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Titlebook: Mathematical Foundations of Programming Semantics; 5th International Co M. Main,A. Melton,D. Schmidt Conference proceedings 1990 Springer-V

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978-0-387-97375-3Springer-Verlag New York 1990
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Mathematical Foundations of Programming Semantics978-0-387-34808-7Series ISSN 0302-9743 Series E-ISSN 1611-3349
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A category-theoretic semantics for unbounded indeterminacy,categorical analogues of continuity and has the meaning of while loops defined as colimits of ω-diagrams. Furthermore, it collapses via an abstraction function to a semantics that is fully abstract, and coincides with the operational semantics. The abstraction function is the only discontinuous function appearing in our semantics.
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An algebraic formulation for data refinement,ly reformulated and unified in terms of two principal category theoretic notions: those of an enriched category and monad, also known as a triple. The requisite definitions and theory are given, together with several examples to illustrate precisely how Hoare‘s work, including his main theorem may be seen in this light.
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