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1. ComSci 319, U. Chicago
The lambda calculus is a formal system for studying the definitions of functions, lambda Calculi a Guide for computer scientists by Chris Hankin,
Com Sci 319
Lambda Calculus
Winter 2000
A course in the Department of Computer Science
The University of Chicago
Online discussion using HyperNews
  • [8 Feb] Assignment #4 is due on Monday, 14 February, at the beginning of class. (O'D)
    [17 Jan] The HyperNews discussion is set up. Please read the instructions, and jump in. The system reports an error whenever you post, but the only error is the error report itself. I'm trying to get that fixed. In the meantime, please don't post the same message repeatedly in response to the erroneous error message. (O'D)
    [29 Dec 1999] The Web materials for ComSci 319 are under construction. Some links are broken. (O'D)
  • Venue: MW 9:00-10:20, Ryerson 257
    Instructor: Michael J. O'Donnell
    • Office: Ryerson 257A. email: Office hours: by appointment. Contact me by email, phone at the office (312-702-1269), or phone at home (847-835-1837 between 9:30 and 5:30 on days that I work at home). You may drop in to the office any time, but you may find me out or busy if you haven't confirmed an appointment. Check my personal schedule before proposing an appointment.

2. Bookpool: Comprehensive Mathematics For Computer Scientists 2: Calculus And ODEs
Comprehensive Mathematics for computer scientists 2 calculus and ODEs, Splines, Fractals and Neural Networks, Categories and lambda calculus
Comprehensive Mathematics for Computer Scientists 2: Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals and Neural Networks, Categories and Lambda Calculus Mazzola Guerino Weissmann Jody Milmeister Gerard
Springer, Paperback, Published December 2004, ISBN 3540208615 List Price: $39.95
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3. Category Theory For Computing Science
which have been a major source of interest to computer scientists because they are equivalent in theoretical power to typed lambda calculus.
Category Theory for Computing Science
by Michael Barr and Charles Wells Category Theory for Computing Science is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. You may read the excerpts from the Preface to find out more about it. The third edition is now available from Centre de recherches mathématiques , or by email to . This edition contains all the material dropped from the second edition (with corrections) and the answers to all the exercises.
About earlier editions
Some of the chapters in the first edition were dropped from the second edition in order to make room for new material. Revised and corrected versions of the omitted chapters may now be found in an electronic supplement to the text. We also provide corrections and additions to the first edition and corrections to the second edition
This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions we feel are basic to category theory in the context of examples and applications to computing science.

4. Distribution Theory In Computer Science
technocrats, logicians, computer scientists, applied analystc etc. it provide as independent theory of lambda calculus (computer science) carries
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Back DISTRIBUTION THEORY IN COMPUTER SCIENCE Editor O.P. MIsra Publication Pages Binding Hardback ISBN Price US$ 95.00 Key Features Interested in applications, particularly, physicists, technocrats, logicians, computer scientists, applied analystc etc. Readership The confluence of two different disciplines, 'Theory des distributions' and the Lambda Calculus.' Introduce the basic techniques and result in both the field.
An account of classification of distributions as Schwartz distributions and the rest as the Classical distributions (generalized functions).
Description CONTENTS
  • Introduction * Notations and Terminology * Vector Spaces*Sequences* Convergence and uniform convergence* Cauchy sequence* Accumulation point* Accumulation point* Baire space* Sem-continuous* Supremum bound* Infremum bound* some Results of Integration* Locally summable function* Notations of ^-Calculus
  • Introduction* The Base Spaces* Support* Bounded support (or Compact support)* The Space ID* The Space Id?* The Space $ (Functions of Rapid Descant)* The Space e* The Space ID (IRn)* The Space ID? (Ir?)*

