This paper describes the T-Ruby language for specifying VLSI circuits in terms of relational abstractions of their behaviour. The language is based on a typed lambda calculus with a type system closely related to that of Edinburgh LF. Terms in the language may have simple, non-parameterised types or types which are constructed from other types, possibly together with terms. The dependent types which can be constructed in this way are useful for describing parameterised regular structures which commonly appear in VLSI circuits. The language forms the basis for a tool which permits term rewriting in a user-directed transformational style according to a set of proved term equivalences. Terms which describe causal relations may then be translated into a VLSI specification in a standard VLSI description language. The rewriting process is illustrated by the derivation of a relation describing a circuit for 2-dimensional convolution. 1 Introduction Ruby [3] is a language intended for specif...

. 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...