An Embedding of Ruby in Isabelle

. This paper describes a semantical embedding of the relation based language Ruby in Zermelo-Fraenkel set theory (ZF) using the Isabelle theorem prover. A small subset of Ruby, called Pure Ruby, is embedded as a conservative extension of ZF and many useful structures used in connection with VLSI design are defined in terms of Pure Ruby. The inductive package of Isabelle is used to characterise the Pure Ruby subset to allow proofs to be performed by structural induction over the Pure Ruby elements. 1 Introduction Ruby [5] is a relation based language intended for specifying VLSI circuits. A circuit is described by a binary relation between appropriate, possibly complex domains of values, and simple relations can be combined into more complex relations by a variety of combining forms. The Ruby relations generate an algebra which defines a set of equivalences. These are used in the Ruby design process which typically involves a transformation from a "specification" to an "impleme..