The-calculus is a-calculus with a local operator closely related to normal-isation procedures in classical logic and control operators in functional programming. We introduce exp, an explicit substitution calculus for , show it preserves strong normali-sation and that its simply typed version is strongly normalising. Interestingly, exp is the rst example for which the decency method of showing ...

x Abstract. We generalise the notion of explicit substitution from the-calculus to higher order rewriting, realised by combinatory reduction systems (CRSs). For every connuent CRS, R, we construct an explicit substitution variant, Rx, which we prove connuent. We identify a large subset of the CRSs, the structure-preserving CRSs, and show for any structure-preserving CRS R that Rx preserves stro...

This paper investigates an approach to substitution alternative to the implicit treatment of the λ-calculus and the explicit treatment of explicit substitution calculi. In this approach, substitutions are delayed (but not executed) explicitly. We implement this idea with two calculi, one where substitution is a primitive construction of the calculus, the other where substitutions is represented...

Herbelin presented (at CSL’94) an explicit substitution calculus with a sequent calculus as a type system, in which reduction steps correspond to cut-elimination steps. The calculus, extended with some rules for substitution propagation, simulates β-reduction of ordinary λcalculus. In this paper we present a proof of strong normalization for the typable terms of the calculus. The proof is a dir...

We present a simple term language with explicit operators for erasure, duplication and substitution enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s Proof Nets. We establish the good operational behaviour of the language by means of some fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of well-ty...

The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation is made difficult by the complexity of the substitution operation relative to lambda terms. To remedy this, researchers have suggested representing the meta ...

The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation is made difficult by the complexity of the substitution operation relative to lambda terms. To remedy this, researchers have suggested representing the meta ...

The kinetics of chloride substitution from a series of square-planar platinum(II) complexes, viz. [Pt(terpyridine)Cl](+), (Pt1), [Pt{2-(2'-pyridyl)-1,10-phenanthroline}Cl]Cl, (Pt2), [Pt{4'-(2'''-CH3-phenyl)-2,2':6',2''-terpyridine}Cl]CF3SO3 (Pt3) and [Pt{4'-(2'''-CH3-phenyl)-6-(3''-isoquinoyl)-2,2'bipyridine}Cl]SbF6 (Pt4) were studied using a series of five-membered heterocyclic neutral nitroge...

Lake's evolutionary parsimony (EP) method of constructing a phylogenetic tree is primarily applied to four DNA sequences. In this method, three quantities--X, Y, and Z--that correspond to three possible unrooted trees are computed, and an invariance property of these quantities is used for choosing the best tree. However, Lake's method depends on a number of unrealistic assumptions. We therefor...

The-calculus is a-calculus with a control-like operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong normalisation, which provides us with the rst example {moreover a very natural one indeed{ of explicit substitution ca...