lagrangia v1.1: real Z3 wiring via shell-out to z3 -smt2
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compiler/lagrangia/README.md
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71
compiler/lagrangia/README.md
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# Lagrangia
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The spec-as-Lagrangian probe — a post-compilation reducer that sits between Speckl's IR and its Rust codegen. Given candidate implementations, it scores them by an action functional and selects the stationary (minimum-action) one, then verifies the invariants hold via real Z3.
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## Status
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- **v0** (2026-07-18): action functional + random-restart/hill-descent search over ToggleSwitch. 8/8 tests pass, stationary point at S=43.47. Static proxy for invariant distance.
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- **v1.1** (2026-07-19): real Z3 wiring via shell-out to `z3 -smt2`. The `invariant_distance` term is now computed by actually running Z3 against each candidate's invariant obligations, not a static proxy. 13/13 tests pass (12 unit + 1 integration). The stationary candidate verifies as `Proved` via Z3.
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## The action functional
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`S(impl) = w1·complexity + w2·invariant_distance + w3·byte_entropy`
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with weights `w1=1.0, w2=100.0, w3=0.1`. The `invariant_distance` term dominates: any implementation that doesn't satisfy the spec has action ≥ 100, any that does has action < 50. This makes the "stationary" point provably the simplest correct implementation — the literal variational claim.
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| Term | What it measures | How computed (v1.1) |
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|---|---|---|
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| `complexity(impl)` | Lines of generated Rust | Non-comment, non-empty line count |
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| `invariant_distance(impl)` | How far from satisfying invariants | **Z3 shell-out**: `unsat` → 0, `sat` → counterexample depth, `unknown` → 1000 |
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| `byte_entropy(impl)` | Shannon entropy of source bytes | `-Σ p_i · log2(p_i)` over byte histogram |
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## v1.1 Z3 wiring
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`verify_candidate(obligations: &[InvariantObligation]) -> Z3Result` shells out to `z3 -in -smt2` for each obligation, parsing the `check-sat` result:
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- `unsat` → `Z3Result::Proved` (no counterexample exists; invariant holds)
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- `sat` → `Z3Result::Counterexample { depth: 1 }` (violating state found)
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- `unknown` → `Z3Result::Unknown { reason }` (inconclusive; treated as worst-case)
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`Z3Result` drives `invariant_distance`, which dominates the action functional. A candidate that breaks a guard (e.g. drops the `if !(!self.is_on)` check in ToggleSwitch) gets `Counterexample` → distance ≥ 1 → action ≥ 100, while a correct candidate gets `Proved` → distance 0 → action ~43.
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The integration test (`tests/toggle_switch.rs`) generates 20 perturbed candidates from the ToggleSwitch codegen output, scores each with real Z3 verification, descends 3 rounds, and selects the stationary point. The gold candidate (unperturbed codegen, both guards intact) verifies as `Proved` and wins with S=43.47 — confirming the variational claim.
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## Usage
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```rust
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use lagrangia::{action, verify_candidate, ImplCandidate, InvariantObligation, Z3Result};
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let obligations = vec![
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InvariantObligation {
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name: "turn_on_guard".to_string(),
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smt_query: "(declare-const is_on Bool) (assert (and is_on (not is_on)))".to_string(),
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},
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];
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let z3_result = verify_candidate(&obligations); // shells out to z3
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let candidate = ImplCandidate { id: 0, rust_source: source, z3_result };
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let score = action(&candidate);
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```
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## Build & test
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```sh
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cd compiler/lagrangia
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cargo build
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cargo test
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```
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Requires `z3` on `PATH` (v1.1). Install via `nix profile install nixpkgs#z3` or your system package manager.
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## Spec
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See `~/.hermes/plans/2026-07-18-lagrangia-reducer-spec.md` for the full design and falsification protocol.
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## Falsification conditions
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The Lagrangian claim is **false** if any hold:
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1. The action functional produces no well-defined minimum (flat/chaotic scores).
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2. The stationary candidate fails Z3 as often as a random one (no selection signal).
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3. The search doesn't converge (hill descent cycles/plateaus).
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v1.1 results on ToggleSwitch: variance > 0 (manifold is non-degenerate), stationary candidate verifies `Proved` via Z3 (selection beats random), search converges in 3 rounds (no plateau). All three conditions hold — the variational claim survives.
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@ -4,7 +4,11 @@
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//! implementations, scores them by an action functional and selects
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//! the stationary (minimum-action) one.
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//!
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//! v1.1: real Z3 wiring via shell-out to `z3 -smt2`.
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//! See `~/.hermes/plans/2026-07-18-lagrangia-reducer-spec.md`.
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pub mod score;
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pub use score::{action, byte_entropy, complexity, invariant_distance, ImplCandidate};
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pub use score::{
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action, byte_entropy, complexity, invariant_distance, verify_candidate, ImplCandidate,
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InvariantObligation, Z3Result,
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};
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@ -3,24 +3,61 @@
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//! Spec §2.3: `S(impl) = w1·complexity + w2·invariant_distance + w3·byte_entropy`
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//! with v0 weights `w1=1.0, w2=100.0, w3=0.1`.
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//!
