DS - A Deductive System

A deductive system for logical inference, implemented in C++. The library provides bindings for Python (via pybind11) and TypeScript/JavaScript (via Emscripten/WebAssembly).

Architecture

• C++ Core: The core implementation in src/ and include/ds/ provides the fundamental data structures and algorithms
• Python Bindings: Built with pybind11, wrapping the C++ core (see apyds/)
• TypeScript/JavaScript Bindings: Built with Emscripten, compiling C++ to WebAssembly (see atsds/)

Features

• Multi-Language Support: Use the same deductive system in C++, Python, or TypeScript/JavaScript
• Logical Terms: Work with variables, items (constants/functors), and lists
• Rule-Based Inference: Define rules and facts, perform logical deduction
• Unification and Matching: Unify terms and match rules
• Search Engine: Built-in search mechanism for iterative inference
• WebAssembly: Run inference in the browser or Node.js environments
• Type-Safe: Strong typing support in TypeScript and Python

Installation

TypeScript/JavaScript (npm)

The TypeScript/JavaScript package wraps the C++ core via WebAssembly.

npm install atsds

The package includes WebAssembly binaries and TypeScript type definitions.

Python (pip)

The Python package wraps the C++ core via pybind11.

pip install apyds

Requires Python 3.10-3.14.

C++ (Core Library)

The C++ library is the core implementation. Both Python and TypeScript bindings are built on top of it.

Using vcpkg

Clone the repository and use the overlay port:

git clone https://github.com/USTC-KnowledgeComputingLab/ds.git
vcpkg install ds --overlay-ports=./ds/ports

Add to your vcpkg.json:

{
  "dependencies": ["ds"]
}

In your CMakeLists.txt:

find_package(ds CONFIG REQUIRED)
target_link_libraries(your_target PRIVATE ds::ds)

Building from Source

git clone https://github.com/USTC-KnowledgeComputingLab/ds.git
cd ds
cmake -B build
cmake --build build

Include the headers from include/ds/ in your C++ project.

Quick Start

TypeScript/JavaScript Example

import { Rule, Search } from "atsds";

// Create a search engine
const search = new Search(1000, 10000);

// Modus ponens: P -> Q, P |- Q
search.add("(`P -> `Q) `P `Q");
// Axiom schema 1: p -> (q -> p)
search.add("(`p -> (`q -> `p))");
// Axiom schema 2: (p -> (q -> r)) -> ((p -> q) -> (p -> r))
search.add("((`p -> (`q -> `r)) -> ((`p -> `q) -> (`p -> `r)))");
// Axiom schema 3: (!p -> !q) -> (q -> p)
search.add("(((! `p) -> (! `q)) -> (`q -> `p))");

// Premise: !!X
search.add("(! (! X))");

// Target: X (double negation elimination)
const target = new Rule("X");

// Execute search until target is found
while (true) {
    let found = false;
    search.execute((candidate) => {
        if (candidate.key() === target.key()) {
            console.log("Found:", candidate.toString());
            found = true;
            return true; // Stop search
        }
        return false; // Continue searching
    });
    if (found) break;
}

Python Example

import apyds

# Create a search engine
search = apyds.Search(1000, 10000)

# Modus ponens: P -> Q, P |- Q
search.add("(`P -> `Q) `P `Q")
# Axiom schema 1: p -> (q -> p)
search.add("(`p -> (`q -> `p))")
# Axiom schema 2: (p -> (q -> r)) -> ((p -> q) -> (p -> r))
search.add("((`p -> (`q -> `r)) -> ((`p -> `q) -> (`p -> `r)))")
# Axiom schema 3: (!p -> !q) -> (q -> p)
search.add("(((! `p) -> (! `q)) -> (`q -> `p))")

# Premise: !!X
search.add("(! (! X))")

# Target: X (double negation elimination)
target = apyds.Rule("X")

# Execute search until target is found
while True:
    found = False
    def callback(candidate):
        global found
        if candidate == target:
            print("Found:", candidate)
            found = True
            return True  # Stop search
        return False  # Continue searching
    search.execute(callback)
    if found:
        break

C++ Example

#include <cstdio>
#include <cstring>
#include <ds/ds.hh>
#include <ds/search.hh>
#include <ds/utility.hh>

int main() {
    ds::search_t search(1000, 10000);
    
    // Modus ponens: P -> Q, P |- Q
    search.add("(`P -> `Q) `P `Q");
    // Axiom schema 1: p -> (q -> p)
    search.add("(`p -> (`q -> `p))");
    // Axiom schema 2: (p -> (q -> r)) -> ((p -> q) -> (p -> r))
    search.add("((`p -> (`q -> `r)) -> ((`p -> `q) -> (`p -> `r)))");
    // Axiom schema 3: (!p -> !q) -> (q -> p)
    search.add("(((! `p) -> (! `q)) -> (`q -> `p))");
    
