f5253fd060
This enables use of projection notation. Note that the notations are not always available here since they require one universe instead of two.
48 lines
1.7 KiB
Text
48 lines
1.7 KiB
Text
/-
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Copyright (c) 2017 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
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-/
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prelude
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import init.data.option.basic
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import init.meta.tactic
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universes u v
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@[inline] def option.bind {α : Type u} {β : Type v} : option α → (α → option β) → option β
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| none b := none
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| (some a) b := b a
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def option.map {α β} (f : α → β) (o : option α) : option β :=
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option.bind o (some ∘ f)
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@[simp] theorem option.map_id {α} : (option.map id : option α → option α) = id :=
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funext (λo, match o with | none := rfl | some x := rfl end)
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instance : monad option :=
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{pure := @some, bind := @option.bind, map := @option.map,
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id_map := λ α x, option.rec rfl (λ x, rfl) x,
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pure_bind := λ α β x f, rfl,
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bind_assoc := λ α β γ x f g, option.rec rfl (λ x, rfl) x}
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def option.orelse {α : Type u} : option α → option α → option α
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| (some a) o := some a
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| none (some a) := some a
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| none none := none
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instance : alternative option :=
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{ option.monad with
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failure := @none,
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orelse := @option.orelse }
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lemma option.eq_of_eq_some {α : Type u} : Π {x y : option α}, (∀z, x = some z ↔ y = some z) → x = y
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| none none h := rfl
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| none (some z) h := option.no_confusion ((h z).2 rfl)
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| (some z) none h := option.no_confusion ((h z).1 rfl)
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| (some z) (some w) h := option.no_confusion ((h w).2 rfl) (congr_arg some)
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lemma option.eq_some_of_is_some {α : Type u} : Π {o : option α} (h : option.is_some o), o = some (option.get h)
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| (some x) h := rfl
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lemma option.eq_none_of_is_none {α : Type u} : Π {o : option α}, o.is_none → o = none
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| none h := rfl
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