System Description: Russell - A Logical Framework for Deductive Systems

TL;DR

Russell is a high-level logical framework built on Metamath foundations, enabling declarative proofs and separation of syntax from inference rules, with tools for translation and verification.

Contribution

It introduces a declarative proof language and syntax-inference separation in a Metamath-based framework, enhancing flexibility and verification capabilities.

Findings

Supports translation of nearly 30,000 Metamath theorems

Allows verification of translated theorems in Russell and Metamath

Provides tools for proof verification and framework extensibility

Abstract

Russell is a logical framework for the specification and implementation of deductive systems. It is a high-level language with respect to Metamath language, so inherently it uses a Metamath foundations, i.e. it doesn't rely on any particular formal calculus, but rather is a pure logical framework. The main difference with Metamath is in the proof language and approach to syntax: the proofs have a declarative form, i.e. consist of actual expressions, which are used in proofs, while syntactic grammar rules are separated from the meaningful rules of inference. Russell is implemented in c++14 and is distributed under GPL v3 license. The repository contains translators from Metamath to Russell and back. Original Metamath theorem base (almost 30 000 theorems) can be translated to Russell, verified, translated back to Metamath and verified with the original Metamath verifier. Russell can be downloaded from the repository https://github.com/dmitry-vlasov/russell