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
122 lines
1.8 KiB
Text
122 lines
1.8 KiB
Text
/-!
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Tests that definitions by well-founded recursion are irreducible.
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-/
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set_option pp.mvars false
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def foo : Nat → Nat
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| 0 => 0
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| n+1 => foo n
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termination_by n => n
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/--
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error: Type mismatch
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rfl
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has type
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?_ = ?_
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but is expected to have type
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foo 0 = 0
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-/
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#guard_msgs in
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example : foo 0 = 0 := rfl
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/--
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error: Type mismatch
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rfl
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has type
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?_ = ?_
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but is expected to have type
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foo (n + 1) = foo n
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-/
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#guard_msgs in
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example : foo (n+1) = foo n := rfl
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-- also for closed terms
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/--
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error: Tactic `rfl` failed: The left-hand side
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foo 0
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is not definitionally equal to the right-hand side
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0
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⊢ foo 0 = 0
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-/
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#guard_msgs in
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example : foo 0 = 0 := by rfl
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-- It only works on closed terms:
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/--
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error: Tactic `rfl` failed: The left-hand side
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foo (n + 1)
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is not definitionally equal to the right-hand side
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foo n
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n : Nat
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⊢ foo (n + 1) = foo n
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-/
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#guard_msgs in
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example : foo (n+1) = foo n := by rfl
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section Unsealed
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unseal foo
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-- unsealing works, but does not have the desired effect
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/--
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error: Type mismatch
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rfl
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has type
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?_ = ?_
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but is expected to have type
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foo 0 = 0
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-/
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#guard_msgs in
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example : foo 0 = 0 := rfl
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/--
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error: Type mismatch
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rfl
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has type
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?_ = ?_
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but is expected to have type
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foo (n + 1) = foo n
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-/
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#guard_msgs in
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example : foo (n+1) = foo n := rfl
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end Unsealed
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--should be sealed again here
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/--
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error: Type mismatch
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rfl
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has type
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?_ = ?_
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but is expected to have type
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foo 0 = 0
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-/
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#guard_msgs in
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example : foo 0 = 0 := rfl
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def bar : Nat → Nat
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| 0 => 0
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| n+1 => bar n
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termination_by n => n
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-- Once unsealed, the full internals are visible. This allows one to prove, for example
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-- an equality like the following
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/--
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error: Type mismatch
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rfl
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has type
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?_ = ?_
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but is expected to have type
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foo = bar
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-/
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#guard_msgs in
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example : foo = bar := rfl
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unseal foo bar in
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example : foo = bar := rfl
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