mirror of https://github.com/nmvdw/HITs-Examples
45 lines
975 B
Coq
45 lines
975 B
Coq
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(** The structure of a monad. *)
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Require Import HoTT.
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Section functor.
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Variable (F : Type -> Type).
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Context `{Functorish F}.
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Class Functor :=
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{
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fmap_compose {A B C : Type} (f : A -> B) (g : B -> C) :
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fmap F (g o f) = fmap F g o fmap F f
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}.
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End functor.
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Section monad_operations.
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Variable (F : Type -> Type).
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Class hasPure :=
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{
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pure : forall (A : Type), A -> F A
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}.
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Class hasBind :=
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{
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bind : forall (A : Type), F(F A) -> F A
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}.
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End monad_operations.
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Arguments pure {_} {_} _ _.
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Arguments bind {_} {_} _ _.
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Section monad.
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Variable (F : Type -> Type).
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Context `{Functor F} `{hasPure F} `{hasBind F}.
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Class Monad :=
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{
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bind_assoc : forall {A : Type},
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bind A o bind (F A) = bind A o fmap F (bind A) ;
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bind_neutral_l : forall {A : Type},
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bind A o pure (F A) = idmap ;
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bind_neutral_r : forall {A : Type},
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bind A o fmap F (pure A) = idmap
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}.
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End monad.
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