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1. An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics) by Greg Michaelson
Product Description Functional programming is rooted in lambda calculus, which constitutes the world's smallest programming language. This wellrespected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, and it assumes no prior knowledge of mathematics or functional programming. Cogent examples illuminate the central ideas, and numerous exercises appear throughout the text, offering reinforcement of key concepts. All problems feature complete solutions.
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2. LambdaCalculus and Combinators: An Introduction by J. Roger Hindley, Jonathan P. Seldin
Product Description Combinatory logic and lambdacalculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambdacalculus for over 20 years: this longawaited new version is thoroughly revised and offers a fully uptodate account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambdacalculus are discussed, followed by an introduction to typetheory. Typed and untyped versions of the systems, and their differences, are covered. Lambdacalculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as nontechnical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
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3. The Lambda Calculus. Its Syntax and Semantics (Studies in Logic) by Henk Barendregt
Product Description 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 settheoretic. 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.
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Similar Items: 1. An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics) 2. Purely Functional Data Structures 3. Lambda Calculus with Types (Perspectives in Logic) 4. Types and Programming Languages (MIT Press) 5. Type Theory and Formal Proof: An Introduction 6. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 7. Basic Category Theory for Computer Scientists (Foundations of Computing) 8. Learn You a Haskell for Great Good!: A Beginner's Guide 9. LambdaCalculus and Combinators: An Introduction 10. Introduction to Combinators and (lambda) Calculus (London Mathematical Society Student Texts) . 
4. Lambda Calculus with Types (Perspectives in Logic) by Henk Barendregt, Wil Dekkers, Richard Statman
Product Description 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.
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5. The Lambda Calculus, Its Syntax and Semantics (Studies in Logic and the Foundations of Mathematics, Volume 103). Revised Edition by H.P. Barendregt
Product Description 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.
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6. A Simple LambdaCalculus Model of Programming Languages (Classic Reprint) by S. Kamal Abdali
Product Description Excerpt from A Simple LambdaCalculus Model of Programming Languages
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7. From Mathematics to Generic Programming by Alexander A. Stepanov, Daniel E. Rose
Product Description In this substantive yet accessible book, pioneering software designer Alexander Stepanov and his colleague Daniel Rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based, helping you write code that is both simpler and more powerful.
If you’re a reasonably proficient programmer who can think logically, you have all the background you’ll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a realworld publickey cryptosystem.
As you read this book, you’ll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You’ll also gain deep insight into the value of mathematics to programming—insight that will prove invaluable no matter what programming languages and paradigms you use.
You will learn about
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8. Abstract Computing Machines by Werner Kluge
Product Description The book emphasizes the design of fullfledged, fully normalizing lambda calculus machinery, as opposed to the just weakly normalizing machines.
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9. Structure and Interpretation of Computer Programs  2nd Edition (MIT Electrical Engineering and Computer Science) by Harold Abelson, Gerald Jay Sussman
Product Description Structure and Interpretation of Computer Programs has had a dramatic impact on computer science curricula over the past decade. This longawaited revision contains changes throughout the text. There are new implementations of most of the major programming systems in the book, including the interpreters and compilers, and the authors have incorporated many small changes that reflect their experience teaching the course at MIT since the first edition was published. A new theme has been introduced that emphasizes the central role played by different approaches to dealing with time in computational models: objects with state, concurrent programming, functional programming and lazy evaluation, and nondeterministic programming. There are new example sections on higherorder procedures in graphics and on applications of stream processing in numerical programming, and many new exercises. In addition, all the programs have been reworked to run in any Scheme implementation that adheres to the IEEE standard. Amazon.com Review Abelson and Sussman's classic Structure and Interpretation of Computer Programs teaches readers how to program by employing the tools of abstraction and modularity. The authors' central philosophy is that programming is the task of breaking large problems into small ones. The book spends a great deal of time considering both this decomposition and the process of knitting the smaller pieces back together. The authors employ this philosophy in their writing technique. The text asks the broad question "What is programming?" Having come to the conclusion that programming consists of procedures and data, the authors set off to explore the related questions of "What is data?" and "What is a procedure?" The authors build up the simple notion of a procedure to dizzying complexity. The discussion culminates in the description of the code behind the programming language Scheme. The authors finish with examples of how to implement some of the book's concepts on a register machine. Through this journey, the reader not only learns how to program, but also how to think about programming.
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Similar Items: 1. The Little Schemer  4th Edition 2. Instructor's Manual t/a Structure and Interpretation of Computer Programs  2nd Edition 3. The Pragmatic Programmer: From Journeyman to Master 4. The Seasoned Schemer (MIT Press) 5. An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics) 6. Programming Pearls: (2nd Edition) 7. Purely Functional Data Structures 8. Code: The Hidden Language of Computer Hardware and Software 9. Code Complete: A Practical Handbook of Software Construction, Second Edition 10. Design Patterns: Elements of Reusable ObjectOriented Software . 
10. The Parametric Lambda Calculus: A Metamodel for Computation (Texts in Theoretical Computer Science. An EATCS Series) by Simona Ronchi Della Rocca, Luca Paolini
Product Description The book contains a completely new presentation of classical results in the field of Lambda Calculus, together with new results. The text is unique in that it presents a new calculus (Parametric Lambda Calculus) which can be instantiated to obtain already known lambdacalculi. Some properties, which in the literature have been proved separately for different calculi, can be proved once for the Parametric one. The lambda calculi are presented from a Computer Science point of view, with a particular emphasis on their semantics, both operational and denotational.
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