89 lines
2.8 KiB
Text
89 lines
2.8 KiB
Text
/-
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Copyright (c) 2016 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Jeremy Avigad, Leonardo de Moura
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Monad Combinators, as in Haskell's Control.Monad.
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-/
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prelude
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import init.control.monad init.control.alternative init.data.list.basic init.coe
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universes u v w
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def mjoin {m : Type u → Type u} [Monad m] {α : Type u} (a : m (m α)) : m α :=
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bind a id
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@[macroInline]
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def when {m : Type → Type u} [Monad m] (c : Prop) [h : Decidable c] (t : m Unit) : m Unit :=
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if c then t else pure ()
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@[macroInline]
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def unless {m : Type → Type u} [Monad m] (c : Prop) [h : Decidable c] (e : m Unit) : m Unit :=
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if c then pure () else e
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@[macroInline]
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def mcond {m : Type → Type u} [Monad m] {α : Type} (mbool : m Bool) (tm fm : m α) : m α :=
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do b ← mbool, cond b tm fm
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@[macroInline]
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def mwhen {m : Type → Type u} [Monad m] (c : m Bool) (t : m Unit) : m Unit :=
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mcond c t (pure ())
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namespace Nat
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@[specialize]
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def mrepeat {m} [Monad m] (n : Nat) (f : Nat → m Unit) : m Unit :=
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n.repeat (λ i a, a *> f i) (pure ())
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end Nat
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namespace List
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@[specialize]
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def mmap {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m β) : List α → m (List β)
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| [] := pure []
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| (h :: t) := do h' ← f h, t' ← mmap t, pure (h' :: t')
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@[specialize]
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def mmap' {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m β) : List α → m PUnit
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| [] := pure ⟨⟩
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| (h :: t) := f h *> mmap' t
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@[specialize]
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def mfor {m : Type u → Type v} [Monad m] {α : Type w} {β : Type u} (f : α → m β) : List α → m PUnit :=
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List.mmap' f
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@[specialize]
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def mfilter {m : Type → Type v} [Monad m] {α : Type} (f : α → m Bool) : List α → m (List α)
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| [] := pure []
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| (h :: t) := do b ← f h, t' ← mfilter t, cond b (pure (h :: t')) (pure t')
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@[specialize]
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def mfoldl {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} : (s → α → m s) → s → List α → m s
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| f s [] := pure s
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| f s (h :: r) := do
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s' ← f s h,
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mfoldl f s' r
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@[specialize]
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def mfoldr {m : Type u → Type v} [Monad m] {s : Type u} {α : Type w} : (α → s → m s) → s → List α → m s
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| f s [] := pure s
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| f s (h :: r) := do
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s' ← mfoldr f s r,
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f h s'
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@[specialize]
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def mfirst {m : Type u → Type v} [Monad m] [Alternative m] {α : Type w} {β : Type u} (f : α → m β) : List α → m β
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| [] := failure
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| (a::as) := f a <|> mfirst as
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@[specialize]
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def mexists {m : Type → Type u} [Monad m] {α : Type v} (f : α → m Bool) : List α → m Bool
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| [] := pure false
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| (a::as) := do b ← f a, if b then pure true else mexists as
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@[specialize]
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def mforall {m : Type → Type u} [Monad m] {α : Type v} (f : α → m Bool) : List α → m Bool
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| [] := pure true
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| (a::as) := do b ← f a, if b then mforall as else pure false
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end List
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