An Executable Rewriting Logic Semantics of K-Scheme

This paper presents an executable rewriting logic semantics of KScheme, a dialect of Scheme based (partially) on the informal definition given in the RRS report (Kelsey et al. 1998). The presented semantics follows the K language definitional style (Roşu 2005 and 2006) and is a pure rewriting logic specification (Meseguer 1992) containing 772 equations and 1 rewrite rule, so it can also be regarded as an algebraic denotational specification with an initial model semantics. Rewriting logic specifications can be executed on common (context-insensitive) rewrite engines, provided that equations are oriented into rewrite rules, typically from left-to-right. While in theory rewriting logic specifications can let certain behaviors 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 “implementations”. To become executable, K-Scheme overspecifies certain features left undefined on purpose in RRS. In spite of overspecifying 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 provides 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 extensions 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 evaluation contexts, their complete translation in Maude as executable specifications is rather verbose and low-level. An automated translator 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 specification is public, together with a web-based interface to “execute” K-Scheme programs without having to download Maude.