Call-by-push-value: Decomposing call-by-value and call-by-name

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.

Computation in focused intuitionistic logic

“…The methodology we follow here has its importance: we wish to interpret LJF as a system entirely justified using prooftheoretical arguments, rather than an ad-hoc system for particular strategies. This approach confirms the two natural representations of the most standard strategies -CBN and CBV -in the focused type system, but it also reveals the tight connection between LJF and call-by-push-value [25], in which the two standard strategies can be embedded. The relation between CBPV and focusing was conjectured but still unclear: we establish it in details and discuss their differences.…”

“…Then, we describe an abstract machine implementing cut elimination in the LJF system and show how it relates to the CK-style machine defined in the literature for CBPV [25].…”

Handlers of Algebraic Effects

“…We can extend both handlers and computations with other call-by-push-value types and terms [11,22]. A problem arises if we introduce thunks: handler terms then contain value terms, which contain thunked computation terms, which contain the handling construct.…”

“…For example, using a binary choice operation or : 2, a nondeterministically chosen boolean is given by the term or(return true, return false):F bool, where F σ stands for the type of computations that return values of type σ (we are working in Levy's call-by-push-value (CBPV) framework [11]). The equations of the theory, for example the ones stating that or is a semi-lattice operation, generate the free-model functor, which is used to interpret the type F σ.…”

Realizability Semantics of Parametric Polymorphism, General References, and Recursive Types

“…-Investigating what semantic structures are needed in general models for effects. Indeed, we see the present work as a pilot study for studying general type theories and models of effects (e.g., [12,19]), in which we identify key ingredients needed for semantic modeling of general first-class references. -Paving the way for developing models of separation logic for ML-like languages with reference types.…”