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

TL;DR

This paper develops a general framework using Levy's call-by-push-value calculus to relate call-by-value and call-by-name semantics, especially in the presence of computational effects, establishing conditions for their observable equivalence and Galois connections.

Contribution

It introduces a novel technique for reasoning about the relationship between call-by-value and call-by-name, leveraging call-by-push-value to analyze effects and establish Galois connections.

Findings

Identifies conditions under which call-by-value and call-by-name have related observable behaviors.

Shows that certain effects like divergence satisfy the Galois connection properties.

Demonstrates the applicability of the framework to effects such as nondeterminism.

Abstract

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.