Programming with higher-order logic /:
"Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a c...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | "Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called [Lambda]Prolog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and [lambda]-terms and [pi]-calculus expressions can be encoded in [Lambda]Prolog"-- |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139518420 1139518429 9781139516570 1139516574 1280775084 9781280775086 9781139514927 113951492X 9781139021326 113902132X |
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| 245 | 1 | 0 | |a Programming with higher-order logic / |c Dale Miller, Gopalan Nadathur. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
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| 520 | |a "Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called [Lambda]Prolog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and [lambda]-terms and [pi]-calculus expressions can be encoded in [Lambda]Prolog"-- |c Provided by publisher | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Introduction -- First-order terms and representations of data -- First-order horn clauses -- First-order hereditary Harrop formulas -- Typed [lambda]-terms and formulas -- Using quantification at higher-order types -- Mechanisms for structuring large programs -- Computations over [lambda]-terms -- Unification of [lambda]-terms -- Implementing proof systems -- Computations over functional programs -- Encoding a process calculus language -- Appendix. | |
| 588 | 0 | |a Print version record. | |
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| 700 | 1 | |a Nadathur, Gopalan. | |
| 776 | 0 | 8 | |i Print version: |a Miller, Dale (Dale A.). |t Programming with higher-order logic. |d Cambridge : Cambridge University Press, 2012 |z 9780521879408 |w (DLC) 2012016719 |w (OCoLC)774491609 |
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| 880 | 0 | |6 505-00/(S |a Cover -- Programming with Higher-Order Logic -- Title -- Copyright -- Contents -- Preface -- Introduction -- I.1 Connections between logic and computation -- I.2 Logical primitives and programming expressivity -- I.3 The meaning of higher-order logic -- I.4 Presentation style -- I.5 Prerequisites -- I.6 Organization of the book -- 1: First-Order Terms and Representations of Data -- 1.1 Sorts and type constructors -- 1.2 Type expressions -- 1.3 Typed first-order terms -- 1.4 Representing symbolic objects -- 1.5 Unification of typed first-order terms -- 1.6 Bibliographic notes -- 2 First-Order Horn Clauses -- 2.1 First-order formulas -- 2.2 Logic programming and search semantics -- 2.3 Horn clauses and their computational interpretation -- 2.4 Programming with first-order Horn clauses -- 2.4.1 Concrete syntax for program clauses -- 2.4.2 Interacting with the λProlog system -- The read phase -- The prove phase -- The print phase -- Multiple solutions -- 2.4.3 Reachability in a finite-state machine -- 2.4.4 Defining relations over recursively structured data -- 2.4.5 Programming over abstract syntax representations -- 2.5 Pragmatic aspects of computing with Horn clauses -- 2.6 The relationship with logical notions -- 2.6.1 The cut rule and cut-elimination -- 2.6.2 Different presentations of fohc -- 2.7 The meaning and use of types -- 2.7.1 Types and the categorization of expressions -- 2.7.2 Polymorphic typing -- 2.7.3 Type checking and type inference -- 2.7.4 Types and run-time computations -- 2.8 Bibliographic notes -- 3: First-Order Hereditary Harrop Formulas -- 3.1 The syntax of goals and program clauses -- 3.2 Implicational goals -- 3.2.1 Inferences among propositional clauses -- 3.2.2 Hypothetical reasoning -- 3.3 Universally quantified goals -- 3.3.1 Substitution and quantification -- 3.3.2 Quantification can link goals and clauses. | |
