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
513 lines
11 KiB
Text
513 lines
11 KiB
Text
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set_option pp.mvars.levels false
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/-!
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This file tests the `rfl` tactic:
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* Extensibility
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* Error messages
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* Effect of `with_reducible`
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-/
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set_option pp.mvars.levels false
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-- First, let's see what `rfl` does:
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ false = true
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-/
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#guard_msgs in
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example : false = true := by rfl
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-- Now to `apply_rfl`.
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-- A plain reflexive predicate
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inductive P : α → α → Prop where | refl : P a a
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attribute [refl] P.refl
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-- Plain error
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/--
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error: Tactic `rfl` failed: the left-hand side
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42
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is not definitionally equal to the right-hand side
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23
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⊢ P 42 23
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-/
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#guard_msgs in
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example : P 42 23 := by apply_rfl
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-- Revealing implicit arguments
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opaque withImplicitNat {n : Nat} : Nat
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/--
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error: Tactic `rfl` failed: the left-hand side
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@withImplicitNat 42
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is not definitionally equal to the right-hand side
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@withImplicitNat 23
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⊢ P withImplicitNat withImplicitNat
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-/
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#guard_msgs in
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example : P (@withImplicitNat 42) (@withImplicitNat 23) := by apply_rfl
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-- Exhaustive testing of various combinations:
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-- In addition to Eq, HEq and Iff we test four relations:
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-- Defeq to relation `P` at reducible transparency
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abbrev Q : α → α → Prop := P
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-- Defeq to relation `P` at default transparency
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def Q' : α → α → Prop := P
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-- No refl attribute
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inductive R : α → α → Prop where | refl : R a a
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/-
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Now we systematically test all relations with
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* syntactic equal arguments
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* reducibly equal arguments
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* semireducibly equal arguments
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* nonequal arguments
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and all using `apply_rfl` and `with_reducible apply_rfl`
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-/
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-- Syntactic equal
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example : true = true := by apply_rfl
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example : true ≍ true := by apply_rfl
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example : True ↔ True := by apply_rfl
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example : P true true := by apply_rfl
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example : Q true true := by apply_rfl
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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Q'
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⊢ Q' true true
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-/
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#guard_msgs in example : Q' true true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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R
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⊢ R true true
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-/
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#guard_msgs in example : R true true := by apply_rfl -- Error
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example : true = true := by with_reducible apply_rfl
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example : true ≍ true := by with_reducible apply_rfl
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example : True ↔ True := by with_reducible apply_rfl
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example : P true true := by with_reducible apply_rfl
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example : Q true true := by with_reducible apply_rfl
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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Q'
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⊢ Q' true true
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-/
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#guard_msgs in
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example : Q' true true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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R
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⊢ R true true
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-/
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#guard_msgs in
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example : R true true := by with_reducible apply_rfl -- Error
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-- Reducibly equal
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abbrev true' := true
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abbrev True' := True
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example : true' = true := by apply_rfl
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example : true' ≍ true := by apply_rfl
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example : True' ↔ True := by apply_rfl
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example : P true' true := by apply_rfl
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example : Q true' true := by apply_rfl
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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Q'
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⊢ Q' true' true'
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-/
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#guard_msgs in
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example : Q' true' true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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R
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⊢ R true' true'
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-/
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#guard_msgs in
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example : R true' true := by apply_rfl -- Error
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example : true' = true := by with_reducible apply_rfl
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example : true' ≍ true := by with_reducible apply_rfl
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example : True' ↔ True := by with_reducible apply_rfl
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example : P true' true := by with_reducible apply_rfl
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example : Q true' true := by with_reducible apply_rfl -- NB: No error, Q and true' reducible
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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Q'
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⊢ Q' true' true'
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-/
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#guard_msgs in
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example : Q' true' true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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R
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⊢ R true' true'
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-/
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#guard_msgs in
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example : R true' true := by with_reducible apply_rfl -- Error
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-- Equal at default transparency only
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def true'' := true
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def True'' := True
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example : true'' = true := by apply_rfl
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example : true'' ≍ true := by apply_rfl
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example : True'' ↔ True := by apply_rfl
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example : P true'' true := by apply_rfl
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example : Q true'' true := by apply_rfl
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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Q'
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⊢ Q' true'' true''
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-/
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#guard_msgs in
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example : Q' true'' true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: no @[refl] lemma registered for relation
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R
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⊢ R true'' true''
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-/
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#guard_msgs in
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example : R true'' true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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true''
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is not definitionally equal to the right-hand side
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true
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⊢ true'' = true
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-/
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#guard_msgs in
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example : true'' = true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `apply` failed: could not unify the conclusion of 'HEq.refl'
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@HEq ?α ?a ?α ?a
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with the goal
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@HEq Bool true'' Bool true
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Note: The full type of 'HEq.refl' is
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∀ {α : Sort _} (a : α), a ≍ a
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⊢ true'' ≍ true
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-/
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#guard_msgs in
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example : true'' ≍ true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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True''
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is not definitionally equal to the right-hand side
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True
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⊢ True'' ↔ True
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-/
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#guard_msgs in
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example : True'' ↔ True := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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true''
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is not definitionally equal to the right-hand side
