Purely functional data structures

Abstract

When a C programmer needs an efficient data structure for a particular prob- lem, he or she can often simply look one up in any of a number of good text- books or handbooks. Unfortunately, programmers in functional languages such as Standard ML or Haskell do not have this luxury. Although some data struc- tures designed for imperative languages such as C can be quite easily adapted to a functional setting, most cannot, usually because they depend in crucial ways on as- signments, which are disallowed, or at least discouraged, in functional languages. To address this imbalance, we describe several techniques for designing functional data structures, and numerous original data structures based on these techniques, including multiple variations of lists, queues, double-ended queues, and heaps, many supporting more exotic features such as random access or efficient catena- tion. In addition, we expose the fundamental role of lazy evaluation in amortized functional data structures. Traditional methods of amortization break down when old versions of a data structure, not just the most recent, are available for further processing. This property is known as persistence, and is taken for granted in functional languages. On the surface, persistence and amortization appear to be incompatible, butwe showhow lazy evaluation can be used to resolve this conflict, yielding amortized data structures that are efficient even when used persistently. Turning this relationship between lazy evaluation and amortization around, the notion of amortization also provides the first practical techniques for analyzing the time requirements of non-trivial lazy programs. Finally, our data structures offer numerous hints to programming language de- signers, illustrating the utility of combining strict and lazy evaluation in a single language, and providing non-trivial examples using polymorphic recursion and higher-order, recursive modules.