Contextual Completion - Formal Verification Documentation

Category: Contextual Completion Correctness Status: Proof-sketch documentation complete; contextual Rocq modules are not present in this repository yet Started: 2025-01-21 Dependencies: Core dictionary backends (Phase 10)

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Table of Contents

1. Overview
2. Motivation
3. Theorem Summary
4. Reading Order
5. Dependencies
6. Implementation
7. References

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Overview

This category contains formal verification documentation for the contextual completion engine in liblevenshtein-rust. Contextual completion provides hierarchical, scope-aware symbol completion with draft buffers, undo/redo support, and efficient incremental updates.

Key Features Verified

1. Hierarchical Contexts: Parent-child relationships with inheritance
2. Draft Buffers: Incremental character-by-character updates
3. Checkpoint Stacks: Undo/redo with exact state restoration
4. Query Fusion: Correct merging of draft and finalized symbols
5. Distance Calculation: Naive Levenshtein distance correctness
6. Visibility Rules: Proper symbol visibility across context boundaries
7. Finalization Atomicity: All-or-nothing draft→dictionary transitions

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Motivation

The Problem

The rholang-language-server depends critically on liblevenshtein's contextual completion for:

• LSP Code Completion: Scope-aware symbol suggestions while typing
• Incremental Updates: Sub-millisecond response to keystrokes
• Nested Scopes: Correct symbol visibility in contract/block hierarchies

Without formal verification, subtle bugs in context management could cause:

• Missing completions: Symbols not visible in child scopes
• Leaked symbols: Private variables visible in wrong scopes
• Inconsistent state: Draft buffer desynchronization
• Performance degradation: 10,000x slowdown if incremental updates break

The Solution

Formal verification provides mathematical certainty that:

1. Context hierarchies correctly implement lexical scoping
2. Draft buffers maintain UTF-8 validity and consistency
3. Undo/redo operations are idempotent and complete
4. Query results are sound and complete (no false positives/negatives)
5. Distance calculations match formal Levenshtein definition
6. Symbol visibility follows strict parent-child rules
7. Finalization is atomic (no partial states observable)

Downstream Impact

These theorems unblock formal verification of:

• rholang-language-server scope detection (depends on Theorems 1, 2, 4, 6)
• LSP goto-definition (depends on Theorem 1, 6)
• LSP refactoring/rename (depends on Theorem 3, 6, 7)
• Code completion ranking (depends on Theorem 4, 5)

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Theorem Summary

#	Theorem	Property	Status	Pages
1	Context Tree Visibility	visible_contexts(ctx) returns all ancestors in order	🚧 Documenting	4
2	Draft Buffer Consistency	Insert/delete maintain valid UTF-8 boundaries	🚧 Documenting	3
3	Checkpoint Stack Correctness	Undo restores exact previous state	🚧 Documenting	3
4	Query Fusion Completeness	complete() returns union of draft + finalized	🚧 Documenting	4
5	Levenshtein Distance Correctness	Naive $\mathcal{O}(n\cdot m)$ matches formal definition	🚧 Documenting	5
6	Hierarchical Visibility Soundness	Children see parents, parents don't see children	🚧 Documenting	3
7	Finalization Atomicity	Draft→dictionary is all-or-nothing	🚧 Documenting	4

Total: 7 main theorems, ~26 pages of formal documentation

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Reading Order

For LSP Developers (Minimal Path)

Focused on properties needed for rholang-language-server scope detection:

1. Theorem 1 (Context Visibility) - How context trees work
2. Theorem 2 (Draft Consistency) - Incremental updates
3. Theorem 4 (Query Fusion) - What complete() guarantees
4. Theorem 6 (Hierarchical Visibility) - Scope isolation rules

Time: ~1 hour (14 pages)

For Library Maintainers (Complete Understanding)

Full coverage of all correctness properties:

1. Theorem 1 → Establishes context tree foundation
2. Theorem 6 → Builds on Theorem 1 for visibility rules
3. Theorem 2 → Draft buffer operations
4. Theorem 3 → Builds on Theorem 2 for undo/redo
5. Theorem 7 → Builds on Theorem 2 for finalization
6. Theorem 4 → Combines all context/draft/finalized properties
7. Theorem 5 → Independent distance calculation verification

Time: ~2-3 hours (26 pages)

For Formal Verification Engineers

Start with the proof-sketch pages, then compare their assumptions with the existing Rocq core under rocq/liblevenshtein/:

1. Read all markdown theorems first (overview)
2. Study the checked non-contextual Rocq modules for naming, invariant, and proof-structure conventions
3. If these sketches are promoted, build contextual modules in dependency order:
   • Visibility.v (Theorems 1, 6)
   • DraftBuffer.v (Theorems 2, 3)
   • Query.v (Theorems 4, 5)
   • Finalization.v (Theorem 7)

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Dependencies

Theorem Dependencies (Within This Category)

Theorem 1 (Context Visibility)
    ↓
Theorem 6 (Hierarchical Visibility)
    ↓
Theorem 4 (Query Fusion) ← Theorem 2 (Draft Consistency)
                           ↑
                       Theorem 3 (Checkpoint) ← Theorem 2
                       Theorem 7 (Finalization) ← Theorem 2

Theorem 5 (Distance) - Independent

External Dependencies

These theorems assume correct dictionary backends:

• Theorem 4 assumes Theorem 8 (Trie Reachability) from Category 07
• Theorem 4 assumes Theorem 17 (Prefix Traversal) from Category 08
• Theorem 7 assumes Theorem 10 (Dynamic Consistency) from Category 07

See docs/formal-verification/proofs/07_dictionary_backends/README.md for backend theorems.

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Implementation

Source Files

Core Implementation (src/collection/dawg/contextual_completion/):

• context.rs (lines 1-350) - Context tree structure

  • Context type definition
  • visible_contexts() method (Theorem 1, 6)
  • Parent-child management

• draft_buffer.rs (lines 1-280) - Draft buffer operations

  • DraftBuffer type
  • insert_char(), delete_char() methods (Theorem 2)
  • UTF-8 boundary handling

• checkpoint.rs (lines 1-180) - Checkpoint stack

  • Checkpoint type
  • save(), restore() methods (Theorem 3)
  • Stack invariants

• engine.rs (lines 1-650) - Main completion engine

  • DynamicContextualCompletionEngine type
  • complete() method (Theorem 4)
  • levenshtein_distance() helper (Theorem 5)
  • finalize() method (Theorem 7)

Test Coverage

Unit Tests (src/collection/dawg/contextual_completion/mod.rs::#[cfg(test)]):

• test_context_hierarchy_* - Context tree operations
• test_draft_buffer_* - Incremental updates
• test_checkpoint_* - Undo/redo
• test_complete_* - Query fusion
• test_distance_* - Levenshtein calculation
• test_visibility_* - Hierarchical scoping
• test_finalize_* - Atomicity guarantees

Integration Tests (rholang-language-server):

• /home/dylon/Workspace/f1r3fly.io/rholang-language-server/tests/test_completion.rs
  • test_nested_scope_priority_inner - Tests Theorem 1, 4, 6
  • test_local_symbol_priority_inner - Tests Theorem 6
  • Completion performance tests - Test Theorem 2, 4

Property-test specifications:

• Theorem 1, 6: Context visibility is transitive
• Theorem 2: UTF-8 boundary preservation
• Theorem 3: Undo-redo idempotence
• Theorem 4: Query result set properties
• Theorem 5: Distance triangle inequality

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References

Theory Documents

Contextual Completion:

• docs/algorithms/07-contextual-completion/README.md - Algorithm overview
• docs/algorithms/07-contextual-completion/patterns/ - Design patterns
• docs/algorithms/07-contextual-completion/implementation/ - Implementation notes

Related Algorithms:

• docs/algorithms/06-zipper-navigation/README.md - PrefixZipper (Theorem 4 depends on this)
• docs/algorithms/01-dictionary-layer/README.md - Dictionary backends (Theorem 7 depends on this)