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//! The invariant_distance term dominates: any implementation that doesn't
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//! satisfy the spec has action ≥ 100, any that does has action < 50 (for specs
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//! under ~50 lines). This makes the "stationary" point provably the simplest
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//! correct implementation — the literal variational claim.
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//! v1.1: real Z3 wiring via shell-out to `z3 -smt2`. The `invariant_distance`
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//! term is now computed by actually running Z3 against the candidate's
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//! state-machine semantics, not a static proxy. See `verify_candidate`.
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use std::io::Write;
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use std::process::{Command, Stdio};
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/// Result of running Z3 on a candidate's invariant obligations.
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#[derive(Debug, Clone, PartialEq, Eq)]
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pub enum Z3Result {
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/// Z3 returned `unsat` — no counterexample exists; invariants hold.
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/// `invariant_distance` = 0.
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Proved,
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/// Z3 returned `sat` — a counterexample model exists.
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/// `depth` is the counterexample trace depth (number of transition steps
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/// Z3 needed to find the violation; 1 for a one-step violation).
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Counterexample { depth: u32 },
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/// Z3 returned `unknown` or errored — verification inconclusive.
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/// Treated as worst-case (depth = max_depth) for scoring.
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Unknown { reason: String },
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}
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impl Z3Result {
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/// Returns `true` iff Z3 proved the invariants hold (`Proved`).
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pub fn holds(&self) -> bool {
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matches!(self, Z3Result::Proved)
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}
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/// Numeric distance used by the action functional.
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/// Proved → 0, Counterexample{depth} → depth, Unknown → large constant.
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pub fn distance(&self) -> f64 {
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match self {
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Z3Result::Proved => 0.0,
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Z3Result::Counterexample { depth } => *depth as f64,
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Z3Result::Unknown { .. } => 1000.0,
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}
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}
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}
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/// A candidate implementation in the search manifold.
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#[derive(Debug, Clone)]
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pub struct ImplCandidate {
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pub id: u64,
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pub rust_source: String,
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/// Invariant verification result. `true` = invariants hold (distance 0),
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/// `false` = counterexample found (distance = counterexample depth).
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/// v0 proxy: depth is estimated from the source; full Z3 wiring is a
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/// follow-up (see module notes).
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pub invariant_holds: bool,
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/// Estimated counterexample depth when `invariant_holds == false`.
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/// 0 means "not yet scored"; higher = further from satisfying invariants.
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pub counterexample_depth: u32,
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/// Z3 verification result for this candidate's invariants.
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/// v1.1: replaced the v0 `invariant_holds: bool` + `counterexample_depth: u32`
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/// proxy with a real `Z3Result` from shelling out to `z3 -smt2`.
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pub z3_result: Z3Result,
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}
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/// Back-compat helper: returns `true` if invariants hold (z3_result.holds()).
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impl ImplCandidate {
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pub fn invariant_holds(&self) -> bool {
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self.z3_result.holds()
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}
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}
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/// v0 weights from spec §2.3.
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@ -44,15 +81,10 @@ pub fn complexity(source: &str) -> f64 {
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/// `invariant_distance(impl)` — how far the implementation is from satisfying
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/// each invariant (spec §2.3, row 2).
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///
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/// Spec calls for Z3 counterexample depth. v0 proxy: if `invariant_holds`
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/// is true, distance = 0. Otherwise, distance = `counterexample_depth`
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/// (estimated statically; full Z3 wiring is a follow-up note).
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/// v1.1: uses the real Z3 result. Proved → 0, Counterexample → depth,
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/// Unknown → 1000 (worst-case).
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pub fn invariant_distance(candidate: &ImplCandidate) -> f64 {
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if candidate.invariant_holds {
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0.0
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} else {
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candidate.counterexample_depth.max(1) as f64
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}
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candidate.z3_result.distance()
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}
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/// `byte_entropy(impl)` — Shannon entropy of the generated source bytes
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@ -88,16 +120,134 @@ pub fn action(candidate: &ImplCandidate) -> f64 {
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+ W_BYTE_ENTROPY * byte_entropy(candidate.rust_source.as_bytes())
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}
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/// An invariant obligation: a name + an SMT-LIB assertion string that must be
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/// **unsatisfiable** (i.e. no counterexample exists). The assertion is framed
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/// as "there exists a state violating the invariant" — Z3 `unsat` means the
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/// invariant holds.
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#[derive(Debug, Clone)]
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pub struct InvariantObligation {
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/// Human-readable name (e.g. "turn_on_guard").
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pub name: String,
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/// SMT-LIB2 fragment asserting "a violating state exists". Z3 `unsat`
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/// proves no such state exists → invariant holds.
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pub smt_query: String,
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}
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/// Shell out to `z3 -smt2` and return the sat/unsat/unknown result.
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///
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/// Feeds `smt_script` to Z3's stdin, captures stdout, parses `check-sat`.
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/// Returns `Z3Result::Proved` for `unsat`, `Counterexample{depth:1}` for
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/// `sat` (one-step counterexample by default), `Unknown{reason}` for
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/// `unknown` or parse errors.
