An Experiment with a User Manual of a Programming Language Based on a Denotational Semantics

Denotational models should provide an opportunity for the revision of current practices seen in the manuals of programming languages. New styles should on one hand base on denotational models but on the other - do not assume that today readers are acquainted in this field. A manual should, therefore, provide some basic knowledge and notation needed to understand the definition of a programming language written in a new style. At the same time - I strongly believe that - it should be written for professional programmers rather than for amateurs. The role of a manual is not to teach the skills of programming. Such textbooks are, of course, necessary, but they should tell the readers what the programming is about rather than the technicalities of a concrete language. The paper contains an example of a manual for a virtual programming language Lingua developed in our project.Comment: 47 pages. This paper is based on my preprinted book 'A Denotational Engineering of Programming Languages' (available on arXiv:1905.01473), which describes a virtual programming language whose manual is discussed in the paper. To make the paper possibly self-contained large parts of the book are quoted in the paper. arXiv admin note: substantial text overlap with arXiv:1905.0146

An experiment with denotational semantics

The paper is devoted to showing how to systematically design a programming language in 'reverse order', i.e. from denotations to syntax. This construction is developed in an algebraic framework consisting of three many-sorted algebras: of denotations, of an abstract syntax and of a concrete syntax. These algebras are constructed in such a way that there is a unique homomorphism from concrete syntax to denotations, which constitutes the denotational semantics of the language. Besides its algebraic framework, the model is set-theoretic, i.e. the denotational domains are just sets, rather than Scott's reflexive domains. The method is illustrated by a layer-by-layer development of a virtual language Lingua: an applicative layer, an imperative layer (with recursive procedures) and an SQL layer where Lingua is regarded as an API (Application Programming Interface) for an SQL engine. The latter is given a denotational semantics as well. The langue is equipped with a strong typing mechanism which covers basic types (numbers, Booleans, etc.), lists, arrays, record and their arbitrary combinations plus SQL-like types: rows, tables and databases. The model of types includes SQL integrity constraints.Comment: A preprint of 44 pages. All comments will be highly appreciated. You may contact me on [email protected]

A Denotational Engineering of Programming Languages

The book is devoted to two research areas: (1) Designing programming languages along with their denotational models. A denotational model of a language consists of two many-sorted algebras - an algebra of syntax and an algebra of denotations - and a (unique) homomorphism from syntax to denotations called the semantics of the language. (2) Designing sound program-constructors for languages with denotational models. In our approach programs syntactically contain their total-correctness specifications. A program is said to be correct if it is correct wrt its specification. A program-constructor is sound if given correct component-programs yields a correct resulting program. Both methods are illustrated on an example-language Lingua.Comment: A preprint of a book; 340 pages. All comments will be highly appreciated. You may write to me on [email protected]