By Maarten Marx (auth.), Luke Ong (eds.)
ISBN-10: 3540282319
ISBN-13: 9783540282310
ISBN-10: 3540318976
ISBN-13: 9783540318972
This ebook constitutes the refereed lawsuits of the nineteenth overseas Workshop on computing device technology common sense, CSL 2005, held because the 14th Annual convention of the EACSL in Oxford, united kingdom in August 2005.
The 33 revised complete papers awarded including four invited contributions have been rigorously reviewed and chosen from 108 papers submitted. All present elements of good judgment in laptop technology 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, style concept and lambda calculus, linear common sense and ludics, constraints, finite types, decidability and complexity, verification and version checking, positive reasoning and computational arithmetic, and implicit computational complexity and rewriting.
Read or Download Computer Science Logic: 19th International Workshop, CSL 2005, 14th Annual Conference of the EACSL, Oxford, UK, August 22-25, 2005. Proceedings PDF
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Additional resources 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 describe a polymorphic extension of the substructural lambda calculus αλ associated with the logic of bunched implications. This extension is particularly novel in that both variables and type variables are treated substructurally, being maintained through a system of zoned, bunched contexts. Polymorphic universal quantifiers are introduced in both additive and multiplicative forms, and then metatheoretic properties, including subject-reduction and normalization, are established. A sound interpretation in a class of indexed category models is defined and the construction of a generic model is outlined, yielding completeness.
3 Strong Normalization by Approximation Definition 3. 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 ’.
There are a number of parts to the base case. These are identity, terminal, diagonal, projection, pseudoprojection, right unit, associativity, associativity inverse, symmetry. For brevity, we give only the diagonal and pseudoprojection clauses below. From these, the forms of the other cases may be easily inferred. Diagonal: for every X there is a morphism ΔX : X −→ X; X , where X is any hub which is disjoint from X and with X ∼ = X. The morphism is given α. by fX ; fX where fX is formed by replacing every leaf α of X with X Pseudoprojection: for all X and Y there is an arrow ψ 1 : X, Y −→ X formed by replacing each leaf α of X with X, Y α.
Computer Science Logic: 19th International Workshop, CSL 2005, 14th Annual Conference of the EACSL, Oxford, UK, August 22-25, 2005. Proceedings by Maarten Marx (auth.), Luke Ong (eds.)
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