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Programming With Higher-Order Logic

Dale Miller, Gopalan Nadathur
Cambridge ; New York : Cambridge University Press, 2012.
9780521879408 (hbk.), 052187940X (hbk.)
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"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.
  • 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: The Teyjus system.
xiii, 306 p. : ill. ; 24 cm.
Includes bibliographical references (p. 289-299) and index.
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