/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Research Stack Team CompileBridge.lean — GPU-Accelerated Compilation Bridge Formal Specification This module formalizes the interface between the Lean 4 build system (lake) and GPU-accelerated theorem verification. It defines the receipt schema, theorem batch descriptors, and verification result types that the Rust lake_compile_bridge binary reads and writes. Architecture: lake build ──► CompileBridge (Lean) ──► Rust bridge (wgpu) ──► WGSL compute ▲ │ └──────────── build_receipt.json ◄───────────────────────┘ Per AGENTS.md §1.4: Q16_16 fixed-point for scoring. Per AGENTS.md §4: Eval witnesses and theorems required. -/ namespace Semantics.CompileBridge -- ═══════════════════════════════════════════════════════════════════════════ -- §1 Theorem Registry -- ═══════════════════════════════════════════════════════════════════════════ /-- Canonical theorem IDs for GPU-accelerated verification. Each ID maps to a theorem in FixedPoint.lean and a verification kernel in the WGSL compile_bridge shader. -/ inductive TheoremID | zeroMul -- zero * a = zero | mulZero -- a * zero = zero | addZero -- a + zero = a | zeroAdd -- zero + a = a | subSelf -- a - a = zero | oneMul -- one * a = a | mulOne -- a * one = a | addComm -- a + b = b + a | negInvolutive -- -(-a) = a | subViaNeg -- a - b = a + (-b) | q0_2_mulSelfNonneg -- q0_2_mul_self_nonneg (4 cases) | q0_2_mulNonneg -- q0_2_mul_nonneg (16 cases) | q0_2_addNonneg -- q0_2_add_nonneg (16 cases) deriving Repr, DecidableEq, BEq, Inhabited instance : ToString TheoremID where toString | .zeroMul => "zero_mul" | .mulZero => "mul_zero" | .addZero => "add_zero" | .zeroAdd => "zero_add" | .subSelf => "sub_self" | .oneMul => "one_mul" | .mulOne => "mul_one" | .addComm => "add_comm" | .negInvolutive => "neg_involutive" | .subViaNeg => "sub_via_neg" | .q0_2_mulSelfNonneg => "q0_2_mul_self_nonneg" | .q0_2_mulNonneg => "q0_2_mul_nonneg" | .q0_2_addNonneg => "q0_2_add_nonneg" namespace TheoremID /-- Map theorem ID to its WGSL shader kernel name. -/ def toKernelName : TheoremID → String | .zeroMul => "check_zero_mul" | .mulZero => "check_mul_zero" | .addZero => "check_add_zero" | .zeroAdd => "check_zero_add" | .subSelf => "check_sub_self" | .oneMul => "check_one_mul" | .mulOne => "check_mul_one" | .addComm => "check_add_comm" | .negInvolutive => "check_neg_involutive" | .subViaNeg => "check_sub_via_neg" | .q0_2_mulSelfNonneg => "check_q0_2_mul_self_nonneg" | .q0_2_mulNonneg => "check_q0_2_mul_nonneg" | .q0_2_addNonneg => "check_q0_2_add_nonneg" /-- Map theorem ID to numeric dispatch index (matches WGSL switch). -/ def toDispatchIndex : TheoremID → Nat | .zeroMul => 0 | .mulZero => 1 | .addZero => 2 | .zeroAdd => 3 | .subSelf => 4 | .oneMul => 5 | .mulOne => 6 | .addComm => 7 | .negInvolutive => 8 | .subViaNeg => 9 | .q0_2_mulSelfNonneg => 10 | .q0_2_mulNonneg => 11 | .q0_2_addNonneg => 12 /-- Number of GPU-verifiable theorems. -/ def count : Nat := 13 end TheoremID -- ═══════════════════════════════════════════════════════════════════════════ -- §2 GPU Verification Batch -- ═══════════════════════════════════════════════════════════════════════════ /-- A single test vector for Q16_16 theorem verification. -/ structure TestVector where a : UInt32 -- First Q16_16 operand b : UInt32 -- Second Q16_16 operand expected : UInt32 -- Expected result (0 for property-based checks) deriving Repr, BEq, Inhabited /-- Descriptor for a GPU theorem verification batch. -/ structure TheoremBatch where theoremId : UInt32 -- Dispatch index from TheoremID.toDispatchIndex count : UInt32 -- Number of test vectors deriving Repr, BEq, Inhabited /-- Result of GPU theorem verification. -/ structure TheoremResult where theoremId : UInt32 -- Matching dispatch index passed : Bool -- True if all test vectors passed total : UInt32 -- Total test vectors checked failed : UInt32 -- Number of test vectors that failed deriving Repr, BEq, Inhabited /-- Complete GPU verification receipt. -/ structure VerificationReceipt where schema : String -- "lake_compile_bridge_receipt_v1" version : String -- "0.1.0" target : String -- Lake build target (e.g., "Semantics.FixedPoint") jobs : UInt32 -- Parallel jobs used for lake build vectorsPerTheorem : UInt32 -- Test vectors per