diff --git a/library/init/category/alternative.lean b/library/init/category/alternative.lean
index 182266bee2..c34d46d9b4 100644
--- a/library/init/category/alternative.lean
+++ b/library/init/category/alternative.lean
@@ -8,16 +8,16 @@ import init.logic init.category.applicative
 universes u v
 
 class alternative (f : Type u → Type v) extends applicative f : Type (max u+1 v) :=
-(failure : Π {a : Type u}, f a)
-(orelse  : Π {a : Type u}, f a → f a → f a)
+(failure : Π {α : Type u}, f α)
+(orelse  : Π {α : Type u}, f α → f α → f α)
 
 section
-variables {f : Type u → Type v} [alternative f] {a : Type u}
+variables {f : Type u → Type v} [alternative f] {α : Type u}
 
-@[inline] def failure : f a :=
+@[inline] def failure : f α :=
 alternative.failure f
 
-@[inline] def orelse : f a → f a → f a :=
+@[inline] def orelse : f α → f α → f α :=
 alternative.orelse
 
 infixr ` <|> `:2 := orelse
@@ -31,7 +31,7 @@ if p then pure () else failure
 | tt := pure ()
 | ff := failure
 
-@[inline] def optional (x : f a) : f (option a) :=
+@[inline] def optional (x : f α) : f (option α) :=
 some <$> x <|> pure none
 
 end
diff --git a/library/init/category/applicative.lean b/library/init/category/applicative.lean
index 4bf778dd52..6f15a56b76 100644
--- a/library/init/category/applicative.lean
+++ b/library/init/category/applicative.lean
@@ -1,38 +1,38 @@
 /-
 Copyright (c) 2016 Microsoft Corporation. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Author: Leonardo de Moura
+Authors: Leonardo de Moura, Sebastian Ullrich
 -/
 prelude
 import init.category.functor
-import init.function
 open function
 universes u v
 
-class applicative (f : Type u → Type v) extends functor f : Type (max u+1 v):=
-(pure : Π {a : Type u}, a → f a)
-(seq  : Π {a b : Type u}, f (a → b) → f a → f b)
+class applicative (f : Type u → Type v) extends functor f :=
+(pure : Π {α : Type u}, α → f α)
+(seq  : Π {α β : Type u}, f (α → β) → f α → f β)
+(seq_left : Π {α β : Type u}, f α → f β → f α := λ α β a b, seq (map (const β) a) b)
+(seq_right : Π {α β : Type u}, f α → f β → f β := λ α β a b, seq (map (const α id) a) b)
+(map := λ _ _ x y, seq (pure x) y)
 
 section
-variables {a b : Type u} {f : Type u → Type v} [applicative f]
+variables {f : Type u → Type v} [applicative f] {α β : Type u}
 
-@[inline] def pure : a → f a :=
+@[inline] def pure : α → f α :=
 applicative.pure f
 
-@[inline] def seq_app : f (a → b) → f a → f b :=
+@[inline] def seq_app : f (α → β) → f α → f β :=
 applicative.seq
 
-infixl ` <*> `:2 := seq_app
-
 /-- Sequence actions, discarding the first value. -/
-def seq_left (x : f a) (y : f b) : f a :=
-pure (λ x y, x) <*> x <*> y
+@[inline] def seq_left : f α → f β → f α :=
+applicative.seq_left
 
 /-- Sequence actions, discarding the second value. -/
-def seq_right (x : f a) (y : f b) : f b :=
-pure (λ x y, y) <*> x <*> y
-
-infixl ` <* `:2 := seq_left
-infixl ` *> `:2 := seq_right
+@[inline] def seq_right : f α → f β → f β :=
+applicative.seq_right
 
+infixl ` <*> `:2 := seq_app
+infixl ` <* `:2  := seq_left
+infixl ` *> `:2  := seq_right
 end
diff --git a/library/init/category/functor.lean b/library/init/category/functor.lean
index 292c2e1f22..7e4d925e73 100644
--- a/library/init/category/functor.lean
+++ b/library/init/category/functor.lean
@@ -1,16 +1,23 @@
 /-
 Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Luke Nelson and Jared Roesch
+Authors: Luke Nelson, Jared Roesch, Sebastian Ullrich
 -/
 prelude
-import init.core
+import init.core init.function
+open function
 universes u v
 
 class functor (f : Type u → Type v) : Type (max u+1 v) :=
-(map : Π {a b : Type u}, (a → b) → f a → f b)
+(map : Π {α β : Type u}, (α → β) → f α → f β)
+(map_const : Π {α : Type u} (β : Type u), α → f β → f α := λ α β, map ∘ const β)
 
