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