Pierre Lescanne

Equational problems anddisunification

Roughly speaking, an equational problem is a first order formula whose only predicatesymbol is =. We propose some rules for the transformation of equational problems and study their correctness in various models. Then, we give completeness results with respect to some simple problems called solved forms. Such completeness results still hold when adding some control which moreover ensures termination. The termination proofs are given for a weak control and thus hold for the (large) class of algorithms obtained by restricting the scope of the rules. Finally, it must be noted that a by-product of our method is a decision procedure for the validity in the Herbrand Universe of any first order formula with the only predicate symbol=.

Termination of rewriting systems by polynomial interpretations and its implementation

Abstract This paper describes the actual implementation in the rewrite rule laboratory REVE of an elementary procedure that checks inequalities between polynomials and is used for proving termination of rewriting systems, especially in the more difficult case of associative-commutative rewriting systems, for which a complete characterization is given.

Computer experiments with the REVE term rewriting system generator

A term rewriting system generator called REVE is described. REVE builds confluent and uniformly terminating term rewriting systems from sets of equations. Particular emphasis is placed on mechanization of termination proof. Indeed, REVE is one of the few such systems which can actually be called automatic because termination is fully integrated into the algorithms. REVE uses an incremental termination method based on recursive decomposition ordering which constructs the termination proof step by step from the presentation of the set of equations and which requires little knowledge of termination methods from the user. All examples from this paper are taken from abstract data type specifications.

lambda-nu, A Calculus of Explicit Substitutions which Preserves Strong Normalisation.

Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Levy to internalise substitutions into

From λσ to λν: a journey through calculi of explicit substitutions

lambda

Termination by completion

-calculus and to propose a mechanism for computing on substitutions.

Polynomial Interpretations and the Complexity of Algorithms

lambdaupsilon

On the recursive decomposition ordering with lexicographical status and other related orderings

is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps.

Termination of Rewrite Systems by Elementary Interpretations

lambdaupsilon

Completion Procedures as Transition Rules + Control

is simple and preserves strong normalisation. Apparently that important property cannot stay with another important one, namely confluence on open terms. The spirit of