-@[inline] def fmap {f : Type u → Type v} [functor f] {a b : Type u} : (a → b) → f a → f b :=
+@[inline] def fmap {f : Type u → Type v} [functor f] {α β : Type u} : (α → β) → f α → f β :=
 functor.map
 
+@[inline] def fmap_const {f : Type u → Type v} [functor f] {α : Type u} : Π (β : Type u), α → f β → f α :=
+functor.map_const
+
 infixr ` <$> `:100 := fmap
+infixr ` <$ `:100 := fmap_const
+infixr ` $> `:100 := λ α a b, fmap_const α b a
diff --git a/library/init/category/monad.lean b/library/init/category/monad.lean
index 462a1d1e86..7de9980012 100644
--- a/library/init/category/monad.lean
+++ b/library/init/category/monad.lean
@@ -1,38 +1,32 @@
 /-
 Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Luke Nelson and Jared Roesch
+Authors: Leonardo de Moura, Luke Nelson, Jared Roesch, Sebastian Ullrich
 -/
 prelude
 import init.category.applicative
 universes u v
 
 class pre_monad (m : Type u → Type v) :=
-(bind : Π {a b : Type u}, m a → (a → m b) → m b)
+(bind : Π {α β : Type u}, m α → (α → m β) → m β)
 
-@[inline] def bind {m : Type u → Type v} [pre_monad m] {a b : Type u} : m a → (a → m b) → m b :=
+@[inline] def bind {m : Type u → Type v} [pre_monad m] {α β : Type u} : m α → (α → m β) → m β :=
 pre_monad.bind
 
-@[inline] def pre_monad.and_then {a b : Type u} {m : Type u → Type v} [pre_monad m] (x : m a) (y : m b) : m b :=
+@[inline] def pre_monad.and_then {α β : Type u} {m : Type u → Type v} [pre_monad m] (x : m α) (y : m β) : m β :=
 do x, y
 
-class monad (m : Type u → Type v) extends functor m, pre_monad m : Type (max u+1 v) :=
-(ret  : Π {a : Type u}, a → m a)
-
-@[inline] def return {m : Type u → Type v} [monad m] {a : Type u} : a → m a :=
-monad.ret m
-
-def fapp {m : Type u → Type v} [monad m] {a b : Type u} (f : m (a → b)) (a : m a) : m b :=
-do g ← f,
-   b ← a,
-   return (g b)
-
-@[inline] instance monad_is_applicative (m : Type u → Type v) [monad m] : applicative m :=
-⟨@fmap _ _, @return _ _, @fapp _ _⟩
-
 infixl ` >>= `:2 := bind
 infixl ` >> `:2  := pre_monad.and_then
 
+class monad (m : Type u → Type v) extends applicative m, pre_monad m : Type (max u+1 v) :=
+(seq := λ α β f x, bind f $ λ f, bind x $ λ x, pure (f x))
+-- implied by `seq`, but a bit simpler
+(map := λ α β f x, bind x $ λ x, pure (f x))
+
+def return {m : Type u → Type v} [monad m] {α : Type u} : α → m α :=
+pure
+
 /- Identical to pre_monad.and_then, but it is not inlined. -/
-def pre_monad.seq {a b : Type u} {m : Type u → Type v} [pre_monad m] (x : m a) (y : m b) : m b :=
+def pre_monad.seq {α β : Type u} {m : Type u → Type v} [pre_monad m] (x : m α) (y : m β) : m β :=
 do x, y
diff --git a/library/init/category/state.lean b/library/init/category/state.lean
index a5edf84a37..42cb19c533 100644
--- a/library/init/category/state.lean
+++ b/library/init/category/state.lean
@@ -12,9 +12,6 @@ def state (σ : Type) (α : Type) : Type :=
 section
 variables {σ : Type} {α β : Type}
 
-@[inline] def state_fmap (f : α → β) (a : state σ α) : state σ β :=
-λ s, match (a s) with (a', s') := (f a', s') end
-
 @[inline] def state_return (a : α) : state σ α :=
 λ s, (a, s)
 
@@ -22,9 +19,7 @@ variables {σ : Type} {α β : Type}
 λ s, match (a s) with (a', s') := b a' s' end
 
 instance (σ : Type) : monad (state σ) :=
-{ map := @state_fmap σ,
-  ret  := @state_return σ,
-  bind := @state_bind σ }
+{pure := @state_return σ, bind := @state_bind σ}
 end
 
 namespace state
@@ -44,11 +39,6 @@ section
   variable  [monad m]
   variables {α β : Type}
 