    // Premise: !!X
    search.add("(! (! X))");
    
    // Target: X (double negation elimination)
    auto target = ds::text_to_rule("X", 1000);
    
    // Execute search until target is found
    while (true) {
        bool found = false;
        search.execute([&](ds::rule_t* candidate) {
            if (candidate->data_size() == target->data_size() &&
                memcmp(candidate->head(), target->head(), candidate->data_size()) == 0) {
                printf("Found: %s", ds::rule_to_text(candidate, 1000).get());
                found = true;
                return true; // Stop search
            }
            return false; // Continue searching
        });
        if (found) break;
    }
    
    return 0;
}

Core Concepts

Terms

Terms are the basic building blocks of the deductive system:

• Variables: Prefixed with backtick, e.g., `X, `P, `Q
• Items: Constants or functors, e.g., a, father, !
• Lists: Ordered sequences enclosed in parentheses, e.g., (a b c), (father john mary)

Rules

Rules consist of zero or more premises (above the line) and a conclusion (below the line):

premise1
premise2
----------
conclusion

A fact is a rule without premises:

----------
(parent john mary)

Grounding

Grounding substitutes variables with values using a dictionary:

const a = new Term("`a");
const dict = new Term("((`a b))"); // Substitute `a with b
const result = a.ground(dict);
console.log(result.toString()); // "b"

Matching

Matching unifies the first premise of a rule with a fact to produce a new rule. For example, applying modus ponens to double negation elimination:

// Modus ponens rule: (p -> q), p |- q
const mp = new Rule("(`p -> `q)\n`p\n`q\n");
// Double negation elimination axiom: !!x -> x
const pq = new Rule("((! (! `x)) -> `x)");
// Match produces: !!x |- x
console.log(mp.match(pq).toString()); // "(! (! `x))\n----------\n`x\n"

API Overview

TypeScript/JavaScript

• buffer_size(size?: number): Get/set buffer size for internal operations
• String_: String wrapper class
• Variable: Logical variable class
• Item: Item (constant/functor) class
• List: List class
• Term: General term class (variable, item, or list)
• Rule: Logical rule class
• Search: Search engine for inference

Python

• buffer_size(size: int): Set buffer size
• scoped_buffer_size(size: int): Context manager for temporary buffer size
• String: String wrapper class
• Variable: Logical variable class
• Item: Item (constant/functor) class
• List: List class
• Term: General term class
• Rule: Logical rule class
• Search: Search engine for inference

C++ (Core)

All classes are in the ds namespace:

• string_t: String handling
• variable_t: Logical variables
• item_t: Items (constants/functors)
• list_t: Lists
• term_t: General terms
• rule_t: Logical rules
• search_t: Search engine (in <ds/search.hh>)

See header files in include/ds/ for detailed API documentation.

Building from Source

Prerequisites

• For TypeScript: Emscripten SDK
• For Python: Python 3.10-3.14, C++20 compatible compiler, CMake 3.30+
• For C++: C++20 compatible compiler, CMake 3.30+

Build All Components

# Clone repository
git clone https://github.com/USTC-KnowledgeComputingLab/ds.git
cd ds

# Build TypeScript/JavaScript (requires Emscripten)
npm install
npm run build

# Build Python package
uv sync --extra dev

# Build C++ library
cmake -B build
cmake --build build

Running Tests

# TypeScript/JavaScript tests
npm test

# Python tests
pytest

# C++ tests (if available)
cd build && ctest

Examples

Example programs are provided in the examples/ directory:

• examples/main.mjs: TypeScript/JavaScript example
• examples/main.py: Python example
• examples/main.cc: C++ example

Each example demonstrates logical inference using propositional logic axioms.

Support Packages

• BNF Conversion Library (apyds-bnf, atsds-bnf): Bidirectional conversion between DS syntax formats. See /bnf for details.

Development

Code Formatting

The project uses code formatting tools for consistency:

• C++: clang-format (.clang-format config provided)
• Python: ruff (configured in pyproject.toml)
• TypeScript: Biome (configured in biome.json)

Pre-commit Hooks

Pre-commit hooks are configured in .pre-commit-config.yaml.

License

This project is licensed under the GNU General Public License v3.0 or later. See LICENSE.md for details.

Documentation

For comprehensive documentation including tutorials, API reference, and examples, visit:

• DS Documentation

Repository

• GitHub: USTC-KnowledgeComputingLab/ds
• Documentation: ustc-knowledgecomputinglab.github.io/ds
• npm package: atsds
• PyPI package: apyds

Author

Hao Zhang [email protected]

Contributing

Contributions are welcome! Please feel free to submit issues or pull requests.