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

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

This e-book constitutes the refereed court cases of the nineteenth overseas Workshop on computing device technological know-how 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 machine technological know-how are addressed starting from mathematical common sense and logical foundations to methodological concerns and functions of logics in quite a few computing contexts. the quantity is prepared in topical sections on semantics and logics, style idea 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.

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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

Note that the functoriality of T means that M id = M , where id: C → C is the identity, and M (θ ◦ θ ) = (M θ )θ. Example 1. Consider simple types generated from the base types boole and nat by the formation of function types, ρ → σ. Let an object C of Const be a countable set of typed constants cρ , and a morphism θ: C → C a type respecting constant substitution. Terms (and their types) over C are built from typed variables, xρ , and constants, cρ ∈ C, by the formation of constructor terms, 0nat , S(M nat )nat , #tboole , #f boole , definition by cases, (if P boole then M ρ else N ρ )ρ ), abstraction, (λxρ M σ )ρ→σ , and application, (M ρ→σ N ρ )σ .

All products are pseudoproducts, but not vice versa. The category Set ⊥ of pointed sets X⊥ and functions which preserve the distinguished element ⊥ has a pseudoproduct given by the coproduct. A pseudoprojection from X⊥ + Y⊥ to X⊥ may be taken to be ⊥, y → ⊥, x → x for all x ∈ X, y ∈ Y . A cartesian doubly closed category (CDCC) is a category with a pair of symmetric monoidal closed structures, one of which is cartesian. A functor between CDCC’s is strict if it preserves both the cartesian closed and the monoidal closed structure on-the-nose.

Assume a countable collection of type variables α, β, . . to be given. τ , where α is any type variable. The connectives , ∧, → and ∀ are the additive unit, product, function space and polymorphic universal quantifier, respectively. There are multiplicative unit I, product ∗, function space − −∗ and universal ∀∗ connectives. We allow the letters σ, τ to range over types. A hub is a bunch of type variables, generated as follows X := ∅ | α | X, X | X;X , subject to the restriction that every type-variable may occur at most once in a bunch.

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