  let tf : Bool → eff [IO] _ := fun (x : Bool) => Reader.run x $ eff.tryIo $ State.run ([] : List String) $
+  do modify (fun xs => "begin"::xs);
      x ← read;
      r ← monadLift $ exfn x;
-     modify (λ xs, "end"::xs);
+     modify (fun xs => "end"::xs);
      pure r in
   do repr <$> eff.runM (tf tt) >>= IO.println;
      repr <$> eff.runM (tf ff) >>= IO.println
diff --git a/tests/lean/run/ext_eff_linear.lean b/tests/lean/run/ext_eff_linear.lean
index 39d7f06f6e..f327e93093 100644
--- a/tests/lean/run/ext_eff_linear.lean
+++ b/tests/lean/run/ext_eff_linear.lean
@@ -87,34 +87,34 @@ meta def eff.bind {α β : Type} {effs : List effect} : eff effs α → (α →
 | (@eff.impure _ _ β u k) f := eff.impure u (ftcQueue.Node k (ftcQueue.leaf f))
 
 meta instance (effs) : Monad (eff effs) :=
-{ pure := λ α, eff.pure,
-  bind := λ α β, eff.bind }
+{ pure := fun α => eff.pure,
+  bind := fun α β => eff.bind }
 
 @[inline] meta def eff.send {e : effect} {effs α} [member e effs] : e α → eff effs α :=
-λ x, eff.impure (union.inj x) (ftcQueue.leaf pure)
+fun x => eff.impure (union.inj x) (ftcQueue.leaf pure)
 
 @[inline] meta def eff.handleRelay {e : effect} {effs α β} (ret : β → eff effs α)
   (h : ∀ {β}, e β → (β → eff effs α) → eff effs α) : eff (e :: effs) β → eff effs α
 | (eff.pure a) := ret a
 | (@eff.impure _ _ γ u k) := match u.decomp with
-  | Sum.inl e := h e (λ c, eff.handleRelay (arrs.apply k c))
-  | Sum.inr u := eff.impure u (ftcQueue.leaf (λ c, eff.handleRelay (arrs.apply k c)))
+  | Sum.inl e := h e (fun c => eff.handleRelay (arrs.apply k c))
+  | Sum.inr u := eff.impure u (ftcQueue.leaf (fun c => eff.handleRelay (arrs.apply k c)))
 
 
 @[inline] meta def eff.handleRelayΣ {e : effect} {effs α β} {σ : Type} (ret : σ → β → eff effs α)
   (h : ∀ {β}, σ → e β → (σ → β → eff effs α) → eff effs α) : σ → eff (e :: effs) β → eff effs α
 | st (eff.pure a) := ret st a
 | st (@eff.impure _ _ γ u k) := match u.decomp with
-  | Sum.inl e := h st e (λ st c, eff.handleRelayΣ st (arrs.apply k c))
-  | Sum.inr u := eff.impure u (ftcQueue.leaf (λ c, eff.handleRelayΣ st (arrs.apply k c)))
+  | Sum.inl e := h st e (fun st c => eff.handleRelayΣ st (arrs.apply k c))
+  | Sum.inr u := eff.impure u (ftcQueue.leaf (fun c => eff.handleRelayΣ st (arrs.apply k c)))
 
 
 @[inline] meta def eff.interpose {e : effect} {effs α β} [member e effs] (ret : β → eff effs α)
   (h : ∀ {β}, e β → (β → eff effs α) → eff effs α) : eff effs β → eff effs α
 | (eff.pure a) := ret a
 | (@eff.impure _ _ γ u k) := match u.prj e with
-  | some e := h e (λ c, eff.interpose (arrs.apply k c))
-  | none   := eff.impure u (ftcQueue.leaf (λ c, eff.interpose (arrs.apply k c)))
+  | some e := h e (fun c => eff.interpose (arrs.apply k c))
+  | none   := eff.impure u (ftcQueue.leaf (fun c => eff.interpose (arrs.apply k c)))
 
 
 inductive Reader (ρ : Type) : Type → Type
@@ -124,7 +124,7 @@ inductive Reader (ρ : Type) : Type → Type
 meta instance {ρ effs} [member (Reader ρ) effs] : MonadReader ρ (eff effs) := ⟨eff.read⟩
 
