Automatic proof checking is about using a computer to check the validity of proofs of
mathematical statements. Since this verification is purely computational, it offers a high …

Term rewriting systems play an important role in many areas of computer science. In
essence, they provide an abstract way to define algorithms. The theory is simple: terms …

In this paper, we first briefly survey automated termination proof methods for higher-order
calculi. We then concentrate on the higher-order recursive path ordering, for which we …

Abstract C oq Modulo Theory (C oq MT) is an extension of the C oq proof assistant
incorporating, in its computational mechanism, validity entailment for user-defined first-order …

This paper aims at carrying out termination proofs for simply typed higher-order calculi
automatically by using ordering comparisons. To this end, we introduce the computability …

This paper proposes a new approach to writing and verifying divide-and-conquer programs
in Coq. Extending the rich line of previous work on algebraic approaches to recursion …

Le calcul de réécriture est un lambda-calcul avec filtrage. Cette thèse est consacrée à
l'étude de systèmes de types pour ce calcul et à son utilisation dans le domaine de la …

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 …

Abstract Since Val Tannen's pioneering work on the combination of simply-typed λ-calculus
and first-order rewriting [11], many authors have contributed to this subject by extending it to …

It is commonly agreed that the success of future proof assistants will rely on their ability to
incorporate computations within deduction in order to mimic the mathematician when …