| 880 | 8 | |6 505-00/(S |a 3.4 The relationship with logical notions -- 3.4.1 Classical versus intuitionistic logic -- 3.4.2 Intuitionistic versus minimal logic -- 3.4.3 Notable subsets of fohh -- 3.5 Bibliographic notes -- 4: Typed λ-Terms and Formulas -- 4.1 Syntax for λ-terms and formulas -- 4.2 The rules of λ-conversion -- 4.3 Some properties of λ-conversion -- 4.4 Unification problems as quantified equalities -- 4.4.1 Simplifying quantifier prefixes -- 4.4.2 Unifiers, solutions, and empty types -- 4.4.3 Examples of unification problems and their solutions -- 4.5 Solving unification problems -- 4.6 Some hard unification problems -- 4.6.1 Solving Post correspondence problems -- 4.6.2 Solving Diophantine equations -- 4.7 Bibliographic notes -- 5 Using Quantification at Higher-Order Types -- 5.1 Atomic formulas in higher-order logic programs -- 5.1.1 Flexible atoms as heads of clauses -- 5.1.2 Logical symbols within atomic formulas -- 5.2 Higher-order logic programming languages -- 5.2.1 Higher-order Horn clauses -- 5.2.2 Higher-order hereditary Harrop formulas -- 5.2.3 Extended higher-order hereditary Harrop formulas -- 5.3 Examples of higher-order programming -- 5.4 Flexible atoms as goals -- 5.5 Reasoning about higher-order programs -- 5.6 Defining some of the logical constants -- 5.7 The conditional and negation-as-failure -- 5.8 Using λ-terms as functions -- 5.8.1 Some basic computations with functional expressions -- 5.8.2 Functional difference lists -- 5.9 Higher-order unification is not a panacea -- 5.10 Comparison with functional programming -- 5.11 Bibliographic notes -- 6: Mechanisms for Structuring Large Programs -- 6.1 Desiderata for modular programming -- 6.2 A modules language -- 6.3 Matching signatures and modules -- 6.4 The logical interpretation of modules -- 6.4.1 Existential quantification in program clauses -- 6.4.2 A module as a logical formula. | |
| 880 | 8 | |6 505-00/(S |a 6.4.3 Interpreting queries against modules -- 6.4.4 Module accumulation as scoped inlining of code -- 6.5 Some programming aspects of the modules language -- 6.5.1 Hiding and abstract datatypes -- 6.5.2 Code extensibility and modular composition -- 6.5.3 Signature accumulation and parametrization of modules -- 6.5.4 Higher-order programming and predicate visibility -- 6.6 Implementation considerations -- 6.7 Bibliographic notes -- 7: Computations over λ-Terms -- 7.1 Representing objects with binding structure -- 7.1.1 Encoding logical formulas with quantifiers -- 7.1.2 Encoding untyped λ-terms -- 7.1.3 Properties of the encoding of binding -- 7.2 Realizing object-level substitution -- 7.3 Mobility of binders -- 7.4 Computing with untyped λ-terms -- 7.4.1 Computing normal forms -- 7.4.2 Reduction based on paths through terms -- 7.4.3 Type inference -- 7.4.4 Translating to and from de Bruijn syntax -- 7.5 Computations over first-order formulas -- 7.6 Specifying object-level substitution -- 7.7 The λ-tree approach to abstract syntax -- 7.8 The Lλ subset of λProlog -- 7.9 Bibliographic notes -- 8: Unification of λ-terms -- 8.1 Properties of the higher-order unification problem -- 8.2 A procedure for checking for unifiability -- 8.2.1 Simplification of rigid-rigid equations -- 8.2.2 Substitutions for equations between flexible and rigid terms -- 8.2.3 The iterative transformation of unification problems -- 8.2.4 Unification problems with only flexible-flexible equations -- 8.2.5 Nontermination of reductions -- 8.2.6 Matching trees -- 8.3 Higher-order pattern unification -- 8.4 Pragmatic aspects of higher-order unification -- 8.5 Bibliographic notes -- 9: Implementing Proof Systems -- 9.1 Deduction in propositional intuitionistic logic -- 9.2 Encoding natural deduction for intuitionistic logic -- 9.3 A theorem prover for classical logic. | |
| 880 | 8 | |6 505-00/(S |a 9.4 A general architecture for theorem provers -- 9.4.1 Goals and tactics -- 9.4.2 Combining tactics into proof strategies -- 9.5 Bibliographic notes -- 10: Computations over Functional Programs -- 10.1 The miniFP programming language -- 10.2 Specifying evaluation for miniFP programs -- 10.2.1 A big-step-style specification -- 10.2.2 A specification using evaluation contexts -- 10.3 Manipulating functional programs -- 10.3.1 Partial evaluation of miniFP programs -- 10.3.2 Transformation to continuation passing style -- 10.4 Bibliographic notes -- 11: Encoding a Process Calculus Language -- 11.1 Representing the expressions of the π-calculus -- 11.2 Specifying one-step transitions -- 11.3 Animating π-calculus expressions -- 11.4 May- versus must-judgments -- 11.5 Mapping the λ-calculus into the π-calculus -- 11.6 Bibliographic notes -- Appendix: The Teyjus system -- A.1 An overview of the Teyjus system -- A.2 Interacting with the Teyjus system -- A.3 Using modules within the Teyjus system -- A.4 Special features of the Teyjus system -- A.4.1 Built-in types and predicates -- A.4.2 Deviations from the language assumed in this book -- Bibliography -- Index. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn796804053 |
