An exploration in fluid logics

Abstract

We designed and implemented a framework, programming language, and standard library for specifying and programming in categorical denotational proof languages. We encoded a number of logical systems, including several versions of the propositional calculus, and mappings between them, including a mapping based on a translation between axiomatic proofs into natural-deduction proofs, and a mapping based on the deduction theorem. We present examples illustrating how programs in this language achieve heterogeneous reasoning, and conclude with discussion of future work and applications.