Call-by-push-value in Coq: operational, equational, and denotational theory

Forster, Yannick; Schäfer, Steven; Spies, Simon; Stark, Kathrin

doi:10.1145/3293880.3294097

Cited by 8 publications

(2 citation statements)

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“…We use the lifting from Hermida's thesis (1993), defined to contain the returners that reduce to a return value for all closed substitutions. Forster et al (2019) have since formalised in Coq a similar termination proof for CBPV; see their manuscript ( Figure 12 on page 6) for more details.…”

Section: Proofmentioning

confidence: 99%

On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control

Forster

Kammar²,

Lindley

et al. 2019

J. Funct. Prog.

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We compare the expressive power of three programming abstractions for user-defined computational effects: Plotkin and Pretnar’s effect handlers, Filinski’s monadic reflection, and delimited control. This comparison allows a precise discussion about the relative expressiveness of each programming abstraction. It also demonstrates the sensitivity of the relative expressiveness of user-defined effects to seemingly orthogonal language features. We present three calculi, one per abstraction, extending Levy’s call-by-push-value. For each calculus, we present syntax, operational semantics, a natural type-and-effect system, and, for effect handlers and monadic reflection, a set-theoretic denotational semantics. We establish their basic metatheoretic properties: safety, termination, and, where applicable, soundness and adequacy. Using Felleisen’s notion of a macro translation, we show that these abstractions can macro express each other, and show which translations preserve typeability. We use the adequate finitary set-theoretic denotational semantics for the monadic calculus to show that effect handlers cannot be macro expressed while preserving typeability either by monadic reflection or by delimited control. Our argument fails with simple changes to the type system such as polymorphism and inductive types. We supplement our development with a mechanised Abella formalisation.

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Section: Proofmentioning

confidence: 99%

On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control

Forster

Kammar²,

Lindley

et al. 2019

J. Funct. Prog.

Self Cite

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“…Our notion of (co)data is also similar to Zeilberger's [Zei09] definition of types via (co)patterns, which is fully dual, extended with sharing. This work also extends the work on the operational and equational theory of call-by-push-value [FSSk19] to incorporate not only "jumbo" connectives, but also call-by-need evaluation and its dual.…”

Section: Related Workmentioning

confidence: 73%

Compiling With Classical Connectives

Downen,

Ariola

2019

Preprint

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The study of polarity in computation has revealed that an "ideal" programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But this binary choice leaves out call-by-need which is used in practice to implement lazy-by-default languages like Haskell. We show how the notion of polarity can be extended beyond the value/name dichotomy to include call-by-need by adding a mechanism for sharing which is enough to compile a Haskell-like functional language with user-defined types. The key to capturing sharing in this mixed-evaluation setting is to generalize the usual notion of polarity "shifts:" rather than just two shifts (between positive and negative) we have a family of four dual shifts.We expand on this idea of logical duality-"and" is dual to "or;" proof is dual to refutation-for the purpose of compiling a variety of types. Based on a general notion of data and codata, we show how classical connectives can be used to encode a wide range of built-in and user-defined types. In contrast with an intuitionistic logic corresponding to pure functional programming, these classical connectives bring more of the pleasant symmetries of classical logic to the computationally-relevant, constructive setting. In particular, an involutive pair of negations bridges the gulf between the wide-spread notions of parametric polymorphism and abstract data types in programming languages. To complete the study of duality in compilation, we also consider the dual to call-by-need evaluation, which shares the computation within the control flow of a program instead of computation within the information flow.

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