From Specifications to Programs: A Fork Algebraic Approach to Bridge the Gap

BAUM, GABRIEL; FRIAS, MARCELO FABIAN; HAEBERER, ARMANDO MARTIN; MARTINEZ LOPEZ, PABLO

LECTURE NOTES IN COMPUTER SCIENCE

Springer

Año: 1996 vol. 1113 p. 180 - 191

0302-9743

The development of programs from first–order specifications has as its main difficulty that of dealing with universal quantifiers. This work is focused in that point, i.e., in the construction of programs whose specifications involve universal quantifiers. This task is performed within a relational calculus based on fork algebras. The fact that first–order theories can be translated into equational theories in abstract fork algebras suggests that such work can be accomplished in a satisfactory way. Furthermore, the fact that these abstract algebras are representable guarantees that all properties valid in the standard models are captured by the axiomatization given for them, allowing the reasoning formalism to be shifted back and forth between any model and the abstract algebra. In order to cope with universal quantifiers, a new algebraic operation — relational implication — is introduced. This operation is shown to have deep significance in the relational statement of first–order expressions involving universal quantifiers. Several algebraic properties of the relational implication are stated showing its usefulness in program calculation. Finally, a non–trivial example of derivation is given to asses the merits of the relational implication as an specification tool, and also in calculation steps, where its algebraic properties are clearly appropriate as transformation rules.