08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
50 lines
1.7 KiB
Text
50 lines
1.7 KiB
Text
/-!
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# Tests of the 'cases' tactic
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-/
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/-!
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Error messages when not an inductive type.
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-/
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/--
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error: Tactic `cases` failed: major premise type is not an inductive type
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Prop
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Explanation: the `cases` tactic is for constructor-based reasoning as well as for applying custom cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above type neither is an inductive type nor has a registered theorem.
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Consider using the 'by_cases' tactic, which does true/false reasoning for propositions.
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p : Prop
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⊢ True
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-/
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#guard_msgs in
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example (p : Prop) : True := by
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cases p
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/--
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error: Tactic `cases` failed: major premise type is not an inductive type
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Type
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Explanation: the `cases` tactic is for constructor-based reasoning as well as for applying custom cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above type neither is an inductive type nor has a registered theorem.
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Type universes are not inductive types, and type-constructor-based reasoning is not possible. This is a strong limitation. According to Lean's underlying theory, the only provable distinguishing feature of types is their cardinalities.
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α : Type
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⊢ True
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-/
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#guard_msgs in
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example (α : Type) : True := by
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cases α
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/--
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error: Tactic `cases` failed: major premise type is not an inductive type
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Bool → Bool
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Explanation: the `cases` tactic is for constructor-based reasoning as well as for applying custom cases principles with a 'using' clause or a registered '@[cases_eliminator]' theorem. The above type neither is an inductive type nor has a registered theorem.
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f : Bool → Bool
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⊢ True
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-/
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#guard_msgs in
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example (f : Bool → Bool) : True := by
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cases f
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