## Standardization and Evaluation in Combinatory Reduction Systems (2000)

Citations: | 4 - 1 self |

### BibTeX

@MISC{Wells00standardizationand,

author = {J. B. Wells and Robert Muller},

title = {Standardization and Evaluation in Combinatory Reduction Systems},

year = {2000}

}

### OpenURL

### Abstract

A rewrite system has standardization i for any rewrite sequence there is an equivalent one which contracts the redexes in a standard order. Standardization is extremely useful for finding normalizing strategies and proving that a rewrite system for a programming language is sound with respect to the language's operational semantics. Although for some rewrite systems the standard-order can be simple, e.g., left-to-right or outermost-first, many systems need a more delicate order. There are abstract notions of standard order which always apply, but proofs (often quite dicult) are required that the rewrite system satis es a number of axioms and not much guidance is provided for finding a concrete order that satisfies the abstract definition. This paper gives a framework based on combinatory reduction systems (CRS's) which is general enough to handle many programming languages. If the CRS is orthogonal and fully extended and a good redex ordering can be found, then a standard order is obtain...