 @[inline] meta def Reader.run {ρ effs α} (env : ρ) : eff (Reader ρ :: effs) α → eff effs α :=
-eff.handleRelay pure (λ β x k, by cases x; exact k env)
+eff.handleRelay pure (fun β x k => by cases x; exact k env)
 
 
 inductive State (σ : Type) : Type → Type
@@ -134,13 +134,13 @@ inductive State (σ : Type) : Type → Type
 @[inline] meta def eff.get {σ effs} [member (State σ) effs] : eff effs σ := eff.send State.get
 @[inline] meta def eff.put {σ effs} [member (State σ) effs] (s : σ) : eff effs Unit := eff.send (State.put s)
 meta instance {σ effs} [member (State σ) effs] : MonadState σ (eff effs) :=
-⟨λ α x, do st ← eff.get;
+⟨fun α x => do st ← eff.get;
            let ⟨a, s'⟩ := x.run st;
            eff.put s';
            pure a⟩
 
 meta def State.run {σ effs α} (st : σ) : eff (State σ :: effs) α → eff effs (α × σ) :=
-eff.handleRelayΣ (λ st a, pure (a, st)) (λ β st x k, begin
+eff.handleRelayΣ (fun st a => pure (a, st)) (fun β st x k => begin
   cases x,
   case State.get { exact k st st },
   case State.put : st' { exact k st' () }
@@ -151,12 +151,12 @@ inductive Exception (ε α : Type) : Type
 
 @[inline] meta def eff.throw {ε α effs} [member (Exception ε) effs] (ex : ε) : eff effs α := eff.send (Exception.throw ex)
 @[inline] meta def eff.catch {ε α effs} [member (Exception ε) effs] (x : eff effs α) (handle : ε → eff effs α) : eff effs α :=
-x.interpose pure (λ β x k, match (x : Exception ε β) with Exception.throw e := handle e)
+x.interpose pure (fun β x k => match (x : Exception ε β) with Exception.throw e := handle e)
 meta instance {ε effs} [member (Exception ε) effs] : MonadExcept ε (eff effs) :=
-⟨λ α, eff.throw, λ α, eff.catch⟩
+⟨fun α => eff.throw, fun α => eff.catch⟩
 
 @[inline] meta def Exception.run {ε effs α} : eff (Exception ε :: effs) α → eff effs (Except ε α) :=
-eff.handleRelay (pure ∘ Except.ok) (λ β x k, match x with Exception.throw e := pure (Except.error e))
+eff.handleRelay (pure ∘ Except.ok) (fun β x k => match x with Exception.throw e := pure (Except.error e))
 
 
 meta def eff.run {α : Type} : eff [] α → α
diff --git a/tests/lean/run/float_cases_bug.lean b/tests/lean/run/float_cases_bug.lean
index a4cec08fc8..aef21a2a2e 100644
--- a/tests/lean/run/float_cases_bug.lean
+++ b/tests/lean/run/float_cases_bug.lean
@@ -1,2 +1,2 @@
 def foo (xs : List Nat) :=
-xs.span (λ n, coe (decide (n = 1)))
+xs.span (fun n => coe (decide (n = 1)))
diff --git a/tests/lean/run/handlers.lean b/tests/lean/run/handlers.lean
index fb2386b0da..24014be6f5 100644
--- a/tests/lean/run/handlers.lean
+++ b/tests/lean/run/handlers.lean
@@ -21,22 +21,22 @@ structure comp (h : Type*) [handler h] (α : Type*) :=
 (handle : (α → h → handler.Result h) → h → handler.Result h)
 
 @[inline] def comp.do {h e u} {op : Type → Type → Type*} [isOp op] [handler h] [handles h op e] (f : op e u) : comp h (isOp.return op e u) :=
-⟨λ k h, handles.clause f k h⟩
+⟨fun k h => r handles.clause f k h⟩
 
 instance (h) [handler h] : Monad (comp h) :=
-{ pure := λ α v, ⟨λ k h, k v h⟩,
-  bind := λ α β ⟨c⟩ f, ⟨λ k h, c (λ x h', (f x).handle k h') h⟩ }
+{ pure := fun α v => ⟨fun k h => k v h⟩,
+  bind := fun α β ⟨c⟩ f => ⟨fun k h => c (fun x h' => (f x).handle k h') h⟩ }
 
