A type-indexed function is a function that is defined for each member of some family of types. Haskell's type class mechanism provides collections of open type-indexed functions, in which the indexing family can be extended by defining a new type class instance but the collection of functions is fixed. The purpose of this paper is to present TypeCase: a design pattern that allows the definition of closed type-indexed functions, in which the index family is fixed but the collection of functions is extensible. It is inspired by Cheney and Hinze's work on lightweight approaches to generic programming. We generalise their techniques as a design pattern. Furthermore, we show that type-indexed functions with typeindexed types, and consequently generic functions with generic types, can also be encoded in a lightweight manner, thereby overcoming one of the main limitations of the lightweight approaches.

Functional programmers often reason about programs as if they were written in a total language, expecting the results to carry over to non-total (partial) languages. We justify such reasoning.

This article is a tutorial on four methods for proving properties of corecursive programs: fixpoint induction, the approximation lemma, coinduction, and fusion.

Abstract. In programs written in lazy functional languages such as for example Clean and Haskell, the programmer can choose freely whether particular subexpressions will be evaluated lazily (the default) or strictly (must be specified explicitly). It is widely known that this choice affects program behavior, resource consumption and semantics in several ways. However, not much experience is available about the impact on logical program properties and formal reasoning. This paper aims to give a better understanding of the concept of explicit strictness. The impact of explicit strictness on formal reasoning will be investigated. It will be shown that this impact is bigger than expected and that tool support is needed for formal reasoning in the context of explicit strictness. We introduce the various ways in which strictness specific support is offered by the proof assistant Sparkle. 1