Logic Prover (logic-prover)
logic-prover is a formal logic theorem prover, explorer, deducer, and Lean 4 exporter in Python with optional Cython acceleration.
📚 Full Documentation & API Reference: https://francofantomius.com/logic-prover/
Features
- First-Order & Second-Order Logic AST: Full support for parameterized sorts, canonical variable renaming, and substitutions.
- Resolution Prover with Equality: Otter/Discount given-clause loop with superposition and natural deduction proof reconstruction.
- Formula Explorer: Diversity-guided formula generation and interestingness heuristic ranking.
- Deducer: Network-level minimal hypothesis detection and equivalence classification.
- Lean 4 Export: High-fidelity translation of formulas, statements, and tactic proofs into Lean 4 code.
- Interactive HTML Graphs: Proof DAG and dependency graph visualizer.
- Optional Cython Acceleration: Core AST, substitutions, and resolution engine compiled to native C extensions for high performance.
- Automated Documentation & Logging: Structured logging subsystem and Reflection/AST documentation generator.
Installation
From PyPI
Install the latest release from PyPI:
pip install logic-prover
To install with visualization support (interactive HTML graphs with Jinja2):
pip install "logic-prover[vis]"
From GitHub
You can also install the latest development version directly from GitHub:
pip install git+https://github.com/FrancoFantomius/logic-prover.git
From Source (Development)
Clone the repository and install in editable mode:
git clone https://github.com/FrancoFantomius/logic-prover.git
cd logic-prover
pip install -e ".[dev,vis]"
Quickstart & CLI
Syntax Note: Formulas require
v0,v1, ... for individual variables,=>(orimplies/→) for implication,&(orand/∧) for conjunction,|(oror/∨) for disjunction, and~(ornot/¬) for negation.
# Initialize Knowledge Database
logic-prover init --reset
# Prove a Theorem
logic-prover prove "(forall v0 (P(v0) => Q(v0))) => ((forall v0 P(v0)) => (forall v0 Q(v0)))"
# Explore Candidate Formulas
logic-prover explore --strategy mixed --count 20 --top-k 5
# Analyze Network Dependencies
logic-prover analyze
# Export to Lean 4
logic-prover export lean --output theorem.lean --stubs-only
# Export Interactive Proof Graph
logic-prover export graph --type dependency --output network.html
# Generate API Documentation
logic-prover docs --output-dir docs
(You can also invoke via python -m logic_prover)
Python API Example
import logic_prover
from logic_prover.kb import get_combined_signature
from logic_prover.core.parser import parse_formula, to_string
from logic_prover.prover.engine import TheoremProver
from logic_prover.config import SolverConfig
from logic_prover.utils.logging import setup_logging
# Configure structured logging
setup_logging(log_level="INFO")
# Load logical signature containing predefined predicates & functions
signature = get_combined_signature()
# Configure and instantiate TheoremProver
config = SolverConfig(prover_timeout_sec=5.0, prover_max_steps=500)
prover = TheoremProver(signature=signature, config=config)
# Parse hypothesis and target formula (using 'v0', 'v1', ... for variables)
hypothesis = parse_formula("forall v0, (P(v0) => Q(v0))", signature=signature)
conclusion = parse_formula("(forall v0, P(v0)) => (forall v0, Q(v0))", signature=signature)
# Run resolution theorem prover (returns a ProofDAG on success)
proof_dag = prover.prove(target=conclusion, premises=[hypothesis])
print(f"Proof Found for target: {to_string(proof_dag.conclusion)}")
for step in proof_dag.topological_order():
print(f" [{step.id}] {step.rule}: {to_string(step.conclusion)}")
Documentation
Full interactive documentation, API reference, architecture deep dives, and tutorials are available at:
🌐 https://francofantomius.com/logic-prover/
You can also build the documentation locally using MkDocs:
pip install "logic-prover[docs]"
mkdocs serve
Project Architecture
logic_prover/
├── core/ # AST, Sorts, Signature, Parser, Substitutions, Rewriting, Database
├── kb/ # Foundational mathematical knowledge bases (Logic, Equality, Numbers, Sets, Groups)
├── prover/ # Resolution Prover, Clausification, Proof Reconstruction
├── explorer/ # Formula Generator, Diversity Metrics, Ranking Heuristics
├── deducer/ # Network Analysis, Minimal Hypotheses, Equivalence Classes
├── exporters/ # Lean 4 Exporter & HTML Interactive Graph Visualizers
├── sol/ # Second-Order Logic (SOL) Extension
└── utils/ # Logging Subsystem & Automated Doc Generator
Testing
Run unit tests via pytest:
pytest
or with Python's built-in unittest:
python -m unittest discover -s tests
Contributing & Community
We welcome contributions to logic-prover! Please check out the following resources:
- Contributing Guidelines: Setup instructions, code style, testing, and PR workflow.
- Code of Conduct: Community standards and enforcement policies.
- Security Policy: How to report vulnerabilities securely.
- Changelog: Release history and version migration notes.
License & Commercial Use
This project is licensed under the Creative Commons Attribution-NonCommercial 4.0 International Public License (CC BY-NC 4.0). See the LICENSE file for the full legal text.
Key Terms:
- Attribution: You must give appropriate credit to the author (Franco Fantomius), provide a link to the license, and indicate if changes were made.
- Non-Commercial: You may freely use, modify, and distribute this software for academic, research, personal, and non-commercial purposes.
- Commercial Use / Dual Licensing: Any commercial use, including incorporating this software into commercial software, hosted commercial services, or revenue-generating products, requires prior written permission and a commercial license agreement from the author.
For commercial inquiries and licensing agreements, please contact: Franco Fantomius <mail@francofantomius.com>
1 maintainer
Metadata
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Release files for logic-prover 0.1.5
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