Plotkin's call-by-value λ-calculus as a modal calculus

Santo, José Espírito; Pinto, Luís; Uustalu, Tarmo

doi:10.1016/j.jlamp.2022.100775

Cited by 1 publication

(1 citation statement)

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“…Here we use CBPV as a calculus in which to reason about both call-by-value and call-by-name, but other calculi (e.g. the modal calculus of [ESPU22]) may be suitable for this purpose.…”

Section: Mcdermott and A Mycroftmentioning

confidence: 99%

Galois connecting call-by-value and call-by-name

McDermott,

Mycroft

2024

Logical Methods in Computer Science

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We establish a general framework for reasoning about the relationship between call-by-value and call-by-name. In languages with computational effects, call-by-value and call-by-name executions of programs often have different, but related, observable behaviours. For example, if a program might diverge but otherwise has no effects, then whenever it terminates under call-by-value, it terminates with the same result under call-by-name. We propose a technique for stating and proving properties like these. The key ingredient is Levy's call-by-push-value calculus, which we use as a framework for reasoning about evaluation orders. We show that the call-by-value and call-by-name translations of expressions into call-by-push-value have related observable behaviour under certain conditions on computational effects, which we identify. We then use this fact to construct maps between the call-by-value and call-by-name interpretations of types, and identify further properties of effects that imply these maps form a Galois connection. These properties hold for some computational effects (such as divergence), but not others (such as mutable state). This gives rise to a general reasoning principle that relates call-by-value and call-by-name. We apply the reasoning principle to example computational effects including divergence and nondeterminism.

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“…Here we use CBPV as a calculus in which to reason about both call-by-value and call-by-name, but other calculi (e.g. the modal calculus of [ESPU22]) may be suitable for this purpose.…”

Section: Mcdermott and A Mycroftmentioning

confidence: 99%

Galois connecting call-by-value and call-by-name

McDermott,

Mycroft

2024

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

Plotkin's call-by-value λ-calculus as a modal calculus

Cited by 1 publication

References 13 publications

Galois connecting call-by-value and call-by-name

Galois connecting call-by-value and call-by-name

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