There are situations in programming where some dynamic typing is needed, even in the presence of advanced static type systems. We investigate the interplay of dynamic types with other advanced type constructions, discussing their integration into languages with explicit polymorphism (in the style of system F), implicit polymorphism (in the style of ML), abstract data types, and subtyping.

Solid modelling using constructive solid geometry (CSG) includes many examples of stylised divide-and-conquer algorithms. We identify the sources of these recurrent patterns and describe a Geometric Evaluation Library (GEL) which captures them as higher-order functions. This library then becomes the basis of developing CSG applications quickly and concisely. GEL is currently implemented as a set of separately compiled modules in the pure functional language Hope+. We evaluate our work in terms of performance and general applicability. We also assess the benefits of the functional paradigm in this domain and the merits of programming with a set of higher-order functions.

We introduce a λ-calculus notation which enables us to detect in a term, more β-redexes than in the usual notation. On this basis, we define an extended β-reduction which is yet a subrelation of conversion. The Church Rosser property holds for this extended reduction. Moreover, we show that we can transform generalised redexes into usual ones by a process called ‘term reshuffling’.

This paper presents an application of functional programming in the field of molecular biology: exploring the conformations of nucleic acids. The Nucleic Acid three-dimensional structure determination problem (NA3D) and a constraint satisfaction algorithm are formally described. Prototyping and experimental development using the Miranda functional programming language, over the last four years, are discussed. A Prolog implementation has been developed to evaluate software engineering and performance criteria between functional and logic programming. A C++ implementation has been developed for distribution purpose and to solve large practical problems. This system, called MC-SYM for ‘Macromolecular Conformation by SYMbolic generation’, is used in more than 50 laboratories, including academic and government research centres and pharmaceutical companies.