## Relative Normalization in Deterministic Residual Structures (1996)

Venue: | In: Proc. of the 19 th International Colloquium on Trees in Algebra and Programming, CAAP'96, Springer LNCS |

Citations: | 17 - 13 self |

### BibTeX

@INPROCEEDINGS{Glauert96relativenormalization,

author = {John Glauert and Zurab Khasidashvili},

title = {Relative Normalization in Deterministic Residual Structures},

booktitle = {In: Proc. of the 19 th International Colloquium on Trees in Algebra and Programming, CAAP'96, Springer LNCS},

year = {1996},

pages = {180--195}

}

### OpenURL

### Abstract

. This paper generalizes the Huet and L'evy theory of normalization by neededness to an abstract setting. We define Stable Deterministic Residual Structures (SDRS) and Deterministic Family Structures (DFS) by axiomatizing some properties of the residual relation and the family relation on redexes in an Abstract Rewriting System. We present two proofs of the Relative Normalization Theorem, one for SDRSs for regular stable sets, and another for DFSs for all stable sets of desirable `normal forms'. We further prove the Relative Optimality Theorem for DFSs. We extend this result to deterministic Computation Structures which are deterministic Event Structures with an extra relation expressing self-essentiality. 1 Introduction A normalizable term, in a rewriting system, may have an infinite reduction, so it is important to have a normalizing strategy which enables one to construct reductions to normal form. It is well known that the leftmost-outermost strategy is normalizing in the -calc...