A Scalable Module System

TL;DR

The paper introduces MMT, a scalable module system for mathematical theories designed to manage large, interconnected mathematical knowledge bases efficiently, supporting integration and interoperability across various formal systems.

Contribution

It presents the design and implementation of MMT, a simple, scalable, and foundation-agnostic module system that facilitates large-scale mathematical knowledge management and integration.

Findings

MMT enables integration of existing formal languages.

It supports web-scale processing of mathematical theories.

MMT separates logic-dependent and logic-independent concerns.

Abstract

Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented mathematical knowledge that needs to be managed to use such systems effectively. While mathematical knowledge management (MKM) "in the small" is well-studied, scaling up to large, highly interconnected corpora remains difficult. We hold that in order to realize MKM "in the large", we need representation languages and software architectures that are designed systematically with large-scale processing in mind. Therefore, we have designed and implemented the MMT language -- a module system for mathematical theories. MMT is designed as the simplest possible language that combines a module system, a foundationally uncommitted formal semantics, and web-scalable implementations. Due to a careful choice of representational primitives, MMT allows us to integrate existing representation languages for formal mathematical knowledge in a simple, scalable formalism. In particular, MMT abstracts from the underlying mathematical and logical foundations so that it can serve as a standardized representation format for a formal digital library. Moreover, MMT systematically separates logic-dependent and logic-independent concerns so that it can serve as an interface layer between computation systems and MKM systems.