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Resource Transition Systems and Full Abstraction for Linear Higher-Order Effectful Programs

Authors Ugo Dal Lago , Francesco Gavazzo

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Ugo Dal Lago
  • University of Bologna, Italy
  • INRIA Sophia Antipolis, France
Francesco Gavazzo
  • University of Bologna, Italy
  • INRIA Sophia Antipolis, France

Funding

The authors are supported by the ERC Consolidator Grant DLV-818616 DIAPASoN.

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Ugo Dal Lago and Francesco Gavazzo. Resource Transition Systems and Full Abstraction for Linear Higher-Order Effectful Programs. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.FSCD.2021.23

Abstract

We investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear λ-calculus with explicit copying and algebraic effects à la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Operational semantics
Keywords
  • algebraic effects
  • linearity
  • program equivalence
  • full abstraction

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