Compositional Program Verification with Polynomial Functors in Dependent Type Theory
arXiv:2604.01303v1 Announce Type: cross Abstract: We present a framework for compositional program verification based on polynomial functors in dependent type theory. In this framework, polynomial functors serve as program interfaces, Kleisli morphisms for the free monad monad serve as implementations, and dependent polynomials encode pre/postcondition specifications. We show that implementations and their verifications compose via wiring diagrams, and that Mealy machines provide a compositional coalgebraic operational semantics. We identify the abstract categorical structure underlying this compositionality as a monoidal functor from specifications to interfaces with a compatible monoidal natural transformation of lax monoidal presheaves; this opens the door to generalizations to other ca
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Abstract:We present a framework for compositional program verification based on polynomial functors in dependent type theory. In this framework, polynomial functors serve as program interfaces, Kleisli morphisms for the free monad monad serve as implementations, and dependent polynomials encode pre/postcondition specifications. We show that implementations and their verifications compose via wiring diagrams, and that Mealy machines provide a compositional coalgebraic operational semantics. We identify the abstract categorical structure underlying this compositionality as a monoidal functor from specifications to interfaces with a compatible monoidal natural transformation of lax monoidal presheaves; this opens the door to generalizations to other categories, monoidal products, etc., including settings for concurrency and relational verification, which we sketch. As a proof-of-concept, the entire framework has been formalized in Agda.
Subjects:
Logic in Computer Science (cs.LO); Programming Languages (cs.PL); Category Theory (math.CT)
Cite as: arXiv:2604.01303 [cs.LO]
(or arXiv:2604.01303v1 [cs.LO] for this version)
https://doi.org/10.48550/arXiv.2604.01303
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: C.B. Aberlé [view email] [v1] Wed, 1 Apr 2026 18:16:05 UTC (28 KB)
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