-  def state_t_fmap (f : α → β) (act : state_t σ m α) : state_t σ m β :=
-  λ s, show m (β × σ), from
-    do (a, new_s) ← act s,
-       return (f a, new_s)
-
   def state_t_return (a : α) : state_t σ m α :=
   λ s, show m (α × σ), from
     return (a, s)
@@ -60,9 +50,7 @@ section
 end
 
 instance (σ : Type) (m : Type → Type) [monad m] : monad (state_t σ m) :=
-{ map  := @state_t_fmap σ m _,
-  ret  := @state_t_return σ m _,
-  bind := @state_t_bind σ m _}
+{pure := @state_t_return σ m _, bind := @state_t_bind σ m _}
 
 section
   variable  {σ : Type}
@@ -79,9 +67,7 @@ section
 end
 
 instance (σ : Type) (m : Type → Type) [alternative m] [monad m] : alternative (state_t σ m) :=
-{ map     := @state_t_fmap σ m _,
-  pure    := @state_t_return σ m _,
-  seq     := @fapp _ _,
+{ state_t.monad σ m with
   failure := @state_t_failure σ m _ _,
   orelse  := @state_t_orelse σ m _ _ }
 
diff --git a/library/init/data/list/basic.lean b/library/init/data/list/basic.lean
index ae31e28fde..bc71f65781 100644
--- a/library/init/data/list/basic.lean
+++ b/library/init/data/list/basic.lean
@@ -229,4 +229,4 @@ join (map b a)
 end list
 
 instance : monad list :=
-{map := @list.map, ret := @list.ret, bind := @list.bind}
+{map := @list.map, pure := @list.ret, bind := @list.bind}
diff --git a/library/init/data/list/instances.lean b/library/init/data/list/instances.lean
index 769fb46368..1ae4565e3e 100644
--- a/library/init/data/list/instances.lean
+++ b/library/init/data/list/instances.lean
@@ -11,7 +11,9 @@ open list
 universes u v
 
 instance : alternative list :=
-⟨@map, @list.ret, @fapp _ _, @nil, @list.append⟩
+{ list.monad with
+  failure := @nil,
+  orelse  := @list.append }
 
 instance {α : Type u} [decidable_eq α] : decidable_eq (list α) :=
 by tactic.mk_dec_eq_instance
diff --git a/library/init/data/option/basic.lean b/library/init/data/option/basic.lean
index d041fa268f..aa98a6cb1e 100644
--- a/library/init/data/option/basic.lean
+++ b/library/init/data/option/basic.lean
@@ -53,16 +53,12 @@ instance {α : Type u} [d : decidable_eq α] : decidable_eq (option α)
   | (is_false n) := is_false (λ h, option.no_confusion h (λ e, absurd e n))
   end
 
-@[inline] def option_fmap {α : Type u} {β : Type v} (f : α → β) : option α → option β
-| none     := none
-| (some a) := some (f a)
-
 @[inline] def option_bind {α : Type u} {β : Type v} : option α → (α → option β) → option β
 | none     b := none
 | (some a) b := b a
 
 instance : monad option :=
-{map := @option_fmap, ret := @some, bind := @option_bind}
+{pure := @some, bind := @option_bind}
 
 def option_orelse {α : Type u} : option α → option α → option α
 | (some a) o         := some a
@@ -70,19 +66,13 @@ def option_orelse {α : Type u} : option α → option α → option α
 | none     none      := none
 
 instance : alternative option :=
-alternative.mk @option_fmap @some (@fapp _ _) @none @option_orelse
+{ option.monad with
+  failure := @none,
+  orelse  := @option_orelse }
 
 def option_t (m : Type u → Type v) [monad m] (α : Type u) : Type v :=
 m (option α)
 
