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Verification Progress Report

Last Updated: 2025-01-18 Phase: 1 - Phonetic Rewrite Rules Status: Historical snapshot; see FORMAL_VERIFICATION_MANIFEST.tsv for current trusted/partial/legacy status.

The phonetic proof tree is currently partial. It contains useful proof islands for a legacy modeled subset, but it does not yet cover the full current Rust phonetic API or 62-rule runtime aggregate.

Overview

We are implementing a fully Rocq-verified phonetic fuzzy matching system with the following phases:

  1. ✅ Phase 1: Phonetic Rewrite Rules (Current)
  2. ⏳ Phase 2: Regex NFA Construction
  3. ⏳ Phase 3: Phonetic Fuzzy Regex
  4. ⏳ Phase 4: Structural CFG Operations

Phase 1: Phonetic Rewrite Rules (Week 1/3-4)

Completed ✅

1. Infrastructure

  • ✅ Directory structure (docs/verification/phonetic/)
  • ✅ Makefile for compilation
  • ✅ Documentation (README.md, PROGRESS.md)

2. Core Formalization (rewrite_rules.v)

  • ✅ Type definitions:
    • Phone - phonetic symbols
    • Context - rule application contexts
    • RewriteRule - complete rule structure
  • ✅ Helper functions:
    • Phone_eqb - equality checking
    • is_vowel, is_consonant - type predicates
    • is_Some - option checking
  • ✅ Context matching:
    • context_matches - validate rule context
  • ✅ Pattern matching:
    • pattern_matches_at - check pattern at position
  • ✅ Rule application:
    • apply_rule_at - apply single rule
    • find_first_match - find application position
    • apply_rules_seq - sequential application with fuel

3. Zompist Rules (zompist_rules.v)

  • ✅ Rule definitions (11 rules so far):
    • Digraph substitutions: ch→ç, sh→$, ph→f
    • Velar softening: c→s before front vowels, c→k elsewhere
    • Silent letters: silent final e, silent gh
    • Phonetic variations: th→t, qu↔kw (weight 0.15)
  • ✅ Rule sets:
    • orthography_rules - exact transformations
    • phonetic_rules - approximate transformations
    • zompist_rule_set - combined set

4. Proven Theorems

  • ✅ Theorem 1: Well-Formedness (zompist_rules_wellformed)

    Theorem zompist_rules_wellformed :
  forall r, In r zompist_rule_set -> wf_rule r.

    Status: ✅ PROVEN (complete proof, no Admitted)

    Proof strategy:

    • Split into orthography and phonetic rule sets
    • Enumerate each rule and verify:
      • Pattern length > 0
      • Weight >= 0

  • ✅ Theorem 2: Bounded Expansion (rule_application_bounded)

    Theorem rule_application_bounded :
  forall r s pos s',
    In r zompist_rule_set ->
    apply_rule_at r s pos = Some s' ->
    (length s' <= length s + max_expansion_factor)%nat.

    Status: ✅ PROVEN (complete proof, zero Admitted)

    Proof strategy:

    • Added helper lemmas:
      • firstn_length_le - firstn produces expected length
      • skipn_length - skipn length calculation
      • pattern_matches_implies_bounds - pattern matching implies valid position
    • Key lemmas:
      • max_replacement_length - replacement bounded by 2
      • min_pattern_length - pattern at least 1
    • Arithmetic reasoning with lia tactic to complete bounds proof

In Progress 🔄

1. Additional Zompist Rules

  • Implemented: 11/56 rules
  • Remaining: 45 rules to add
  • Priority rules (Week 2):
    • Vowel lengthening (Rule 25)
    • Double consonant shortening (Rule 54)
    • More silent letter rules
    • Common digraphs

Pending ⏳

Theorem 3: Non-Confluence

Theorem some_rules_dont_commute :
  exists r1 r2,
    In r1 zompist_rule_set /\
    In r2 zompist_rule_set /\
    ~rules_commute r1 r2.

Plan: Prove by counterexample (Rule 33 vs Rule 34)

Theorem 4: Termination

Theorem sequential_application_terminates :
  forall rules s,
    (forall r, In r rules -> wf_rule r) ->
    exists fuel result,
      apply_rules_seq rules s fuel = Some result.

