: 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...
Abstract : The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prov...
Abstract. In this paper, we show how Miquel's Implicit Calculus of Constructions (ICC) can be used as a programming language featuring dependent types. Since this system has a...
Since Val Tannen's pioneering work on the combination of simply-typed λ-calculus and rst-order rewriting [11], many authors have contributed to this subject by extending it ...
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...