Isabelle/Spartan -- A Dependent Type Theory Framework for Isabelle

Abstract

This paper introduces Isabelle/Spartan, an implementation of intensional dependent type theory with cumulative universes as an object logic in the Isabelle proof assistant. In contrast to other systems supporting dependent type theory, Isabelle is based on simple type theory -- yet I show how its existing logical framework infrastructure is able to handle automation tasks that are typically implemented on the source code level of dependently-typed systems. I also go some way in integrating the propositions-as-types paradigm with the declarative Isar proof language. Isabelle/Spartan supports book HoTT and the univalence axiom, and its capabilities are demonstrated by the formalization of foundational results from the Homotopy Type Theory book.