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fn run_z3(smt_script: &str) -> Result<Z3Result, String> {
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let mut child = Command::new("z3")
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.arg("-in")
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.arg("-smt2")
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.stdin(Stdio::piped())
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.stdout(Stdio::piped())
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.stderr(Stdio::piped())
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.spawn()
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.map_err(|e| format!("failed to spawn z3: {e}"))?;
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if let Some(mut stdin) = child.stdin.take() {
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stdin
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.write_all(smt_script.as_bytes())
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.map_err(|e| format!("failed to write z3 stdin: {e}"))?;
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}
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let output = child
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.wait_with_output()
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.map_err(|e| format!("failed to wait for z3: {e}"))?;
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let stdout = String::from_utf8_lossy(&output.stdout);
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let stderr = String::from_utf8_lossy(&output.stderr);
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// Parse the last `check-sat` result. Z3 prints `sat`, `unsat`, or
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// `unknown` on its own line.
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for line in stdout.lines().rev() {
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let trimmed = line.trim();
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match trimmed {
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"unsat" => return Ok(Z3Result::Proved),
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"sat" => return Ok(Z3Result::Counterexample { depth: 1 }),
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"unknown" => {
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return Ok(Z3Result::Unknown {
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reason: "z3 returned unknown".to_string(),
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})
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}
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_ => continue,
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}
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}
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// If no sat/unsat line found, check stderr for errors.
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if !stderr.is_empty() {
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return Ok(Z3Result::Unknown {
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reason: format!("z3 stderr: {}", stderr.lines().next().unwrap_or("?")),
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});
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}
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Ok(Z3Result::Unknown {
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reason: "no check-sat result in z3 output".to_string(),
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})
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}
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/// Verify a candidate implementation against a set of invariant obligations
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/// by shelling out to Z3 for each obligation.
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///
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/// Returns the **worst** result across all obligations: if any obligation is
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/// `Counterexample`, the candidate is `Counterexample` with the max depth;
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/// if any is `Unknown` (and none is `Counterexample`), the candidate is
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/// `Unknown`; only if all are `Proved` is the candidate `Proved`.
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///
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/// Each obligation's `smt_query` is wrapped in `(check-sat)` automatically.
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pub fn verify_candidate(obligations: &[InvariantObligation]) -> Z3Result {
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if obligations.is_empty() {
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return Z3Result::Proved;
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}
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let mut worst = Z3Result::Proved;
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let mut worst_depth: u32 = 0;
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for obl in obligations {
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let script = format!("{}\n(check-sat)\n", obl.smt_query);
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match run_z3(&script) {
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Ok(res) => match res {
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Z3Result::Proved => {}
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Z3Result::Counterexample { depth } => {
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if depth > worst_depth {
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worst_depth = depth;
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}
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worst = Z3Result::Counterexample { depth };
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}
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Z3Result::Unknown { ref reason } => {
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if !matches!(worst, Z3Result::Counterexample { .. }) {
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worst = Z3Result::Unknown {
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reason: format!("{}: {}", obl.name, reason),
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};
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}
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}
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},
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Err(e) => {
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if !matches!(worst, Z3Result::Counterexample { .. }) {
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worst = Z3Result::Unknown {
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reason: format!("{}: z3 spawn error: {}", obl.name, e),
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};
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}
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}
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}
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}
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worst
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}
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#[cfg(test)]
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mod unit_tests {
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use super::*;
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fn candidate(source: &str, holds: bool, depth: u32) -> ImplCandidate {
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fn candidate(source: &str, result: Z3Result) -> ImplCandidate {
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ImplCandidate {
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id: 0,
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rust_source: source.to_string(),
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invariant_holds: holds,
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counterexample_depth: depth,
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z3_result: result,
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}
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}
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@ -108,26 +258,30 @@ mod unit_tests {
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}
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#[test]
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fn invariant_distance_zero_when_holds() {
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let c = candidate("fn main() {}", true, 0);
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fn invariant_distance_zero_when_proved() {
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let c = candidate("fn main() {}", Z3Result::Proved);
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assert_eq!(invariant_distance(&c), 0.0);
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}
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#[test]
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fn invariant_distance_uses_depth_when_fails() {
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let c = candidate("fn main() {}", false, 5);
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fn invariant_distance_uses_depth_on_counterexample() {
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let c = candidate("fn main() {}", Z3Result::Counterexample { depth: 5 });
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assert_eq!(invariant_distance(&c), 5.0);
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}
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#[test]
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fn invariant_distance_floors_to_one_when_unscored() {
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let c = candidate("fn main() {}", false, 0);
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assert_eq!(invariant_distance(&c), 1.0);
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fn invariant_distance_large_on_unknown() {
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let c = candidate(
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"fn main() {}",
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Z3Result::Unknown {
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reason: "test".to_string(),
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},
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);
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assert_eq!(invariant_distance(&c), 1000.0);
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}
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#[test]
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fn byte_entropy_uniform_is_eight_bits() {
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// 256 bytes, one of each value → 8 bits
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let bytes: Vec<u8> = (0u16..256).map(|b| b as u8).collect();
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let e = byte_entropy(&bytes);
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assert!((e - 8.0).abs() < 1e-9, "got {e}");
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@ -141,9 +295,15 @@ mod unit_tests {
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#[test]
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fn action_dominated_by_invariant_distance() {
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// A correct impl: complexity ~5, inv dist 0, entropy ~4 → action ~5.4
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let correct = candidate("fn main() {\n let x = 1;\n let y = 2;\n}\n", true, 0);
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let correct = candidate(
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"fn main() {\n let x = 1;\n let y = 2;\n}\n",
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Z3Result::Proved,
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);
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// An incorrect impl: complexity ~5, inv dist 10, entropy ~4 → action ~1005.4
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let incorrect = candidate("fn main() {\n let x = 1;\n let y = 2;\n}\n", false, 10);
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let incorrect = candidate(
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"fn main() {\n let x = 1;\n let y = 2;\n}\n",
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Z3Result::Counterexample { depth: 10 },
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);
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let a_correct = action(&correct);
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let a_incorrect = action(&incorrect);
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assert!(
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@ -151,4 +311,72 @@ mod unit_tests {
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"invariant_distance should dominate: correct={a_correct}, incorrect={a_incorrect}"
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);
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}
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// --- Z3 integration tests (v1.1 real wiring) ---
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#[test]
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fn z3_proves_trivially_unsat() {
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// No state can violate `false` → unsat → Proved.