 
 inductive Put : Type → Type → Type 1
 | mk {σ : Type} (s : σ) : Put σ Unit
 
-instance Put.op : isOp Put := ⟨λ _ _, Unit⟩
+instance Put.op : isOp Put := ⟨fun _ _ => Unit⟩
 
 inductive Get : Type → Type → Type 1
 | mk {σ : Type} : Get σ Unit
 
-instance Get.op : isOp Get := ⟨λ σ _, σ⟩
+instance Get.op : isOp Get := ⟨fun σ _ => σ⟩
 
 @[inline] def get {h σ } [handler h] [handles h Get σ] : comp h σ :=
 comp.do Get.mk
@@ -46,7 +46,7 @@ comp.do (Put.mk s)
 instance (h σ) [handler h] [handles h Get σ] [handles h Put σ] : MonadState σ (comp h) :=
 { get := get,
   put := put,
-  modify := λ f, f <$> get >>= put }
+  modify := fun f => f <$> get >>= put }
 
 structure stateH (h : Type) (σ : Type) (α : Type) := mk {} ::
 (State : σ)
@@ -54,22 +54,22 @@ structure stateH (h : Type) (σ : Type) (α : Type) := mk {} ::
 instance (h σ α) [handler h] : handler (stateH h σ α) := ⟨comp h α⟩
 
 instance stateHHandleGet (h σ α) [handler h] : handles (stateH h σ α) Get σ :=
-⟨λ _ _ k ⟨st⟩, k st ⟨st⟩⟩
+⟨fun _ _ k ⟨st⟩ => k st ⟨st⟩⟩
 
 instance stateHHandlePut (h σ α) [handler h] : handles (stateH h σ α) Put σ :=
-⟨λ _ op k _, by cases op with _ st'; apply k () ⟨st'⟩⟩
+⟨fun _ op k _ => by cases op with _ st'; apply k () ⟨st'⟩⟩
 
 instance stateHForward (h op σ α) [handler h] [isOp op] [handles h op α] : handles (stateH h σ α) op α :=
-⟨λ _ op k hi, comp.do op >>= (λ x, k x hi)⟩
+⟨fun _ op k hi => comp.do op >>= (fun x => k x hi)⟩
 
 @[inline] def handleState {h σ α} [handler h] (st : σ) (x : comp (stateH h σ α) α) : comp h α :=
-x.handle (λ a _, (pure a : comp h α)) ⟨st⟩
+x.handle (fun a _ => (pure a : comp h α)) ⟨st⟩
 
 
 inductive Read : Type → Type → Type 1
 | mk {ρ : Type} : Read ρ Unit
 
-instance Read.op : isOp Read := ⟨λ ρ _, ρ⟩
+instance Read.op : isOp Read := ⟨fun ρ _ => ρ⟩
 
 @[inline] def read {h ρ} [handler h] [handles h Read ρ] : comp h ρ :=
 comp.do Read.mk
@@ -83,13 +83,13 @@ structure readH (h : Type) (ρ : Type) (α : Type) := mk {} ::
 instance readH.handler (h ρ α) [handler h] : handler (readH h ρ α) := ⟨comp h α⟩
 
 instance readHHandleRead (h ρ α) [handler h] : handles (readH h ρ α) Read ρ :=
-⟨λ _ _ k ⟨env⟩, k env ⟨env⟩⟩
+⟨fun _ _ k ⟨env⟩ => k env ⟨env⟩⟩
 
 instance readHForward (h op ρ α) [handler h] [isOp op] [handles h op α] : handles (readH h ρ α) op α :=
-⟨λ _ op k hi, comp.do op >>= (λ x, k x hi)⟩
+⟨fun _ op k hi => comp.do op >>= (fun x => k x hi)⟩
 
 @[inline] def handleRead {h ρ α} [handler h] (env : ρ) (x : comp (readH h ρ α) α) : comp h α :=
-x.handle (λ a _, (pure a : comp h α)) ⟨env⟩
+x.handle (fun a _ => (pure a : comp h α)) ⟨env⟩
 
 
 structure pureH (α : Type) := mk {}
@@ -97,7 +97,7 @@ structure pureH (α : Type) := mk {}
 instance pureH.handler (α) : handler (pureH α) := ⟨α⟩
 
