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As a generic theorem prover, Isabelle supports a variety of logics. Distinctive features include Isabelle's representation of logics within a meta-logic and the use of higher-order unification to combine inference rules. Isabelle can be applied to reasoning in pure mathematics or verification of computer systems. This volume constitutes the Isabelle documentation. It begins by outlining theoretical aspects and then demonstrates the use in practice. Virtually all Isabelle functions are described, with advice on correct usage and numerous examples. Isabelle's built-in logics are also described in detail. There is a comprehensive bebliography and index. The book addresses prospective users of Isabelle as well as researchers in logic and automated reasoning.

Automatic theorem proving --- Theorema's--Automatische bewijsvoering --- Théorèmes--Démonstration automatique --- Automatic theorem proving. --- Théorèmes --- Démonstration automatique --- Isabelle (Computer file) --- Isabelle (Computer file). --- Théorèmes --- Démonstration automatique --- Computer science. --- Logic design. --- Software engineering. --- Artificial intelligence. --- Logic, Symbolic and mathematical. --- Mathematical Logic and Formal Languages. --- Logics and Meanings of Programs. --- Software Engineering. --- Artificial Intelligence. --- Mathematical Logic and Foundations. --- Informatics --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computer software engineering --- Engineering --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Cambridge LCF (Computer system) --- Cambridge LCF (Computersysteem) --- Cambridge LCF (Système d'ordinateur) --- Computable functions --- -Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Decidability (Mathematical logic) --- Cambridge Logic for Computable Functions (Computer system) --- Cambridge LCF (Computer system). --- Computer science --- Data processing --- Data processing. --- Computable functions - Data processing.

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This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.

Cambridge LCF (Computer system) --- Computable functions --- Data processing.

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This volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.

Computer logic --- Automatic theorem proving --- Computer Science --- Engineering & Applied Sciences --- 681.3*D21 --- 681.3*D31 --- 681.3*F31 --- 681.3*F41 --- 681.3*I23 --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Artificial intelligence --- Proof theory --- Computer science logic --- Logic, Symbolic and mathematical --- Requirements/specifications: languages; methodologies; tools (Software engineering)--See also {681.3*D31} --- Formal definitions and theory: semantics; syntax (Programming languages)--See also {681.3*D21}; {681.3*F31}; {681.3*F32}; {681.3*F42}; {681.3*F43} --- Specifying anf verifying and reasoning about programs: assertions; invariants; mechanical verification; pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21}; {681.3*D24}; {681.3*D31}; {681.3*E1} --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F31 Specifying anf verifying and reasoning about programs: assertions; invariants; mechanical verification; pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21}; {681.3*D24}; {681.3*D31}; {681.3*E1} --- 681.3*D31 Formal definitions and theory: semantics; syntax (Programming languages)--See also {681.3*D21}; {681.3*F31}; {681.3*F32}; {681.3*F42}; {681.3*F43} --- 681.3*D21 Requirements/specifications: languages; methodologies; tools (Software engineering)--See also {681.3*D31} --- Computer logic. --- Automatic theorem proving. --- Computer science. --- Logic. --- Programming languages (Electronic computers). --- Computers. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Mathematical Logic and Formal Languages. --- Theory of Computation. --- Artificial Intelligence (incl. Robotics). --- Logics and Meanings of Programs. --- Programming Languages, Compilers, Interpreters. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Calculators --- Cyberspace --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Informatics --- Methodology --- Information theory. --- Logic design. --- Artificial Intelligence. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Communication theory --- Communication