In these lecture notes we describe an algebraic approach to programming, suitable both for
the derivation of individual programs and for the study of programming techniques in …

The area of coalgebra has emerged within theoretical computer science with a unifying
claim: to be the mathematics of computational dynamics. It combines ideas from the theory of …

We study polynomial functors over locally cartesian closed categories. After setting up the
basic theory, we show how polynomial functors assemble into a double category, in fact a …

Lenses--bidirectional transformations between pairs of connected structures--have been
extensively studied and are beginning to find their way into industrial practice. However …

We introduce the notion of containers as a mathematical formalisation of the idea that many
important datatypes consist of templates where data is stored. We show that containers have …

Modern quantum programming languages integrate quantum resources and classical
control. They must, on the one hand, be linearly typed to reflect the no-cloning property of …

The development of science proceeds in a cycle of activities, the so-called abstraction-
specialisation cycle. Abstraction is the process of seeking patterns or commonalities, which …

This paper describes a new approach to generic functional programming, which allows us to
define functions generically for all datatypes expressible in Haskell. A generic function is …

Bidirectional programming languages are a practical approach to the view update problem.
Programs in these languages, called lenses, define both a view and an update policy-ie …

Isabelle/HOL has recently acquired new versions of definitional packages for inductive
datatypes and primitive recursive functions. In contrast to its predecessors and most other …