Schema-based logic program transformation

In traditional programming methodology, developing a correct and efficient program is divided into two phases: in the first phase, called the synthesis phase, a correct, but maybe inefficient program is constructed, and in the second phase, called the transformation phase, the constructed program is transformed into a more efficient equivalent program. If the synthesis phase is guided by a schema that embodies the algorithm design knowledge abstracting the construction of a particular family of programs, then the transformation phase can also be done in a schema-guided fashion using transformation schemas, which encode the transformation techniques from input program schemas to output program schemas by defining the conditions that have to be verified to have a more efficient equivalent program. Seven program schemas are proposed, which capture sub-families of divide-and-conquer programs and the programs that are constructed using some generalization methods. The proposed transformation schemas either automate transformation strategies, such as accumulator introduction and tupling generalization, which is a special case of sructural generalization, or simulate and extend a basic theorem in functional programming (the first duality law of the fold operators) for logic programs. A prototype transformation system is presented that can transform programs, using the proposed transformation schemas.