This paper introduces a Hilbert system for lambda calculus called sequent combinators. Sequent combinators address many of the problems of Hilbert systems, which have led to the m...
Abstract. We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus ...
Abstract. We introduce a semi-automated proof system for basic category-theoretic reasoning. It is based on a first-order sequent calculus that captures the basic properties of cat...
Abstract. In higher-order process calculi the values exchanged in communications may contain processes. There are only two capabilities for received processes: execution and forwar...
Placing our result in a web of related mechanised results, we give a direct proof that the de Bruijn λ-calculus (`a la Huet, Nipkow and Shankar) is isomorphic to an α-quotiented ...