## Paper: Programming in equational logic: beyond strong sequentiality (at LICS 1990)

**R. C. Sekar I. V. Ramakrishnan**

### Abstract

The authors consider whether it is possible to devise a complete normalization algorithm that minimizes (rather than eliminates) the wasteful reductions for the entire class of regular systems. A solution is proposed to this problem using the concept of a necessary set of redexes. In such a set, at least one of the redexes must be reduced to normalize a term. An algorithm is devised to compute a necessary set for any term not in normal form, and it is shown that a strategy that repeatedly reduces all redexes in such a set is complete for regular programs. It is also shown that the algorithm is optimal among all normalization algorithms that are based on left-hand sides alone. This means that the algorithm is lazy (like Huet-Levy's) on strongly sequential parts of a program, relaxes laziness minimally to handle the other parts, and thus does not sacrifice generality for the sake of efficiency

### BibTeX

@InProceedings{SekarRamakrishnan-Programminginequati, author = {R. C. Sekar and I. V. Ramakrishnan}, title = {Programming in equational logic: beyond strong sequentiality}, booktitle = {Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science (LICS 1990)}, year = {1990}, month = {June}, pages = {230--241}, location = {Philadelphia, PA, USA}, publisher = {IEEE Computer Society Press} }