 @[inline] def handlePure {α} (x : comp (pureH α) α) : α :=
-x.handle (λ a _, a) ⟨⟩
+x.handle (fun a _ => a) ⟨⟩
 end handlers
 
 
diff --git a/tests/lean/run/new_compiler.lean b/tests/lean/run/new_compiler.lean
index 6fd169133a..3eda40fd20 100644
--- a/tests/lean/run/new_compiler.lean
+++ b/tests/lean/run/new_compiler.lean
@@ -20,18 +20,18 @@ let y2 := y1 in
 y2 + n
 
 def cseTst (n : Nat) : Nat :=
-let y := Nat.succ ((λ x, x) n) in
+let y := Nat.succ ((fun x => x) n) in
 let z := Nat.succ n in
 y + z
 
 def tst1 (n : Nat) : Nat :=
 let p := (Nat.succ n, n) in
 let q := (p, p) in
-Prod.casesOn q (λ x y, Prod.casesOn x (λ z w, z))
+Prod.casesOn q (fun x y => Prod.casesOn x (fun z w => z))
 
 def tst2 (n : Nat) : Nat :=
-let p := (λ x, Nat.succ x, Nat.zero)  in
-let f := λ p : (Nat → Nat) × Nat, p.1 in
+let p := (fun x => Nat.succ x, Nat.zero)  in
+let f := fun (p : (Nat → Nat) × Nat) => p.1 in
 f p n
 
 def add' : Nat → Nat → Nat
@@ -42,22 +42,22 @@ def aux (i : Nat) (h : i > 0) :=
 i
 
 unsafe def foo2 : Nat :=
-@False.rec (λ _, Nat) sorry
+@False.rec (fun _ => Nat) sorry
 
 set_option pp.notation false
 
 def foo3 (n : Nat) : Nat :=
-(λ a : Nat, a + a + a) (n*n)
+(fun a : Nat => a + a + a) (n*n)
 
 def boo (a : Nat) (l : List Nat) : List Nat :=
 let f := @List.cons Nat in
 f a (f a l)
 
 def bla (i : Nat) (h : i > 0 ∧ i ≠ 10) : Nat :=
-@And.rec _ _ (λ _, Nat) (λ h₁ h₂, aux i h₁ + aux i h₁) h
+@And.rec _ _ (fun _ => Nat) (fun h₁ h₂ => aux i h₁ + aux i h₁) h
 
 def bla' (i : Nat) (h : i > 0 ∧ i ≠ 10) : Nat :=
-@And.casesOn _ _ (λ _, Nat) h (λ h₁ h₂, aux i h₁ + aux i h₁)
+@And.casesOn _ _ (fun _ => Nat) h (fun h₁ h₂ => aux i h₁ + aux i h₁)
 
 inductive vec (α : Type u) : Nat → Type u
 | nil {}  : vec 0
diff --git a/tests/lean/run/new_inductive.lean b/tests/lean/run/new_inductive.lean
index b4b713a320..11f6e58bb6 100644
--- a/tests/lean/run/new_inductive.lean
+++ b/tests/lean/run/new_inductive.lean
@@ -17,7 +17,7 @@ with boo : Nat → Type (max u v)
 #print bla
 
 inductive Term (α : Type) (β : Type)
-| var : α → bla Term (λ _, Term) 10 → Term
+| var : α → bla Term (fun _ => Term) 10 → Term
 | foo (p : Nat → myPair Term (myList Term)) (n : β) : myList (myList Term) → Term
 
 #print Term
diff --git a/tests/lean/run/quasi_pattern_unification_approx_issue.lean b/tests/lean/run/quasi_pattern_unification_approx_issue.lean
index f993dcf15a..04d5527bcc 100644
--- a/tests/lean/run/quasi_pattern_unification_approx_issue.lean
+++ b/tests/lean/run/quasi_pattern_unification_approx_issue.lean
@@ -22,13 +22,13 @@ Then, we need to solve:
 ==> instantiate metavars
 ?m σ =?= StateT σ id σ
 ==> (approximate since it is a quasi-pattern unification constraint)
-?m := λ σ, StateT σ id σ
+?m := fun σ => StateT σ id σ
 
