Building on previous work by Coquand and Spiwack [8] we construct a strict domaintheoretic model for the untyped -calculus with pattern matching and term rewriting which has the p...
We present constructive arithmetic in Deduction modulo with rewrite rules only. In natural deduction and in sequent calculus, the cut elimination theorem and the analysis of the st...
A typed lambda calculus with categorical type constructors is introduced. It has a uniform category theoretic mechanism to declare new types. Its type structure includes categoric...
Abstract. We present a formal treatment of normalization by evaluation in type theory. The involved semantics of simply-typed λ-calculus is exactly the simply typed fragment of th...
: This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generali...