We introduce the normal produoidal category of monoidal contexts over an arbitrary
monoidal category. In the same sense that a monoidal morphism represents a process, a …

We extend the theory of formal languages in monoidal categories to the multi-sorted,
symmetric case, and show how this theory permits a graphical treatment of topics in …

Strong monads and premonoidal categories play a central role in clarifying the denotational
semantics of effectful programming languages. Unfortunately, this theory excludes many …

The Functional Machine Calculus (FMC) was recently introduced as a generalization of the
lambda-calculus to include higher-order global state, probabilistic and non-deterministic …

We introduce regular languages of morphisms in free monoidal categories, with their
associated grammars and automata. These subsume the classical theory of regular …

We introduce monoidal width as a measure of complexity for morphisms in monoidal
categories. Inspired by well-known structural width measures for graphs, like tree width and …

We further the theory of optics or" circuits-with-holes" to encompass premonoidal categories:
monoidal categories without the interchange law. Every premonoidal category gives rise to …

We introduce effectful Mealy machines-a general notion of Mealy machine with global
effects-and give them semantics in terms of both effectful bisimilarity and traces. Bisimilarity …

Static single assignment form, or SSA, has been the dominant compiler intermediate
representation for decades. In this paper, we give a type theory for a variant of SSA …

Premonoidal categories are monoidal categories without the interchange law; effectful
categories are premonoidal categories with a chosen monoidal subcategory of …