Numerical Representations as Purely Functional Data Structures: a New Approach

This paper is concerned with design, implementation and verification of persistent purely functional data structures which are motivated by the representation of natural numbers using positional number systems. A new implementation of random-access list based on redundant segmented binary numbers is described. It uses 4 digits and an invariant which guarantees constant worst-case bounds for cons, head, and tail list operations as well as logarithmic time for lookup and update. The relationship of random-access list with positional number system is formalized and benefits of this analogy are demonstrated. Key words: data structures, purely functional language, random-accesss list, program derivation, recursive slowdown.

• Type: Journal
• Year: 2002
• Where: INFORMATICALT
• Authors: Mirjana Ivanovic, Viktor Kuncak
• Keywords: Data Structures, INFORMATICALT 2002, Positional Number System, Purely Functional