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| author2 | Nadathur, Gopalan |
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| callnumber-sort | QA 276.63 M554 42012EB |
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| contents | Introduction -- First-order terms and representations of data -- First-order horn clauses -- First-order hereditary Harrop formulas -- Typed [lambda]-terms and formulas -- Using quantification at higher-order types -- Mechanisms for structuring large programs -- Computations over [lambda]-terms -- Unification of [lambda]-terms -- Implementing proof systems -- Computations over functional programs -- Encoding a process calculus language -- Appendix. |
| ctrlnum | (OCoLC)796804053 |
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| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.1/15 |
| dewey-search | 005.1/15 |
| dewey-sort | 15.1 215 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
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ind2="7"><subfield code="a">Prolog (Computer program language)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nadathur, Gopalan.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Miller, Dale (Dale A.).</subfield><subfield code="t">Programming with higher-order logic.</subfield><subfield code="d">Cambridge : Cambridge University Press, 2012</subfield><subfield code="z">9780521879408</subfield><subfield code="w">(DLC) 2012016719</subfield><subfield code="w">(OCoLC)774491609</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=458666</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">Cover -- Programming with Higher-Order Logic -- Title -- Copyright -- Contents -- Preface -- Introduction -- I.1 Connections between logic and computation -- I.2 Logical primitives and programming expressivity -- I.3 The meaning of higher-order logic -- I.4 Presentation style -- I.5 Prerequisites -- I.6 Organization of the book -- 1: First-Order Terms and Representations of Data -- 1.1 Sorts and type constructors -- 1.2 Type expressions -- 1.3 Typed first-order terms -- 1.4 Representing symbolic objects -- 1.5 Unification of typed first-order terms -- 1.6 Bibliographic notes -- 2 First-Order Horn Clauses -- 2.1 First-order formulas -- 2.2 Logic programming and search semantics -- 2.3 Horn clauses and their computational interpretation -- 2.4 Programming with first-order Horn clauses -- 2.4.1 Concrete syntax for program clauses -- 2.4.2 Interacting with the λProlog system -- The read phase -- The prove phase -- The print phase -- Multiple solutions -- 2.4.3 Reachability in a finite-state machine -- 2.4.4 Defining relations over recursively structured data -- 2.4.5 Programming over abstract syntax representations -- 2.5 Pragmatic aspects of computing with Horn clauses -- 2.6 The relationship with logical notions -- 2.6.1 The cut rule and cut-elimination -- 2.6.2 Different presentations of fohc -- 2.7 The meaning and use of types -- 2.7.1 Types and the categorization of expressions -- 2.7.2 Polymorphic typing -- 2.7.3 Type checking and type inference -- 2.7.4 Types and run-time computations -- 2.8 Bibliographic notes -- 3: First-Order Hereditary Harrop Formulas -- 3.1 The syntax of goals and program clauses -- 3.2 Implicational goals -- 3.2.1 Inferences among propositional clauses -- 3.2.2 Hypothetical reasoning -- 3.3 Universally quantified goals -- 3.3.1 Substitution and quantification -- 3.3.2 Quantification can link goals and clauses.