theorem gpuAvailable : Bool -- Whether GPU was available gpuDevice : String -- GPU device name theorems : List TheoremResult -- Per-theorem results totalTheorems : Nat -- Total theorems checked passed : Nat -- Theorems passing failed : Nat -- Theorems failing buildExitCode : Int -- lake build exit code elapsedMs : Nat -- Total elapsed time in milliseconds timestampUtc : String -- ISO 8601 timestamp deriving Repr, Inhabited -- ═══════════════════════════════════════════════════════════════════════════ -- §3 Bridge Invariants -- ═══════════════════════════════════════════════════════════════════════════ /-- Invariant: theorem IDs in result match canonical registry. -/ def resultIdsValid (receipt : VerificationReceipt) : Bool := receipt.theorems.all (fun r => r.theoremId.toNat < TheoremID.count) /-- Invariant: if passed then failed = 0, else failed = total. -/ def resultCountsValid (receipt : VerificationReceipt) : Bool := receipt.theorems.all (fun r => if r.passed then r.failed = 0 else r.failed = r.total) /-- Invariant: totalTheorems = |theorems|. -/ def totalCountMatches (receipt : VerificationReceipt) : Bool := receipt.totalTheorems = receipt.theorems.length /-- All bridge invariants hold simultaneously. -/ def invariantsHold (receipt : VerificationReceipt) : Bool := resultIdsValid receipt && resultCountsValid receipt && totalCountMatches receipt -- ═══════════════════════════════════════════════════════════════════════════ -- §4 Lean-side Theorem Verification Wrapper -- ═══════════════════════════════════════════════════════════════════════════ /-- Promote a GPU-verified theorem result into the Lean formal theory. This is the receiving end of the bridge. The Rust binary writes a receipt, and this function reads it, checks invariants, and returns a VerifiedClaim that can be used in proofs. -/ structure VerifiedClaim where theoremId : TheoremID gpuReceipt : TheoremResult leanTheorem : String -- Name of the Lean theorem this verifies deriving Repr, Inhabited /-- GPU results are an *accelerator* for native_decide, not a replacement. The Lean-side theorem remains the authoritative proof. GPU verification provides a fast, parallel cross-check that catches regressions early. -/ def promoteToClaim (receipt : VerificationReceipt) (idx : Nat) : Option VerifiedClaim := if h : idx < receipt.theorems.length then let res := receipt.theorems.get ⟨idx, h⟩ let theoremId : TheoremID := match res.theoremId with | 0 => TheoremID.zeroMul | 1 => TheoremID.mulZero | 2 => TheoremID.addZero | 3 => TheoremID.zeroAdd | 4 => TheoremID.subSelf | 5 => TheoremID.oneMul | 6 => TheoremID.mulOne | 7 => TheoremID.addComm | 8 => TheoremID.negInvolutive | 9 => TheoremID.subViaNeg | 10 => TheoremID.q0_2_mulSelfNonneg | 11 => TheoremID.q0_2_mulNonneg | 12 => TheoremID.q0_2_addNonneg | _ => TheoremID.zeroMul some { theoremId := theoremId gpuReceipt := res leanTheorem := toString theoremId } else none -- ═══════════════════════════════════════════════════════════════════════════ -- §5 Eval Witnesses -- ═══════════════════════════════════════════════════════════════════════════ /-- Empty receipt for invariant check (trivially valid). -/ def emptyReceipt : VerificationReceipt := { schema := "lake_compile_bridge_receipt_v1" version := "0.1.0" target := "" jobs := 0 vectorsPerTheorem := 0 gpuAvailable := false gpuDevice := "" theorems := [] totalTheorems := 0 passed := 0 failed := 0 buildExitCode := 0 elapsedMs := 0 timestampUtc := "" } #eval invariantsHold emptyReceipt #eval List.map TheoremID.toDispatchIndex [TheoremID.zeroMul, TheoremID.mulZero, TheoremID.addZero, TheoremID.zeroAdd, TheoremID.subSelf, TheoremID.oneMul, TheoremID.mulOne, TheoremID.addComm, TheoremID.negInvolutive, TheoremID.subViaNeg, TheoremID.q0_2_mulSelfNonneg, TheoremID.q0_2_mulNonneg, TheoremID.q0_2_addNonneg] -- Expected: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] #eval (List.map TheoremID.toDispatchIndex [TheoremID.zeroMul, TheoremID.mulZero, TheoremID.addZero, TheoremID.zeroAdd, TheoremID.subSelf, TheoremID.oneMul, TheoremID.mulOne, TheoremID.addComm, TheoremID.negInvolutive, TheoremID.subViaNeg, TheoremID.q0_2_mulSelfNonneg, TheoremID.q0_2_mulNonneg, TheoremID.q0_2_addNonneg]).all (fun idx => idx < TheoremID.count) -- Expected: true end Semantics.CompileBridge