Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Into the infinite - theory exploration for coinduction

Theory exploration is a technique for automating the discovery of lemmas in formalizations of mathematical theories, using testing and automated proof techniques. Automated theory exploration has previously been successfully applied to discover lemmas for inductive theories, about recursive datatypes and functions. We present an extension of theory exploration to coinductive theories, allowing us to explore the dual notions of corecursive datatypes and functions. This required development of new methods for testing infinite values, and for proof automation. Our work has been implemented in the Hipster system, a theory exploration tool for the proof assistant Isabelle/HOL