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feat: add ECHIDNA integration configuration
Add integration with ECHIDNA neurosymbolic theorem proving platform: - echidna.toml: Main configuration with prover settings, theorem specs, OpenCyc ontology, and DeepProbLog rules - echidna/specs/filesystem.json: Universal proof specification with types, definitions, predicates, and theorem status - docs/ECHIDNA_INTEGRATION.md: Comprehensive integration guide This enables: - Automated multi-prover proof generation (CVC5, HOL Light, Metamath) - Neural completion assistance for admitted lemmas - Semantic understanding via OpenCyc integration - Probabilistic reasoning for proof pattern learning Supports all 12 ECHIDNA provers across 4 tiers.
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‎docs/ECHIDNA_INTEGRATION.md‎

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# ECHIDNA Integration Guide
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This document describes how to integrate Valence Shell with ECHIDNA, the neurosymbolic theorem proving platform.
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## Overview
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[ECHIDNA](https://github.com/hyperpolymath/echidna) (Extensible Cognitive Hybrid Intelligence for Deductive Neural Assistance) is a unified multi-prover system that combines neural proof synthesis with symbolic verification across 12 different theorem provers.
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### Benefits for Valence Shell
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1. **Automated Multi-Prover Generation**: Generate proofs in new systems (CVC5, HOL Light, Metamath) from existing Coq/Lean proofs
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2. **Neural Completion**: AI-assisted completion of admitted lemmas
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3. **Semantic Understanding**: OpenCyc integration for common-sense reasoning about filesystem operations
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4. **Probabilistic Reasoning**: DeepProbLog for learning proof patterns
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## Configuration Files
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### echidna.toml
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The main configuration file at the repository root:
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```toml
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[project]
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name = "valence-shell"
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version = "0.6.0"
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[provers]
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enabled = ["coq", "lean4", "agda", "isabelle", "z3", "cvc5"]
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default = "coq"
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[theorems.mkdir_rmdir_reversible]
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description = "Directory creation is reversible"
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category = "reversibility"
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proven_in = ["coq", "lean4", "agda", "isabelle", "mizar", "z3"]
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```
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### echidna/specs/filesystem.json
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Proof specifications in ECHIDNA's universal format:
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```json
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{
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"types": {
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"Path": { "kind": "alias", "target": "List PathComponent" },
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"Filesystem": { "kind": "function", "domain": "Path", "codomain": "Option FSNode" }
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},
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"theorems": [
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{
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"name": "mkdir_rmdir_reversible",
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"statement": "forall p fs, mkdir_precondition p fs -> rmdir p (mkdir p fs) = fs",
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"status": { "coq": "proven", "lean4": "proven", ... }
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}
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]
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}
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```
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## Supported Provers
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### Tier 1 (Currently Implemented)
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| Prover | Status | Files |
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|--------|--------|-------|
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| **Coq** | 77/78 complete | 7 files, ~1,900 lines |
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| **Lean 4** | 59/59 complete | 5 files, ~850 lines |
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| **Agda** | 55/55 complete | 5 files, ~750 lines |
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| **Isabelle** | 44/44 complete | 5 files, ~750 lines |
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| **Z3** | 15/15 assertions | 1 file, ~160 lines |
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### Tier 2 (Partially Implemented)
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| Prover | Status | Notes |
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|--------|--------|-------|
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| **Mizar** | 44/44 complete | 5 files, ~800 lines |
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| **CVC5** | Pending | Generate from Z3 |
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| **HOL Light** | Pending | Generate from Isabelle |
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| **Metamath** | Pending | Generate from Coq |
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### Tier 3-4 (Future)
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- PVS, ACL2, HOL4
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## Usage
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### Prerequisites
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```bash
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# Install ECHIDNA
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git clone https://github.com/hyperpolymath/echidna
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cd echidna
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just build
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# Or via package manager (when available)
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cargo install echidna
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```
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### Verify Existing Proofs
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```bash
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# Using ECHIDNA CLI
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echidna verify --config echidna.toml
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# Or using just
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just verify-all
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```
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### Generate Proofs for New Systems
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```bash
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# Generate CVC5 from Z3
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echidna generate --source z3 --target cvc5 --theorem mkdir_rmdir_reversible
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# Generate HOL Light from Isabelle
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echidna generate --source isabelle --target hol-light --all
