fbfb0757ca
This PR implements the basic tactics for the new `grind` interactive
mode. While many additional `grind` tactics will be added later, the
foundational framework is already operational. The following `grind`
tactics are currently implemented: `skip`, `done`, `finish`, `lia`, and
`ring`.
This PR also removes the notion of `grind` fallback procedure since it
is subsumed by the new framework. Examples:
```lean
example (x y : Nat) : x ≥ y + 1 → x > 0 := by
grind => skip; lia; done
open Lean Grind
example [CommRing α] (a b c : α)
: a + b + c = 3 →
a^2 + b^2 + c^2 = 5 →
a^3 + b^3 + c^3 = 7 →
a^4 + b^4 + c^4 = 9 := by
grind => ring
```
54 lines
1.6 KiB
Text
54 lines
1.6 KiB
Text
module
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meta import Lean.Meta.Tactic.Grind
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#exit -- TODO: reenable after we add support for running code in interactive mode
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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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meta 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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trace: [Meta.debug] [‹i < a.size›, ‹j < a.size›, ‹j < b.size›]
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[Meta.debug] [a[j], b[j], a[i]]
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-/
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#guard_msgs (trace) 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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trace: [Meta.debug] [‹i < a.size›, ‹j < a.size›, ‹j < b.size›]
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[Meta.debug] [a[j], a[i]]
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-/
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#guard_msgs (trace) 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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namespace Test
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opaque p : Prop
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axiom hp : p
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opaque h : p → Prop
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example : h (@Lean.Grind.nestedProof p hp) → p := by
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grind
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example : h hp → p := by
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grind
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end Test
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