We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. − A clausification procedure in type theory, equipped w...
Abstract. We describe a second-order type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated supp...
Termination of recursive functions is an important property in proof assistants based on dependent type theories; it implies consistency and decidability of type checking. Type-bas...
We present a development of Universal Algebra inside Type Theory, formalized using the proof assistant Coq. We define the notion of a signature and of an algebra over a signature. ...
Proof assistants based on dependent type theory are closely related to functional programming languages, and so it is tempting to use them to prove the correctness of functional p...
Andreas Abel, Marcin Benke, Ana Bove, John Hughes,...