Many students complete PhDs in functional programming each year. As a service to the community, the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.

The problem of finding a densest segment of a list is similar to the well-known maximum segment sum problem, but its solution is surprisingly challenging. We give a general specification of such problems, and formally develop a linear-time online solution, using a sliding-window style algorithm. The development highlights some elegant properties of densities, involving partitions that are decreasing and all right-skew.

Teaching functional programming as a second programming paradigm is often difficult as students can have strong preconceptions about programming. When most of these preconceived ideas fail to be confirmed, functional programming may be seen as an unnecessarily difficult topic. A typical topic that causes such difficulties is the language of types employed by many modern functional languages. In this paper, we focus on addressing this difficulty through the use of step-by-step calculations of type expressions. The outcome of the study is an elaboration of a worked example format and a methodical approach for teaching types to beginner functional programmers.

In a paper, entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent lambda terms and derive results from their generating functions, especially that the number of terms of size n grows roughly like 1.963447954. . .n. In a second part we use this approach to generate random lambda terms using Boltzmann samplers.