On the theory of specification, implementation, and parametrization of abstract data types

ABSTRACT. In the framework of a category spec of equational speoficatlons of abstract data types, tmplementations are defined to be certain pairs of morphlsms with a common target Th~s concept covers, among others, arbitrary recurslon schemes for defining the derived operations It is shown that for given single steps of a multilevel tmplementatlon, there is always a multtlevel tmplementatlon composed of these steps, but there ts no effective construction of th~s overall implementauon Some suggestions are gtven for practtcal composition of tmplementat~ons Utdlzmg pushouts Parametric specifications and parameter assignments are defined to be spectal morphlsms in spec, and parameter substitution ~s made precise by means of pushouts Since actual parameters can agam be parametrtc, parameter subsututton can be tterated. Thts tterauon ts shown to be assoctatwe Whtle the subject is being treated on a syntactical level in terms of speclfieauons, the imtlal algebra approach ts adopted as providing an appropriate semantics for spec~ficauons, and the effects of the present concepts and results on the initial algebras are studie

Operationelle und funktionale Semantik von Σ-Graphen mit Anwendungen auf LISP

Dieser Bericht ist im Wortlaut identisch mit: Peter Padawitz, Church-Rosser-Eigenschaften von Graph-Grammatiken und Anwendungen auf die Semantik von LISP, Diplomarbeit 1978.Previous studies of operational versus functional semantics of symbolic expressions mostly have been confined to treelike expressions and evaluation by "simplification" and substitution of recursive definitions for function symbols. In order to drop these restrictions we introduce Σ-graphs and Σ-grammars to represent expressions and evaluation rules, respectively. Functional semantics of Σ-graphs is defined as an extension of Scott's fixed point semantics of flow diagrams. We prove that derivations via a Σ-grammar P preserve the functional semantics of Σ-graphs if the underlying "semantic algebra" satisfies the equations given by P. To get an operational semantics of a Σ-graph G relative to a Σ-grammar P derivations of G via P must yield a unique normal form. Therefore sufficient conditions for a weak Church-Rosser property of Σ-grammars are formulated and proved for some classes of such grammars. Applying these results to the programming language LISP we show that the evaluation rules of a LISP interpreter are compatible with the semantics of LISP and weak Church-Rosser where garbage collection is included