Related papers: Formal P-Category Theory and Normalization by Eval…
Soundness and completeness with respect to equational theories for programming languages are fundamental properties in the study of categorical semantics. However, completeness results have not been established for programming languages…
Systematic compositionality is the ability to recombine meaningful units with regular and predictable outcomes, and it's seen as key to humans' capacity for generalization in language. Recent work has studied systematic compositionality in…
Weak $\infty$-categories are known to be more expressive than their strict counterparts, but are more difficult to work with, as constructions in such a category involve the manipulation of explicit coherence data. This motivates the search…
We specialise a recently introduced notion of generalised dinaturality for functors $T : (\mathcal{C}^\text{op})^p \times \mathcal{C}^q \to \mathcal{D}$ to the case where the domain (resp., codomain) is constant, obtaining notions of ends…
We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
When formalizing mathematics in (generalized predicative) constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we…
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
In \cite{tva}, Bertrand Toen and Michel Vaquie defined a scheme theory for a closed monoidal category $(C,\otimes,1)$. In this article, we define a notion of smoothness in this relative (and not necesarilly additive) context which…
Completeness proofs in categorical semantics usually proceed by building a syntactic category whose composition is given by substitution. For untyped effectful Call-by-Value languages, this runs into a basic obstacle: there is no canonical…
We introduces a category-theoretic framework for modelling trust as applied to trusted computation systems and remote attestation. By formalizing elements, claims, results, and decisions as objects within a category, and the processes of…
We show that the condition of being categorical in a tail of cardinals can be characterized algebraically for several classes of modules. $Theorem.$ Assume $R$ is an associative ring with unity. 1. The class of locally pure-injective…
We present a Rocq library for monoidal categories, which includes a decision procedure for proving equality of morphisms as well as notations that make it possible to reason as if they were strict, inferring MacLane isomorphims…
Certain results involving "higher structures" are not currently accessible to computer formalization because the prerequisite $\infty$-category theory has not been formalized. To support future work on formalizing $\infty$-category theory…
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…
It has long been known that every weak monoidal category A is equivalent via monoidal functors and monoidal natural transformations to a strict monoidal category st(A). We generalise the definition of weak monoidal category to give a…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…