34bd6e8bfd
This PR improves the error messages produced by the `split` tactic, including suggesting syntax fixes and related tactics with which it might be confused. Note that, to avoid clashing with the new error message styling conventions used in these messages, this PR also updates the formatting of the message produced by `throwTacticEx`. Closes #6224
168 lines
2.5 KiB
Text
168 lines
2.5 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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-- Attributes on the definition take precedence
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@[semireducible] def baz : Nat → Nat
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| 0 => 0
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| n+1 => baz n
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termination_by n => n
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example : baz 0 = 0 := rfl
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seal baz in
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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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baz 0 = 0
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-/
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#guard_msgs in
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example : baz 0 = 0 := rfl
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example : baz 0 = 0 := rfl
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@[reducible] def quux : Nat → Nat
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| 0 => 0
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| n+1 => quux n
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termination_by n => n
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example : quux 0 = 0 := rfl
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set_option allowUnsafeReducibility true in
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seal quux in
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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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quux 0 = 0
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-/
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#guard_msgs in
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example : quux 0 = 0 := rfl
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example : quux 0 = 0 := rfl
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