Denotational Engineering or from Denotations to Syntax

This paper is devoted to the methodology of using denotational techniques in software design. Since denotations describe the mechanisms of a system and syntax is only a user-visible representation of these mechanisms, we suggest that denotations be developed in the first place and that syntax be derived from them later. That viewpoint is opposite to the traditional (descriptive) style where denotational techniques are used in assigning a meaning to some earlier defined syntax. Our methodology is discussed on an algebraic ground where both denotations and syntax constitute many-sorted algebras and where denotational semantics is a homomorphism between them. On that ground the construction of a denotational model of a software system may be regarded as a derivation of a sequence of algebras. We discuss some mathematical techniques which may support that process especially this part where syntax is derived from denotations. The suggested methodology is illustrated on an example where we develop a toy programming language with rendezvous mechanisms.