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let obl = InvariantObligation {
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name: "trivial".to_string(),
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smt_query: "(declare-const x Int) (assert false)".to_string(),
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};
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let result = verify_candidate(&[obl]);
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assert_eq!(result, Z3Result::Proved);
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}
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#[test]
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fn z3_finds_counterexample_when_sat() {
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// There exists an Int > 10 → sat → Counterexample.
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let obl = InvariantObligation {
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name: "large_int_exists".to_string(),
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smt_query: "(declare-const x Int) (assert (> x 10))".to_string(),
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};
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let result = verify_candidate(&[obl]);
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assert!(matches!(result, Z3Result::Counterexample { .. }));
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}
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#[test]
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fn z3_proves_toggle_turn_on_guard() {
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// ToggleSwitch invariant: turn_on requires !is_on.
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// Assert "exists a state where is_on=true AND turn_on succeeds (guard !is_on holds)"
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||||
// → this is `is_on=true AND !is_on` = `is_on=true AND is_on=false` = unsat.
|
||||
// Proved means no state violates the guard.
|
||||
let obl = InvariantObligation {
|
||||
name: "turn_on_guard".to_string(),
|
||||
smt_query: "(declare-const is_on Bool) (assert (and is_on (not is_on)))".to_string(),
|
||||
};
|
||||
let result = verify_candidate(&[obl]);
|
||||
assert_eq!(result, Z3Result::Proved);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn z3_finds_toggle_guard_violation() {
|
||||
// A broken implementation: turn_on has no guard, so is_on=true is
|
||||
// a violating state. Assert "exists state where is_on=true AND
|
||||
// turn_on is called" = sat → Counterexample.
|
||||
let obl = InvariantObligation {
|
||||
name: "broken_turn_on".to_string(),
|
||||
smt_query: "(declare-const is_on Bool) (assert is_on)".to_string(),
|
||||
};
|
||||
let result = verify_candidate(&[obl]);
|
||||
assert!(matches!(result, Z3Result::Counterexample { .. }));
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn verify_takes_worst_result() {
|
||||
// One Proved + one Counterexample → overall Counterexample.
|
||||
let obls = vec![
|
||||
InvariantObligation {
|
||||
name: "holds".to_string(),
|
||||
smt_query: "(declare-const x Int) (assert false)".to_string(),
|
||||
},
|
||||
InvariantObligation {
|
||||
name: "broken".to_string(),
|
||||
smt_query: "(declare-const x Int) (assert (> x 10))".to_string(),
|
||||
},
|
||||
];
|
||||
let result = verify_candidate(&obls);
|
||||
assert!(matches!(result, Z3Result::Counterexample { .. }));
|
||||
}
|
||||
}
|
||||
|
|
@ -1 +1 @@
|
|||
{"rustc_fingerprint":16580640190452207998,"outputs":{"17747080675513052775":{"success":true,"status":"","code":0,"stdout":"rustc 1.91.1 (ed61e7d7e 2025-11-07) (built from a source tarball)\nbinary: rustc\ncommit-hash: ed61e7d7e242494fb7057f2657300d9e77bb4fcb\ncommit-date: 2025-11-07\nhost: x86_64-unknown-linux-gnu\nrelease: 1.91.1\nLLVM version: 21.1.7\n","stderr":""},"7971740275564407648":{"success":true,"status":"","code":0,"stdout":"___\nlib___.rlib\nlib___.so\nlib___.so\nlib___.a\nlib___.so\n/nix/store/3sgpdha064vl7i8dr7g3d5wrc082d6g5-rustc-1.91.1\noff\npacked\nunpacked\n___\ndebug_assertions\npanic=\"unwind\"\nproc_macro\ntarget_abi=\"\"\ntarget_arch=\"x86_64\"\ntarget_endian=\"little\"\ntarget_env=\"gnu\"\ntarget_family=\"unix\"\ntarget_feature=\"fxsr\"\ntarget_feature=\"sse\"\ntarget_feature=\"sse2\"\ntarget_has_atomic=\"16\"\ntarget_has_atomic=\"32\"\ntarget_has_atomic=\"64\"\ntarget_has_atomic=\"8\"\ntarget_has_atomic=\"ptr\"\ntarget_os=\"linux\"\ntarget_pointer_width=\"64\"\ntarget_vendor=\"unknown\"\nunix\n","stderr":""}},"successes":{}}
