This paper discusses the relationships of two important program classes of linearly recursive programs, that is, decomposable programs and rule commutative programs. We prove that the decomposable programs are always rule commutative. Furthermore, the rule commutative programs that satisfy certain conditions are decomposable. These results are meaningful for integrating the related specified optimization algorithms.

Scientific database systems for the analysis of genes and proteins are becoming very important these days. We have developed a deductive database system PACADE for analyzing the three dimensional and secondary structures of proteins. In this paper, we describe the statistical data classification component of PACADE. We implemented the component for cluster analysis and discrimination analysis. In addition, we enhanced the aggregation function in order to calculate the characteristic values which are useful for data classification. By using the cluster analysis function, the proteins are thereby classified into different types of structural characteristics. The results of these structural analysis experiments are also described in this paper.

Program transformation is a kind of optimization techniques for logic programs, which aims at transforming equally a program into an other form by exploiting some properties or information of the program, so as to make the program cheaper to evaluate. In this paper, a new kind of property of logic programs, called reducibility, is exploited in program transformation. A recursive predicate is reducible if the values of some variables in the recursive predicate are independent to the remainder part and can be detached from the predicate after finite times of expansions. After being proved that the semantic notion of reducibility can be replaced by the syntactic notion of disconnectivity of a R-graph, which is a kind of graph model to represent the behavior of formula expansions, an efficient testing and factoring algorithm is proposed. The paper also extends some existed results on compiled formulas of linear sirups, and compares with some related work.