Implementation Documentation

API Documentation:

• Run cargo doc --open and navigate to:
  • liblevenshtein::collection::dawg::contextual_completion
  • liblevenshtein::collection::dawg::contextual_completion::engine::DynamicContextualCompletionEngine

Developer Guide:

• docs/developer-guide/ - Contribution guidelines
• docs/examples/06-contextual/ - Usage examples

Academic Background

Contextual Completion (general concept):

• Wikipedia: Autocomplete
• ACM Survey: Code Completion

Levenshtein Distance:

• Wagner & Fischer, "The String-to-String Correction Problem" (1974)
• Wikipedia: Levenshtein Distance

Formal Verification:

• /var/tmp/debug/f1r3node/docs/formal-verification/coq/ - Similar Rocq proofs for Rholang
• Software Foundations - Coq tutorial
• CompCert - Verified C compiler (similar methodology)

Downstream Projects

rholang-language-server:

• /home/dylon/Workspace/f1r3fly.io/rholang-language-server/docs/completion_performance_summary.md
  • Documents how LSP uses contextual completion
  • Performance benchmarks (depends on Theorem 2, 4)
  • Phase 9 optimization (uses PrefixZipper from Theorem 17)

Scope-detection specifications:

• /home/dylon/Workspace/f1r3fly.io/rholang-language-server/docs/formal-verification/scope-detection.md
  • Scope detection verification target
  • Depends on Theorems 1, 2, 4, 6 from this category

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Roadmap

Phase 9.1: Documentation

Goal: Create markdown documentation for all 7 theorems

Status: Complete proof-sketch documentation

Progress:

• [x] Category README.md (this file)
• [x] Theorem 1: Context Visibility
• [x] Theorem 2: Draft Consistency
• [x] Theorem 3: Checkpoint Stack
• [x] Theorem 4: Query Fusion
• [x] Theorem 5: Distance Correctness
• [x] Theorem 6: Hierarchical Visibility
• [x] Theorem 7: Finalization Atomicity

Rocq Promotion Targets

Goal: Formalize types and theorems in Rocq

Candidate modules:

• rocq/liblevenshtein/ContextualCompletion/Core.v - Type definitions
• rocq/liblevenshtein/ContextualCompletion/Visibility.v - Theorems 1, 6
• rocq/liblevenshtein/ContextualCompletion/DraftBuffer.v - Theorems 2, 3
• rocq/liblevenshtein/ContextualCompletion/Query.v - Theorems 4, 5
• rocq/liblevenshtein/ContextualCompletion/Finalization.v - Theorem 7

Priority order: Theorems 1, 2, 4 are the most critical for LSP integration.

Property-Test Promotion Targets

Goal: Add property-based tests matching formal specifications

Candidate coverage:

• Property tests for all 7 theorems using proptest
• Integration with Rust test suite
• CI enforcement of properties

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Contributing

Adding Proofs

1. Document first: Create markdown file in this directory
2. Formalize (optional): Add theorem to Rocq files
3. Test: Add property-based tests to Rust implementation
4. Review: Submit PR with all three components

Style Guidelines

Follow the established pattern from docs/formal-verification/proofs/01_subsumption_properties.md:

• Sections: Overview, Definitions, Theorem Statement, Proof Sketch, Implementation, Test Coverage
• Code blocks: Use Coq for formal statements, Rust for implementation
• Diagrams: ASCII art where helpful
• Cross-references: Link to source files (with line numbers) and tests

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Changelog

2025-01-21 - Phase 9 Started

Added:

• Category structure (proofs/06_contextual_completion/)
• This README
• Theorem documentation planned (7 files)

Status: Proof-sketch documentation complete; contextual Rocq modules are not present in this repository yet.

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License

This formal verification work is part of the liblevenshtein-rust project and follows the same license (MIT/Apache-2.0).

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Last Updated: 2025-01-21 Promotion Policy: These pages are proof-sketch artifacts unless matching checked Rocq modules are added to the manifest.