 Remark: the constraint is not a Milner pattern because σ is in
 the local context of `?m`. We are ignoring the other possible solutions:
-?m := λ σ', StateT σ id σ
-?m := λ σ', StateT σ' id σ
-?m := λ σ', StateT σ id σ'
+?m := fun σ' => StateT σ id σ
+?m := fun σ' => StateT σ' id σ
+?m := fun σ' => StateT σ id σ'
 
 We need the quasi-pattern approximation for elaborating recursors.
 One Option is to enable this kind of approximation only when
diff --git a/tests/lean/run/rc_tests.lean b/tests/lean/run/rc_tests.lean
index 99fea49844..54cf107dcc 100644
--- a/tests/lean/run/rc_tests.lean
+++ b/tests/lean/run/rc_tests.lean
@@ -59,7 +59,7 @@ end x5
 namespace x6
 
 @[noinline] def act : State Nat Unit :=
-modify (+1)
+modify (fun a => a + 1)
 
 def f : State Nat Unit :=
 act *> act
diff --git a/tests/lean/trust0/basic.lean b/tests/lean/trust0/basic.lean
index 588daca52c..ac965eb8ad 100644
--- a/tests/lean/trust0/basic.lean
+++ b/tests/lean/trust0/basic.lean
@@ -16,11 +16,11 @@ inductive lessThanOrEqual (a : ℕ) : ℕ → Prop
 
 @[elabAsEliminator]
 theorem lessThanOrEqual.ndrec  {a : Nat} {C : Nat → Prop} (m₁ : C a) (m₂ : ∀ (b : Nat), lessThanOrEqual a b → C b → C (succ b)) {b : ℕ} (h : lessThanOrEqual a b) : C b :=
-@lessThanOrEqual.rec a (λ b _, C b) m₁ m₂ b h
+@lessThanOrEqual.rec a (fun b _ => C b) m₁ m₂ b h
 
 @[elabAsEliminator]
 theorem lessThanOrEqual.ndrecOn {a : Nat} {C : Nat → Prop} {b : ℕ} (h : lessThanOrEqual a b) (m₁ : C a) (m₂ : ∀ (b : Nat), lessThanOrEqual a b → C b → C (succ b)) : C b :=
-@lessThanOrEqual.rec a (λ b _, C b) m₁ m₂ b h
+@lessThanOrEqual.rec a (fun b _ => C b) m₁ m₂ b h
 
 instance : HasLessEq ℕ :=
 ⟨Nat.lessThanOrEqual⟩
@@ -54,17 +54,17 @@ instance : HasMul ℕ :=
 
 def hasDecEq : Π a b : Nat, Decidable (a = b)
 | zero     zero     := isTrue rfl
-| (succ x) zero     := isFalse (λ h, Nat.noConfusion h)
-| zero     (succ y) := isFalse (λ h, Nat.noConfusion h)
+| (succ x) zero     := isFalse (fun h => Nat.noConfusion h)
+| zero     (succ y) := isFalse (fun h => Nat.noConfusion h)
 | (succ x) (succ y) :=
     match hasDecEq x y with
     | isTrue xeqy := isTrue (xeqy ▸ Eq.refl (succ x))
-    | isFalse xney := isFalse (λ h, Nat.noConfusion h (λ xeqy, absurd xeqy xney))
+    | isFalse xney := isFalse (fun h => Nat.noConfusion h (fun xeqy => absurd xeqy xney))
 
 instance : DecidableEq ℕ :=
 {decEq := hasDecEq}
 
-def {u} repeat {α : Type u} (f : ℕ → α → α) : ℕ → α → α
+def repeat.{u} {α : Type u} (f : ℕ → α → α) : ℕ → α → α
 | 0         a := a
 | (succ n)  a := f n (repeat n a)
 