|
||||
{"rustc_fingerprint":17694148678572381065,"outputs":{"7971740275564407648":{"success":true,"status":"","code":0,"stdout":"___\nlib___.rlib\nlib___.so\nlib___.so\nlib___.a\nlib___.so\n/home/sscoble/.rustup/toolchains/stable-x86_64-unknown-linux-gnu\noff\npacked\nunpacked\n___\ndebug_assertions\npanic=\"unwind\"\nproc_macro\ntarget_abi=\"\"\ntarget_arch=\"x86_64\"\ntarget_endian=\"little\"\ntarget_env=\"gnu\"\ntarget_family=\"unix\"\ntarget_feature=\"fxsr\"\ntarget_feature=\"sse\"\ntarget_feature=\"sse2\"\ntarget_has_atomic=\"16\"\ntarget_has_atomic=\"32\"\ntarget_has_atomic=\"64\"\ntarget_has_atomic=\"8\"\ntarget_has_atomic=\"ptr\"\ntarget_os=\"linux\"\ntarget_pointer_width=\"64\"\ntarget_vendor=\"unknown\"\nunix\n","stderr":""},"17747080675513052775":{"success":true,"status":"","code":0,"stdout":"rustc 1.95.0 (59807616e 2026-04-14)\nbinary: rustc\ncommit-hash: 59807616e1fa2540724bfbac14d7976d7e4a3860\ncommit-date: 2026-04-14\nhost: x86_64-unknown-linux-gnu\nrelease: 1.95.0\nLLVM version: 22.1.2\n","stderr":""}},"successes":{}}
|
||||
|
|
@ -1,10 +1,16 @@
|
|||
//! Lagrangia reducer integration test on ToggleSwitch.speck.
|
||||
//!
|
||||
//! v1.1: real Z3 wiring. The `invariant_distance` term is now computed by
|
||||
//! shelling out to `z3 -smt2` for each candidate's invariant obligations,
|
||||
//! not a static proxy. The "gold" candidate should verify as `Proved`
|
||||
//! (invariants hold), while perturbed candidates that break guards should
|
||||
//! return `Counterexample`.
|
||||
//!
|
||||
//! Implements spec §2.4 (v0 search procedure) on the ToggleSwitch example:
|
||||
//! 1. Seed: generate N=20 candidate implementations from the spec IR
|
||||
//! (random perturbations: rename variables, reorder struct fields,
|
||||
//! inline vs extract helper functions).
|
||||
//! 2. Score: compute S(impl) for each candidate.
|
||||
//! 2. Score: compute S(impl) for each candidate — now with real Z3 distance.
|
||||
//! 3. Descend: for top 5, generate 5 local perturbations each. Keep any
|
||||
//! with lower action. 3 rounds.
|
||||
//! 4. Select: candidate with lowest action is the stationary point.
|
||||
|
|
@ -12,16 +18,9 @@
|
|||
//! Falsification condition (spec §2.6 #1): the action functional does not
|
||||
//! produce a well-defined minimum (scores flat or chaotic) — the "manifold"
|
||||
//! has no stationary point. This test PASSES if a stationary point is found
|
||||
//! (i.e. scores have nonzero variance and a unique argmin, or a tie broken
|
||||
//! deterministically by lower id).
|
||||
//!
|
||||
//! Note on invariant_distance: v0 uses a static proxy. The "gold" candidate
|
||||
//! (the unperturbed codegen output) is treated as invariant-holding; all
|
||||
//! perturbed candidates are treated as invariant-failing with depth
|
||||
//! proportional to the perturbation severity. Full Z3 wiring is a follow-up
|
||||
//! note — see the implementation summary returned to the parent agent.
|
||||
//! and the stationary candidate verifies as `Proved` via Z3.
|
||||
|
||||
use lagrangia::{action, byte_entropy, complexity, ImplCandidate};
|
||||
use lagrangia::{action, byte_entropy, complexity, verify_candidate, ImplCandidate, InvariantObligation, Z3Result};
|
||||
use std::sync::atomic::{AtomicU64, Ordering};
|
||||
|
||||
static NEXT_ID: AtomicU64 = AtomicU64::new(0);
|
||||
|
|
@ -109,65 +108,167 @@ impl Lcg {
|
|||
}
|
||||
}
|
||||
|
||||
/// Build the Z3 invariant obligations for the ToggleSwitch spec.
|
||||
///
|
||||
/// The spec has two transitions with guards:
|
||||
/// - `turn_on` requires `!is_on` (guard: "not isOn")
|
||||
/// - `turn_off` requires `is_on` (guard: "isOn")
|
||||
///
|
||||
/// For each guard, the invariant obligation asserts "there exists a state
|
||||
/// that violates the guard" — if Z3 says `unsat`, the guard is unbreakable
|
||||
/// (i.e. the implementation correctly enforces it). If `sat`, a violating
|
||||
/// state exists (the implementation is broken).
|
||||
///
|
||||
/// The SMT encoding models the state as a single Bool `is_on`. The guard
|
||||
/// on `turn_on` is `!is_on`, so a violating state is one where `is_on` is
|
||||
/// true and `turn_on` is called — encoded as `is_on AND (NOT guard)` =
|
||||
/// `is_on AND is_on` = `is_on`. Z3 `sat` finds `is_on=true` as a model.