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true
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⊢ P true'' true
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-/
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#guard_msgs in
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example : P true'' true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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true''
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is not definitionally equal to the right-hand side
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true
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⊢ Q true'' true
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-/
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#guard_msgs in
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example : Q true'' true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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true''
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is not definitionally equal to the right-hand side
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true
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⊢ Q' true'' true
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-/
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#guard_msgs in
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example : Q' true'' true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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true''
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is not definitionally equal to the right-hand side
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true
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⊢ R true'' true
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-/
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#guard_msgs in
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example : R true'' true := by with_reducible apply_rfl -- Error
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-- Unequal
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ false = true
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-/
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#guard_msgs in
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example : false = true := by apply_rfl -- Error
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/--
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error: Tactic `apply` failed: could not unify the conclusion of 'HEq.refl'
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?a ≍ ?a
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with the goal
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false ≍ true
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Note: The full type of 'HEq.refl' is
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∀ {α : Sort _} (a : α), a ≍ a
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⊢ false ≍ true
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-/
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#guard_msgs in
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example : false ≍ true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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False
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is not definitionally equal to the right-hand side
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True
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⊢ False ↔ True
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-/
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#guard_msgs in
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example : False ↔ True := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ P false true
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-/
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#guard_msgs in
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example : P false true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ Q false true
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-/
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#guard_msgs in
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example : Q false true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ Q' false true
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-/
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#guard_msgs in
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example : Q' false true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ R false true
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-/
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#guard_msgs in
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example : R false true := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ false = true
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-/
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#guard_msgs in
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example : false = true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `apply` failed: could not unify the conclusion of 'HEq.refl'
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?a ≍ ?a
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with the goal
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false ≍ true
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Note: The full type of 'HEq.refl' is
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∀ {α : Sort _} (a : α), a ≍ a
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⊢ false ≍ true
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-/
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#guard_msgs in
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example : false ≍ true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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False
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is not definitionally equal to the right-hand side
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True
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⊢ False ↔ True
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-/
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#guard_msgs in
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example : False ↔ True := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ P false true
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-/
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#guard_msgs in
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example : P false true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ Q false true
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-/
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#guard_msgs in
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example : Q false true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ Q' false true
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-/
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#guard_msgs in
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example : Q' false true := by with_reducible apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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false
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is not definitionally equal to the right-hand side
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true
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⊢ R false true
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-/
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#guard_msgs in
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example : R false true := by with_reducible apply_rfl -- Error
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-- Inheterogeneous unequal
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/--
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error: Tactic `apply` failed: could not unify the conclusion of 'HEq.refl'
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?a ≍ ?a
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with the goal
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true ≍ 1
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Note: The full type of 'HEq.refl' is
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∀ {α : Sort _} (a : α), a ≍ a
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⊢ true ≍ 1
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-/
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#guard_msgs in
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example : true ≍ 1 := by apply_rfl -- Error
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/--
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error: Tactic `apply` failed: could not unify the conclusion of 'HEq.refl'
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?a ≍ ?a
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with the goal
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true ≍ 1
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Note: The full type of 'HEq.refl' is
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∀ {α : Sort _} (a : α), a ≍ a
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⊢ true ≍ 1
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-/
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#guard_msgs in
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example : true ≍ 1 := by with_reducible apply_rfl -- Error
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-- Rfl lemma with side condition:
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-- Error message should show left-over goal
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inductive S : Bool → Bool → Prop where | refl : a = true → S a a
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attribute [refl] S.refl
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/--
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error: Tactic `rfl` failed: the left-hand side
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true
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is not definitionally equal to the right-hand side
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false
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⊢ S true false
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-/
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#guard_msgs in
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example : S true false := by apply_rfl -- Error
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/--
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error: Tactic `rfl` failed: the left-hand side
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true
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is not definitionally equal to the right-hand side
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false
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⊢ S true false
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-/
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#guard_msgs in
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example : S true false := by with_reducible apply_rfl -- Error
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/--
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error: unsolved goals
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case a
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⊢ true = true
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-/
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#guard_msgs in
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example : S true true := by apply_rfl -- Error (left-over goal)
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/--
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error: unsolved goals
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case a
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⊢ true = true
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-/
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#guard_msgs in
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example : S true true := by with_reducible apply_rfl -- Error (left-over goal)
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/--
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error: unsolved goals
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case a
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⊢ false = true
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-/
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#guard_msgs in
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example : S false false := by apply_rfl -- Error (left-over goal)
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/--
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error: unsolved goals
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case a
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⊢ false = true
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-/
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#guard_msgs in
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example : S false false := by with_reducible apply_rfl -- Error (left-over goal)
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