Extending reliability: Transformational tailoring of abstract mathematical software

Methods for automatically constructing concrete executable programs from an abstract prototype program by applying transformations based on theorems of matrix algebra and on algebraic properties of programming languages are described. These methods provide a user with highly efficient programs tailored to his environment while maintaining the advantages of high reliability and low cost associated with routines from the best mathematical software libraries. Also, the transformations which produce such programs represent a formal codification of rules for writing linear algebra programs.