Introduction to higher order categorical logic
Introduction to higher order categorical logic
Categories of partial morphisms and the λp-calculus
Proceedings of a tutorial and workshop on Category theory and computer programming
Information and Computation
Partiality, cartesian closedness, and toposes
Information and Computation
Abstract and concrete categories
Abstract and concrete categories
Axiomatic domain theory in categories of partial maps
Axiomatic domain theory in categories of partial maps
Restriction categories I: categories of partial maps
Theoretical Computer Science
A functorial semantics for multi-algebras and partial algebras, with applications to syntax
Theoretical Computer Science
HASCASL: Towards Integrated Specification and Development of Functional Programs
AMAST '02 Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology
HOLCF: Higher Order Logic of Computable Functions
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
An Extension of Models of Axiomatic Domain Theory to Models of Synthetic Domain Theory
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Lambda Calculus with Constrained Types (Extended Abstract)
Proceedings of the Conference on Logic of Programs
An equational notion of lifting monad
Theoretical Computer Science - Category theory and computer science
Restriction categories II: partial map classification
Theoretical Computer Science - Category theory and computer science
Amalgamation in the semantics of CASL
Theoretical Computer Science - Automata, languages and programming
Monad-independent Dynamic Logic in HasCasl
Journal of Logic and Computation
Monad-independent Hoare logic in HasCasl
FASE'03 Proceedings of the 6th international conference on Fundamental approaches to software engineering
HasCasl: Integrated higher-order specification and program development
Theoretical Computer Science
Bootstrapping types and cotypes in HASCASL
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
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We develop the semantic foundations of the specification language HASCaSL, which combines algebraic specification and functional programming on the basis of Moggi's partial λ-calculus. Generalizing Lambek's classical equivalence between the simply typed λ-calculus and cartesian closed categories, we establish an equivalence between partial cartesian closed categories (pccc's) and partial λ-theories. Building on these results, we define (set-theoretic) notions of intensional Henkin model and syntactic λ-algebra for Moggi's partial λ-calculus. These models are shown to be equivalent to the originally described categorical models in pccc's via the global element construction. The semantics of HASCASL is defined in terms of syntactic λ-algebras. Correlations between logics and classes of categories facilitate reasoning both on the logical and on the categorical side; as an application, we pinpoint unique choice as the distinctive feature of topos logic (in comparison to intuitionistic higher-order logic of partial functions, which by our results is the logic of pccc's with equality). Finally, we give some applications of the model-theoretic equivalence result to the semantics of HASCASL and its relation to first-order CASL.