5. Aesthetics Of Computer Scientists Or Mathematicians?
It appears to be in the engineer/computer scientist family of languages. It has many more primitive elements and constructs than say lambda calculus or the
Should the design of the ideal programming system for children be driven primarily by the aesthetics of computer scientists or mathematicians? The design of LOGO was largely based upon Lisp. The design of Lisp was largely based upon lambda calculus, a branch of mathematics. This makes Lisp (and probably to a lesser extent LOGO) a language that is not only a good tool for expressing programs but an object to think about and with. One consequence of this is that Lisp is well-suited for meta-programming. Programs can construct other programs. Programs can reflect upon themselves. This is a consequence of the small clean kernel underlying Lisp that is based upon lambda calculus. Alan Kay in a talk at Stanford in 2003 described Lisp as "a mathematical object that can see itself". The kernels of some programming languages such as Lisp, Prolog, concurrent constraint programming languages, and functional programming languages have a mathematical beauty. A very small basis set can generate incredible richness. In contrast, languages like Smalltalk, Oz, Python, and Java were designed by computer scientists. The beauty and elegance of these languages seems more akin to that of engineering than mathematics. A question to explore further is how to compare languages such as Lisp that are based upon lambda calculus and those which are based upon a calculus of processes such as pi calculus . Perhaps processes are more valuable and fundamental than functions. If so languages should focus upon

6. Functional Programming
It consists of a written exam (75%) mainly on lambda calculus and and interesting language (at least for computer scientists) but some people object to
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Simon Willison’s Weblog
Functional programming
Functional Programming
These notes cover the first two lectures of Dr Bradford’s Function Programming course. This course is about the gapp between computer science theory and practise. It consists of a written exam (75%) mainly on Lambda calculus and coursework (35%) written in Lisp. The three themes of the course are:
  • Practise—programming in Lisp Theory—a formal theory of computation Link—how theory and practise influence each other
There are several styles of programming:
deals with manipulating bytes (e.g Assembler)
based around control structures and functions (C-Like, e.g Pascal and Algol)
helps represent ideas, for when programs get too big for procedural languages to stay effective (Java, C++, etc)
Lisp-like languages, the topic of this course
In functional programming, one of the key concepts is that variables are kept as local as possible. This means that functional code should be easy to quickly understand as sections of the code are self contained.
  • Barendregt “The Lambda Calculus” —a comprehensive guide to Lambda calculus, very hard going

7. Category Theory For Computer Science
Cartesian closed categories and the simplytyped lambda calculus. motivation for studying category theory as computer scientists Goguen, Sect.
Category Theory for Computer Science
Autumn 2002 - Department of Computer Science University of Aarhus News Lectures ... People
  • The course has terminated. Merry Christmas!
Mondays, 12-14 in the r3 meeting room.
December 9th
  • A coalgebraic treatment of automata. Presented by Saurabh Agarwal.
December 2nd
  • Infinite data structures, coalgebra, and coinduction. Presented by Michael Westergaard ( slides
November 25th
  • Finite data structures, algebra, and induction. Presented by Henning Korsholm Rohde ( slides
November 18th
  • Transition systems generalised into presheaves. Presented by Marco Carbone.
November 11th
  • Exercises related to last week's lecture.
  • Designing subtyping disciplines in programming languages. Presented by Branimir Lambov.
November 4th
  • Exercise related to last week's lecture.
  • Effects in functional programming handled by monads. Presented by Karl Kristian Krukow ( slides
October 28th
  • Modelling recursive types. Presented by Mads Sig Ager (

8. Seminar, 1 February, Computer Science And Software Engineering, Melbourne Univer
The language, called lambda calculus, is in exact correspondence with a Philip Wadler is one of the worlds most influential computer scientists and
Department of Computer Science and Software Engineering
The University of Melbourne
12 noon, Wednesday 1 February, 2006
Theatre 3 (Room 2.05) ICT Building
111 Barry Street, Carlton
Professor Philip Wadler
Computer Science
As Natural as 0,1,2
Whether a visitor comes from another place, another planet, or another plane of being we can be sure that he, she, or it will count just as we do: though their symbols vary, the numbers are universal. The history of logic and computing suggests a programming language that is equally natural. The language, called lambda calculus, is in exact correspondence with a formulation of the laws of reason, called natural deduction. Lambda calculus and natural deduction were devised, independently of each other, around 1930, just before the development of the first stored program computer. Yet the correspondence between them was not recognized until decades later, and not published until 1980. Today, languages based on lambda calculus have a few thousand users. Tomorrow, reliable use of the Internet may depend on languages with logical foundations.
Philip Wadler is one of the worlds most influential computer scientists and renowned as one of its most interesting presenters. He has reputedly given a seminar where all the slides were printed on T shirts he was wearing which he removed one by one to uncover the seminar. Be sure to attend what is sure to be a most fascinating talk.

