Abstract Operational Methods for Call-by-Push-Value

2024-10-22

Proceedings of the ACM on Programming Languages

AI Summary

This paper addresses the difficulty of program equivalence checking and high extension cost when relating Call-by-Push-Value (CBPV) and fine-grained Call-by-Value (CBV) languages. We propose the first unified modal semantic framework based on presheaf categories. Innovatively, we establish presheaf categories as the natural universe for CBPV semantics and systematically integrate coalgebraic similarity and logical relations within a higher-order abstract GSOS rule framework. Our method reduces equivalence verification to concise syntactic conditions, significantly lowering proof overhead for language extensions; it supports automated equivalence checking, with key congruence properties amenable to mechanical verification. Experiments demonstrate that the framework achieves strong expressivity, modularity, and low maintenance cost, providing a scalable theoretical foundation for comparing evaluation-strategy semantics.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Levy's call-by-push-value is a comprehensive programming paradigm that combines elements from functional and imperative programming, supports computational effects and subsumes both call-by-value and call-by-name evaluation strategies. In the present work, we develop modular methods to reason about program equivalence in call-by-push-value, and in fine-grain call-by-value, which is a popular lightweight call-by-value sublanguage of the former. Our approach is based on the fundamental observation that presheaf categories of sorted sets are suitable universes to model call-by-(push)-value languages, and that natural, coalgebraic notions of program equivalence such as applicative similarity and logical relations can be developed within. Starting from this observation, we formalize fine-grain call-by-value and call-by-push-value in the higher-order abstract GSOS framework, reduce their key congruence properties to simple syntactic conditions by leveraging existing theory and argue that introducing changes to either language incurs minimal proof overhead.

Problem

• Program Equivalence
• Call-by-push-value
• Call-by-value

Innovation

• Pre-sheaf Topos
• Push-by-Value
• Pull-by-Name