The Lambda Calculus

Author: H.P. Barendregt
Publisher: Elsevier
ISBN: 9780080933757
Format: PDF, ePub
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The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.

Lambda Calculus with Types

Author: Henk Barendregt
Publisher: Cambridge University Press
ISBN: 1107276349
Format: PDF, ePub, Docs
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This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

The Lambda Calculus

Author: Henk Barendregt
Publisher:
ISBN: 9781848900660
Format: PDF, Kindle
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The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic. The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is a function, M its argument, and FM the result of the application. This is only the intention: to actually obtain the result one has to rewrite the expression FM according to the reduction rules. Abstraction provides a way to create functions according to the effect when applying them. The power of the theory comes from the fact that computations, both terminating and infinite, can be expressed by lambda terms at a 'comfortable' level of abstraction.

Introduction to Combinators and lambda Calculus

Author: J. R. Hindley
Publisher: CUP Archive
ISBN: 9780521268967
Format: PDF, Docs
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Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.

Introduction to Mathematical Logic

Author: Alonzo Church
Publisher: Princeton University Press
ISBN: 9780691029061
Format: PDF, Mobi
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Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

Algebraic Foundations of Systems Specification

Author: Egidio Astesiano
Publisher: Springer Science & Business Media
ISBN: 364259851X
Format: PDF, Kindle
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This IFIP report is a collection of fundamental, high-quality contributions on the algebraic foundations of system specification. The contributions cover and survey active topics and recent advances, and address such subjects as: the role of formal specification, algebraic preliminaries, partiality, institutions, specification semantics, structuring, refinement, specification languages, term rewriting, deduction and proof systems, object specification, concurrency, and the development process. The authors are well-known experts in the field, and the book is the result of IFIP WG 1.3 in cooperation with Esprit Basic Research WG COMPASS, and provides the foundations of the algebraic specification language CASL designed in the CoFI project. For students, researchers, and system developers.

Pillars of Computer Science

Author: Arnon Avron
Publisher: Springer Science & Business Media
ISBN: 3540781269
Format: PDF, ePub, Docs
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The Person 1 Boris Abramovich Trakhtenbrot (????? ????????? ???????????) – his Hebrew given name is Boaz ( ) – is universally admired as a founding - ther and long-standing pillar of the discipline of computer science. He is the ?eld's preeminent distinguished researcher and a most illustrious trailblazer and disseminator. He is unmatched in combining farsighted vision, unfaltering c- mitment, masterful command of the ?eld, technical virtuosity, æsthetic expr- sion, eloquent clarity, and creative vigor with humility and devotion to students and colleagues. For over half a century, Trakhtenbrot has been making seminal contributions to virtually all of the central aspects of theoretical computer science, inaugur- ing numerous new areas of investigation. He has displayed an almost prophetic ability to foresee directions that are destined to take center stage, a decade or morebeforeanyoneelsetakesnotice.Hehasneverbeentempted toslowdownor limithisresearchtoareasofendeavorinwhichhehasalreadyearnedrecognition and honor. Rather, he continues to probe the limits and position himself at the vanguard of a rapidly developing ?eld, while remaining, as always, unassuming and open-minded.

Combinatory Logic

Author: Katalin Bimbó
Publisher: CRC Press
ISBN: 1439800006
Format: PDF, ePub, Docs
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Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the author presents the most up-to-date research studies. She includes an introduction to combinatory logic before progressing to its central theorems and proofs. The text makes intelligent and well-researched connections between combinatory logic and lambda calculi and presents models and applications to illustrate these connections.

Concise Encyclopedia of Semantics

Author: Keith Allan
Publisher: Elsevier
ISBN: 9780080959696
Format: PDF
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Concise Encyclopedia of Semantics is a comprehensive new reference work aiming to systematically describe all aspects of the study of meaning in language. It synthesizes in one volume the latest scholarly positions on the construction, interpretation, clarification, obscurity, illustration, amplification, simplification, negotiation, contradiction, contraction and paraphrasing of meaning, and the various concepts, analyses, methodologies and technologies that underpin their study. It examines not only semantics but the impact of semantic study on related fields such as morphology, syntax, and typologically oriented studies such as ‘grammatical semantics’, where semantics has made a considerable contribution to our understanding of verbal categories like tense or aspect, nominal categories like case or possession, clausal categories like causatives, comparatives, or conditionals, and discourse phenomena like reference and anaphora. COSE also examines lexical semantics and its relation to syntax, pragmatics, and cognitive linguistics; and the study of how ‘logical semantics’ develops and thrives, often in interaction with computational linguistics. As a derivative volume from Encyclopedia of Language and Linguistics, Second Edition, it comprises contributions from 150 of the foremost scholars of semantics in their various specializations and draws on 20+ years of development in the parent work in a compact and affordable format. Principally intended for tertiary level inquiry and research, this will be invaluable as a reference work for undergraduate and postgraduate students as well as academics inquiring into the study of meaning and meaning relations within languages. As semantics is a centrally important and inherently cross-cutting area within linguistics it will therefore be relevant not just for semantics specialists, but for most linguistic audiences. The first encyclopedia ever published in this fascinating and diverse field Combines the talents of the world’s leading semantics specialists The latest trends in the field authoritatively reviewed and interpreted in context of related disciplines Drawn from the richest, most authoritative, comprehensive and internationally acclaimed reference resource in the linguistics area Compact and affordable single volume reference format

Categorical Logic and Type Theory

Author: Bart Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Format: PDF, Kindle
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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.