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Zbl 0896.68094
Reeves, A.C.
Towards a sketch based model of self-interpreters. (English)
[J] Diagrammes 33, 1-178 (1995). ISSN 0224-3911

This is an interesting, although quite technical, PhD Thesis. The author considers an important issue -- whether and how is it possible to construct (calculate) a processor from a source language into a target language if the precise semantic specifications of both languages are known, but the source to target relationship is not specified. The Thesis provides a categorical model of a language based on sketches which is used to develop a technique for the calculation of a self-interpreter. The author considers his Thesis is an important first step towards achieving his goal and outlines some of the next steps, together with open questions.\par The framework for the research is provided by the categorical model of a programming language considered as a 4-tuple consisting of the language semantics, language syntax, and two functions: eval (from syntax to semantics), and learn (from semantics to syntax). This abstract nature enables precise specification (and understanding) of very general properties of languages and classes of languages. However, the author's presentation is very technical, and most of it is hardly understandable to a non-specialist computing scientist. Although category theory leads to the reduction of the amount of rabbits taken out of various magic hats [the metaphor used by E. W. Dijkstra], the author does not state this explicitly; and only a reader having some technical knowledge of category theory can infer this from the Thesis. This is a pity since it may be possible to present category-theoretical approaches in a manner that separates semantics from technicalities, as (for example) in {\it J. Goguen} [Semiotic morphisms. TR-CS97-553, University of California at San Diego (August 1997)]; and therefore to advance the usuage of category theory by computing scientists (and even practitioners) not so well initiated in category theory. This certainly applies to the possible wide(r) distribution of the author's results which is very desirable since, in particular, using sketches (as the author did) requires being explicit in stating all details of language specifications and therefore making these complete and explicit specifications available both to humans and to software systems. It would be very interesting and quite important to use these ideas for creating a processor from the source language of a business specification to a target language of a system specification in constructing information management systems (especially since -- much more often than not -- these languages have not yet been completely and explicitly specified).\par Unfortunately, the amount of technicalities even for a very small toy language is quite substantial (acknowledge by the author), and it is not clear what will happen for non-toy examples. It may be well that such a scaling-up is possible, but there seems to be no indication by the author whether this is the case. Thus, one of the most important merits of category theory -- simplification for human understanding by means of abstraction -- is not as clear in the Thesis as it could have been (although the need to distinguish parts of a sketch as being of special interest is acknowledged, and a mechanism is shown).
[H.Kilov (Millington)]

MSC 2000:: *68Q55 Semantics
68Q65 Abstract data types; algebraic specification
18B99 Special categories

Keywords: language processors; self-interpreter; category theory

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Zentralblatt MATH Berlin [Germany]