Coinductive Reasoning for Parametrized Functors and Monads

2026-09-28

International Conference on Concurrency Theory

AI Summary

This study addresses the lack of parametric control in behavioral equivalence for state systems and contextual equivalence for effectful programs. To this end, it proposes a theory of relaxed extensions grounded in parameterized functors and monads. Methodologically, by integrating category theory, relation lifting, and coinductive reasoning, the work constructs refined equivalence notions that permit tunable contexts, thereby replacing traditional universal quantification over all contexts. Furthermore, it uniformly realizes behavioral preorders, equivalences, or metrics through parametric adjustment. Overall, this research establishes a behavior-equivalence framework supporting parametric modulation, significantly enhancing both the flexibility and precision of system verification.

Abstract

Lax extensions (also called relators or relation liftings) are a categorical notion to reason about functors acting on functions and relations in a compatible way. They play a central role to develop sound proof principles for behavioral equivalence of state-based systems and are also important for establishing contextual equivalence for effectful programs. In this paper, we develop the theory of lax extensions for parametrized functors and monads and consider notions of behavioral preorders, equivalence relations or metrics which can now be modulated by additional parameters. From an operational viewpoint, we replace standard contextual equivalence where we quantify over all possible contexts by a refined notion of equivalence where the user can regulate the allowed contexts via chosen parameters.

Problem

• lax extensions
• parametrized functors
• parametrized monads
• behavioral equivalence
• contextual equivalence

Innovation

• lax extensions
• parametrized functors
• parametrized monads
• behavioral equivalence
• contextual equivalence