In 1984, J. Rosický gave an abstract presentation of the structure associated to tangent
bundle functors in differential and algebraic geometry. By slightly generalizing this notion …

We introduce partial Markov categories. In the same way that Markov categories encode
stochastic processes, partial Markov categories encode stochastic processes with …

We combine two recent ideas: cartesian differential categories, and restriction categories.
The result is a new structure which axiomatizes the category of smooth maps defined on …

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

We provide a Lawvere-style definition for partial theories, extending the classical notion of
equational theory by allowing partially defined operations. As in the classical case, our …

Recently, a number of reversible functional programming languages have been proposed.
Common to several of these is the assumption of totality, a property that is not necessarily …

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

The categorical semantics of reversible computing must be a category which combines the
concepts of partiality and the ability to reverse any map in the category. Inverse cate gories …

With the increased interest in machine learning, and deep learning in particular, the use of
automatic differentiation has become more wide-spread in computation. There have been …

Structured reversible flowchart languages is a class of imperative reversible programming
languages allowing for a simple diagrammatic representation of control flow built from a …