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A Categorical Model for Higher Order Imperative Programming
 Mathematical Structures in Computer Science
, 1993
"... This paper gives the first complete axiomatization for higher types in the refinement calculus of predicate transformers. ..."
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Cited by 13 (12 self)
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This paper gives the first complete axiomatization for higher types in the refinement calculus of predicate transformers.
Lifting as a KZdoctrine
 Proceedings of the 6 th International Conference, CTCS'95, volume 953 of Lecture Notes in Computer Science
, 1995
"... this paper, is the analysis of notions of approximation aiming at explaining and justifying (ordertheoretic) properties of categories of domains. For example, in [Fio94c, Fio94a], while studying the interaction between partiality and orderenrichment we considered contextual approximation which, in ..."
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Cited by 3 (2 self)
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this paper, is the analysis of notions of approximation aiming at explaining and justifying (ordertheoretic) properties of categories of domains. For example, in [Fio94c, Fio94a], while studying the interaction between partiality and orderenrichment we considered contextual approximation which, in the framework we were working in, coincided with the specialisation preorder . But in the applications carried out in [FP94, Fio94a] we had to work with an axiomatised notion of approximation, instead of the aforementioned one, for the following two reasons: first, the specialisation preorder is not appropriate in categories of domains and stable functions (see [Fio94c]) and, second, we do not know of nonordertheoretic axioms making the specialisation preorder !complete. To overcome these drawbacks another notion of approximation was to be considered. And, it was the second problem that motivated the intensional notion of approximation provided by the path relation. In fact, it is shown in [Fio94b] that under suitable axioms the path relation can be equipped with a canonical passagetothelimit operator appropriate for fixedpoint computations; stronger axioms make this operator be given by lubs of !chains
Computational Soundness and Adequacy for Typed Object Calculus
"... By giving a translation from typed object calculus into Plotkin’s FPC, we demonstrate that every computationally sound and adequate model of FPC (with eager operational semantics), is also a sound and adequate model of typed object calculus. This establishes that denotational equality is contained i ..."
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By giving a translation from typed object calculus into Plotkin’s FPC, we demonstrate that every computationally sound and adequate model of FPC (with eager operational semantics), is also a sound and adequate model of typed object calculus. This establishes that denotational equality is contained in operational equivalence, i.e. that for any such model of typed object calculus, if two terms have equal denotations, then no program (or rather program context) can distinguish between those two terms. Hence we show that FPC models can be used in the study of program transformations (program algebra) for typed object calculus. Our treatment is based on selfapplication interpretation and subtyping is not considered. The typed object calculus under consideration is a variation of Abadi and Cardelli’s firstorder calculus with sum and product types, recursive types, and the usual method update and method invocation in a form where the object types have assimilated the recursive types. As an additional result, we prove subject reduction for this calculus.