Abstract: We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped -calcul...
An extension of the simply-typed lambda calculus is presented which contains both well-structured inductive and coinductive types, and which also identifies a class of types for w...
Pi is a system for the interactive construction and editing of formal derivations in the calculus of finitary partial inductive definitions. This calculus can be used as a logical ...
In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them ...
The contribution of this paper is an effective proof of the well-foundedness of MPO, as a term of the Calculus of Inductive Constructions. This proof is direct, short and simple. ...