Computer Science Logic: 19th International Workshop, CSL by Maarten Marx (auth.), Luke Ong (eds.)

By Maarten Marx (auth.), Luke Ong (eds.)

This publication constitutes the refereed complaints of the nineteenth overseas Workshop on machine technology good judgment, CSL 2005, held because the 14th Annual convention of the EACSL in Oxford, united kingdom in August 2005.

The 33 revised complete papers offered including four invited contributions have been rigorously reviewed and chosen from 108 papers submitted. All present facets of common sense in desktop technological know-how are addressed starting from mathematical good judgment and logical foundations to methodological concerns and purposes of logics in quite a few computing contexts. the quantity is equipped in topical sections on semantics and logics, sort conception and lambda calculus, linear good judgment and ludics, constraints, finite versions, decidability and complexity, verification and version checking, optimistic reasoning and computational arithmetic, and implicit computational complexity and rewriting.

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Extra info for Computer Science Logic: 19th International Workshop, CSL 2005, 14th Annual Conference of the EACSL, Oxford, UK, August 22-25, 2005. Proceedings

Example text

We use the notation FTV (−) for the set of type variables which occur free in a bunch (−), type (−), the types of the variables in the context (−) or the type of the term (−), respectively. In a term App(M, X, τ ) or App∗ (M, X, τ ), the type variables of X are free, so substitution must take account of this. We introduce a syntactic measure μ which assigns to each term the set of type variables which are free and which occur in some application of the multiplicative universal quantifier. M ) = μ(M ) {α} μ(App∗ (M, X, τ )) = μ(M )∪FTV (X) are the informative clauses.

Composite: the composite in B of a pair of arrows f : X −→ Y , g : Y −→ Z is an arrow g ◦ f : X −→ Z constructed by replacing each leaf Y ρ of g with the leaf X ρ[f /Y ], where the mapping (−) is extended to trees in the obvious way. Some comments and observations about the above definition are in order. In a number of the clauses above we have formed a morphism from X to Y using On Bunched Polymorphism 45 some words like “replace any variable α of Y with the judgement X τ ” and it is to be understood that any leaves of Y which are units ∅ should be replaced by the judgement X .

Let T: Const → CountSet be a term system and (D, val) a model of T. A rewrite structure for T and (D, val) is a triple R = (C, →, α) where C is 30 Ulrich Berger a constant system, → a binary relation on T(C) and α ∈ DC . R is monotone if M → N implies [M ]α [N ]α for all M, N ∈ T(C). t. e. there is no infinite reduction sequence beginning with M . t. → iff the restriction of → to the set {N | M →∗ N } is wellfounded. Therefore it makes sense to speak of ‘induction on the strong normalizability of M ’.

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