-@[inline] def option_t_fmap {m : Type u → Type v} [monad m] {α β : Type u} (f : α → β) (e : option_t m α) : option_t m β :=
-show m (option β), from
-do o ← e,
-   match o with
-   | none     := return none
-   | (some a) := return (some (f a))
-   end
-
 @[inline] def option_t_bind {m : Type u → Type v} [monad m] {α β : Type u} (a : option_t m α) (b : α → option_t m β)
                                : option_t m β :=
 show m (option β), from
@@ -97,7 +87,7 @@ show m (option α), from
 return (some a)
 
 instance {m : Type u → Type v} [monad m] : monad (option_t m) :=
-{map := @option_t_fmap m _, ret := @option_t_return m _, bind := @option_t_bind m _}
+{pure := @option_t_return m _, bind := @option_t_bind m _}
 
 def option_t_orelse {m : Type u → Type v} [monad m] {α : Type u} (a : option_t m α) (b : option_t m α) : option_t m α :=
 show m (option α), from
@@ -112,11 +102,9 @@ show m (option α), from
 return none
 
 instance {m : Type u → Type v} [monad m] : alternative (option_t m) :=
-{map     := @option_t_fmap m _,
- pure    := @option_t_return m _,
- seq     := @fapp (option_t m) (@option_t.monad m _),
- failure := @option_t_fail m _,
- orelse  := @option_t_orelse m _}
+{ option_t.monad with
+  failure := @option_t_fail m _,
+  orelse  := @option_t_orelse m _ }
 
 def option_t.lift {m : Type u → Type v} [monad m] {α : Type u} (a : m α) : option_t m α :=
 (some <$> a : m (option α))
diff --git a/library/init/data/set.lean b/library/init/data/set.lean
index ad968cdd77..f4fd527986 100644
--- a/library/init/data/set.lean
+++ b/library/init/data/set.lean
@@ -74,6 +74,6 @@ def image (f : α → β) (s : set α) : set β :=
 {b | ∃ a, a ∈ s ∧ f a = b}
 
 instance : functor set :=
-⟨@set.image⟩
+{map := @set.image}
 
 end set
diff --git a/library/init/meta/converter.lean b/library/init/meta/converter.lean
index 79cfd15b6e..7b15d87617 100644
--- a/library/init/meta/converter.lean
+++ b/library/init/meta/converter.lean
@@ -69,13 +69,11 @@ protected meta def bind {α β : Type} (c₁ : conv α) (c₂ : α → conv β)
 
 meta instance : monad conv :=
 { map  := @conv.map,
-  ret  := @conv.pure,
+  pure := @conv.pure,
   bind := @conv.bind }
 
 meta instance : alternative conv :=
-{ map     := @conv.map,
-  pure    := @conv.pure,
-  seq     := @conv.seq,
+{ conv.monad with
   failure := @conv.fail,
   orelse  := @conv.orelse }
 
diff --git a/library/init/meta/exceptional.lean b/library/init/meta/exceptional.lean
index 70364d4c02..f3db6d8085 100644
--- a/library/init/meta/exceptional.lean
+++ b/library/init/meta/exceptional.lean
@@ -37,11 +37,6 @@ protected meta def to_option : exceptional α → option α
 | (success a)      := some a
 | (exception .α _) := none
 
-@[inline] protected meta def fmap (f : α → β) (e : exceptional α) : exceptional β :=
-exceptional.cases_on e
-  (λ a, success (f a))
-  (λ f, exception β f)
-
 @[inline] protected meta def bind (e₁ : exceptional α) (e₂ : α → exceptional β) : exceptional β :=
 exceptional.cases_on e₁
   (λ a, e₂ a)
@@ -55,4 +50,4 @@ exception α (λ u, f)
 end exceptional
 
 meta instance : monad exceptional :=
-{map := @exceptional.fmap, ret := @exceptional.return, bind := @exceptional.bind}
+{pure := @exceptional.return, bind := @exceptional.bind}
diff --git a/library/init/meta/interaction_monad.lean b/library/init/meta/interaction_monad.lean
index e2f53e8e39..06c3c2e137 100644
--- a/library/init/meta/interaction_monad.lean
+++ b/library/init/meta/interaction_monad.lean
@@ -63,7 +63,7 @@ meta def interaction_monad_orelse {α : Type u} (t₁ t₂ : m α) : m α :=
 interaction_monad_bind t₁ (λ a, t₂)
 
 meta instance interaction_monad.monad : monad m :=
-{map := @interaction_monad_fmap, ret := @interaction_monad_return, bind := @interaction_monad_bind}
+{map := @interaction_monad_fmap, pure := @interaction_monad_return, bind := @interaction_monad_bind}
 
 meta def interaction_monad.mk_exception {α : Type u} {β : Type v} [has_to_format β] (msg : β) (ref : option expr) (s : state) : result state α :=
 exception (some (λ _, to_fmt msg)) none s
diff --git a/library/init/meta/lean/parser.lean b/library/init/meta/lean/parser.lean
index b0640d47f8..47e25699cb 100644
--- a/library/init/meta/lean/parser.lean
+++ b/library/init/meta/lean/parser.lean
@@ -47,7 +47,9 @@ result.cases_on (p₁ s)
      exception)
 
 meta instance : alternative parser :=
-⟨@interaction_monad_fmap parser_state, (λ α a s, success a s), (@fapp _ _), @interaction_monad.failed parser_state, @parser_orelse⟩
+{ interaction_monad.monad with
+  failure := @interaction_monad.failed _,
+  orelse  := @parser_orelse }
 
