Amortization, lazy evaluation, and persistence: lists with catenation via lazy linking

Abstract

Amortization has been underutilized in the design of persistent data structures, largely because traditional accounting schemes break down in a persistent setting. Such schemes depend on saving credits for future use, but a persistent data structure may have multiple futures, each competing for the same credits. We describe how lazy evaluation can often remedy this problem, yielding persistent data structures with good amortized efficiency. In fact, such data structures can be implemented purely functionally in any functional language supporting lazy evaluation. As can example of this technique, we present a purely functional (and therefore persistent) implementation of lists that simultaneously support catenation and all other usual list primitives in constant amortized time. This data structure is much simpler than the only existing data structure with comparable bounds, the recently discovered catenable lists of Kaplan and Tarjan, which support all operations in constant worst-case time.