738435b90a
Previously, it was not possible to use `decide` with most Array functions (including `==`). Later, we may replace some of these functions with defeqs that go via the `List` operations, and use `csimp` lemmas for fast runtime behaviour. In the meantime, this allows using `decide`.
45 lines
1.4 KiB
Text
45 lines
1.4 KiB
Text
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/-!
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Because `Array.isEqvAux` was defined by well-founded recursion, this used to fail with
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```
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tactic 'decide' failed for proposition
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#[0, 1] = #[0, 1]
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since its 'Decidable' instance
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#[0, 1].instDecidableEq #[0, 1]
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did not reduce to 'isTrue' or 'isFalse'.
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After unfolding the instances 'instDecidableEqNat', 'Array.instDecidableEq' and 'Nat.decEq', reduction got stuck at the 'Decidable' instance
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match h : #[0, 1].isEqv #[0, 1] fun a b => decide (a = b) with
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| true => isTrue ⋯
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| false => isFalse ⋯
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```
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-/
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example : #[0, 1] = #[0, 1] := by decide
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/-!
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There are other `Array` functions that use well-founded recursion,
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which we've marked as `@[semireducible]`. We test that `decide` can unfold them here.
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-/
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example : Array.ofFn (id : Fin 2 → Fin 2) = #[0, 1] := by decide
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example : #[0, 1].map (· + 1) = #[1, 2] := by decide
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example : #[0, 1].any (· % 2 = 0) := by decide
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example : #[0, 1].findIdx? (· % 2 = 0) = some 0 := by decide
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example : #[0, 1, 2].popWhile (· % 2 = 0) = #[0, 1] := by decide
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example : #[0, 1, 2].takeWhile (· % 2 = 0) = #[0] := by decide
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example : #[0, 1, 2].feraseIdx ⟨1, by decide⟩ = #[0, 2] := by decide
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example : #[0, 1, 2].insertAt ⟨1, by decide⟩ 3 = #[0, 3, 1, 2] := by decide
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example : #[0, 1, 2].isPrefixOf #[0, 1, 2, 3] = true := by decide
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example : #[0, 1, 2].zipWith #[3, 4, 5] (· + ·) = #[3, 5, 7] := by decide
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example : #[0, 1, 2].allDiff = true := by decide
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