b6399e18c3
This PR adds support for decidable equality of empty lists and empty arrays. Decidable equality for lists and arrays is suitably modified so that all diamonds are definitionally equal. Following #9302, the strong condition of definitionally equal under `with_reducible_and_instances` is tested. This also moves some of the comments added in #9302 out of docstrings. --------- Co-authored-by: Aaron Liu <aaronliu2008@outlook.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
45 lines
1.5 KiB
Text
45 lines
1.5 KiB
Text
def listL (a : List α) := if a = [] then 1 else 2
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def listR (a : List α) := if [] = a then 1 else 2
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/-- info: 1 -/
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#guard_msgs in #eval @listL Nat []
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/-- info: 2 -/
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#guard_msgs in #eval listL [""]
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/-- info: 1 -/
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#guard_msgs in #eval @listL Nat []
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/-- info: 2 -/
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#guard_msgs in #eval listL [()]
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-- test instance diamonds
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example :
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@List.instDecidableEqNil α [] = @List.instDecidableNilEq α [] := by
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with_reducible_and_instances rfl
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section
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variable {α : Type u} [DecidableEq α]
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example (x : List α) :
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instDecidableEqList x [] = List.instDecidableEqNil x := by
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with_reducible_and_instances rfl
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example (x : List α) :
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instDecidableEqList [] x = List.instDecidableNilEq x := by
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with_reducible_and_instances rfl
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end
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-- List decidable equality using `withPtrEqDecEq`
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def listDecEqAux {α} [s : DecidableEq α] : ∀ (as bs : List α), Decidable (as = bs)
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| [], [] => isTrue rfl
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| [], b::bs => isFalse $ fun h => List.noConfusion h
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| a::as, [] => isFalse $ fun h => List.noConfusion h
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| a::as, b::bs =>
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match s a b with
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| isTrue h₁ =>
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match withPtrEqDecEq as bs (fun _ => listDecEqAux as bs) with
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| isTrue h₂ => isTrue $ h₁ ▸ h₂ ▸ rfl
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| isFalse h₂ => isFalse $ fun h => List.noConfusion h $ fun _ h₃ => absurd h₃ h₂
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| isFalse h₁ => isFalse $ fun h => List.noConfusion h $ fun h₂ _ => absurd h₂ h₁
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instance List.optimizedDecEq {α} [DecidableEq α] : DecidableEq (List α) :=
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fun a b => withPtrEqDecEq a b (fun _ => listDecEqAux a b)
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