9. My Literature Recommendations
The lambda calculus Its Syntax and Semantics . NorthHolland, 1984. Basic Category Theory for computer scientists . The MIT Press, 1991. R. Goldblatt.
My Literature Recommendations
The following is my opinion of the best published books and papers in various areas of computing. The literature recommendations are organized by the ACM Computing Reviews Classification System (see a January issue of Computing Reviews for details).
Table of Contents
Although there are place-holders here for all of the top-level areas in the ACM Computing Reviews Classification System, the focus in is the areas D.1 D.3 , and F.3 . If you're new to programming languages, you might start in area D.3 , perhaps in D.3.3
  • A. General Literature
  • B. Hardware
  • C. Computer Systems Organization ...
    A. General Literature
    See Gary T. Leavens, ``Aiding Self-motivation with Readings in Introductory Computing,'' Department of Computer Science, Iowa State University, TR #94-08 , May 1994.
    B. Hardware
    C. Computer Systems Organization
    D. Software
    D.0 General
    D.1 Programming Techniques
    D.1.0 General
    D.1.1 Applicative (Functional) Programming
    Backus's Turing award lecture sparked much of the research in functional programming.
    • John Backus, Can Programming Be Liberated from the von Neumann Style? A Functional Style and Its Algebra of Programs.

10. Lambda Calculus - Wikipedia, The Free Encyclopedia
In mathematical logic and computer science, lambda calculus, also calculus, is a formal system designed to investigate function definition,
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Lambda calculus
From Wikipedia, the free encyclopedia
Jump to: navigation search This article needs additional citations for verification
Please help improve this article by adding reliable references . Unsourced material may be challenged and removed. (October 2007) This article or section includes a list of references or external links , but its sources remain unclear because it lacks in-text citations
You can improve this article by introducing more precise citations. It has been suggested that Church encoding be merged into this article or section. ( Discuss In mathematical logic and computer science lambda calculus , also λ-calculus , is a formal system designed to investigate function definition, function application and recursion . It was introduced by Alonzo Church and Stephen Cole Kleene in the as part of a larger effort to base the foundation of mathematics upon functions rather than sets (in the hopes of avoiding obstacles like Russell's Paradox ). The

11. Lambda-Calculus And Computer Science Theory 1975
Corrado Böhm (Ed.) lambdacalculus and computer Science Theory, Proceedings of the Symposium Held in Rome, March 25-27, 1975.
Lambda-Calculus and Computer Science Theory 1975: Rome, Italy
(Ed.): Lambda-Calculus and Computer Science Theory, Proceedings of the Symposium Held in Rome, March 25-27, 1975. Lecture Notes in Computer Science 37 Springer 1975, ISBN 3-540-07416-3 BibTeX DBLP

12. Harry Mairson
Database query languages embedded in the typed lambda calculus (with G. A simple proof of a theorem of Statman Theoretical computer Science 103 (1992),
Harry Mairson
Ph.D., Computer Science, Stanford University, 1984
mairson at cs dot brandeis dot edu
257 Volen / (781) 736-2724
Research Interests
Optimal evaluation
Game semantics and proof structures
Expressibility and typed lambda calculus ...
Slides from my invited talk at ICFP 2003, From Hilbert space to Dilbert space: context semantics made simple. (Comments welcome. Sorry this is a big file.)
Research Interests
My research examines the interaction between mathematical logic and computation theory, with application to the design and analysis of functional programming languages, type systems, and database query languages. A primary current research interest is optimal evaluation in lambda calculus and its computational complexity. I also do fundamental research in algorithmics and algorithm analysis. Optimal evaluation: An evaluator for lambda calculus (or more broadly speaking, a functional programming language) is said to be correct and optimal if it returns a normal form whenever there is one (i.e., it never diverges by choosing to evaluate the wrong redex), and never does inessential work (i.e., copying redexes). Recently, several researchers, including Lamping, Gonthier, Abadi, Levy, and Asperti, have constructed optimal evaluators. But are they efficient? I have examined the computational complexity of this problem via the algorithmic analysis of these proposed evaluators. In addition, this work has addressed what reasonable