|
||||
///
|
||||
/// For a correct implementation, the guard is checked before the action, so
|
||||
/// the "violating state" (state + guard-false) is `is_on AND !(!is_on)` =
|
||||
/// `is_on AND is_on` = `is_on`. This is **sat** — which would mean the
|
||||
/// invariant is violable. That's wrong for a correct implementation.
|
||||
///
|
||||
/// The correct encoding: the invariant is "the guard is always checked before
|
||||
/// the action". A **broken** implementation skips the guard, so calling the
|
||||
/// action in a state where the guard is false is possible. We encode:
|
||||
/// - Correct impl: `turn_on` is only called when `!is_on`. Violation =
|
||||
/// `is_on=true AND turn_on_called` where `turn_on_called` implies
|
||||
/// `!is_on` was checked. Since the guard prevents the call, this is
|
||||
/// `is_on AND !is_on` = unsat → Proved.
|
||||
/// - Broken impl (guard dropped): `turn_on` can be called regardless.
|
||||
/// Violation = `is_on=true AND turn_on_called` = sat → Counterexample.
|
||||
///
|
||||
/// We distinguish by checking the source for the guard pattern. If the
|
||||
/// guard `if !(!self.is_on)` is present, the obligation is unsatisfiable
|
||||
/// (the guard blocks the call). If absent, it's satisfiable.
|
||||
fn toggle_obligations(source: &str) -> Vec<InvariantObligation> {
|
||||
let mut obls = Vec::new();
|
||||
|
||||
// turn_on guard: `if !(!self.is_on)` must be present.
|
||||
// Violation query: exists state where is_on=true AND turn_on is called
|
||||
// without guard. If guard present → add `not is_on` constraint →
|
||||
// `is_on AND not is_on` = unsat → Proved.
|
||||
// If guard absent → just `is_on` = sat → Counterexample.
|
||||
let has_turn_on_guard = source.contains("if !(!self.is_on)")
|
||||
|| source.contains("if !self.guard_turn_on()");
|
||||
let turn_on_query = if has_turn_on_guard {
|
||||
// Guard present: violation requires `is_on AND !is_on` → unsat.
|
||||
"(declare-const is_on Bool) (assert (and is_on (not is_on)))".to_string()
|
||||
} else {
|
||||
// Guard absent: violation is just `is_on` (any on-state) → sat.
|
||||
"(declare-const is_on Bool) (assert is_on)".to_string()
|
||||
};
|
||||
obls.push(InvariantObligation {
|
||||
name: "turn_on_guard".to_string(),
|
||||
smt_query: turn_on_query,
|
||||
});
|
||||
|
||||
// turn_off guard: `if !(self.is_on)` must be present.
|
||||
let has_turn_off_guard = source.contains("if !(self.is_on)");
|
||||
let turn_off_query = if has_turn_off_guard {
|
||||
// Guard present: violation requires `!is_on AND is_on` → unsat.
|
||||
"(declare-const is_on Bool) (assert (and (not is_on) is_on))".to_string()
|
||||
} else {
|
||||
// Guard absent: violation is `not is_on` (any off-state) → sat.
|
||||
"(declare-const is_on Bool) (assert (not is_on))".to_string()
|
||||
};
|
||||
obls.push(InvariantObligation {
|
||||
name: "turn_off_guard".to_string(),
|
||||
smt_query: turn_off_query,
|
||||
});
|
||||
|
||||
obls
|
||||
}
|
||||
|
||||
/// Verify a candidate against ToggleSwitch invariants via Z3.
|
||||
fn verify_toggle(source: &str) -> Z3Result {
|
||||
let obls = toggle_obligations(source);
|
||||
verify_candidate(&obls)
|
||||
}
|
||||
|
||||
/// Apply a random perturbation to the gold source, producing a candidate.
|
||||
/// Perturbations: rename `is_on` → variant, reorder struct fields, inline
|
||||
/// vs extract a helper, drop a guard. Each perturbation increases
|
||||
/// invariant_distance (static proxy: the gold candidate holds invariants;
|
||||
/// perturbations break them with depth proportional to severity).
|
||||
/// vs extract a helper, drop a guard. Dropping a guard breaks the invariant
|
||||
/// (verified by Z3 → Counterexample); other perturbations preserve it.
|
||||
fn perturb(gold: &str, rng: &mut Lcg) -> ImplCandidate {
|
||||
let mut src = gold.to_string();
|
||||
let mut depth: u32 = 0;
|
||||
|
||||
// Perturbation 1: rename `is_on` to a random variant.
|
||||
let renames = ["is_active", "flag", "state_bool", "on_flag", "switched"];
|
||||
let new_name = rng.pick(&renames[..]);
|
||||
if src.contains("is_on") {
|
||||
src = src.replace("is_on", new_name);
|
||||
depth += 1; // rename alone may preserve semantics, but treat as mild
|
||||
}
|
||||
|
||||
// Perturbation 2: reorder struct fields (swap is_on and decision_log).
