b13f7e25ec
This PR adds the `instantiate`, `show_true`, `show_false`,
`show_asserted`, and `show_eqcs` tactics for the `grind` interactive
mode. The `show` tactic take an optional "filter" and are used to probe
the `grind` state. Example:
```lean
example (as bs cs : Array α) (v₁ v₂ : α)
(i₁ i₂ j : Nat)
(h₁ : i₁ < as.size)
(h₂ : bs = as.set i₁ v₁)
(h₃ : i₂ < bs.size)
(h₃ : cs = bs.set i₂ v₂)
(h₄ : i₁ ≠ j ∧ i₂ ≠ j)
(h₅ : j < cs.size)
(h₆ : j < as.size)
: cs[j] = as[j] := by
grind =>
instantiate
-- Display asserted facts with `generation > 0`
show_asserted gen > 0
-- Display propositions known to be `True`, containing `j`, and `generation > 0`
show_true j && gen > 0
-- Display equivalence classes with terms that contain `as` or `bs`
show_eqcs as || bs
instantiate
```
This PR also fixes a bug in the `grind` interactive mode initialization
procedure.
88 lines
2.5 KiB
Text
88 lines
2.5 KiB
Text
/--
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error: `grind` failed
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case grind
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α : Type u
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op : α → α → α
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inst : Std.Associative op
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a b c d : α
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h : d = op b c
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h_1 : ¬op a d = op (op a b) c
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] Std.Associative op
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[prop] d = op b c
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[prop] ¬op a d = op (op a b) c
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[eqc] True propositions
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[prop] Std.Associative op
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[eqc] False propositions
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[prop] op a d = op (op a b) c
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[eqc] Equivalence classes
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[eqc] {d, op b c}
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[assoc] Operator `op`
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[diseqs] Disequalities
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[_] op a d ≠ op a (op b c)
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-/
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#guard_msgs in
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example {α : Type u} (op : α → α → α) [Std.Associative op] (a b c d : α)
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: d = op b c → op a d = op (op a b) c := by
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grind => skip
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example {α : Type u} (op : α → α → α) [Std.Associative op] (a b c d : α)
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: d = op b c → op a d = op (op a b) c := by
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grind => finish
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example (x y : Nat) : x ≥ y + 1 → x > 0 := by
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grind => lia
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example (x y : Nat) : x ≥ y + 1 → x > 0 := by
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grind => skip; lia; done
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open Lean Grind
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example [CommRing α] (a b c : α)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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a^4 + b^4 + c^4 = 9 := by
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grind => ring
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/--
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trace: [facts] Asserted facts
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[_] (bs.set i₂ v₂ ⋯).size = bs.size
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[_] (as.set i₁ v₁ ⋯).size = as.size
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[_] (bs.set i₂ v₂ ⋯)[j] = if i₂ = j then v₂ else bs[j]
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---
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trace: [props] True propositions
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[_] j < (bs.set i₂ v₂ ⋯).size
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[_] j < bs.size
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---
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trace: [eqc] Equivalence classes
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[eqc] {bs, as.set i₁ v₁ ⋯}
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[eqc] {as.size, bs.size, (as.set i₁ v₁ ⋯).size, (bs.set i₂ v₂ ⋯).size}
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[eqc] {bs[j], (bs.set i₂ v₂ ⋯)[j]}
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[eqc] {if i₂ = j then v₂ else bs[j]}
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[eqc] others
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[eqc] {bs.set i₂ v₂ ⋯}
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[eqc] {↑as.size, ↑bs.size, ↑(bs.set i₂ v₂ ⋯).size}
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-/
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#guard_msgs in
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example (as bs cs : Array α) (v₁ v₂ : α)
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(i₁ i₂ j : Nat)
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(h₁ : i₁ < as.size)
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(h₂ : bs = as.set i₁ v₁)
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(h₃ : i₂ < bs.size)
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(h₃ : cs = bs.set i₂ v₂)
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(h₄ : i₁ ≠ j ∧ i₂ ≠ j)
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(h₅ : j < cs.size)
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(h₆ : j < as.size)
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: cs[j] = as[j] := by
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grind =>
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instantiate
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-- Display asserted facts with `generation > 0`
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show_asserted gen > 0
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-- Display propositions known to be `True`, containing `j`, and `generation > 0`
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show_true j && gen > 0
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-- Display equivalence classes with terms that contain `as` or `bs`
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show_eqcs as || bs
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instantiate
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