fd2c42a8bf
sed -Ei 's/^(\s*)((private |protected )?(noncomputable )?(abbreviation|definition|meta_definition|theorem|lemma|proposition|corollary)\s+\S+\s*)((\s*\[(\S+(\s+[0-9]+)*|priority.*)\])+)\s*/\1attribute \6\n\1\2/' library/**/*.lean tests/**/*.lean sed -Ei 's/\s+$//' library/**/*.lean # remove trailing whitespace
84 lines
2.9 KiB
Text
84 lines
2.9 KiB
Text
/-
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Copyright (c) 2014 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.logic init.monad init.alternative
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open decidable
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attribute [instance]
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definition option_is_inhabited (A : Type) : inhabited (option A) :=
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inhabited.mk none
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attribute [instance]
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definition option_has_decidable_eq {A : Type} [H : decidable_eq A] : ∀ o₁ o₂ : option A, decidable (o₁ = o₂)
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| none none := tt rfl
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| none (some v₂) := ff (λ H, option.no_confusion H)
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| (some v₁) none := ff (λ H, option.no_confusion H)
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| (some v₁) (some v₂) :=
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match (H v₁ v₂) with
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| (tt e) := tt (congr_arg (@some A) e)
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| (ff n) := ff (λ H, option.no_confusion H (λ e, absurd e n))
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end
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attribute [inline]
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definition option_fmap {A B : Type} (f : A → B) (e : option A) : option B :=
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option.cases_on e
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none
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(λ a, some (f a))
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attribute [inline]
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definition option_bind {A B : Type} (a : option A) (b : A → option B) : option B :=
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option.cases_on a
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none
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(λ a, b a)
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attribute [instance]
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definition option_is_monad : monad option :=
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monad.mk @option_fmap @some @option_bind
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definition option_orelse {A : Type} : option A → option A → option A
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| (some a) _ := some a
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| none (some a) := some a
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| none none := none
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attribute [instance]
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definition option_is_alternative {A : Type} : alternative option :=
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alternative.mk @option_fmap @some (@fapp _ _) @none @option_orelse
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definition optionT (m : Type → Type) [monad m] (A : Type) :=
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m (option A)
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attribute [inline]
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definition optionT_fmap {m : Type → Type} [monad m] {A B : Type} (f : A → B) (e : optionT m A) : optionT m B :=
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@monad.bind m _ _ _ e (λ a : option A, option.cases_on a (return none) (λ a, return (some (f a))))
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attribute [inline]
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definition optionT_bind {m : Type → Type} [monad m] {A B : Type} (a : optionT m A) (b : A → optionT m B)
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: optionT m B :=
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@monad.bind m _ _ _ a (λ a : option A, option.cases_on a (return none) (λ a, b a))
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attribute [inline]
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definition optionT_return {m : Type → Type} [monad m] {A : Type} (a : A) : optionT m A :=
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@monad.ret m _ _ (some a)
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attribute [instance]
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definition optionT_is_monad {m : Type → Type} [monad m] {A : Type} : monad (optionT m) :=
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monad.mk (@optionT_fmap m _) (@optionT_return m _) (@optionT_bind m _)
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definition optionT_orelse {m : Type → Type} [monad m] {A : Type} (a : optionT m A) (b : optionT m A) : optionT m A :=
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@monad.bind m _ _ _ a (λ a : option A, option.cases_on a b (λ a, return (some a)))
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definition optionT_fail {m : Type → Type} [monad m] {A : Type} : optionT m A :=
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@monad.ret m _ _ none
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attribute [instance]
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definition optionT_is_alternative {m : Type → Type} [monad m] {A : Type} : alternative (optionT m) :=
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alternative.mk
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(@optionT_fmap m _)
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(@optionT_return m _)
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(@fapp (optionT m) (@optionT_is_monad m _ A))
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(@optionT_fail m _)
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(@optionT_orelse m _)
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