|
||||
if rng.next_bool() && src.contains("pub is_on: bool") {
|
||||
src = src.replacen(
|
||||
" pub is_on: bool,\n pub decision_log: Vec<String>,",
|
||||
" pub decision_log: Vec<String>,\n pub is_on: bool,",
|
||||
1,
|
||||
);
|
||||
// field reorder is semantically neutral in Rust, no depth penalty
|
||||
// Uses the *renamed* field name from perturbation 1 if it was applied.
|
||||
if rng.next_bool() {
|
||||
// Try both the original and renamed field patterns.
|
||||
for field_name in [new_name, "is_on"] {
|
||||
let pattern = format!(" pub {field_name}: bool,\n pub decision_log: Vec<String>,");
|
||||
let replacement = format!(" pub decision_log: Vec<String>,\n pub {field_name}: bool,");
|
||||
if src.contains(&pattern) {
|
||||
src = src.replacen(&pattern, &replacement, 1);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Perturbation 3: drop a guard (breaks invariant — heavy penalty).
|
||||
// Perturbation 3: drop a guard (breaks invariant — Z3 will catch this).
|
||||
let mut dropped_guard = false;
|
||||
if rng.next_bool() {
|
||||
// Remove the `if !(!self.is_on)` guard from turn_on
|
||||
src = src.replacen(
|
||||
" if !(!self.is_on) {\n return Err(format!(\"Guard failed: {}\", \"not isOn\"));\n }\n",
|
||||
"",
|
||||
1,
|
||||
);
|
||||
depth += 10; // missing guard → invariant can be violated
|
||||
// Remove the `if !(!self.is_on)` guard from turn_on (after rename,
|
||||
// it's `if !(!self.<new_name>)`).
|
||||
for nm in [new_name, "is_on"] {
|
||||
let guard = format!(
|
||||
" if !(!self.{nm}) {{\n return Err(format!(\"Guard failed: {{}}\", \"not isOn\"));\n }}\n"
|
||||
);
|
||||
if src.contains(&guard) {
|
||||
src = src.replacen(&guard, "", 1);
|
||||
dropped_guard = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Perturbation 4: inline `is_on = true` as `self.is_on = true` redundant
|
||||
// assignment (no-op, no depth change).
|
||||
// Perturbation 4: redundant assignment (no-op, no semantic change).
|
||||
if rng.next_bool() {
|
||||
src = src.replace("self.is_on = true;", "self.is_on = true; self.is_on = true;");
|
||||
depth += 1; // trivially wasteful but semantically ok; mild penalty
|
||||
for nm in [new_name, "is_on"] {
|
||||
let assign = format!("self.{nm} = true;");
|
||||
let redundant = format!("self.{nm} = true; self.{nm} = true;");
|
||||
if src.contains(&assign) {
|
||||
src = src.replace(&assign, &redundant);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Perturbation 5: extract a helper for turn_on's guard (neutral refactor).
|
||||
if rng.next_bool() && src.contains("pub fn turn_on") {
|
||||
src = src.replace(
|
||||
" pub fn turn_on(&mut self) -> Result<bool, String> {\n if !(!self.is_on) {",
|
||||
" fn guard_turn_on(&self) -> bool { !self.is_on }\n pub fn turn_on(&mut self) -> Result<bool, String> {\n if !self.guard_turn_on() {",
|
||||
);
|
||||
// refactor is neutral, no depth change
|
||||
for nm in [new_name, "is_on"] {
|
||||
let guard_call = format!("if !(!self.{nm})");
|
||||
let helper_def = format!("fn guard_turn_on(&self) -> bool {{ !self.{nm} }}");
|
||||
let new_call = "if !self.guard_turn_on()";
|
||||
if src.contains(&guard_call) {
|
||||
// Only refactor if the guard is still present (not dropped).
|
||||
let _ = dropped_guard; // suppress unused warning
|
||||
src = src.replace(
|
||||
&format!(" pub fn turn_on(&mut self) -> Result<bool, String> {{\n {guard_call}"),
|
||||
&format!(" {helper_def}\n pub fn turn_on(&mut self) -> Result<bool, String> {{\n {new_call}"),
|
||||
);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// v1.1: real Z3 verification. Run Z3 on the candidate's invariants.
|
||||
let z3_result = verify_toggle(&src);
|
||||
|
||||
ImplCandidate {
|
||||
id: next_id(),
|
||||
rust_source: src,
|
||||
invariant_holds: false, // any perturbation is treated as suspect
|
||||
counterexample_depth: depth.max(1),
|
||||
z3_result,
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -193,11 +294,12 @@ fn descend(
|
|||
for _ in 0..perturbations_per_candidate {
|
||||
let mut child = perturb(&parent.rust_source, rng);
|
||||
// A child of a correct parent may itself be correct if the
|
||||
// perturbation is semantically neutral. Approximate: if the
|
||||
// child's source is byte-identical to the parent, it holds.
|
||||
// perturbation is semantically neutral. We already ran Z3
|
||||
// in perturb(), so trust the result. But if the source is
|
||||
// byte-identical to the parent, inherit the parent's result
|
||||
// to avoid redundant Z3 calls.
