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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. Types and Programming Languages (MIT Press) 4. Lambda Calculus with Types (Perspectives in Logic) 5. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics) 6. LambdaCalculus and Combinators: An Introduction 7. Conceptual Mathematics: A First Introduction to Categories 8. Type Theory and Formal Proof: An Introduction 9. Category Theory for the Sciences (MIT Press) 10. Basic Category Theory for Computer Scientists (Foundations of Computing) . 
4. 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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5. 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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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. 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. Code Complete: A Practical Handbook of Software Construction, Second Edition 5. The Seasoned Schemer (MIT Press) 6. An Introduction to Functional Programming Through Lambda Calculus (Dover Books on Mathematics) 7. Design Patterns: Elements of Reusable ObjectOriented Software 8. Purely Functional Data Structures 9. C Programming Language, 2nd Edition 10. Code: The Hidden Language of Computer Hardware and Software . 
9. Lambdacalculus, Combinators and Functional Programming (Cambridge Tracts in Theoretical Computer Science) by G. E. Revesz
Product Description Originally published in 1988, this book presents an introduction to lambdacalculus and combinators without getting lost in the details of mathematical aspects of their theory. Lambdacalculus is treated here as a functional language and its relevance to computer science is clearly demonstrated. The main purpose of the book is to provide computer science students and researchers with a firm background in lambdacalculus and combinators and show the applicabillity of these theories to functional programming. The presentation of the material is selfcontained. It can be used as a primary text for a course on functional programming. It can also be used as a supplementary text for courses on the structure and implementation of programming languages, theory of computing, or semantics of programming languages.
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10. An Introduction to Lambda Calculi for Computer Scientists (Texts in Computing) by C. Hankin
Product Description The lambdacalculus lies at the very foundations of computer science. Besides its historical role in computability theory it has had significant influence on programming language design and implementation, denotational semantics, and domain theory. The book emphasises the proof theory for the typefree lambdacalculus. The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the lambdacalculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed lambdacalculus, then Milnerstyle polymorphism and, finally, the polymorphic lambdacalculus. Chapter 8 concerns two variants of the typefree lambdacalculus that have appeared in the research literature: the lazy lambdacalculus, and the lambda sigmacalculus. The final chapter contains references and a guide to further reading. There are exercises throughout. In contrast to earlier books on these topics, which were written by logicians, this book is written from a computer science perspective and emphasises the practical relevance of many of the key theoretical ideas. The book is intended as a course text for final year undergraduates or first year graduate students in computer science. Research students should find it a useful introduction to more specialist literature.
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Similar Items: 1. The Lambda Calculus. Its Syntax and Semantics (Studies in Logic) 2. Purely Functional Data Structures 3. Types and Programming Languages (MIT Press) 4. LambdaCalculus and Combinators: An Introduction 5. Exercises for Programmers: 57 Challenges to Develop Your Coding Skills . 
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