 
 -- TODO: move
diff --git a/library/init/meta/smt/smt_tactic.lean b/library/init/meta/smt/smt_tactic.lean
index 4eaa29d78b..0b9aacdaa6 100644
--- a/library/init/meta/smt/smt_tactic.lean
+++ b/library/init/meta/smt/smt_tactic.lean
@@ -82,11 +82,9 @@ meta instance : monad_fail smt_tactic :=
 { smt_tactic.monad with fail := λ α s, (tactic.fail (to_fmt s) : smt_tactic α) }
 
 meta instance : alternative smt_tactic :=
-{failure := λ α, @tactic.failed α,
- orelse  := @smt_tactic_orelse,
- pure    := @return _ _,
- seq     := @fapp _ _,
- map     := @fmap _ _}
+{ smt_tactic.monad with
+  failure := λ α, @tactic.failed α,
+  orelse  := @smt_tactic_orelse }
 
 namespace smt_tactic
 open tactic (transparency)
diff --git a/library/init/meta/tactic.lean b/library/init/meta/tactic.lean
index b20ad83e2d..f051dd3066 100644
--- a/library/init/meta/tactic.lean
+++ b/library/init/meta/tactic.lean
@@ -51,7 +51,9 @@ infixl ` >>=[tactic] `:2 := interaction_monad_bind
 infixl ` >>[tactic] `:2  := interaction_monad_seq
 
 meta instance : alternative tactic :=
-⟨@interaction_monad_fmap tactic_state, (λ α a s, success a s), (@fapp _ _), @interaction_monad.failed tactic_state, @interaction_monad_orelse tactic_state⟩
+{ interaction_monad.monad with
+  failure := @interaction_monad.failed _,
+  orelse  := @interaction_monad_orelse _ }
 
 meta def {u₁ u₂} tactic.up {α : Type u₂} (t : tactic α) : tactic (ulift.{u₁} α) :=
 λ s, match t s with
diff --git a/library/init/meta/task.lean b/library/init/meta/task.lean
index 8d34056a19..43c9331dd9 100644
--- a/library/init/meta/task.lean
+++ b/library/init/meta/task.lean
@@ -14,7 +14,7 @@ protected meta def {u v} bind {α : Type u} {β : Type v} (t : task α) (f : α
 task.flatten (task.map f t)
 
 meta instance : monad task :=
-{ map := @task.map, bind := @task.bind, ret := @task.pure }
+{ map := @task.map, bind := @task.bind, pure := @task.pure }
 
 @[inline]
 meta def {u} delay {α : Type u} (f : unit → α) : task α :=
diff --git a/library/init/meta/vm.lean b/library/init/meta/vm.lean
index 32041bf555..cb1b02f085 100644
--- a/library/init/meta/vm.lean
+++ b/library/init/meta/vm.lean
@@ -77,7 +77,7 @@ meta constant vm_core.ret {α : Type} : α → vm_core α
 meta constant vm_core.bind {α β : Type} : vm_core α → (α → vm_core β) → vm_core β
 
 meta instance : monad vm_core :=
-{map := @vm_core.map, ret := @vm_core.ret, bind := @vm_core.bind}
+{map := @vm_core.map, pure := @vm_core.ret, bind := @vm_core.bind}
 
 @[reducible] meta def vm (α : Type) : Type := option_t vm_core α
 
diff --git a/library/init/native/result.lean b/library/init/native/result.lean
index aa79273e64..bc867ac8e3 100644
--- a/library/init/native/result.lean
+++ b/library/init/native/result.lean
@@ -5,11 +5,7 @@ Authors: Jared Roesch
 -/
 prelude
 
-import init.category.applicative
-import init.category.functor
 import init.category.monad
-import init.logic
-import init.function
 
 namespace native
 
@@ -21,24 +17,12 @@ def unwrap_or {E T : Type} : result E T → T → T
 | (result.err _) default := default
 | (result.ok t) _ := t
 
