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Record Nr. |
UNISA996464514903316 |
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Autore |
Schreiner Wolfgang <1967-> |
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Titolo |
Thinking programs : logical modeling and reasoning about languages, data, computations, and executions / / Wolfgang Schreiner |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (660 pages) |
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Collana |
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Texts and Monographs in Symbolic Computation |
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Disciplina |
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Soggetti |
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Logic, Symbolic and mathematical |
Computer science - Mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Foreword -- Preface -- Motivation -- Content -- Software -- Teaching and Further Study -- Web Page and Exercises -- Acknowledgments -- Contents -- Logic for Programming: A Perspective -- Logic and Language -- Logic and Mathematics -- Logic with Computers -- Logic for Computer Science -- Logic and Software Development -- Further Reading -- Part IThe Foundations -- 1 Syntax and Semantics -- 1.1 Abstract Syntax -- 1.2 Structural Induction -- 1.3 Semantics -- 1.4 Type Systems -- 1.5 The Semantics of Typed Languages -- 2 The Language of Logic -- 2.1 First-Order Logic -- 2.2 Informal Interpretation -- 2.3 Well-Formed Terms and Formulas -- 2.4 Propositional Logic -- 2.5 Free and Bound Variables -- 2.6 Formal Semantics -- 2.7 Validity, Logical Consequence, and Logical Equivalence -- 3 The Art of Reasoning -- 3.1 Reasoning and Proofs -- 3.2 Inference Rules and Proof Trees -- 3.3 Reasoning in First Order Logic -- 3.4 Reasoning by Induction -- 4 Building Models -- 4.1 Axioms and Definitions -- 4.2 The Theory of Sets -- 4.3 Products and Sums -- 4.4 Set-Theoretic Functions and Relations -- 4.5 More Type Constructions -- 4.6 Implicit Definitions and Function Specifications -- Exercises -- Further Reading -- 5 Recursion -- 5.1 Recursive Definitions -- 5.2 Primitive Recursion -- 5.3 Least and Greatest Fixed Points -- 5.4 Defining Continuous Functions -- 5.5 Inductive and Coinductive Relation Definitions -- 5.6 Rule-Oriented Inductive and |
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Coinductive Relation Definitions -- 5.7 Inductive and Coinductive Function Definitions -- 5.8 Inductive and Coinductive Proofs -- Part IIThe Higher Planes -- 6 Abstract Data Types -- 6.1 Introduction -- 6.2 Declarations, Signatures, and Presentations -- 6.3 Algebras, Homomorphisms, and Abstract Data Types -- 6.4 Loose Specifications -- 6.5 Generated and Free Specifications -- 6.6 Cogenerated and Cofree Specifications. |
6.7 Specifying in the Large -- 6.8 Reasoning About Specifications -- 7 Programming Languages -- 7.1 Programs and Commands -- 7.2 A Denotational Semantics -- 7.3 An Operational Semantics -- 7.4 The Correctness of Translations -- 7.5 Procedures -- Further Reading -- 8 Computer Programs -- 8.1 Specifying Problems -- 8.2 Verifying Programs -- 8.3 Predicate Transformers and Commands as Relations -- 8.4 Non-abortion and Termination -- 8.5 Loop Invariants and Termination Measures -- 8.6 The Refinement of Commands -- 8.7 Reasoning About Procedures -- Further Reading -- 9 Concurrent Systems -- 9.1 Labeled Transition Systems -- 9.2 Modeling Shared Systems -- 9.3 Modeling Distributed Systems -- 9.4 Specifying System Properties -- 9.5 Verifying Invariance -- 9.6 Verifying Response -- 9.7 The Refinement of Systems -- References -- Index. |
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