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CFGKAT: A Complete Calculus for Non-Local Control Flow

Year: 2026

Type: preprint

Abstract: CFGKAT is an extension of guarded Kleene Algebra with Tests (GKAT) that adds non-local control flow (e.g., break, goto) while maintaining an efficient decision procedure. An axiomatization of equivalence for CFGKAT presents unique barriers created by the presence of non-local control flow and contextual semantics of goto which compromises compositional reasoning. In this paper, we overcome these barriers and present a sound and complete axiomatization of program equivalence in CFGKAT. We verify the loop case of the Erosa-Hendren goto elimination algorithm, a difficult syntactic metatheorem which requires reasoning about fixpoints, control-flow contexts, and mutable state. We mechanize the metatheory and case study in Rocq.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2611.14201

Authors: Van Koevering, Spencer, Silva, Alexandra, Zhang, Cheng, Kappé, Tobias

Language: English

Topic: Logic, programming, and type systems

Subfield: Software

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225832244

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