Development of Correct Transformation Schemata for Prolog Programs 1 Schema-based Transformations

Schema-based program transformation 5] has been proposed as an eeective technique for the optimisation of logic programs. Schemata are applied to a logic program, mapping ineecient constructs to more eecient ones. One challenging aspect of the technique is that of proving that the schemata are correct. This paper describes work in progress addressing the issue of correctness. We deene operations for developing correct schemata by construction. The schema development operations are higher order equivalents of the classic program transformations of fold/unfold 2]. We consider a transformation schema to be correct if its application yields a target program which is equivalent to the source program under the pure Prolog semantics. The work described in this paper makes three contributions: a methodology for the development of provably correct program transformation schemata, abstraction of program transformation operations to transformation operations on schemata, and a higher-order uniication algorithm which forms the basis of the schema transformation operations. A program transformation technique based on transformation schemata is described in 5]. Transformation schemata are deened using patterns | higher-order terms which can be instantiated to program fragments. A transformation schema is applied to a program by scanning the program for a piece of code which matches the source pattern, and replacing it with the instantiated target pattern. A program transformation schema is deened in 5] as a 4-tuple, which spe-ciies that a conjunction of goals G 1 (1) Such schemata can encode a wide range of useful transformations, e.g. loop fusion, accumulator introduction and goal reordering. This paper reports work in progress addressing the issue of proving the cor-rectness of transformation schemata. There are two basic design decisions we must make when considering the correctness of program transformation schemata: 1. Do we seek to prove the correctness of existing schemata, or do we instead only provide tools for constructing new schemata which are guaranteed to be correct? We have decided to take the latter approach.