An Executable Rewriting Logic Semantics of K-Scheme

This paper presents an executable rewriting logic semantics of K- Scheme, a dialect of Scheme based (partially) on the informal defi- nition given in the R 5 RS report (Kelsey et al. 1998). The presented semantics follows the K language definitional style (Rosu 2005 and 2006) and is a pure rewriting logic specification (Meseguer 1992) containing 772 equations and 1 rewrite rule, so it can also be re- garded as an algebraic denotational specification with an initial model semantics. Rewriting logic specifications can be executed on common (context-insensitive) rewrite engines, provided that equa- tions are oriented into rewrite rules, typically from left-to-right. While in theory rewriting logic specifications can let certain behav- iors underspecified, thus allowing more models, in practice they need to completely specify all the desired behaviors if one wants to use their associated rewrite systems as "interpreters", or "imple- mentations". To become executable, K-Scheme overspecifies cer- tain features left undefined on purpose in R 5 RS. In spite of over- specifying for executability reasons, the rewriting logic semantics in this paper is the most complete formal definition of a language in the Scheme family that we are aware of, in the sense that it pro- vides definitions for more Scheme language features than any other similar attempts. The presented executable definition of K-Scheme can serve as a platform for experimentation with variants and ex- tensions of Scheme, for example concurrency. The Maude system is used in this paper, but other rewrite engines could have been used as well. Even though, on paper, K rewrite-based definitions tend to be as compact and high-level as reduction-based definitions with eval- uation contexts, their complete translation in Maude as executable specifications is rather verbose and low-level. An automated trans- lator from K to Maude is under development, which will reduce the size of definitions following the K style several times and will certainly increase their readability. The complete Maude specifi- cation is public, together with a web-based interface to "execute" K-Scheme programs without having to download Maude.