A definitional extension LNGMIt of the Calculus of Inductive Constructions (CIC), that underlies the proof assistant Coq, is presented that allows also to program with nested dat...
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluat...
Bench-Capon and Sartor have proposed that reasoning with legal cases be seen as a process of theory construction, evaluation and application. They have proposed a set of theory co...
Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive ZermeloFraenkel Set Theory...
Abstract. We give an elementary theory of Henselian local rings and construct the Henselization of a local ring. All our theorems have an algorithmic content.