Abstract
The ITERATOR pattern gives a clean interface for element-by-element access to a collection. Imperative iterations using the pattern have two simultaneous aspects: mapping and accumulating . Various existing functional iterations model one or other of these, but not both simultaneously. We argue that McBride and Paterson’s idioms , and in particular the corresponding traverse operator, do exactly this, and therefore capture the essence of the ITERATOR pattern. We present some axioms for traversal, and illustrate with a simple example, the repmin problem.
Highlights
Perhaps the most familiar of the so-called Gang of Four design patterns [5] is the ITERATOR pattern, which ‘provides a way to access the elements of an aggregate object sequentially without exposing its underlying representation’
Monadic maps are very close to the idiomatic traversals that we propose as the essence of imperative iterations; for monadic idioms, traversal reduces exactly to monadic map
We have argued that idiomatic traversals capture the essence of imperative loops — both mapping and accumulating aspects
Summary
Perhaps the most familiar of the so-called Gang of Four design patterns [5] is the ITERATOR pattern, which ‘provides a way to access the elements of an aggregate object sequentially without exposing its underlying representation’ This is achieved by identifying an ITERATOR interface (for example, presenting operations to initialize an iteration, to access the current element, to advance to the element, and to test for completion), that collection objects are expected to implement — perhaps indirectly, via a subobject. C# has some syntactic sugar (matched in Java in version 1.5) to avoid the need to write the boilerplate code to manage an iteration over collection elements; we show an example below This makes code cleaner and simpler, but gives privileged status to the specific iteration interface chosen, and entangles the language and its libraries.
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