@@ -80,7 +80,7 @@ theorem leSucc (n : ℕ) : n ≤ succ n :=
 lessThanOrEqual.step (Nat.leRefl n)
 
 theorem succLeSucc {n m : ℕ} : n ≤ m → succ n ≤ succ m :=
-λ h, lessThanOrEqual.ndrec (Nat.leRefl (succ n)) (λ a b, lessThanOrEqual.step) h
+fun h => lessThanOrEqual.ndrec (Nat.leRefl (succ n)) (fun a b => lessThanOrEqual.step) h
 
 theorem zeroLe : ∀ (n : ℕ), 0 ≤ n
 | 0     := Nat.leRefl 0
@@ -97,9 +97,9 @@ theorem notSuccLeZero : ∀ (n : ℕ), succ n ≤ 0 → False
 theorem notLtZero (a : ℕ) : ¬ a < 0 := notSuccLeZero a
 
 theorem predLePred {n m : ℕ} : n ≤ m → pred n ≤ pred m :=
-λ h, lessThanOrEqual.ndrecOn h
+fun h => lessThanOrEqual.ndrecOn h
   (Nat.leRefl (pred n))
-  (λ n, Nat.rec (λ a b, b) (λ a b c, lessThanOrEqual.step) n)
+  (fun n => Nat.rec (fun a b => b) (fun a b c => lessThanOrEqual.step) n)
 
 theorem leOfSuccLeSucc {n m : ℕ} : succ n ≤ succ m → n ≤ m :=
 predLePred
@@ -110,13 +110,13 @@ instance decidableLe : ∀ a b : ℕ, Decidable (a ≤ b)
 | (a+1) (b+1) :=
   match decidableLe a b with
   | isTrue h  := isTrue (succLeSucc h)
-  | isFalse h := isFalse (λ a, h (leOfSuccLeSucc a))
+  | isFalse h := isFalse (fun a => h (leOfSuccLeSucc a))
 
 instance decidableLt : ∀ a b : ℕ, Decidable (a < b) :=
-λ a b, Nat.decidableLe (succ a) b
+fun a b => Nat.decidableLe (succ a) b
 
 protected theorem eqOrLtOfLe {a b : ℕ} (h : a ≤ b) : a = b ∨ a < b :=
-lessThanOrEqual.casesOn h (Or.inl rfl) (λ n h, Or.inr (succLeSucc h))
+lessThanOrEqual.casesOn h (Or.inl rfl) (fun n h => Or.inr (succLeSucc h))
 
 theorem ltSuccOfLe {a b : ℕ} : a ≤ b → a < succ b :=
 succLeSucc
@@ -124,16 +124,16 @@ succLeSucc
 theorem succSubSuccEqSub (a b : ℕ) : succ a - succ b = a - b :=
 Nat.recOn b
   (show succ a - succ zero = a - zero, from (Eq.refl (succ a - succ zero)))
-  (λ b, congrArg pred)
+  (fun b => congrArg pred)
 
 theorem notSuccLeSelf : ∀ n : ℕ, ¬succ n ≤ n :=
-λ n, Nat.rec (notSuccLeZero 0) (λ a b c, b (leOfSuccLeSucc c)) n
+fun n => Nat.rec (notSuccLeZero 0) (fun a b c => b (leOfSuccLeSucc c)) n
 
 protected theorem ltIrrefl (n : ℕ) : ¬n < n :=
 notSuccLeSelf n
 
 protected theorem leTrans {n m k : ℕ} (h1 : n ≤ m) : m ≤ k → n ≤ k :=
-lessThanOrEqual.ndrec h1 (λ p h2, lessThanOrEqual.step)
+lessThanOrEqual.ndrec h1 (fun p h2 => lessThanOrEqual.step)
 
 theorem predLe : ∀ (n : ℕ), pred n ≤ n
 | 0        := lessThanOrEqual.refl 0
@@ -144,7 +144,7 @@ theorem predLt : ∀ {n : ℕ}, n ≠ 0 → pred n < n
 | (succ a) h := ltSuccOfLe (lessThanOrEqual.refl _)
 
 theorem subLe (a b : ℕ) : a - b ≤ a :=
-Nat.recOn b (Nat.leRefl (a - 0)) (λ b₁, Nat.leTrans (predLe (a - b₁)))
+Nat.recOn b (Nat.leRefl (a - 0)) (fun b₁ => Nat.leTrans (predLe (a - b₁)))
 
 theorem subLt : ∀ {a b : ℕ}, 0 < a → 0 < b → a - b < a
 | 0     b     h1 h2 := absurd h1 (Nat.ltIrrefl 0)