|
||||
if child.rust_source == parent.rust_source {
|
||||
child.invariant_holds = parent.invariant_holds;
|
||||
child.counterexample_depth = parent.counterexample_depth;
|
||||
child.z3_result = parent.z3_result.clone();
|
||||
}
|
||||
if action(&child) < action(parent) {
|
||||
candidates.push(child);
|
||||
|
|
@ -211,11 +313,20 @@ fn descend(
|
|||
fn toggle_switch_finds_stationary_point() {
|
||||
// --- Spec §2.4 step 1: Seed N=20 candidates ---
|
||||
let mut rng = Lcg::new(0xC0FFEE_BABE_1234); // fixed seed for byte-stability (Gate C)
|
||||
|
||||
// Gold candidate: verify via Z3. The gold source has both guards intact,
|
||||
// so Z3 should return Proved for both obligations.
|
||||
let gold_result = verify_toggle(GOLD_SOURCE);
|
||||
assert_eq!(
|
||||
gold_result,
|
||||
Z3Result::Proved,
|
||||
"gold candidate must verify as Proved via Z3 — got {gold_result:?}"
|
||||
);
|
||||
|
||||
let gold = ImplCandidate {
|
||||
id: next_id(),
|
||||
rust_source: GOLD_SOURCE.to_string(),
|
||||
invariant_holds: true, // gold candidate satisfies invariants
|
||||
counterexample_depth: 0,
|
||||
z3_result: gold_result,
|
||||
};
|
||||
let mut candidates: Vec<ImplCandidate> = vec![gold.clone()];
|
||||
// Generate 19 perturbed candidates for N=20 total.
|
||||
|
|
@ -230,7 +341,11 @@ fn toggle_switch_finds_stationary_point() {
|
|||
// --- Falsification condition §2.6 #1: scores must not be flat ---
|
||||
let variance = {
|
||||
let mean = scores.iter().sum::<f64>() / scores.len() as f64;
|
||||
scores.iter().map(|s| (s - mean).powi(2)).sum::<f64>() / scores.len() as f64
|
||||
scores
|
||||
.iter()
|
||||
.map(|s| (s - mean).powi(2))
|
||||
.sum::<f64>()
|
||||
/ scores.len() as f64
|
||||
};
|
||||
assert!(
|
||||
variance > 0.0,
|
||||
|
|
@ -253,17 +368,17 @@ fn toggle_switch_finds_stationary_point() {
|
|||
let stationary_action = action(stationary);
|
||||
|
||||
// The stationary point should be the gold candidate (lowest action:
|
||||
// invariant_holds=true → distance 0, and it's the simplest correct form).
|
||||
// z3_result=Proved → distance 0, and it's the simplest correct form).
|
||||
assert!(
|
||||
stationary.invariant_holds,
|
||||
"FALSIFICATION: stationary candidate does not hold invariants — \
|
||||
stationary.z3_result.holds(),
|
||||
"FALSIFICATION: stationary candidate does not hold invariants (Z3 result = {:?}) — \
|
||||
variational selection found no correct stationary point. \
|
||||
stationary action = {stationary_action}, source =\n{}",
|
||||
stationary.z3_result,
|
||||
stationary.rust_source
|
||||
);
|
||||
|
||||
// --- Falsification condition §2.6 #1 (refined): minimum is well-defined ---
|
||||
// Either unique, or tie broken deterministically by lower id.
|
||||
let min_count = candidates
|
||||
.iter()
|
||||
.filter(|c| (action(c) - stationary_action).abs() < 1e-9)
|
||||
|
|
@ -285,8 +400,17 @@ fn toggle_switch_finds_stationary_point() {
|
|||
);
|
||||
}
|
||||
|
||||
// --- Z3 verification of the stationary point (spec §2.4 step 5) ---
|
||||
// Re-verify the stationary candidate via Z3 to confirm Proved.
|
||||
let reverify = verify_toggle(&stationary.rust_source);
|
||||
assert_eq!(
|
||||
reverify,
|
||||
Z3Result::Proved,
|
||||
"stationary candidate must re-verify as Proved via Z3 — got {reverify:?}"
|
||||
);
|
||||
|
||||
// --- Report (printed to stdout for the falsification record) ---
|
||||
println!("=== Lagrangia reducer: ToggleSwitch stationary point ===");
|
||||
println!("=== Lagrangia reducer v1.1: ToggleSwitch stationary point (real Z3) ===");
|
||||
println!("candidates scored: {}", candidates.len());
|
||||
println!("score variance (pre-descent): {variance:.6}");
|
||||
println!("stationary candidate id: {}", stationary.id);
|
||||
|
|
@ -297,10 +421,14 @@ fn toggle_switch_finds_stationary_point() {
|
|||
lagrangia::invariant_distance(stationary),
|
||||
byte_entropy(stationary.rust_source.as_bytes())
|
||||
);
|
||||
println!("stationary invariant_holds: {}", stationary.invariant_holds);
|
||||
println!("stationary z3_result: {:?}", stationary.z3_result);
|
||||
println!(
|
||||
"stationary source (first 200 chars): {:?}",
|
||||
&stationary.rust_source.chars().take(200).collect::<String>()
|
||||
&stationary
|
||||
.rust_source
|
||||
.chars()
|
||||
.take(200)
|
||||
.collect::<String>()
|
||||
);
|
||||
println!("=== Lagrangia reducer: PASS — stationary point found ===");
|
||||
println!("=== Lagrangia reducer v1.1: PASS — stationary point found + Z3-verified ===");
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue