Tarski asked whether the arithmetic identities taught in high school are complete for showing all arithmetic equations valid for the natural numbers. The answer to this question f...
The last few years have seen the development of a new calculus which can be considered as an outcome of the last decade of various researches on (higher order) term rewriting syst...
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...
The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calcu...
We present a notion of -long ? -normal term for the typed lambda calculus with sums and prove, using Grothendieck logical relations, that every term is equivalent to one in norm...