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lean4-htt/tests/lean/run/rflTacticErrors.lean
Joachim Breitner a3ca15d2b2
refactor: back rfl tactic primarily via apply_rfl (#3718) 
building upon #3714, this (almost) implements the second half of #3302.

The main effect is that we now get a better error message when `rfl`
fails. For
```lean
example : n+1+m = n + (1+m) := by rfl
```
instead of the wall of text
```
The rfl tactic failed. Possible reasons:
- The goal is not a reflexive relation (neither `=` nor a relation with a @[refl] lemma).
- The arguments of the relation are not equal.
Try using the reflexivity lemma for your relation explicitly, e.g. `exact Eq.refl _` or
`exact HEq.rfl` etc.
n m : Nat
⊢ n + 1 + m = n + (1 + m)
```
we now get
```
error: tactic 'rfl' failed, the left-hand side
  n + 1 + m
is not definitionally equal to the right-hand side
  n + (1 + m)
n m : Nat
⊢ n + 1 + m = n + (1 + m)
```

Unfortunately, because of very subtle differences in semantics (which
transparency setting is used when reducing the goal and whether the
“implicit lambda” feature applies) I could not make this simply the only
`rfl` implementation. So `rfl` remains a macro and is still expanded to
`eq_refl` (difference transparency setting) and `exact Iff.rfl` and
`exact HEq.rfl` (implicit lambda) to not break existing code. This can
be revised later, so this still closes: #3302.

A user might still be puzzled *why* to terms are not defeq. Explaining
that better (“reduced to… and reduces to… etc.”) would also be great,
but that’s not specific to `rfl`, so better left for some other time.
2024-09-25 10:34:42 +00:00

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