-def result.map : Π {E : Type} {T : Type} {U : Type}, (T → U) → result E T → result E U
-| E T U f (result.err e) := result.err e
-| E T U f (result.ok t) := result.ok (f t)
-
 def result.and_then {E T U : Type} : result E T → (T → result E U) → result E U
 | (result.err e) _ := result.err e
 | (result.ok t) f := f t
 
-instance result_functor (E : Type) : functor (result E) := functor.mk (@result.map E)
-
-def result.seq {E T U : Type} : result E (T → U) → result E T → result E U
-| f t := result.and_then f (fun f', result.and_then t (fun t', result.ok (f' t')))
-
-instance result_applicative (E : Type) : applicative (result E) :=
-  applicative.mk (@result.map E) (@result.ok E) (@result.seq E)
-
 instance result_monad (E : Type) : monad (result E) :=
-{map := @result.map E, ret := @result.ok E, bind := @result.and_then E}
+{pure := @result.ok E, bind := @result.and_then E}
 
 inductive resultT (M : Type → Type) (E : Type) (A : Type) : Type
 | run : M (result E A) → resultT
@@ -46,9 +30,6 @@ inductive resultT (M : Type → Type) (E : Type) (A : Type) : Type
 section resultT
   variable {M : Type → Type}
 
-  def resultT.map [functor : functor M] {E : Type} {A B : Type} : (A → B) → resultT M E A → resultT M E B
-  | f (resultT.run action) := resultT.run (@functor.map M functor _ _ (result.map f) action)
-
   def resultT.pure [monad : monad M] {E A : Type} (x : A) : resultT M E A :=
     resultT.run $ return (result.ok x)
 
@@ -56,17 +37,13 @@ section resultT
   | (resultT.run action) f := resultT.run (do
   res_a ← action,
   -- a little ugly with this match
-  (match res_a with
-  | native.result.err e := return (native.result.err e)
-  | native.result.ok a := let (resultT.run actionB) := f a in actionB
-  end : M (result E B)))
+  match res_a with
+  | result.err e := return (result.err e)
+  | result.ok a := let (resultT.run actionB) := f a in actionB
+  end)
 
-  instance resultT_functor [f : functor M] (E : Type) : functor (resultT M E) :=
-    functor.mk (@resultT.map M f E)
-
-  -- Should we unify functor and monad like haskell?
-  instance resultT_monad [f : functor M] [m : monad M] (E : Type) : monad (resultT M E) :=
-  {map := @resultT.map M f E, ret := @resultT.pure M m E, bind := @resultT.and_then M m E}
+  instance resultT_monad [m : monad M] (E : Type) : monad (resultT M E) :=
+  {pure := @resultT.pure M m E, bind := @resultT.and_then M m E}
 end resultT
 
 end native
diff --git a/library/system/io.lean b/library/system/io.lean
index 230ff7759b..6d5f67226c 100644
--- a/library/system/io.lean
+++ b/library/system/io.lean
@@ -12,7 +12,7 @@ constant io.put_str          : string → io unit
 constant io.get_line         : io string
 
 instance : monad io :=
-{ ret  := @io.return,
+{ pure := @io.return,
   bind := @io.bind,
   map  := @io.map }
 
diff --git a/library/tools/super/prover_state.lean b/library/tools/super/prover_state.lean
index 4febeb776f..c67894510e 100644
--- a/library/tools/super/prover_state.lean
+++ b/library/tools/super/prover_state.lean
@@ -154,7 +154,7 @@ meta def orelse (A : Type) (p1 p2 : prover A) : prover A :=
 take state, p1 state <|> p2 state
 
 meta instance : alternative prover :=
-{ monad_is_applicative prover with
+{ prover.monad with
   failure := λα, fail "failed",
   orelse := orelse }
 
diff --git a/src/library/compiler/erase_irrelevant.cpp b/src/library/compiler/erase_irrelevant.cpp
index a97543b8c7..49d8c104f6 100644
--- a/src/library/compiler/erase_irrelevant.cpp
+++ b/src/library/compiler/erase_irrelevant.cpp
@@ -365,12 +365,12 @@ class erase_irrelevant_fn : public compiler_step_visitor {
         }
     }
 
-    expr visit_monad_return(expr const & e, buffer<expr> const & args) {
+    expr visit_applicative_pure(expr const & e, buffer<expr> const & args) {
         if (args.size() == 4 && is_builtin_state_monad(args[1])) {
             /* IO monad return
                return v := fun s, (v, s)
 
