Relating operational and denotational semantics for input/output effects

نویسندگان

Roy L. Crole

Andrew D. Gordon

چکیده

We study the longstanding problem of semantics for input/output (I/O) expressed using side-eeects. Our vehicle is a small higher-order imperative language, with operations for interactive character I/O and based on ML syntax. Unlike previous theories, we present both operational and denotational semantics for I/O eeects. We use a novel labelled transition system that uniformly expresses both applicative and imperative computation. We make a standard deenition of bisimilarity. We prove bisimilarity is a congruence using Howe's method. Next, we deene a metalanguage M in which we may give a denotational semantics to O. M generalises Crole and Pitts' FIX-logic by adding in a param-eterised recursive datatype, which is used to model I/O. M comes equipped both with an operational semantics and a domain-theoretic semantics in the category CPPO of cppos (bottom-pointed posets with joins of !-chains) and Scott continuous functions. We use the CPPO semantics to prove that M is computationally adequate for the operational semantics using formal approximation relations. The existence of such relations is based on recent work of Pitts Pit94b] for untyped languages, and uses the idea of minimal invariant objects due to Freyd. A monadic-style textual translation into M induces a denotational semantics on O. Our nal result validates the denotational semantics: if the denotations of two O programs are equal then the O programs are in fact operationally equivalent.

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