</subfield></datafield><datafield tag="880" ind1="8" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">3.4 The relationship with logical notions -- 3.4.1 Classical versus intuitionistic logic -- 3.4.2 Intuitionistic versus minimal logic -- 3.4.3 Notable subsets of fohh -- 3.5 Bibliographic notes -- 4: Typed λ-Terms and Formulas -- 4.1 Syntax for λ-terms and formulas -- 4.2 The rules of λ-conversion -- 4.3 Some properties of λ-conversion -- 4.4 Unification problems as quantified equalities -- 4.4.1 Simplifying quantifier prefixes -- 4.4.2 Unifiers, solutions, and empty types -- 4.4.3 Examples of unification problems and their solutions -- 4.5 Solving unification problems -- 4.6 Some hard unification problems -- 4.6.1 Solving Post correspondence problems -- 4.6.2 Solving Diophantine equations -- 4.7 Bibliographic notes -- 5 Using Quantification at Higher-Order Types -- 5.1 Atomic formulas in higher-order logic programs -- 5.1.1 Flexible atoms as heads of clauses -- 5.1.2 Logical symbols within atomic formulas -- 5.2 Higher-order logic programming languages -- 5.2.1 Higher-order Horn clauses -- 5.2.2 Higher-order hereditary Harrop formulas -- 5.2.3 Extended higher-order hereditary Harrop formulas -- 5.3 Examples of higher-order programming -- 5.4 Flexible atoms as goals -- 5.5 Reasoning about higher-order programs -- 5.6 Defining some of the logical constants -- 5.7 The conditional and negation-as-failure -- 5.8 Using λ-terms as functions -- 5.8.1 Some basic computations with functional expressions -- 5.8.2 Functional difference lists -- 5.9 Higher-order unification is not a panacea -- 5.10 Comparison with functional programming -- 5.11 Bibliographic notes -- 6: Mechanisms for Structuring Large Programs -- 6.1 Desiderata for modular programming -- 6.2 A modules language -- 6.3 Matching signatures and modules -- 6.4 The logical interpretation of modules -- 6.4.1 Existential quantification in program clauses -- 6.4.2 A module as a logical formula.</subfield></datafield><datafield tag="880" ind1="8" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">6.4.3 Interpreting queries against modules -- 6.4.4 Module accumulation as scoped inlining of code -- 6.5 Some programming aspects of the modules language -- 6.5.1 Hiding and abstract datatypes -- 6.5.2 Code extensibility and modular composition -- 6.5.3 Signature accumulation and parametrization of modules -- 6.5.4 Higher-order programming and predicate visibility -- 6.6 Implementation considerations -- 6.7 Bibliographic notes -- 7: Computations over λ-Terms -- 7.1 Representing objects with binding structure -- 7.1.1 Encoding logical formulas with quantifiers -- 7.1.2 Encoding untyped λ-terms -- 7.1.3 Properties of the encoding of binding -- 7.2 Realizing object-level substitution -- 7.3 Mobility of binders -- 7.4 Computing with untyped λ-terms -- 7.4.1 Computing normal forms -- 7.4.2 Reduction based on paths through terms -- 7.4.3 Type inference -- 7.4.4 Translating to and from de Bruijn syntax -- 7.5 Computations over first-order formulas -- 7.6 Specifying object-level substitution -- 7.7 The λ-tree approach to abstract syntax -- 7.8 The Lλ subset of λProlog -- 7.9 Bibliographic notes -- 8: Unification of λ-terms -- 8.1 Properties of the higher-order unification problem -- 8.2 A procedure for checking for unifiability -- 8.2.1 Simplification of rigid-rigid equations -- 8.2.2 Substitutions for equations between flexible and rigid terms -- 8.2.3 The iterative transformation of unification problems -- 8.2.4 Unification problems with only flexible-flexible equations -- 8.2.5 Nontermination of reductions -- 8.2.6 Matching trees -- 8.3 Higher-order pattern unification -- 8.4 Pragmatic aspects of higher-order unification -- 8.5 Bibliographic notes -- 9: Implementing Proof Systems -- 9.1 Deduction in propositional intuitionistic logic -- 9.2 Encoding natural deduction for intuitionistic logic -- 9.3 A theorem prover for classical logic.