feat: CopyIfTactic — native Lean 4 pre-filter tactic

Implements the copy-if pattern as a Lean tactic:
- 'copy_if' tries rfl → decide → omega → norm_num → simp in order
- 'copy_if?' reports which closer worked (for profiling)
- Each closer is a 'zero delta' check — if goal is in normal form,
  closes instantly; if not, tries next closer

This is the Lean-native equivalent of:
- Blog post: vpcompressd register-dest = 40x faster
- VCN: numpy copy-if = 3.3x faster
- Pre-filter: skip trivial theorems = 2.7x faster
- LSP: copy_if tactic = instant close for zero-delta goals

Usage:
  import Semantics.CopyIfTactic
  theorem foo : 1 = 1 := by copy_if
  theorem bar : x + 0 = x := by copy_if
  theorem baz : complex := by copy_if  -- falls through to simp

3298 jobs, 0 errors. Tests pass for rfl, decide, omega, norm_num.
This commit is contained in:
Brandon Schneider 2026-05-29 02:58:19 -05:00
parent 48eb892f49
commit 49dbd48bf5
2 changed files with 96 additions and 0 deletions

View file

@ -0,0 +1,60 @@
/-
CopyIfTactic.lean — Pre-filter tactic for Lean 4
Implements the copy-if pattern as a native Lean tactic:
1. Check if goal is trivially closable (zero delta) → close immediately
2. If non-trivial (non-zero delta) → delegate to solver
Usage:
theorem foo : 1 = 1 := by copy_if
theorem bar : x + 0 = x := by copy_if
theorem baz : complex_statement := by copy_if
The tactic tries fast closers in order of cost:
1. rfl (instant — zero delta)
2. decide (fast — decidable)
3. omega (fast — linear arithmetic)
4. simp (slow — full simplification)
-/
import Mathlib.Tactic
namespace Semantics.CopyIfTactic
open Lean Elab Tactic
/-- The copy_if tactic: try fast closers in order, fail if none work.
Lean implementation of the vectorized copy_if pattern.
Each closer is a "zero delta" check — if the goal is already in
normal form for that tactic, it closes instantly. -/
macro "copy_if" : tactic => `(tactic|
first
| rfl
| decide
| omega
| norm_num
| simp
| fail "copy_if: non-trivial goal, needs solver"
)
/-- The copy_if? tactic: like copy_if but reports which closer worked. -/
elab "copy_if?" : tactic => do
let tactics : List (String × Syntax) := [
("rfl", ← `(tactic| rfl)),
("decide", ← `(tactic| decide)),
("omega", ← `(tactic| omega)),
("norm_num",← `(tactic| norm_num)),
("simp", ← `(tactic| simp)),
]
for (name, tac) in tactics do
try
evalTactic tac
logInfo s!"copy_if?: closed with {name}"
return
catch _ =>
continue
logWarning "copy_if?: non-trivial goal"
throwError "copy_if?: goal is non-trivial"
end Semantics.CopyIfTactic

View file

@ -0,0 +1,36 @@
/-
TestCopyIf.lean — Tests for the copy_if tactic
-/
import Semantics.CopyIfTactic
namespace Semantics.TestCopyIf
open Semantics.CopyIfTactic
-- Trivial: rfl (zero delta)
theorem test_rfl : 1 = 1 := by copy_if
theorem test_rfl2 : True := by copy_if
theorem test_rfl3 : ∀ x : Nat, x = x := by intro x; copy_if
-- Trivial: decide (decidable)
theorem test_decide : 1 + 1 = 2 := by copy_if
theorem test_decide2 : true = true := by copy_if
theorem test_decide3 : 3 > 2 := by copy_if
-- Trivial: omega (linear arithmetic)
theorem test_omega (x : Nat) : x + 0 = x := by copy_if
theorem test_omega2 (x : Int) : x - x = 0 := by copy_if
theorem test_omega3 (x y : Nat) : x + y = y + x := by copy_if
-- Trivial: norm_num (numeric)
theorem test_norm_num : (2 : Nat) + 2 = 4 := by copy_if
theorem test_norm_num2 : (3 : Int) * 4 = 12 := by copy_if
-- Non-trivial: should fail with "non-trivial goal"
-- theorem test_non_trivial (x : Nat) : x * 0 = 0 := by copy_if
-- copy_if? variant: shows which closer worked
theorem test_which_rfl : 1 = 1 := by copy_if?
theorem test_which_decide : 3 > 2 := by copy_if?
theorem test_which_omega (x : Nat) : x + 0 = x := by copy_if?
end Semantics.TestCopyIf