By Paul Blain Levy (auth.)
Call-by-push-value is a programming language paradigm that, strangely, breaks down the call-by-value and call-by-name paradigms into basic primitives. This monograph, written for graduate scholars and researchers, exposes the call-by-push-value constitution underlying a outstanding diversity of semantics, together with operational semantics, domain names, attainable worlds, continuations and video games.
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Extra resources for Call-By-Push-Value: A Functional/Imperative Synthesis
Example text
For exa mple, the term pr int "hello". t rue when evaluated, prints hello and then returns t r ue . We write A for the set of characters that can be print ed , A * for the set of finite strings of characters, * for concate nat ion of strings and " " for the empty string. Formally, we add to the term syntax the following ru le, for every character c E A: rl-M:B I' I- print c. g. in CBV we could let commands have type 1, as in ML. But we prefer commands to be prefixes. This is for the sake of consistency between CE N, CBV, CBPV and the Jump-With-Argument language discussed in Chap.
Proposition 2 (soundness) If M -lJ. m , V then [Mr et = (m, [v]val) D Corollary 3 (by Prop. e, returner of ground type) M , we have M -lJ. m , return n iff [M] = (m, n). 3 Scott Semantics The reader may be familiar with Scott semantics for CBV . This has appeared in two forms. 1 In the older form, types denote pointed cpos, returners denote strict functions and values denote strict, bottom-reflecting functions. 2 In the more recent form, due to Plotkin [Plotkin, 1985], types denote (unpointed) cpos , values denote total functions and returners denote partial functions.
4. Again , t his sect ion may be omitted by read ers unfamiliar with category t heory. The two denotational models of CB N t hat we have seen ar e both cartesian closed categories: CALL-BY-PUSH- VALUE 24 • The printing semantics for CBN is the cartesian closed category in which an object is an A-set (X, *) and a morphism from (X, *) to (Y, *) is a function from X to Y . • The cpo semantics for CBN is the cartesian closed category of cppos and continuous functions. In fact, every model for CBN must be a cartesian closed category, as it must validate the {3- and 1]-laws for funct ions.