</subfield></datafield><datafield tag="880" ind1="8" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">9.4 A general architecture for theorem provers -- 9.4.1 Goals and tactics -- 9.4.2 Combining tactics into proof strategies -- 9.5 Bibliographic notes -- 10: Computations over Functional Programs -- 10.1 The miniFP programming language -- 10.2 Specifying evaluation for miniFP programs -- 10.2.1 A big-step-style specification -- 10.2.2 A specification using evaluation contexts -- 10.3 Manipulating functional programs -- 10.3.1 Partial evaluation of miniFP programs -- 10.3.2 Transformation to continuation passing style -- 10.4 Bibliographic notes -- 11: Encoding a Process Calculus Language -- 11.1 Representing the expressions of the π-calculus -- 11.2 Specifying one-step transitions -- 11.3 Animating π-calculus expressions -- 11.4 May- versus must-judgments -- 11.5 Mapping the λ-calculus into the π-calculus -- 11.6 Bibliographic notes -- Appendix: The Teyjus system -- A.1 An overview of the Teyjus system -- A.2 Interacting with the Teyjus system -- A.3 Using modules within the Teyjus system -- A.4 Special features of the Teyjus system -- A.4.1 Built-in types and predicates -- A.4.2 Deviations from the language assumed in this book -- Bibliography -- Index.</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24076458</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH37563167</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH33350540</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">22677167</subfield><subfield code="c">37.50 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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:28Z |
| institution | BVB |
| isbn | 9781139518420 1139518429 9781139516570 1139516574 1280775084 9781280775086 9781139514927 113951492X 9781139021326 113902132X |
| language | English |
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| publishDate | 2012 |
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| spelling | Miller, Dale (Dale A.) Programming with higher-order logic / Dale Miller, Gopalan Nadathur. Cambridge : Cambridge University Press, 2012. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier "Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called [Lambda]Prolog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and [lambda]-terms and [pi]-calculus expressions can be encoded in [Lambda]Prolog"-- Provided by publisher Includes bibliographical references and index. Introduction -- First-order terms and representations of data -- First-order horn clauses -- First-order hereditary Harrop formulas -- Typed [lambda]-terms and formulas -- Using quantification at higher-order types -- Mechanisms for structuring large programs -- Computations over [lambda]-terms -- Unification of [lambda]-terms -- Implementing proof systems -- Computations over functional programs -- Encoding a process calculus language -- Appendix. Print version record. Logic programming. http://id.loc.gov/authorities/subjects/sh86003454 Prolog (Computer program language) http://id.loc.gov/authorities/subjects/sh85107397 Logic programming. Prolog (Computer program language) Programmation logique. Prolog (Langage de programmation) COMPUTERS Programming Languages General. bisacsh COMPUTERS Programming Open Source. bisacsh COMPUTERS Software Development & Engineering General. bisacsh COMPUTERS Software Development & Engineering Tools. bisacsh Logic programming fast Prolog (Computer program language) fast Nadathur, Gopalan. Print version: Miller, Dale (Dale A.). Programming with higher-order logic. Cambridge : Cambridge University Press, 2012 9780521879408 (DLC) 2012016719 (OCoLC)774491609 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=458666 Volltext 505-00/(S Cover -- Programming with Higher-Order Logic -- Title -- Copyright -- Contents -- Preface -- Introduction -- I.1 Connections between logic and computation -- I.2 Logical primitives and programming expressivity -- I.3 The meaning of higher-order logic -- I.4 Presentation style -- I.5 Prerequisites -- I.6 Organization of the book -- 1: First-Order Terms and Representations of Data -- 1.1 Sorts and type constructors -- 1.2 Type expressions -- 1.3 Typed first-order terms -- 1.4 Representing symbolic objects -- 1.5 Unification of typed first-order terms -- 1.6 Bibliographic notes -- 2 First-Order Horn Clauses -- 2.1 First-order formulas -- 2.2 Logic programming and search semantics -- 2.3 Horn clauses and their computational interpretation -- 2.4 Programming with first-order Horn clauses -- 2.4.1 Concrete syntax for program clauses -- 2.4.2 Interacting with the λProlog system -- The read phase -- The prove phase -- The print phase -- Multiple solutions -- 2.4.3 Reachability in a finite-state machine -- 2.4.4 Defining relations over recursively structured data -- 2.4.5 Programming over abstract syntax