2ed77f3b26
This PR introduces the parametric attribute `[grind]` for annotating theorems and definitions. It also replaces `[grind_eq]` with `[grind =]`. For definitions, `[grind]` is equivalent to `[grind =]`. The new attribute supports the following variants: - **`[grind =]`**: Uses the left-hand side of the theorem's conclusion as the pattern for E-matching. - **`[grind =_]`**: Uses the right-hand side of the theorem's conclusion as the pattern for E-matching. - **`[grind _=_]`**: Creates two patterns. One for the left-hand side and one for the right-hand side. - **`[grind →]`**: Searches for (multi-)patterns in the theorem's antecedents, stopping once a usable multi-pattern is found. - **`[grind ←]`**: Searches for (multi-)patterns in the theorem's conclusion, stopping once a usable multi-pattern is found. - **`[grind]`**: Searches for (multi-)patterns in both the theorem's conclusion and antecedents. It starts with the conclusion and stops once a usable multi-pattern is found. The `grind_pattern` command remains available for cases where these attributes do not yield the desired result.
78 lines
2 KiB
Text
78 lines
2 KiB
Text
opaque g : Nat → Nat
|
||
|
||
set_option trace.Meta.debug true
|
||
|
||
@[grind] def f (a : Nat) :=
|
||
match a with
|
||
| 0 => 10
|
||
| x+1 => g (f x)
|
||
|
||
set_option grind.debug true
|
||
set_option grind.debug.proofs true
|
||
|
||
set_option trace.grind.ematch.instance true
|
||
set_option trace.grind.assert true
|
||
|
||
/--
|
||
info: [grind.assert] f (y + 1) = a
|
||
[grind.assert] ¬a = g (f y)
|
||
[grind.ematch.instance] f.eq_2: f y.succ = g (f y)
|
||
[grind.assert] f (y + 1) = g (f y)
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : f (y + 1) = a → a = g (f y):= by
|
||
grind
|
||
|
||
@[grind] def app (xs ys : List α) :=
|
||
match xs with
|
||
| [] => ys
|
||
| x::xs => x :: app xs ys
|
||
|
||
/--
|
||
info: [grind.assert] app [1, 2] ys = xs
|
||
[grind.assert] ¬xs = 1 :: 2 :: ys
|
||
[grind.ematch.instance] app.eq_2: app [1, 2] ys = 1 :: app [2] ys
|
||
[grind.assert] app [1, 2] ys = 1 :: app [2] ys
|
||
[grind.ematch.instance] app.eq_2: app [2] ys = 2 :: app [] ys
|
||
[grind.assert] app [2] ys = 2 :: app [] ys
|
||
[grind.ematch.instance] app.eq_1: app [] ys = ys
|
||
[grind.assert] app [] ys = ys
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : app [1, 2] ys = xs → xs = 1::2::ys := by
|
||
grind
|
||
|
||
opaque p : Nat → Nat → Prop
|
||
opaque q : Nat → Prop
|
||
|
||
@[grind =] theorem pq : p x x ↔ q x := by sorry
|
||
|
||
/--
|
||
info: [grind.assert] p a a
|
||
[grind.assert] ¬q a
|
||
[grind.ematch.instance] pq: p a a ↔ q a
|
||
[grind.assert] p a a = q a
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : p a a → q a := by
|
||
grind
|
||
|
||
opaque appV (xs : Vector α n) (ys : Vector α m) : Vector α (n + m) :=
|
||
Vector.append xs ys
|
||
|
||
@[grind =]
|
||
theorem appV_assoc (a : Vector α n) (b : Vector α m) (c : Vector α n') :
|
||
HEq (appV a (appV b c)) (appV (appV a b) c) := sorry
|
||
|
||
/--
|
||
info: [grind.assert] x1 = appV a b
|
||
[grind.assert] x2 = appV x1 c
|
||
[grind.assert] x3 = appV b c
|
||
[grind.assert] x4 = appV a x3
|
||
[grind.assert] ¬HEq x2 x4
|
||
[grind.ematch.instance] appV_assoc: HEq (appV a (appV b c)) (appV (appV a b) c)
|
||
[grind.assert] HEq (appV a (appV b c)) (appV (appV a b) c)
|
||
-/
|
||
#guard_msgs (info) in
|
||
example : x1 = appV a b → x2 = appV x1 c → x3 = appV b c → x4 = appV a x3 → HEq x2 x4 := by
|
||
grind
|