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Titlebook: Solving Higher-Order Equations; From Logic to Progra Christian Prehofer Book 1998 Birkhäuser Boston 1998 Hardware.Program Analysis.Theorem

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书目名称Solving Higher-Order Equations
副标题From Logic to Progra
编辑Christian Prehofer
视频video
丛书名称Progress in Theoretical Computer Science
图书封面Titlebook: Solving Higher-Order Equations; From Logic to Progra Christian Prehofer Book 1998 Birkhäuser Boston 1998 Hardware.Program Analysis.Theorem
描述This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica­ tions, higher-order logic provides the necessary level of abstraction for con­ cise and natural formulations. The main assets of higher-order logic are quan­ tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa­ tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea­ soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.
出版日期Book 1998
关键词Hardware; Program Analysis; Theorem Proving; Variable; calculus; computer; computer science; declarative pr
版次1
doihttps://doi.org/10.1007/978-1-4612-1778-7
isbn_softcover978-1-4612-7278-6
isbn_ebook978-1-4612-1778-7
copyrightBirkhäuser Boston 1998
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Applications of Higher-Order Narrowing,MN97] for formalizing logics and λ-calculi, and for process algebras to [Po194]. Other application areas are program synthesis [Hag91b], machine learning [Har90, DW88], natural language processing [Nad87, PM90, GK96, GKL96], and theorem proving systems, for instance see [AINP90, Pau94, Gor88, CAB.86, DFH.93].
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Introduction,tion and verification of hardware, software, and mathematics. In these applications, higher-order logic provides the necessary level of abstraction for concise and natural formulations. The main assets of higher-order logic are quantification over functions or predicates and its abstraction mechanis
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Higher-Order Lazy Narrowing,s in a top-down or outside-in manner. It can be seen as a direct extension of higher-order unification by some narrowing rules. After starting with a general version of lazy narrowing, we develop refinements of lazy narrowing. Some of them also apply to equational reasoning, while the others are tai
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Concluding Remarks,ming. Towards this goal we have first examined decidable classes of higher-order unification. We have shown that for many practical purposes, higher-order unification is not only a powerful tool, but also terminates for several classes of terms. The main restriction we need is linearity, which is co
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