Functional Pearl trouble shared is trouble halved

Authors:
Richard Bird;Ralf Hinze
Affiliations:
Oxford University Computing Laboratory, Oxford, England;Universität Bonn, Römerstraβe, Bonn, Germany
Venue:
Haskell '03 Proceedings of the 2003 ACM SIGPLAN workshop on Haskell
Year:
2003

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Abstract

A nexus is a tree that contains shared nodes, nodes that have more than one incoming arc. Shared nodes are created in almost every functional program---for instance, when updating a purely functional data structure---though programmers are seldom aware of this. In fact, there are only a few algorithms that exploit sharing of nodes consciously. One example is constructing a tree in sublinear time. In this pearl we discuss an intriguing application of nexuses; we show that they serve admirably as memo structures featuring constant time access to memoized function calls. Along the way we encounter Boolean lattices and binomial trees.