representations -- 2.5 Pragmatic aspects of computing with Horn clauses -- 2.6 The relationship with logical notions -- 2.6.1 The cut rule and cut-elimination -- 2.6.2 Different presentations of fohc -- 2.7 The meaning and use of types -- 2.7.1 Types and the categorization of expressions -- 2.7.2 Polymorphic typing -- 2.7.3 Type checking and type inference -- 2.7.4 Types and run-time computations -- 2.8 Bibliographic notes -- 3: First-Order Hereditary Harrop Formulas -- 3.1 The syntax of goals and program clauses -- 3.2 Implicational goals -- 3.2.1 Inferences among propositional clauses -- 3.2.2 Hypothetical reasoning -- 3.3 Universally quantified goals -- 3.3.1 Substitution and quantification -- 3.3.2 Quantification can link goals and clauses. 505-00/(S 3.4 The relationship with logical notions -- 3.4.1 Classical versus intuitionistic logic -- 3.4.2 Intuitionistic versus minimal logic -- 3.4.3 Notable subsets of fohh -- 3.5 Bibliographic notes -- 4: Typed λ-Terms and Formulas -- 4.1 Syntax for λ-terms and formulas -- 4.2 The rules of λ-conversion -- 4.3 Some properties of λ-conversion -- 4.4 Unification problems as quantified equalities -- 4.4.1 Simplifying quantifier prefixes -- 4.4.2 Unifiers, solutions, and empty types -- 4.4.3 Examples of unification problems and their solutions -- 4.5 Solving unification problems -- 4.6 Some hard unification problems -- 4.6.1 Solving Post correspondence problems -- 4.6.2 Solving Diophantine equations -- 4.7 Bibliographic notes -- 5 Using Quantification at Higher-Order Types -- 5.1 Atomic formulas in higher-order logic programs -- 5.1.1 Flexible atoms as heads of clauses -- 5.1.2 Logical symbols within atomic formulas -- 5.2 Higher-order logic programming languages -- 5.2.1 Higher-order Horn clauses -- 5.2.2 Higher-order hereditary Harrop formulas -- 5.2.3 Extended higher-order hereditary Harrop formulas -- 5.3 Examples of higher-order programming -- 5.4 Flexible atoms as goals -- 5.5 Reasoning about higher-order programs -- 5.6 Defining some of the logical constants -- 5.7 The conditional and negation-as-failure -- 5.8 Using λ-terms as functions -- 5.8.1 Some basic computations with functional expressions -- 5.8.2 Functional difference lists -- 5.9 Higher-order unification is not a panacea -- 5.10 Comparison with functional programming -- 5.11 Bibliographic notes -- 6: Mechanisms for Structuring Large Programs -- 6.1 Desiderata for modular programming -- 6.2 A modules language -- 6.3 Matching signatures and modules -- 6.4 The logical interpretation of modules -- 6.4.1 Existential quantification in program clauses -- 6.4.2 A module as a logical formula. 505-00/(S 6.4.3 Interpreting queries against modules -- 6.4.4 Module accumulation as scoped inlining of code -- 6.5 Some programming aspects of the modules language -- 6.5.1 Hiding and abstract datatypes -- 6.5.2 Code extensibility and modular composition -- 6.5.3 Signature accumulation and parametrization of modules -- 6.5.4 Higher-order programming and predicate visibility -- 6.6 Implementation considerations -- 6.7 Bibliographic notes -- 7: Computations over λ-Terms -- 7.1 Representing objects with binding structure -- 7.1.1 Encoding logical formulas with quantifiers -- 7.1.2 Encoding untyped λ-terms -- 7.1.3 Properties of the encoding of binding -- 7.2 Realizing object-level substitution -- 7.3 Mobility of binders -- 7.4 Computing with untyped λ-terms -- 7.4.1 Computing normal forms -- 7.4.2 Reduction based on paths through terms -- 7.4.3 Type inference -- 7.4.4 Translating to and from de Bruijn syntax -- 7.5 Computations over first-order formulas -- 7.6 Specifying object-level substitution -- 7.7 The λ-tree approach to abstract syntax -- 7.8 The Lλ subset of λProlog -- 7.9 Bibliographic notes -- 8: Unification of λ-terms -- 8.1 Properties of the higher-order unification problem -- 8.2 A procedure for checking for unifiability -- 8.2.1 Simplification of rigid-rigid equations -- 8.2.2 Substitutions for equations between flexible and rigid terms -- 8.2.3 The iterative transformation of unification problems -- 8.2.4 Unification problems with only flexible-flexible equations -- 8.2.5 Nontermination of reductions -- 8.2.6 Matching trees -- 8.3 Higher-order pattern unification -- 8.4 Pragmatic aspects of higher-order unification -- 8.5 Bibliographic notes -- 9: Implementing Proof Systems -- 9.1 Deduction in propositional intuitionistic logic -- 9.2 Encoding natural deduction for intuitionistic logic -- 9.3 A theorem prover for classical logic. 