IMPS: An interactive mathematical proof system

Abstract

IMPS, an Interactive Mathematical Proof System [2], is intended as a general purpose tool for formulating and applying mathematics in a familiar fashion. Its logic is a conceptually simple implementation of higher-order predicate logic that closely conforms to mathematical practice. Mathematical specification and inference are performed relative to axiomatic theories, which can be combined with each other and extended by definitions. The system supports a natural style of inference based on deduction graphs, which are akin to derivations in a sequent calculus. However, the individual inferences in a deduction graph may depend on theory-specific simplification procedures, and may encapsulate a large number of basic inferences.