Inheritance hierarchies: Semantics and unification

  • Authors:

  • Gert Smolka;Hassan Ait-Kaci

  • Affiliations:

  • Microelectronics and Computer Technology Corporation,3500 West Balcones Center Drive, Austin, Texas 78759, U.S.A.;Microelectronics and Computer Technology Corporation,3500 West Balcones Center Drive, Austin, Texas 78759, U.S.A.

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 1989

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Abstract

Inheritance hierarchies are introduced as a means of representing taxonomicallyorganized data. The hierarchies are built up from so-called feature types that are ordered by subtyping and whose elements are records. Every feature type comes with a set of features prescribing fields of its record elements. So-called feature terms are available to denote subsets of feature types. Feature unification is introduced as an operation that decides whether two feature terms have a nonempty intersection and computes a feature term denoting the intersection. We model our inheritance hierarchies as algebraic specifications in ordersortedequational logic using initial algebra semantics. Our framework integrates feature types whose elements are obtained as records with constructor types whose elements are obtained by constructor application. Unification in these hierarchies combines record unification with order-sorted term unification and is presented as constraint solving. We specify a unitary unification algorithm by a set of simplification rules and prove its soundness and completeness with respect to the model-theoretic semantics.