マルチセット領域上の等式制約の等価変換

抄録

A new theory of representation and computation for multiset domains was developed. A multiset (or a bag) is a generalization of sets, which allows multiple occurrences of an element. This multiset is useful in representing the collection of objects, and it can be often used as a convenient alternative for sets. In this paper, we investigate the simplest case of a multiset, i.e., the elements in the multiset discussed here are symbols with no structure. While conventional theories for multisets are based on the logic paradigm, this new theory is based on the equivalent transformation(ET)paradigm, where computation is regarded as "equivalent transformation of declarative descriptions." The most important difference from the logic paradigm is the existence of a strict and general foundation. In the ET paradigm, a class of declarative descriptions, called "constraint declarative programs"on "specialization systems, "is used for all possible domains. A generic definition of declarative semantics for all constraint declarative programs is established. A specialization system is a mathematical structure that characterizes each domain. A class of specialization systems is proposed to formalize multiset domains. To delay unnecessary unification, a new transformation rule, called expanding, and equivalent transformation rules for equality constraints are used instead of unfolding. Basic propositions justifying equivalent transformation rules for equality constraints on multiset domains are proven.