34 lines
1.1 KiB
Text
34 lines
1.1 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: Leonardo de Moura, Sebastian Ullrich
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-/
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prelude
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import init.control.functor
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open Function
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universes u v
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class HasPure (f : Type u → Type v) :=
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(pure {} {α : Type u} : α → f α)
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export HasPure (pure)
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class HasSeq (f : Type u → Type v) : Type (max (u+1) v) :=
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(Seq : Π {α β : Type u}, f (α → β) → f α → f β)
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infixl ` <*> `:60 := HasSeq.Seq
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class HasSeqLeft (f : Type u → Type v) : Type (max (u+1) v) :=
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(seqLeft : Π {α β : Type u}, f α → f β → f α)
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infixl ` <* `:60 := HasSeqLeft.seqLeft
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class HasSeqRight (f : Type u → Type v) : Type (max (u+1) v) :=
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(seqRight : Π {α β : Type u}, f α → f β → f β)
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infixl ` *> `:60 := HasSeqRight.seqRight
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class Applicative (f : Type u → Type v) extends Functor f, HasPure f, HasSeq f, HasSeqLeft f, HasSeqRight f :=
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(map := λ _ _ x y, pure x <*> y)
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(seqLeft := λ α β a b, const β <$> a <*> b)
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(seqRight := λ α β a b, const α id <$> a <*> b)
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