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
```
27 lines
768 B
Text
27 lines
768 B
Text
module
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def g {α : Sort u} (a : α) := a
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/--
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error: `grind` failed
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case grind
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β : Type v
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α : Type u
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a c : α
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b d : β
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h : g (a, b) = (c, d)
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h_1 : g (g (a, b)) = (c, d)
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] g (a, b) = (c, d)
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[prop] g (g (a, b)) = (c, d)
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[eqc] Equivalence classes
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[eqc] {c, (g (g (a, b))).fst, (g (a, b)).fst}
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[eqc] {(c, d).fst}
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[eqc] {d, (g (g (a, b))).snd, (g (a, b)).snd}
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[eqc] {(c, d).snd}
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[eqc] {g (g (a, b)), g (a, b), (c, d), ((g (g (a, b))).fst, (g (g (a, b))).snd), ((g (a, b)).fst, (g (a, b)).snd)}
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-/
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#guard_msgs in
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example {β : Type v} {α : Type u} (a c : α) (b d : β) : g.{max u v + 1} (a, b) = (c, d) → g (g.{max (u+1) (v+1)} (a, b)) = (c, d) → False := by
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grind
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