This book gives a tutorial overview of Gödel, presents example programs, provides a formal definition of the syntax and semantics of the language, and covers background material on logic. Gödel is a new, general-purpose, declarative programming language that is based on the paradigm of logic programming and can be regarded as a successor to Prolog. This book gives a tutorial overview of Gödel, presents example programs, provides a formal definition of the syntax and semantics of the language, and covers background material on logic. The Gödel language supports types and modules. It has a rich collection of system modules and provides constraint solving in several domains. It also offers metalogical facilities that provide significant support for metaprograms that do analysis, transformation, compilation, verification, debugging, and the like. The declarative nature of Gödel makes it well suited for use as a teaching language, narrows the gap that currently exists between theory and practice in logic programming, makes possible advanced software engineering tools such as declarative debuggers and compiler generators, reduces the effort involved in providing a parallel implementation of the language, and offers substantial scope for parallelization in such implementations. Logic Programming series

Gödel is a new, general-purpose, declarative programming language that is based on the paradigm of logic programming and can be regarded as a successor to Prolog. This book gives a tutorial overview of Gödel, presents example programs, provides a formal definition of the syntax and semantics of the language, and covers background material on logic.The Gödel language supports types and modules. It has a rich collection of system modules and provides constraint solving in several domains. It also offers metalogical facilities that provide significant support for metaprograms that do analysis, transformation, compilation, verification, debugging, and the like. The declarative nature of Gödel makes it well suited for use as a teaching language, narrows the gap that currently exists between theory and practice in logic programming, makes possible advanced software engineering tools such as declarative debuggers and compiler generators, reduces the effort involved in providing a parallel implementation of the language, and offers substantial scope for parallelization in such implementations.Logic Programming series

The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.

Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.

'What is a self and how can a self come out of inanimate matter?' This is the riddle that drove Douglas Hofstadter to write this extraordinary book. In order to impart his original and personal view on the core mystery of human existence - our intangible sensation of 'I'-ness - Hofstadter defines the playful yet seemingly paradoxical notion of 'strange loop', and explicates this idea using analogies from many disciplines.

Programming Language Pragmatics, Fourth Edition, is the most comprehensive programming language textbook available today. It is distinguished and acclaimed for its integrated treatment of language design and implementation, with an emphasis on the fundamental tradeoffs that continue to drive software development.The book provides readers with a solid foundation in the syntax, semantics, and pragmatics of the full range of programming languages, from traditional languages like C to the latest in functional, scripting, and object-oriented programming. This fourth edition has been heavily revised throughout, with expanded coverage of type systems and functional programming, a unified treatment of polymorphism, highlights of the newest language standards, and examples featuring the ARM and x86 64-bit architectures. - Updated coverage of the latest developments in programming language design, including C & C++11, Java 8, C# 5, Scala, Go, Swift, Python 3, and HTML 5 - Updated treatment of functional programming, with extensive coverage of OCaml - New chapters devoted to type systems and composite types - Unified and updated treatment of polymorphism in all its forms - New examples featuring the ARM and x86 64-bit architectures

Describes the use of computer programs to check several proofs in the foundations of mathematics.