An Applicative Random-Access Stack

Applicative (functional) programming has long been advocated on theoretical grounds as the formal properties of such programs are simple and elegant. Recently, there has been a trend to bring the applicative approach into the practical arena as a software development tool [2] and even as a programming vehicle [1,6]. Unfortunately, the requirement that operations be side-effect free makes efficient implementations difficult to achieve [6]. However, some researchers have begun to develop effective applicative implementations for classic data abstractions such as stacks, queues, tablets, lists, etc. [4,7]. In this article, applicative algorithms for a random-access stuck @A-stack) are presented. An RA-stack is a stack data abstraction in which one is further permitted to access the kth element of a stack. The approach uses a singly-linked list representation which is augmented with auxiliary pointers that permit the access of arbitrary stack elements in O(lg N) time were N is the size of the stack. The auxiliary linking structure is based on a number representation scheme for which subtraction by one involves at most one carry operation. Another scheme with this property appears in [3].