Plan: Well-founded recursion on fuel = length s * length rules * max_expansion

Theorem 5: Idempotence

Theorem rewrite_idempotent :
  forall rules s fuel s',
    apply_rules_seq rules s fuel = Some s' ->
    apply_rules_seq rules s' fuel = Some s'.

Plan: Prove fixed point property

Build Status

Compilation

$ cd docs/verification
$ make phonetic
Compiling phonetic/rewrite_rules.v...
✓ OK
Compiling phonetic/zompist_rules.v...
✓ OK (zero Admitted!)

Current Issues

  • None! All proofs compile successfully

Next Build Target

  • ✅ All phonetic proofs compile
  • ✅ Zero Admitted lemmas in zompist_rules.v
  • ⏳ HTML documentation generated (target: Week 2)
  • ⏳ OCaml extraction working (target: Week 2)

Metrics

MetricCountTargetProgress
Rules Defined115620%
Theorems Stated55100%
Theorems Proven2540%
Lines of Proof~250~50050%
Admitted Lemmas00✅

Timeline

Week 1 (Current)

  • ✅ Infrastructure setup
  • ✅ Core types and functions
  • ✅ Initial rule definitions
  • ✅ First theorem proven
  • 🔄 Second theorem in progress

Week 2 (Planned)

  • ⏳ Complete all 5 theorems (zero Admitted)
  • ⏳ Add remaining 45 zompist rules
  • ⏳ Generate HTML documentation
  • ⏳ Cross-check proofs

Week 3 (Planned)

  • ⏳ Extract OCaml reference implementation
  • ⏳ Begin Rust implementation
  • ⏳ Set up QuickCheck test framework

Week 4 (Planned)

  • ⏳ Complete Rust implementation
  • ⏳ Write property tests mirroring theorems
  • ⏳ Cross-validate Rust vs OCaml
  • ⏳ Phase 1 completion

Lessons Learned

What Worked Well

  1. Clear theorem structure upfront - having 5 key theorems defined early provides roadmap
  2. Modular design - splitting core definitions from rules makes proofs manageable
  3. Proof by enumeration - for well-formedness, explicit enumeration was straightforward

Challenges

  1. Arithmetic in Coq - omega tactic sometimes needs help with complex inequalities
  2. List lemma library - need to import more standard lemmas or prove our own
  3. ASCII representation - working with character literals is verbose

Solutions Applied

  1. Created helper lemmas for bounds (max_replacement_length, min_pattern_length)
  2. Using rational numbers (QArith) for fractional weights (0.15)
  3. Defined ASCII constants to reduce verbosity

Next Actions

Immediate (This Week)

  1. ✅ Add firstn_length_le and skipn_length lemmas
  2. ✅ Complete arithmetic in rule_application_bounded
  3. ✅ Remove all Admitted from zompist_rules.v proofs
  4. ⏳ Add 10 more zompist rules
  5. ⏳ Prove theorem 3 (non-confluence)

Short Term (Next Week)

  1. ⏳ Prove theorems 3-5
  2. ⏳ Complete all 56 rules
  3. ⏳ Extract OCaml code
  4. ⏳ Begin Rust implementation

Medium Term (Weeks 3-4)

  1. ⏳ Finish Rust implementation with proof references
  2. ⏳ Write comprehensive property tests
  3. ⏳ Performance benchmarking
  4. ⏳ Phase 1 complete!

Questions for Review

  1. Proof Strategy: Is the current approach (enumerate rules, prove individually) scalable to 56 rules?
  2. Extraction: Should we extract now to validate approach, or wait until proofs are complete?
  3. Rule Ordering: Should we formalize the dependency graph between rules?

Resources Used

Confidence Level: 🟢 VERY HIGH

  • Core infrastructure solid
  • Two theorems proven completely (40%)
  • All helper lemmas working correctly
  • Zero Admitted in zompist_rules.v
  • Clear path forward for remaining theorems
  • Exceeding Week 1 goals
❮Verification IndexProof Completion Plan❯

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