Superposition as a logical glue

TL;DR

This paper explores integrating superposition calculus into the Matita interactive theorem prover to enhance its automation and flexibility, inspired by mathematical practices of using equalities and isomorphisms as a form of logical glue.

Contribution

It introduces a novel approach to automation in ITP systems by incorporating superposition calculus, enabling more flexible and intelligent reasoning.

Findings

Developed a flexible application tactic for Matita

Implemented a simple, innovative automation approach

Enhanced the system's ability to handle equalities and isomorphisms

Abstract

The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical discipline. A large part of this background knowledge is expressed in form of equalities and isomorphisms, allowing mathematicians to freely move between different incarnations of the same entity without even mentioning the transformation. Providing ITP-systems with similar capabilities seems to be a major way to improve their intelligence, and to ease the communication between the user and the machine. The present paper discusses our experience of integration of a superposition calculus within the Matita interactive prover, providing in particular a very flexible, "smart" application tactic, and a simple, innovative approach to automation.