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A generalization of the trie data structure

Published online by Cambridge University Press:  04 March 2009

Richard H. Connelly  and
F. Lockwood Morris
Richard H. Connelly
Affiliation:
Department of Mathematics and Computer Science, Providence College, River and Eaton Streets, Providence, Rhode Island 02918, USA. Email: rconnell@sequent1.providence.edu
F. Lockwood Morris
Affiliation:
School of Computer and Information Science, 4–116 Center for Science and Technology, Syracuse University, Syracuse, New York 13244–4100, USA. Email: lockwood@top.cis.syr.Edu
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Abstract

Tries, a form of string-indexed look-up structure, are generalized, in a manner first discovered by Wadsworth, to permit indexing by terms built according to an arbitrary signature. The construction is parametric with respect to the type of data to be stored as values; this is essential, because the recursion that defines tries appeals from one value type to others. ‘Trie’ (for any fixed signature) is then a functor, and the corresponding look-up function is a natural isomorphism.

The trie functor is in principle definable by the ‘initial fixed point’ semantics of Smyth and Plotkin. We simplify the construction, however, by introducing the ‘category-cpo’, a class of category within which calculations can retain some domain-theoretic flavor. Our construction of tries extends easily to many-sorted signatures.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 3 , September 1995 , pp. 381 - 418
Copyright
Copyright © Cambridge University Press 1995

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