Toward formal development of programs from algebraic specifications: Parameterisation revisited

Abstract

The program development process is viewed as a sequence of implementation steps leading from a specification to a program. Based on an elementary notion of refinement, two notions of implementation are studied: constructor implementations which involve a construction "on top of" the implementing specification, and abstractor implementations which additionally provide for abstraction from some details of the implemented specification. These subsume most formal notions of implementation in the literature. Both kinds of implementations satisfy a vertical composition and a (modified) horizontal composition property. All the definitions and results generalise to the framework of an arbitrary institution.

The Foundational Legacy of ASL

“…We used the notation ΠX:SP • SP [X] for the latter, following dependent type theory, and ASL-style λ-abstraction as above for the former. There is a Galois connection which links the two semantic domains, with closed elements corresponding to functions mapping models to non-empty classes of models [SST92]. A natural example is to generalise from SET by taking the sort of elements as a parameter, in place of nat.…”

“…generic modules, constructors, ML-style functors). We studied this distinction in [SST92]: parameterized specifications denote functions that map model classes to model classes, while parameterized programs denote functions that map models to models and specifications of parameterized programs denote classes of such functions. The slogan is parameterized (program specification) = (parameterized program) specification.…”

The Semantics of Extended ML: A Gentle Introduction

“…We have not yet seen a compelling need to add parameterised speci cations to EML. In fact, it has become clear to us SST92] that what is really important in formal software development is the ability to specify parameterised program modules (i.e. SML functors), and EML already has this facility: one uses an EML functor declaration having a question mark in place of a body.…”

Horizontal Composability Revisited

“…[Gog96]) that the proper entities here are specifications of parameterised programs, see [SST92], that is, descriptions of functions mapping algebras to algebras, rather than Clear theory procedures which map specifications (descriptions of classes of algebras) to specifications. See Section 3.…”