Logic programming was based on first-order logic. Higher-order logics can also lead to theories of theorem-proving. This book introduces just such a theory, based on a lambda-calculus formulation of a clausal logic wi...
详细信息
ISBN:
(数字)9780511832628
ISBN:
(纸本)9780521117906
Logic programming was based on first-order logic. Higher-order logics can also lead to theories of theorem-proving. This book introduces just such a theory, based on a lambda-calculus formulation of a clausal logic with equality, known as the Clausal Theory of Types. By restricting this logic to Horn clauses, a concise form of logic programming that incorporates functional programming is achieved. The book begins by reviewing the fundamental Skolem-Herbrand-Gödel Theorem and resolution, which are then extrapolated to a higher-order setting; this requires introducing higher-order equational unification which builds in higher-order equational theories and uses higher-order rewriting. The logic programming language derived has the unique property of being sound and complete with respect to Henkin-Andrews general models, and consequently of treating equivalent terms as identical. First published in 1993, the book can be used for graduate courses in theorem-proving, but will be of interest to all working in declarative programming.
This 1993 book shows how formal logic can be used to specify the behaviour of hardware designs and reason about their correctness. ;This 1993 book shows how formal logic can be used to specify the behaviour of hardwar...
详细信息
ISBN:
(数字)9780511880681
ISBN:
(纸本)9780521417181
This 1993 book shows how formal logic can be used to specify the behaviour of hardware designs and reason about their correctness. ;This 1993 book shows how formal logic can be used to specify the behaviour of hardware designs and reason about their correctness. A primary theme of the book is the use of abstraction in hardware specification and verification. The author describes how certain fundamental abstraction mechanisms for hardware verification can be formalised in logic and used to express assertions about design correctness and the relative accuracy of models of hardware behaviour. His approach is pragmatic and driven by examples. He also includes an introduction to higher-order logic, which is a widely used formalism in this subject, and describes how that formalism is actually used for hardware verification. The book is based in part on the author's own research as well as on graduate teaching. Thus it can be used to accompany courses on hardware verification and as a resource for research workers.
The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequ...
详细信息
ISBN:
(数字)9780511879081
ISBN:
(纸本)9780521018470
The authors describe here a framework in which the type notation of functional languages is extended to include a notation for binding times (that is run-time and compile-time) that distinguishes between them. Consequently the ability to specify code and verify program correctness can be improved. Two developments are needed, the first of which introduces the binding time distinction into the lambda calculus, in a manner analogous with the introduction of types into the untyped lambda calculus. Methods are also presented for introducing combinators for run-time. The second concerns the interpretation of the resulting language, which is known as the mixed lambda-calculus and combinatory logic. The notion of 'parametrized semantics' is used to describe code generation and abstract interpretation. The code generation is for a simple abstract machine designed for the purpose; it is close to the categorical abstract machine. The abstract interpretation focuses on a strictness analysis that generalises Wadler's analysis for lists.
This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycl...
详细信息
ISBN:
(数字)9780511881176
ISBN:
(纸本)9780521022545
This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycles and intensionality. The resulting synthesis serves as a logical foundation for grammars, logic programming and constraint-based reasoning systems. A logical perspective is adopted which employs an attribute-value description language along with complete equational axiomatizations of the various systems of feature structures. At the same time, efficiency concerns are kept in mind and complexity and representability results are provided. The application of feature structures to phrase structure grammars is described and completeness results are shown for standard evaluation strategies. Definite clause logic programs are treated as a special case of phrase structure grammars. Constraint systems are introduced and an enumeration technique is developed for solving arbitrary attribute-value logic constraints. This book, with its innovative approach to data structure, will be essential reading for researchers in computational linguistics, logic programming and knowledge representation. Its self-contained presentation makes it flexible enough to serve as both a research tool and a text book.
暂无评论