4b6f07060d
This PR removes support for reducible well-founded recursion, a Breaking Change. Using `@[semireducible]` on a definition by well-founded recursion prints a warning that this is no longer effective. With the upcoming module system, proofs are often not available. With this change, we remove a fringe use case hat may require proofs, and that would not be supported under the module system anyways. At least for now, direct use of `WellFounded.fix` is not affected. This fixes: #5192
59 lines
2.2 KiB
Text
59 lines
2.2 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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example : let a := Array.range (10^6); a == a := by native_decide
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/-!
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There are other `Array` functions that use well-founded recursion.
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For a while we marked them as `@[semireducible]`, but this is now dropped.
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We can still use `native_decide` of course, and should be able to use `simp`:
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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 native_decide
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example : #[0, 1].map (· + 1) = #[1, 2] := by simp
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example : #[0, 1].any (· % 2 = 0) := by native_decide
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example : #[0, 1].any (· % 2 = 0) := by simp
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example : #[0, 1].findIdx? (· % 2 = 0) = some 0 := by native_decide
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example : #[0, 1].findIdx? (· % 2 = 0) = some 0 := by simp [List.findIdx?_cons]
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example : #[0, 1, 2].popWhile (· % 2 = 0) = #[0, 1] := by native_decide
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example : #[0, 1, 2].popWhile (· % 2 = 0) = #[0, 1] := by simp
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example : #[0, 1, 2].takeWhile (· % 2 = 0) = #[0] := by native_decide
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example : #[0, 1, 2].takeWhile (· % 2 = 0) = #[0] := by simp
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example : #[0, 1, 2].eraseIdx 1 = #[0, 2] := by native_decide
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example : #[0, 1, 2].eraseIdx 1 = #[0, 2] := by simp
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example : #[0, 1, 2].insertIdx 1 3 = #[0, 3, 1, 2] := by native_decide
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example : #[0, 1, 2].insertIdx 1 3 = #[0, 3, 1, 2] := by simp
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example : #[0, 1, 2].isPrefixOf #[0, 1, 2, 3] = true := by native_decide
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example : #[0, 1, 2].isPrefixOf #[0, 1, 2, 3] = true := by simp
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example : Array.zipWith (· + ·) #[0, 1, 2] #[3, 4, 5] = #[3, 5, 7] := by native_decide
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example : Array.zipWith (· + ·) #[0, 1, 2] #[3, 4, 5] = #[3, 5, 7] := by simp
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example : #[0, 1, 2].allDiff = true := by native_decide
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-- no API for allDiff yet:
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-- example : #[0, 1, 2].allDiff = true := by simp
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