[2605.01032] Algebraic Semantics of Governed Execution: Monoidal Categories, Effect Algebras, and Coterminous Boundaries
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Computer Science > Artificial Intelligence
arXiv:2605.01032 (cs)
[Submitted on 1 May 2026 (v1), last revised 5 May 2026 (this version, v2)]
Title:Algebraic Semantics of Governed Execution: Monoidal Categories, Effect Algebras, and Coterminous Boundaries
Authors:Alan L. McCann
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Abstract:We present an algebraic semantics for governed execution in which governance is axiomatized, compositional, and coterminous with expressibility. The framework, mechanized in 32 Rocq modules (~12,000 lines, 454 theorems, 0 admitted), is built on interaction trees and parameterized coinduction. A three-axiom GovernanceAlgebra record (safety, transparency, properness) induces a symmetric monoidal category with verified pentagon, triangle, and hexagon coherence, where every tensor composition preserves governance. An algebraic effect system constrains the handler algebra so that only governance-preserving handlers can be constructed in the safe fragment; programs in the empty capability set provably emit only observability directives. Capability-indexed composition bundles programs with machine-checked capability bounds, and a dual guarantee theorem establishes that within_caps and gov_safe hold simultaneously under all composition operators. The capstone result is the coterminous boundary: within our formal model, every program expressible via the four primitive morphism constructors is governed under interpretation, and every governed program is the image of such a program. Turing completeness is preserved inside governance; unmediated I/O is excluded from the governed fragment. Governance denial is modeled as safe coinductive divergence. The governance algebra is parametric: any system instantiating the three axioms inherits all derived properties, including convergence, compositional closure, and goal preservation. Extracted OCaml runs as a NIF in the BEAM runtime, with property-based testing (70,000+ random inputs, zero disagreements) confirming behavioral equivalence between the specification and the runtime interpreter.
Comments: 26 pages, 1 figure, 1 table. Companion proofs: this https URL. Project: this https URL
Subjects:
Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO); Programming Languages (cs.PL)
MSC classes: D.2.4, D.3.1, F.3.1, I.2.0
Cite as: arXiv:2605.01032 [cs.AI]
(or arXiv:2605.01032v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2605.01032
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arXiv-issued DOI via DataCite
Submission history
From: Alan McCann [view email] [v1] Fri, 1 May 2026 18:59:01 UTC (24 KB)
[v2] Tue, 5 May 2026 10:30:32 UTC (24 KB)
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