Programming with Equations, Subsets, and Relations.
Bharat Jayaraman, David A. Plaisted · 1989
We discuss the declarative and computational issues in combining equational, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semantics of subset assertions incorporate a collect all capability, which is expressed formally by the completion of the program. When used in conjunction with equational assertions, subset assertions serve to define set-valued functions, and the resulting paradigm is called subset-equational programming. We also present the class of stratified subset-equational programs for formalizing the class of closure functions, which are useful in defining various transitive-closure sets. The declarative and operational semantics of simple and stratified subset-equational programs are the main focus of this paper. The operational semantics of closures is based on memo-tables (or extension tables). When sub...