4e1a2487b7
This PR adds `num?` parameter to `mkPatternFromTheorem` to control how many leading quantifiers are stripped when creating a pattern. This enables matching theorems where only some quantifiers should be converted to pattern variables. For example, to match `mk_forall_and : (∀ x, P x) → (∀ x, Q x) → (∀ x, P x ∧ Q x)` against a goal `∀ x, q x 0 ∧ q (f (f x)) y`, we use `mkPatternFromTheorem ``mk_forall_and (some 5)` to create the pattern `∀ x, ?P x ∧ ?Q x`, keeping the outermost `∀` in the pattern rather than converting it to a pattern variable.
60 lines
1.7 KiB
Text
60 lines
1.7 KiB
Text
import Lean.Meta.Sym
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open Lean Meta Sym Grind
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set_option grind.debug true
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opaque p [Ring α] : α → α → Prop
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axiom pax [CommRing α] [NoNatZeroDivisors α] (x y : α) : p x y → p (y + 1) x
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opaque a : Int
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opaque b : Int
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def ex₁ := p (a + 1) b
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def test₁ : SymM Unit := do
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let pEx ← mkPatternFromTheorem ``pax
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let e ← shareCommon (← getConstInfo ``ex₁).value!
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let some r₁ ← pEx.match? e | throwError "failed"
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let h := mkAppN (mkConst ``pax r₁.us) r₁.args
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check h
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logInfo h
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logInfo r₁.args
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/--
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info: pax b a ?m.1
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---
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info: #[Int, instCommRingInt, instNoNatZeroDivisorsInt, b, a, ?m.1]
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-/
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#guard_msgs in
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#eval SymM.run' test₁
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theorem mk_forall_and (P Q : α → Prop) : (∀ x, P x) → (∀ x, Q x) → (∀ x, P x ∧ Q x) := by
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grind
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opaque q : Nat → Nat → Prop
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opaque f : Nat → Nat
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def ex₂ := ∀ x, q x 0 ∧ q (f (f x)) (f x + f (f 1))
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def test₂ : SymM Unit := do
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/- We use `some 5` because we want the pattern to be `(∀ x, ?P x ∧ ?Q x)`-/
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let p ← mkPatternFromTheorem ``mk_forall_and (some 5)
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let e ← shareCommon (← getConstInfo ``ex₂).value!
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logInfo p.pattern
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logInfo e
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let some r₁ ← p.unify? e | throwError "failed"
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let h := mkAppN (mkConst ``mk_forall_and r₁.us) r₁.args
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check h
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logInfo h
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logInfo (← inferType r₁.args[3]!)
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logInfo (← inferType r₁.args[4]!)
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/--
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info: ∀ (x : #4), @#3 x ∧ @#2 x
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---
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info: ∀ (x : Nat), q x 0 ∧ q (f (f x)) (f x + f (f 1))
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---
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info: mk_forall_and (fun x => q x 0) (fun x => q (f (f x)) (f x + f (f 1))) ?m.4 ?m.5
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---
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info: ∀ (x : Nat), q x 0
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---
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info: ∀ (x : Nat), q (f (f x)) (f x + f (f 1))
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-/
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#guard_msgs in
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#eval SymM.run' test₂
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