41a2e9af19
This PR makes functions defined by well-founded recursion use an `opaque` well-founded proof by default. This reliably prevents kernel reduction of such definitions and proofs, which tends to be prohibitively slow (fixes #2171), and which regularly causes hard-to-debug kernel type-checking failures. This changes renders `unseal` ineffective for such definitions. To avoid the opaque proof, annotate the function definition with `@[semireducible]`.
49 lines
1.7 KiB
Text
49 lines
1.7 KiB
Text
@[semireducible]
|
||
def sorted_from_var [x: LE α] [DecidableRel x.le] (a: Array α) (i: Nat): Bool :=
|
||
if h: i + 1 < a.size then
|
||
have : i < a.size := Nat.lt_of_succ_lt h
|
||
a[i] ≤ a[i+1] && sorted_from_var a (i + 1)
|
||
else
|
||
true
|
||
termination_by a.size - i
|
||
|
||
attribute [irreducible] sorted_from_var
|
||
|
||
def check_sorted [x: LE α] [DecidableRel x.le] (a: Array α): Bool :=
|
||
sorted_from_var a 0
|
||
|
||
/--
|
||
error: tactic 'rfl' failed, the left-hand side
|
||
check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]
|
||
is not definitionally equal to the right-hand side
|
||
true
|
||
⊢ check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
|
||
-/
|
||
#guard_msgs in
|
||
example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true := by
|
||
rfl -- fails because `rfl` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
|
||
|
||
/--
|
||
error: tactic 'decide' failed for proposition
|
||
check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] = true
|
||
since its 'Decidable' instance
|
||
instDecidableEqBool (check_sorted #[0, 3, 3, 5, 8, 10, 10, 10]) true
|
||
did not reduce to 'isTrue' or 'isFalse'.
|
||
|
||
After unfolding the instances 'instDecidableEqBool' and 'Bool.decEq', reduction got stuck at the 'Decidable' instance
|
||
match check_sorted #[0, 3, 3, 5, 8, 10, 10, 10], true with
|
||
| false, false => isTrue ⋯
|
||
| false, true => isFalse ⋯
|
||
| true, false => isFalse ⋯
|
||
| true, true => isTrue ⋯
|
||
-/
|
||
#guard_msgs in
|
||
example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
|
||
decide -- fails because `decide` uses `.default` transparency, and `sorted_from_var` is marked as irreducible
|
||
|
||
unseal sorted_from_var in
|
||
example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
|
||
decide -- works
|
||
|
||
example: check_sorted #[0, 3, 3, 5, 8, 10, 10, 10] := by
|
||
with_unfolding_all decide -- should work
|