-               Remark: we do not return the state explicility.
+               Remark: we do not return the state explicitly.
             */
             expr u = mk_neutral_expr();
             expr s = mk_var(0);
@@ -420,8 +420,8 @@ class erase_irrelevant_fn : public compiler_step_visitor {
                 return visit_subtype_rec(args);
             } else if (n == get_monad_bind_name() || n == get_pre_monad_bind_name()) {
                 return visit_monad_bind(e, args);
-            } else if (n == get_monad_ret_name()) {
-                return visit_monad_return(e, args);
+            } else if (n == get_applicative_pure_name()) {
+                return visit_applicative_pure(e, args);
             } else if (is_cases_on_recursor(env(), n)) {
                 return visit_cases_on(fn, args);
             } else if (inductive::is_elim_rule(env(), n)) {
diff --git a/src/library/constants.cpp b/src/library/constants.cpp
index d918283fc8..f04e501764 100644
--- a/src/library/constants.cpp
+++ b/src/library/constants.cpp
@@ -16,6 +16,7 @@ name const * g_and_elim_left = nullptr;
 name const * g_and_elim_right = nullptr;
 name const * g_and_intro = nullptr;
 name const * g_andthen = nullptr;
+name const * g_applicative_pure = nullptr;
 name const * g_auto_param = nullptr;
 name const * g_bit0 = nullptr;
 name const * g_bit1 = nullptr;
@@ -176,7 +177,6 @@ name const * g_match_failed = nullptr;
 name const * g_mod = nullptr;
 name const * g_monad = nullptr;
 name const * g_monad_bind = nullptr;
-name const * g_monad_ret = nullptr;
 name const * g_monad_fail = nullptr;
 name const * g_monoid = nullptr;
 name const * g_mul = nullptr;
@@ -391,6 +391,7 @@ void initialize_constants() {
     g_and_elim_right = new name{"and", "elim_right"};
     g_and_intro = new name{"and", "intro"};
     g_andthen = new name{"andthen"};
+    g_applicative_pure = new name{"applicative", "pure"};
     g_auto_param = new name{"auto_param"};
     g_bit0 = new name{"bit0"};
     g_bit1 = new name{"bit1"};
@@ -551,7 +552,6 @@ void initialize_constants() {
     g_mod = new name{"mod"};
     g_monad = new name{"monad"};
     g_monad_bind = new name{"monad", "bind"};
-    g_monad_ret = new name{"monad", "ret"};
     g_monad_fail = new name{"monad_fail"};
     g_monoid = new name{"monoid"};
     g_mul = new name{"mul"};
@@ -767,6 +767,7 @@ void finalize_constants() {
     delete g_and_elim_right;
     delete g_and_intro;
     delete g_andthen;
+    delete g_applicative_pure;
     delete g_auto_param;
     delete g_bit0;
     delete g_bit1;
@@ -927,7 +928,6 @@ void finalize_constants() {
     delete g_mod;
     delete g_monad;
     delete g_monad_bind;
-    delete g_monad_ret;
     delete g_monad_fail;
     delete g_monoid;
     delete g_mul;
@@ -1142,6 +1142,7 @@ name const & get_and_elim_left_name() { return *g_and_elim_left; }
 name const & get_and_elim_right_name() { return *g_and_elim_right; }
 name const & get_and_intro_name() { return *g_and_intro; }
 name const & get_andthen_name() { return *g_andthen; }
+name const & get_applicative_pure_name() { return *g_applicative_pure; }
 name const & get_auto_param_name() { return *g_auto_param; }
 name const & get_bit0_name() { return *g_bit0; }
 name const & get_bit1_name() { return *g_bit1; }
@@ -1302,7 +1303,6 @@ name const & get_match_failed_name() { return *g_match_failed; }
 name const & get_mod_name() { return *g_mod; }
 name const & get_monad_name() { return *g_monad; }
 name const & get_monad_bind_name() { return *g_monad_bind; }
-name const & get_monad_ret_name() { return *g_monad_ret; }
 name const & get_monad_fail_name() { return *g_monad_fail; }
 name const & get_monoid_name() { return *g_monoid; }
 name const & get_mul_name() { return *g_mul; }
diff --git a/src/library/constants.h b/src/library/constants.h
index 8a5fea3e28..9686747dc4 100644
--- a/src/library/constants.h
+++ b/src/library/constants.h
@@ -18,6 +18,7 @@ name const & get_and_elim_left_name();
 name const & get_and_elim_right_name();
 name const & get_and_intro_name();
 name const & get_andthen_name();
+name const & get_applicative_pure_name();
 name const & get_auto_param_name();
 name const & get_bit0_name();
 name const & get_bit1_name();
@@ -178,7 +179,6 @@ name const & get_match_failed_name();
 name const & get_mod_name();
 name const & get_monad_name();
 name const & get_monad_bind_name();
-name const & get_monad_ret_name();
 name const & get_monad_fail_name();
 name const & get_monoid_name();
 name const & get_mul_name();
diff --git a/src/library/constants.txt b/src/library/constants.txt
index 886b7ef7a2..ce39a6b84c 100644
--- a/src/library/constants.txt
+++ b/src/library/constants.txt
@@ -11,6 +11,7 @@ and.elim_left
 and.elim_right
 and.intro
 andthen
+applicative.pure
 auto_param
 bit0
 bit1
@@ -171,7 +172,6 @@ match_failed
 mod
 monad
 monad.bind
-monad.ret
 monad_fail
 monoid
 mul
diff --git a/tests/lean/run/check_constants.lean b/tests/lean/run/check_constants.lean
index c93fd59ce9..15397175cb 100644
--- a/tests/lean/run/check_constants.lean
+++ b/tests/lean/run/check_constants.lean
@@ -16,6 +16,7 @@ run_cmd script_check_id `and.elim_left
 run_cmd script_check_id `and.elim_right
 run_cmd script_check_id `and.intro
 run_cmd script_check_id `andthen
+run_cmd script_check_id `applicative.pure
 run_cmd script_check_id `auto_param
 run_cmd script_check_id `bit0
 run_cmd script_check_id `bit1
@@ -176,7 +177,6 @@ run_cmd script_check_id `match_failed
 run_cmd script_check_id `mod
 run_cmd script_check_id `monad
 run_cmd script_check_id `monad.bind
-run_cmd script_check_id `monad.ret
 run_cmd script_check_id `monad_fail
 run_cmd script_check_id `monoid
 run_cmd script_check_id `mul
diff --git a/tests/lean/run/isabelle.lean b/tests/lean/run/isabelle.lean
index 7a6125d692..3d5f25966b 100644
--- a/tests/lean/run/isabelle.lean
+++ b/tests/lean/run/isabelle.lean
@@ -23,9 +23,6 @@ meta instance {α : Type} : has_coe (tactic α) (lazy_tactic α) :=
 protected meta def return {α} (a : α) : lazy_tactic α :=
 λ s, lazy_list.singleton (a, s)
 
