Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo… (More)
Higher order uniication is equational uniication for-conversion. But it is not rst order equa-tional uniication, as substitution has to avoid capture. Thus the methods for equational uniication (such as narrowing) built upon grafting (i.e. substitution without renaming), cannot be used for higher order uniication, which needs speciic algorithms. Our goal in… (More)
Categorical combinators [Curien 1986/1993; Hardin 1989; Yokouchi 1989] and more recently λ&sgr;-calculus [Abadi 1991; Hardin and Le´vy 1989], have been introduced to provide an explicit treatment of substitutions in the λ-calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special… (More)
In 6] we have proposed a general higher-order uniication method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higher-order patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient way to patterns. We also sketch an eecient implementation of… (More)
The Strong Categorical Combinatory Logic (CCL, CCLpqSP), developed by Curien (1986) is, when typed and augmented with a rule defining a terminal object, a presentation of Cartesian Closed Categories. Furthermore, it is equationally equivalent to the Lambda-calculus with explicit couples and Surjective Pairing. Here we study the confluence properties of… (More)
Higher-order uniication is equational uniication for-conversion. But it is not rst-order equational uniication, as substitution has to avoid capture. In this paper higher-order uniication is reduced to rst-order equational uniication in a suitable theory: the-calculus of explicit substitutions.