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# Batch generation
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echidna generate --config echidna.toml --targets cvc5,hol-light,metamath
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```
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### Neural Completion
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```bash
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# Complete admitted lemmas
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echidna complete --theorem mkdir_creates_rmdir_precondition
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# Suggest helper lemmas
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echidna suggest --file proofs/coq/filesystem_composition.v --line 333
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```
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## OpenCyc Integration
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The configuration includes OpenCyc ontology for semantic understanding:
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```cyc
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(isa FileSystemOperation Action)
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(isa mkdir FileSystemOperation)
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(inverseOf mkdir rmdir)
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(preconditionFor mkdir parentDirectoryExists)
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```
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This enables ECHIDNA to:
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- Understand that `mkdir` and `rmdir` are inverse operations
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- Know that `mkdir` requires parent directory to exist
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- Suggest related theorems based on semantic similarity
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## DeepProbLog Integration
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Probabilistic rules for proof pattern learning:
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```prolog
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0.95::reverses(mkdir, rmdir).
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0.95::reverses(createFile, deleteFile).
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0.90::reverses(writeFile, writeOldContent).
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```
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This enables:
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- Learning proof patterns from successful proofs
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- Predicting likely theorems
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- Suggesting proof strategies
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## Theorem Categories
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| Category | Description | Examples |
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|----------|-------------|----------|
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| `reversibility` | Operations can be undone | `mkdir_rmdir_reversible` |
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| `composition` | Multiple operations compose | `operation_sequence_reversible` |
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| `equivalence` | Filesystem state equality | `fs_equiv_refl`, `fs_equiv_trans` |
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| `content` | File content operations | `write_file_reversible` |
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| `maa` | MAA framework integration | `modification_reversible` |
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| `path` | Path helper lemmas | `parent_path_ne_self` |
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## Aspect Tags
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Theorems are tagged with aspects for intelligent categorization:
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- `filesystem` - Related to filesystem operations
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- `directory` - Directory-specific
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- `file` - File-specific
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- `undo` - Supports undo/rollback
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- `cno` - Certified Null Operation
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- `identity` - Identity element properties
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- `algebraic` - Algebraic structure properties
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- `maa` - MAA framework specific
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- `audit` - Audit trail related
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## CI/CD Integration
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Add to `.gitlab-ci.yml`:
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```yaml
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echidna-verify:
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stage: test
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script:
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- echidna verify --config echidna.toml
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rules:
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- changes:
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- proofs/**/*
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```
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## Known Limitations
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1. **is_empty_dir semantics**: One admitted proof in Coq related to path prefix semantics
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2. **Neural completion**: Requires trained model (not yet available for filesystem proofs)
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3. **Tier 3-4 provers**: Not yet implemented in ECHIDNA
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## Roadmap
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1. **Phase 1** (Current): Configuration and specification files
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2. **Phase 2**: Generate CVC5, HOL Light, Metamath proofs
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3. **Phase 3**: Train neural model on filesystem proof patterns
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4. **Phase 4**: Complete admitted lemmas with neural assistance
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5. **Phase 5**: Extend to PVS, ACL2, HOL4
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## Resources
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- [ECHIDNA Repository](https://github.com/hyperpolymath/echidna)
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- [ECHIDNA Documentation](https://echidna.dev/docs)
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- [Valence Shell Proofs](../proofs/)
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- [Proof Status](../PROOF_STATUS.md)
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## Contributing
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To add support for a new theorem:
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1. Add theorem to `echidna.toml` under `[theorems]`
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2. Add specification to `echidna/specs/filesystem.json`
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3. Implement in at least one Tier 1 prover
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4. Run `echidna generate` to create proofs for other systems
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5. Submit PR with all generated proofs
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---
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**Last Updated**: 2025-12-17
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**ECHIDNA Version**: Compatible with 0.1.x

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