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
51 lines
1.8 KiB
Text
51 lines
1.8 KiB
Text
def sorted_to_var [x: LE α] [DecidableRel x.le] (a: Array α) (i: Nat) (h : i + 1 < a.size) : Bool :=
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match i with
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| 0 => true
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| i+1 =>
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have : i + 1 < a.size := Nat.lt_of_succ_lt h
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a[i] ≤ a[i+1] && sorted_to_var a i this
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termination_by structural i
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attribute [irreducible] sorted_to_var
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def check_sorted [x: LE α] [DecidableRel x.le] (a: Array α): Bool :=
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if h : a.size ≤ 1
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then true
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else sorted_to_var a (a.size - 2) (by omega)
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/--
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error: Tactic `rfl` failed: The left-hand side
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check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]
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is not definitionally equal to the right-hand side
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true
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⊢ check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
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-/
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#guard_msgs in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true := by
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rfl -- fails because `rfl` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
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/--
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error: Tactic `decide` failed for proposition
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check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
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because its `Decidable` instance
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instDecidableEqBool (check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]) true
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did not reduce to `isTrue` or `isFalse`.
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After unfolding the instances `instDecidableEqBool`, `Bool.decEq`, and `Nat.decLe`, reduction got stuck at the `Decidable` instance
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match check_sorted #[0, 3, 3, 5, 8, 10, 10, 10], true with
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| false, false => isTrue ⋯
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| false, true => isFalse ⋯
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| true, false => isFalse ⋯
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| true, true => isTrue ⋯
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-/
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#guard_msgs in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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decide -- fails because `decide` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
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unseal sorted_to_var in
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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decide -- works
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example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
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with_unfolding_all decide -- should work
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