. Call-by-push-value is a new paradigm that subsumes the call-by-name and call-by-value paradigms, in the following sense: both operational and denotational semantics for those paradigms can be seen as arising, via translations that we will provide, from similar semantics for call-by-push-value. To explain call-by-push-value, we first discuss general operational ideas, especially the distinction between values and computations, using the principle that "a value is, a computation does". Using an example program, we see that the lambda-calculus primitives can be understood as push/pop commands for an operand-stack. We provide operational and denotational semantics for a range of computational effects and show their agreement. We hence obtain semantics for call-by-name and call-by-value, of which some are familiar, some are new and some were known but previously appeared mysterious. 1 Introduction 1.1 Contribution In his invited lecture at POPL '98 [32], Reynolds, surveying over 30 year...

We construct a model for FPC, a purely functional, sequential, call-by-value language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract.

We present the call-by-push-value (CBPV) calculus, which decomposes the typed call-by-value (CBV) and typed call-by-name (CBN) paradigms into fine-grain primitives. On the operational side, we give big-step semantics and a stack machine for CBPV, which leads to a straightforward push/pop reading of CBPV programs. On the denotational side, we model CBPV using cpos and, more generally, using algebras for a strong monad. For storage, we present an O’Hearn-style “behaviour semantics” that does not use a monad. We present the translations from CBN and CBV to CBPV. All these translations straightforwardly preserve denotational semantics. We also study their operational properties: simulation and full abstraction. We give an equational theory for CBPV, and show it equivalent to a categorical semantics using monads and algebras. We use this theory to formally compare CBPV to Filinski’s variant of the monadic metalanguage, as well as to Marz’s language SFPL, both of which have essentially the same type structure as CBPV. We also discuss less formally the differences between the CBPV and monadic frameworks.

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ped strategy (in the sense of the AJM model of Abramsky et. al.) for d. Accordingly, the realisability model over A eff wb , the effective well--bracketed strategies, is even universal in the sense that all elements of the model appear as denotations of PCF terms. In a future version of [9] there will also be included the discussion of other pca's of game--theoretic nature giving rise to fully abstract and universal models which originate from S. Abramsky's work on game semantics for classical linear logic. Independently, fully abstract realisability models for PCF have been constructed by Marz, Rohr and Streicher in [14] using as underlying pca's term models for untyped --calculus with arithmetic. In this case the proof is not via the AJM game model but instead makes use of the category SD of sequential domains as described in [13] originating from a reformulation and generalisation of [18]. As describ

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