505-00/(S 9.4 A general architecture for theorem provers -- 9.4.1 Goals and tactics -- 9.4.2 Combining tactics into proof strategies -- 9.5 Bibliographic notes -- 10: Computations over Functional Programs -- 10.1 The miniFP programming language -- 10.2 Specifying evaluation for miniFP programs -- 10.2.1 A big-step-style specification -- 10.2.2 A specification using evaluation contexts -- 10.3 Manipulating functional programs -- 10.3.1 Partial evaluation of miniFP programs -- 10.3.2 Transformation to continuation passing style -- 10.4 Bibliographic notes -- 11: Encoding a Process Calculus Language -- 11.1 Representing the expressions of the π-calculus -- 11.2 Specifying one-step transitions -- 11.3 Animating π-calculus expressions -- 11.4 May- versus must-judgments -- 11.5 Mapping the λ-calculus into the π-calculus -- 11.6 Bibliographic notes -- Appendix: The Teyjus system -- A.1 An overview of the Teyjus system -- A.2 Interacting with the Teyjus system -- A.3 Using modules within the Teyjus system -- A.4 Special features of the Teyjus system -- A.4.1 Built-in types and predicates -- A.4.2 Deviations from the language assumed in this book -- Bibliography -- Index. |
| spellingShingle | Miller, Dale (Dale A.) Programming with higher-order logic / Introduction -- First-order terms and representations of data -- First-order horn clauses -- First-order hereditary Harrop formulas -- Typed [lambda]-terms and formulas -- Using quantification at higher-order types -- Mechanisms for structuring large programs -- Computations over [lambda]-terms -- Unification of [lambda]-terms -- Implementing proof systems -- Computations over functional programs -- Encoding a process calculus language -- Appendix. Logic programming. http://id.loc.gov/authorities/subjects/sh86003454 Prolog (Computer program language) http://id.loc.gov/authorities/subjects/sh85107397 Logic programming. Prolog (Computer program language) Programmation logique. Prolog (Langage de programmation) COMPUTERS Programming Languages General. bisacsh COMPUTERS Programming Open Source. bisacsh COMPUTERS Software Development & Engineering General. bisacsh COMPUTERS Software Development & Engineering Tools. bisacsh Logic programming fast Prolog (Computer program language) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh86003454 http://id.loc.gov/authorities/subjects/sh85107397 |
| title | Programming with higher-order logic / |
| title_auth | Programming with higher-order logic / |
| title_exact_search | Programming with higher-order logic / |
| title_full | Programming with higher-order logic / Dale Miller, Gopalan Nadathur. |
| title_fullStr | Programming with higher-order logic / Dale Miller, Gopalan Nadathur. |
| title_full_unstemmed | Programming with higher-order logic / Dale Miller, Gopalan Nadathur. |
| title_short | Programming with higher-order logic / |
| title_sort | programming with higher order logic |
| topic | Logic programming. http://id.loc.gov/authorities/subjects/sh86003454 Prolog (Computer program language) http://id.loc.gov/authorities/subjects/sh85107397 Logic programming. Prolog (Computer program language) Programmation logique. Prolog (Langage de programmation) COMPUTERS Programming Languages General. bisacsh COMPUTERS Programming Open Source. bisacsh COMPUTERS Software Development & Engineering General. bisacsh COMPUTERS Software Development & Engineering Tools. bisacsh Logic programming fast Prolog (Computer program language) fast |
| topic_facet | Logic programming. Prolog (Computer program language) Programmation logique. Prolog (Langage de programmation) COMPUTERS Programming Languages General. COMPUTERS Programming Open Source. COMPUTERS Software Development & Engineering General. COMPUTERS Software Development & Engineering Tools. Logic programming |
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| work_keys_str_mv | AT millerdale programmingwithhigherorderlogic AT nadathurgopalan programmingwithhigherorderlogic |