Matching and Unification for the Object-Oriented Symbolic Computation System AlgBench

Term matching has become one of the most important primitive operations for symbolic computation. This paper describes the extension of the object-oriented symbolic computation system AlgBench with pattern matching and unification facilities. The various pattern objects are organized in subclasses of the class of the composite expressions. This leads to a clear design and to a distributed implementation of the pattern matcher in the subclasses. New pattern object classes can consequently be added easily to the system. Huet's and our simple mark and retract algorithm for standard unification as well as Stickel's algorithm for associative commutative unification have been implemented in an object-oriented style. Unifiers are selected at runtime. We extend Mathematica's type-constrained pattern matching by taking into account inheritance information from a user-defined hierarchy of object types. The argument unification is basically instance variable unification. The improvement of the pattern matching operation of a rule- and object-based symbolic computation system with unification in an object-oriented way seems to be very appropriate.

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