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Thèse pour obtenir le grade de docteur d'université. Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften. Thèse pour obtenir le grade de docteur d'université. Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften.
Parametric inductive types can be seen as functions taking type parameters as argument and returning the instantiated inductive types. Given functions between parameters one can construct function between the instantiated inductive types representing the change of parameters along these functions. It is well known that it is not a functor w.r.t intensional… (More)
We devise an algorithm using normalization by evaluation (NbE) for deciding equality between terms in a λ-calculus equipped with strong sums. While proofs of cor-rectness and completeness are still work in progress, the originality of this algorithm is its use of exceptions, which yields a particularly simple solution to this intricate problem .
We consider the problem of incorporation of new computational rules in lambda calculus with inductive types and recursion. We consider the extensions of standard reduction systems by certain new reductions preserving strong normalization and Church-Rosser property with possible applications to proof assistants and computer algebra systems. компьютерной… (More)