Selected work

Representative Papers

Dialectica Categories over Heyting Algebras

Jul 25, 2026

This study investigates the algebraic structures and logical properties induced by the categorification of the Dialectica interpretation over Heyting algebras. By specializing de Paiva’s categorical framework to the posetal setting, the authors reconstruct the original construction in purely algebraic terms and demonstrate that the resulting embedding of Heyting algebras into residuated lattices admits a definable adjoint. Key contributions include clarifying the distinct behavior of the single Dialectica tensor with respect to contraction in intuitionistic versus classical logic, and proving that, within ZF set theory, the collapse of the propositional Dialectica construction PD(Set) to PD(2) is equivalent to the Axiom of Choice. The work synthesizes methods from category theory, algebraic logic, and axiomatic set theory, thereby extending the algebraic foundations of Dialectica models and deepening their connections to foundational axiomatic systems.

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Compositionality of Lyapunov functions via assume-guarantee reasoning

Apr 03, 2026

This work addresses the challenge of safety verification for complex dynamical systems—such as parametrized ordinary differential equations and partially observable Markov processes—by proposing a compositional verification framework grounded in category theory. The approach models systems as lenses and integrates assume-guarantee reasoning with advanced categorical structures, including symmetric monoidal double categories, fibrations, and 2-functors, to enable, for the first time, the compositional construction of local input-to-state stability (L)ISS Lyapunov functions. By employing contact conditions to unify diverse system models, the framework supports modular safety verification for generalized Moore machines, significantly enhancing both the expressiveness and applicability of compositional verification while maintaining strong scalability.

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The compact double category $mathbf{Int}(mathbf{Poly}_*)$ models control flow and data transformations

Sep 05, 2025

This paper addresses the challenge of unifying control flow (e.g., loops, conditionals) and data transformations (e.g., copying, deletion, permutation, function application) within a single semantic framework for programming languages. Methodologically, it introduces an algebraic semantics grounded in higher-order category theory: it extends traced cocartesian categories to accommodate data-aware control flow, constructs a compact double category $mathbb{I}mathbf{nt}(mathbf{Poly}_*)$ equipped with trajectory-tracking capability, and establishes its universal properties; using multicategory theory, the $mathbf{Int}$-construction, operads, and traced category techniques, it proves that $mathbf{Poly}_*$—and its multivariate generalization—admit traced structures. The key contribution is the first algebraic semantic model of control flow with dynamic trajectory tracking, enabling a unified characterization of control flow and data transformations in both $mathbb{I}mathbf{nt}(mathbf{Set}_*)$ and $mathbb{I}mathbf{nt}(mathbf{Poly}_*)$.

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Recent publications

Latest Papers

Dialectica Categories over Heyting Algebras

Jul 25, 2026

This study investigates the algebraic structures and logical properties induced by the categorification of the Dialectica interpretation over Heyting algebras. By specializing de Paiva’s categorical framework to the posetal setting, the authors reconstruct the original construction in purely algebraic terms and demonstrate that the resulting embedding of Heyting algebras into residuated lattices admits a definable adjoint. Key contributions include clarifying the distinct behavior of the single Dialectica tensor with respect to contraction in intuitionistic versus classical logic, and proving that, within ZF set theory, the collapse of the propositional Dialectica construction PD(Set) to PD(2) is equivalent to the Axiom of Choice. The work synthesizes methods from category theory, algebraic logic, and axiomatic set theory, thereby extending the algebraic foundations of Dialectica models and deepening their connections to foundational axiomatic systems.

0 citationsRead paper

Compositionality of Lyapunov functions via assume-guarantee reasoning

Apr 03, 2026

This work addresses the challenge of safety verification for complex dynamical systems—such as parametrized ordinary differential equations and partially observable Markov processes—by proposing a compositional verification framework grounded in category theory. The approach models systems as lenses and integrates assume-guarantee reasoning with advanced categorical structures, including symmetric monoidal double categories, fibrations, and 2-functors, to enable, for the first time, the compositional construction of local input-to-state stability (L)ISS Lyapunov functions. By employing contact conditions to unify diverse system models, the framework supports modular safety verification for generalized Moore machines, significantly enhancing both the expressiveness and applicability of compositional verification while maintaining strong scalability.

0 citationsRead paper

The compact double category $mathbf{Int}(mathbf{Poly}_*)$ models control flow and data transformations

Sep 05, 2025

This paper addresses the challenge of unifying control flow (e.g., loops, conditionals) and data transformations (e.g., copying, deletion, permutation, function application) within a single semantic framework for programming languages. Methodologically, it introduces an algebraic semantics grounded in higher-order category theory: it extends traced cocartesian categories to accommodate data-aware control flow, constructs a compact double category $mathbb{I}mathbf{nt}(mathbf{Poly}_*)$ equipped with trajectory-tracking capability, and establishes its universal properties; using multicategory theory, the $mathbf{Int}$-construction, operads, and traced category techniques, it proves that $mathbf{Poly}_*$—and its multivariate generalization—admit traced structures. The key contribution is the first algebraic semantic model of control flow with dynamic trajectory tracking, enabling a unified characterization of control flow and data transformations in both $mathbb{I}mathbf{nt}(mathbf{Set}_*)$ and $mathbb{I}mathbf{nt}(mathbf{Poly}_*)$.

0 citationsRead paper