-protected meta def map {α β} (f : α → β) : lazy_tactic α → lazy_tactic β
-| t s := (t s)^.for (λ ⟨a, new_s⟩, (f a, new_s))
-
 protected meta def bind {α β} : lazy_tactic α → (α → lazy_tactic β) → lazy_tactic β :=
 λ t₁ t₂ s, join (for (t₁ s) (λ ⟨a, new_s⟩, t₂ a new_s))
 
@@ -36,17 +33,13 @@ protected meta def failure {α} : lazy_tactic α :=
 λ s, nil
 
 meta instance : monad lazy_tactic :=
-{ ret  := @lazy_tactic.return,
-  bind := @lazy_tactic.bind,
-  map  := @lazy_tactic.map }
+{ pure := @lazy_tactic.return,
+  bind := @lazy_tactic.bind }
 
 meta instance : alternative lazy_tactic :=
-{ map     := @lazy_tactic.map,
-  pure    := @lazy_tactic.return,
-  seq     := @fapp _ _,
+{ lazy_tactic.monad with
   failure := @lazy_tactic.failure,
-  orelse  := @lazy_tactic.orelse
-}
+  orelse  := @lazy_tactic.orelse }
 
 meta def choose {α} (xs : list α) : lazy_tactic α :=
 λ s, of_list $ xs^.for (λ a, (a, s))
diff --git a/tests/lean/type_error_at_eval_expr.lean.expected.out b/tests/lean/type_error_at_eval_expr.lean.expected.out
index 1cc3d25a56..5f17e591af 100644
--- a/tests/lean/type_error_at_eval_expr.lean.expected.out
+++ b/tests/lean/type_error_at_eval_expr.lean.expected.out
@@ -1,6 +1,6 @@
 type_error_at_eval_expr.lean:3:0: error: eval_expr failed due to type error
 nested exception message:
-type mismatch at definition '_eval_expr.16.423', has type
+type mismatch at definition '_eval_expr.16.436', has type
   list ℕ
 but is expected to have type
   ℕ