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Types, Abstraction, and Parametric Polymorphism, Part 2
, 1991
"... The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logicalrelations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesianclosedcategory models of the simply typed lambda calculus and P ..."
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Cited by 53 (1 self)
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The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logicalrelations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesianclosedcategory models of the simply typed lambda calculus and PLcategory models of the polymorphic typed lambda calculus. Treatments of Kripke relations and of complete relations on domains are included.
HasCASL: Towards Integrated Specification and Development of Functional Programs
, 2002
"... The development of programs in modern functional languages such as Haskell calls for a widespectrum specification formalism that supports the type system of such languages, in particular higher order types, type constructors, and parametric polymorphism, and contains a functional language as an exe ..."
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Cited by 25 (11 self)
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The development of programs in modern functional languages such as Haskell calls for a widespectrum specification formalism that supports the type system of such languages, in particular higher order types, type constructors, and parametric polymorphism, and contains a functional language as an executable subset in order to facilitate rapid prototyping. We lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that is geared towards precisely this purpose. Its semantics is tuned to allow program development by specification refinement, while at the same time staying close to the settheoretic semantics of first order Casl. The number of primitive concepts in the logic has been kept as small as possible; we demonstrate how various extensions to the logic, in particular general recursion, can be formulated within the language itself.
The HasCasl prologue: categorical syntax and semantics of the partial λcalculus
 COMPUT. SCI
, 2006
"... We develop the semantic foundations of the specification language HasCasl, which combines algebraic specification and functional programming on the basis of Moggi’s partial λcalculus. Generalizing Lambek’s classical equivalence between the simply typed λcalculus and cartesian closed categories, we ..."
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Cited by 6 (4 self)
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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 λcalculus. Generalizing Lambek’s classical equivalence between the simply typed λcalculus and cartesian closed categories, we establish an equivalence between partial cartesian closed categories (pccc’s) and partial λtheories. Building on these results, we define (settheoretic) notions of intensional Henkin model and syntactic λalgebra for Moggi’s partial λcalculus. 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 λalgebras. 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 higherorder logic of partial functions, which by our results is the logic of pccc’s with equality). Finally, we give some applications of the modeltheoretic equivalence result to the semantics of HasCasl and its relation to firstorder Casl.
semifunCtors
, 1990
"... Girard categories (GC's) were defined in [14] as categorical models for linear logic. It was shown that the Kleisli category of a GC is Cartesian closed. ..."
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Girard categories (GC's) were defined in [14] as categorical models for linear logic. It was shown that the Kleisli category of a GC is Cartesian closed.