30 lines
1.2 KiB
Text
30 lines
1.2 KiB
Text
/-
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Copyright (c) Luke Nelson and Jared Roesch. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Luke Nelson, Jared Roesch, Sebastian Ullrich, Leonardo de Moura
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-/
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prelude
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import init.core init.function init.meta.name
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open function
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universes u v
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section
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set_option auto_param.check_exists false
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class has_map (f : Type u → Type v) : Type (max (u+1) v) :=
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(map : Π {α β : Type u}, (α → β) → f α → f β)
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(map_const : Π {α β : Type u}, α → f β → f α := λ α β, map ∘ const β)
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infixr ` <$> `:100 := has_map.map
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infixr ` <$ `:100 := has_map.map_const
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@[reducible] def has_map.map_const_rev {f : Type u → Type v} [has_map f] {α β : Type u} : f β → α → f α :=
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λ a b, b <$ a
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infixr ` $> `:100 := has_map.map_const_rev
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class functor (f : Type u → Type v) extends has_map f : Type (max (u+1) v) :=
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(map_const_eq : ∀ {α β : Type u}, @map_const α β = map ∘ const β . control_laws_tac)
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-- `functor` is indeed a categorical functor
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(id_map : Π {α : Type u} (x : f α), id <$> x = x)
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(map_comp : Π {α β γ : Type u} (g : α → β) (h : β → γ) (x : f α), (h ∘ g) <$> x = h <$> g <$> x)
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end
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