A generalization of the trie data structure

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.