The essence of the Iterator pattern

The Iterator pattern gives a clean interface for element-by-element access to a collection, independent of the collection's shape. Imperative iterations using the pattern have two simultaneous aspects: mapping and accumulating. Various existing functional models of iteration capture one or other of these aspects, but not both simultaneously. We argue that C. McBride and R. Paterson's applicative functors (Applicative programming with effects, J. Funct. Program., 18 (1): 1–13, 2008), and in particular the corresponding traverse operator, do exactly this, and therefore capture the essence of the Iterator pattern. Moreover, they do so in a way that nicely supports modular programming. We present some axioms for traversal, discuss modularity concerns and illustrate with a simple example, the wordcount problem.

Computation with classical sequents

$\X$is an untyped continuation-style formal language with a typed subset that provides a Curry–Howard isomorphism for a sequent calculus for implicative classical logic.$\X$can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make${\X}$an expressive platform on which many different (applicative) programming paradigms can be mapped. In this paper we will present the syntax and reduction rules for$\X$; in order to demonstrate its expressive power, we will show how elaborate calculi can be embedded, such as the λ-calculus, Bloo and Rose's calculus of explicit substitutions λx, Parigot's λμ and Curien and Herbelin's$\lmmt$.${\X}$was first presented in Lengrand (2003), where it was called the λξ-calculus. It can be seen as the pure untyped computational content of the reduction system for the implicative classical sequent calculus of Urban (2000).