Fully abstract models for effectful λ-calculi via category-theoretic logical relations

Kammar, Ohad; Katsumata, Shin-ya; Saville, Philip

doi:10.1145/3498705

Cited by 1 publication

(1 citation statement)

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“…Indeed, it is known that this model of immutable state fails to be fully abstract, i.e. that it distinguishes between computations that are contextually equivalent [KKS22]. A different model, such as the identity monad on Set × Set, which is lax idempotent, may enable us to apply Theorem 6.2.…”

Section: A Galois Connection Between Call-by-value and Call-by-namementioning

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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Section: A Galois Connection Between Call-by-value and Call-by-namementioning

confidence: 99%