06d6dbff5d
This PR implements basic model-based theory combination in `grind`.
`grind` can now solve examples such as
```lean
example (f : Int → Int) (x : Int)
: 0 ≤ x → x ≠ 0 → x ≤ 1 → f x = 2 → f 1 = 2 := by
grind
```
38 lines
1.4 KiB
Text
38 lines
1.4 KiB
Text
import Lean.Meta.Tactic.Grind
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def f (α : Type) [Add α] (a : α) := a + a + a
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open Lean Meta Grind in
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def fallback : Fallback := do
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let nodes ← filterENodes fun e => return e.self.isAppOf ``Lean.Grind.nestedProof
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trace[Meta.debug] "{nodes.toList.map (·.self)}"
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let nodes ← filterENodes fun e => return e.self.isApp && e.self.isAppOf ``GetElem.getElem
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let [_, n, _] := nodes.toList | unreachable!
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trace[Meta.debug] "{← getEqc n.self}"
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(← get).mvarId.admit
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set_option trace.Meta.debug true
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set_option grind.debug true
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set_option grind.debug.proofs true
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/-
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Recall that array access terms, such as `a[i]`, have nested proofs.
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The following test relies on `grind` `nestedProof` wrapper to
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detect equalities between array access terms.
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-/
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/--
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info: [Meta.debug] [‹i < a.toList.length›, ‹j < a.toList.length›, ‹j < b.toList.length›]
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[Meta.debug] [a[i], b[j], a[j]]
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-/
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#guard_msgs (info) in
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example (i j : Nat) (a b : Array Nat) (h1 : j < a.size) (h : j < b.size) (h2 : i ≤ j) : a[i] < a[j] + b[j] → i = j → a = b → False := by
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grind -mbtc on_failure fallback
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/--
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info: [Meta.debug] [‹i < a.toList.length›, ‹j < a.toList.length›, ‹j < b.toList.length›]
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[Meta.debug] [a[i], a[j]]
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-/
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#guard_msgs (info) in
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example (i j : Nat) (a b : Array Nat) (h1 : j < a.size) (h : j < b.size) (h2 : i ≤ j) : a[i] < a[j] + b[j] → i = j → False := by
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grind -mbtc on_failure fallback
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