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chore(library/init/monad_combinators): make combinators universe polymorphic (when possible), and use Lean naming conventions (i.e., no camelCase)

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Leonardo de Moura 2016-11-17 10:57:31 -08:00
parent e5d69fef35
commit 85a532b5af
1 changed files with 23 additions and 20 deletions
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43
library/init/monad_combinators.lean
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@ -7,27 +7,30 @@ Monad combinators, as in Haskell's Control.Monad.
-/
prelude
import init.monad init.list
universe variables u v w
namespace monad
def mapM {m : Type → Type} [monad m] {A B : Type} (f : A → m B) : list A → m (list B)
/- Remark: we use (u+1) to make sure B is not a proposition.
That is, we are making sure that B and (list B) inhabit the same universe -/
def mapm {m : Type (u+1) → Type v} [monad m] {A : Type w} {B : Type (u+1)} (f : A → m B) : list A → m (list B)
| [] := return []
| (h :: t) := do h' ← f h, t' ← mapM t, return (h' :: t')
| (h :: t) := do h' ← f h, t' ← mapm t, return (h' :: t')
def mapM' {m : Type → Type} [monad m] {A B : Type} (f : A → m B) : list A → m unit
def mapm' {m : Type → Type v} [monad m] {A : Type u} {B : Type} (f : A → m B) : list A → m unit
| [] := return ()
| (h :: t) := f h >> mapM' t
| (h :: t) := f h >> mapm' t
def forM {m : Type → Type} [monad m] {A B : Type} (l : list A) (f : A → m B) : m (list B) :=
mapM f l
def for {m : Type (u+1) → Type v} [monad m] {A : Type w} {B : Type (u+1)} (l : list A) (f : A → m B) : m (list B) :=
mapm f l
def forM' {m : Type → Type} [monad m] {A B : Type} (l : list A) (f : A → m B) : m unit :=
mapM' f l
def for' {m : Type → Type v} [monad m] {A : Type u} {B : Type} (l : list A) (f : A → m B) : m unit :=
mapm' f l
def sequence {m : Type → Type} [monad m] {A : Type} : list (m A) → m (list A)
def sequence {m : Type (u+1) → Type v} [monad m] {A : Type (u+1)} : list (m A) → m (list A)
| [] := return []
| (h :: t) := do h' ← h, t' ← sequence t, return (h' :: t')
def sequence' {m : Type → Type} [monad m] {A : Type} : list (m A) → m unit
def sequence' {m : Type → Type u} [monad m] {A : Type} : list (m A) → m unit
| [] := return ()
| (h :: t) := h >> sequence' t
@ -37,12 +40,12 @@ infix ` >=> `:2 := λ s t a, s a >>= t
infix ` <=< `:2 := λ t s a, s a >>= t
def join {m : Type → Type} [monad m] {A : Type} (a : m (m A)) : m A :=
def join {m : Type u → Type u} [monad m] {A : Type u} (a : m (m A)) : m A :=
bind a id
def filterM {m : Type → Type} [monad m] {A : Type} (f : A → m bool) : list A → m (list A)
def filter {m : Type → Type v} [monad m] {A : Type} (f : A → m bool) : list A → m (list A)
| [] := return []
| (h :: t) := do b ← f h, t' ← filterM t, cond b (return (h :: t')) (return t')
| (h :: t) := do b ← f h, t' ← filter t, cond b (return (h :: t')) (return t')
def whenb {m : Type → Type} [monad m] (b : bool) (t : m unit) : m unit :=
cond b t (return ())
@ -50,25 +53,25 @@ cond b t (return ())
def unlessb {m : Type → Type} [monad m] (b : bool) (t : m unit) : m unit :=
cond b (return ()) t
def condM {m : Type → Type} [monad m] {A : Type} (mbool : m bool)
def cond {m : Type → Type} [monad m] {A : Type} (mbool : m bool)
(tm fm : m A) : m A :=
do b ← mbool, cond b tm fm
def liftM {m : Type → Type} [monad m] {A R : Type} (f : A → R) (ma : m A) : m R :=
def lift {m : Type u → Type v} [monad m] {A R : Type u} (f : A → R) (ma : m A) : m R :=
do a ← ma, return (f a)
def liftM₂ {m : Type → Type} [monad m] {A R : Type} (f : A → A → R) (ma₁ ma₂: m A) : m R :=
def lift₂ {m : Type u → Type v} [monad m] {A R : Type u} (f : A → A → R) (ma₁ ma₂: m A) : m R :=
do a₁ ← ma₁, a₂ ← ma₂, return (f a₁ a₂)
def liftM₃ {m : Type → Type} [monad m] {A R : Type} (f : A → A → A → R)
def lift₃ {m : Type u → Type v} [monad m] {A R : Type u} (f : A → A → A → R)
(ma₁ ma₂ ma₃ : m A) : m R :=
do a₁ ← ma₁, a₂ ← ma₂, a₃ ← ma₃, return (f a₁ a₂ a₃)
def liftM₄ {m : Type → Type} [monad m] {A R : Type} (f : A → A → A → A → R)
def lift₄ {m : Type u → Type v} [monad m] {A R : Type u} (f : A → A → A → A → R)
(ma₁ ma₂ ma₃ ma₄ : m A) : m R :=
do a₁ ← ma₁, a₂ ← ma₂, a₃ ← ma₃, a₄ ← ma₄, return (f a₁ a₂ a₃ a₄)
def liftM₅ {m : Type → Type} [monad m] {A R : Type} (f : A → A → A → A → A → R)
def lift₅ {m : Type u → Type v} [monad m] {A R : Type u} (f : A → A → A → A → A → R)
(ma₁ ma₂ ma₃ ma₄ ma₅ : m A) : m R :=
do a₁ ← ma₁, a₂ ← ma₂, a₃ ← ma₃, a₄ ← ma₄, a₅ ← ma₅, return (f a₁ a₂ a₃ a₄ a₅)