21846ebdf8
This PR implements non-chronological backtracking for the `grind`
tactic. This feature ensures that `grind` does not need to process
irrelevant branches after performing a case-split that is not relevant.
It is not just about performance, but also the size of the final proof
term. The new test demonstrates this feature in practice.
```lean
-- In the following test, the first 8 case-splits are irrelevant,
-- and non-choronological backtracking is used to avoid searching
-- (2^8 - 1) irrelevant branches
/--
trace:
[grind.split] p8 ∨ q8, generation: 0
[grind.split] p7 ∨ q7, generation: 0
[grind.split] p6 ∨ q6, generation: 0
[grind.split] p5 ∨ q5, generation: 0
[grind.split] p4 ∨ q4, generation: 0
[grind.split] p3 ∨ q3, generation: 0
[grind.split] p2 ∨ q2, generation: 0
[grind.split] p1 ∨ q1, generation: 0
[grind.split] ¬p ∨ ¬q, generation: 0
-/
#guard_msgs (trace) in
set_option trace.grind.split true in
theorem ex
: p ∨ q →
¬ p ∨ q →
p ∨ ¬ q →
¬ p ∨ ¬ q →
p1 ∨ q1 →
p2 ∨ q2 →
p3 ∨ q3 →
p4 ∨ q4 →
p5 ∨ q5 →
p6 ∨ q6 →
p7 ∨ q7 →
p8 ∨ q8 →
False := by
grind (splits := 10)
```
106 lines
2.6 KiB
Text
106 lines
2.6 KiB
Text
reset_grind_attrs%
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set_option grind.warning false
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attribute [grind =] List.length_cons
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attribute [grind →] List.getElem?_eq_getElem
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attribute [grind =] List.length_replicate
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attribute [grind =] List.getElem_replicate
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attribute [grind =] List.getElem?_eq_none
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attribute [grind =] List.getElem?_eq_some_iff
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attribute [grind =] getElem!_pos
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attribute [grind =] Option.map_some Option.map_none
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attribute [grind =] List.getElem?_map
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attribute [grind =] List.getElem?_replicate
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attribute [grind =] List.getLast?_eq_some_iff
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attribute [grind] List.mem_concat_self
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attribute [grind =] List.getElem_cons_zero in
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attribute [grind =] List.getElem?_cons_zero in
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/--
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info: Try this: grind only [= List.getElem?_replicate, = List.getElem?_eq_none]
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-/
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#guard_msgs (info) in
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theorem getElem?_replicate' : (List.replicate n a)[m]? = if m < n then some a else none := by
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grind?
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/--
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info: Try this: grind only [= List.length_cons]
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-/
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#guard_msgs (info) in
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example : 0 < (x :: t).length := by
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grind?
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attribute [grind ext] List.ext_getElem?
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/--
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info: Try this: grind only [= Option.map_none, = Option.map_some, = List.getElem?_replicate, = List.getElem?_eq_some_iff, =
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List.getElem?_map, = List.getElem_replicate, = List.getElem?_eq_none, = List.length_replicate, →
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List.getElem?_eq_getElem, cases Or]
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-/
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#guard_msgs (info) in
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theorem map_replicate' : (List.replicate n a).map f = List.replicate n (f a) := by
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grind?
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/-- info: Try this: grind only [List.mem_concat_self, = List.getLast?_eq_some_iff] -/
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#guard_msgs (info) in
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theorem mem_of_getLast?_eq_some' {xs : List α} {a : α} (h : xs.getLast? = some a) : a ∈ xs := by
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grind?
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def f : Nat → Nat
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| 0 => 1
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| _ => 2
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/--
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info: Try this: grind only
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-/
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#guard_msgs (info) in
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example : x = 0 → f x = 1 := by
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unfold f
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grind? -- should not include match equations
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attribute [grind] f
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/--
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info: Try this: grind only [f]
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-/
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#guard_msgs (info) in
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example : x = 0 → f x = 1 := by
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grind? [f]
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opaque g : Nat → Nat
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theorem gthm : g (g x) = g x := sorry
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grind_pattern gthm => g (g x)
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/--
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info: Try this: grind only [usr gthm]
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-/
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#guard_msgs (info) in
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example : g (g (g x)) = g x := by
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grind?
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/--
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error: `And` is marked as a built-in case-split for `grind` and cannot be erased
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-/
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#guard_msgs (error) in
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attribute [-grind] And
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/--
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error: `And` is marked as a built-in case-split for `grind` and cannot be erased
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-/
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#guard_msgs (error) in
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example : p ∧ q → p := by
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grind [-And]
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example : (List.replicate n a)[m]? = if m < n then some a else none := by
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grind?
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reset_grind_attrs%
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example : (List.replicate n a)[m]? = if m < n then some a else none := by
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fail_if_success grind?
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sorry
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