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At least four research fields detennine the theoretical background
of specification and deduction in computer science: recursion
theory, automated theorem proving, abstract data types and tenn
rewriting systems. As these areas approach each other more and
more, the strong distinctions between functional and relational
views, deductive and denotational approaches as well as between
specification and programming are relieved in favour of their
integration. The book will not expose the lines of this
development; conversely, it starts out from the nucleus of Hom
clause logic and brings forth both known and unknown results, most
of which affect more than one of the fields mentioned above.
Chapter 1 touches on historical issues of specification and
prototyping and delimits the topics handled in this book from
others which are at the core of related work. Chapter 2 provides
the fundamental notions and notations needed for the presentation
and interpretation of many-sorted Horn clause theories with
equality. Chapter 3 supplies a number of sample Hom clause
specifications ranging from arithmetic through string manipulation
to higher data structures and interpreters of programming
languages. Some of these examples serve as a reference to
illustrate definitions and results, others may throw a light on the
strong link between specifications and programs, which are executed
by applying deduction rules. Thus we have included examples of how
to use program trans/ormation methods in specification design.
Declarative programs consist of mathematical functions and
relations and are amenable to formal specification and
verification, since the methods of logic and proof can be applied
to the programs in a well-defined manner. Here Dr Padawitz
emphasizes verification based on logical inference rules, i.e.
deduction (in contrast with model-theoretic approaches, deductive
methods can be automated to some extent). His treatment of the
subject differs from others in that he tries to capture the actual
styles and applications of programming; neither too general with
respect to the underlying logic, nor too restrictive for the
practice of programming. He generalizes and unifies results from
classical theorem-proving and term rewriting to provide proof
methods tailored to declarative program synthesis and verification.
Detailed examples accompany the development of the methods, whose
use is supported by a documented prototyping system. The book can
be used for graduate courses or as a reference for researchers in
formal methods, theorem-proving and declarative languages.
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