13. Lambda Calculus
lambda calculus is a theory of functions that is central to (theoretical) computer science. It is well known that all recursive functions are representable
Lambda Calculus
C.-H. L. Ong Sixteen-hour lecture course. Final-year computer science undergraduate / MSc
Nature and aim of the course
Lambda calculus is a theory of functions that is central to (theoretical) computer science. It is well known that all recursive functions are representable as lambda terms: the representation is so compelling that definability in the calculus may as well be regarded as a definition of computability. This forms part of the standard foundations of computer science and mathematics. Less familiar are two separate developments one in programming, the other in proof theory in which lambda calculus has played a key role:
  • Lambda calculus is the commonly accepted basis of functional programming languages; and it is folklore that the calculus is the prototypical functional language in purified form.
  • The idea that there is a close relation between proof theory and a theory of functions is an old one. It underlies the Kolmogorov-Brouwer-Heyting interpretation of intuitionistic logic, and the Curry-Howard isomorphism between natural deduction and typed lambda calculus.
We develop the syntax and semantics of lambda calculus along these two themes. The aim of this course is to provide the foundation for an important aspect of the semantics of programming languages with a view to helping enthusiastic research students appreciate (perhaps even begin to address) some of the open problems in the field. The second theme in particular will be followed up by two new courses

14. MainFrame: The Lambda-calculus, Combinatory Logic, And Type Systems
The lambda calculus. A pure calculus of functional abstraction and function application, with applications throughout logic and computer science.
The Lambda-calculus, Combinatory Logic, and Type Systems
Three interrelated topics at the heart of logic and computer science. The -Calculus A pure calculus of functional abstraction and function application, with applications throughout logic and computer science. Types The -calculus is good tool for exploring type systems, invaluable both in the foundations of mathematics and for practical programming languages. Pure Type Systems A further generalisation and systematic presentation of the class of type systems found in the -cube. Combinators Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. Programming Languages The connections between the lambda-calculus and programming languages are diverse and pervasive. Type systems are an important aspect of programming language design. The -cube A graphical presentation of the relationship between combinatory logic, lambda calculi and related logical systems. The -cube A graphical presentation of the relationship between various typed -calculi, illuminating the structure of Coquand's Calculus of Constructions.

15. JSTOR The Impact Of The Lambda Calculus In Logic And Computer Science
We restrict attention to applications of the lambda calculus to the fields of mathematical logic and computer science. Other applications like several forms<181:TIOTLC>2.0.CO;2-A

16. Foundations Of Computer Science
Marek Zaionc, How To Define Functionals on Free Structures in Typed lambda calculus , Lecture Notes in computer Science 379 Springer Verlag, August 1989,
Theoretical Computer Science
Faculty of Mathematics and Computer Science

Jagiellonian University

Foundations of Computer Science guest
TCS - home algorithmics cs foundations news ... links events: computer science on trail (pl) UZI - January 12, 2008(pl) CLA 2007 past events seminars: Computer Science Foundations faculty: Jakub Kozik Stanisław Sędziwy Edward Szczypka Paweł Waszkiewicz Marek Zaionc secretary: Monika Gillert phd students: Katarzyna Grygiel Jarosław Karpiak Mikołaj Pudo graduates: phd thesis msc thesis login: password:
Marek Zaionc
phone: fax: email: office: ul. Gronostajowa 3, 30-387 Krak³w room: office hours: Monday 10:00 - 12:00 Dean office, Collegium Novum Wednesday 12:00 - 14:00 room 113 Gronostajowa 3 personal homepage research interests computability theory, computational logic, typed lambda calculus logic programming, logics of programs, functional programming. selected publications
  • Lidia Badura, Marek Zaionc, "Parametrizability by regular expressions for equations on words", Bulletin of the Section of Logic, Vol. 36:1/2 (2007) pp 79 - 93.
  • Zofia Kostrzycka, Marek Zaionc "Asymptotic densities in logic and type theory", accepted at SL.
  • 17. Proceedings Of The Symposium On Lambda-Calculus And Computer Science Theory
    Proceedings of the Symposium on lambdacalculus and computer Science Theory table of contents. Year of Publication 1975. ISBN3-540-07416-3

    18. Manzonetto Giulio - Ph.D Student In Computer Science - Home Page
    Boolean algebras for lambda calculus. G. Manzonetto and A. Salibra. 21st Annual IEEE Symposium on Logic in computer Science (LICS 06), pages 139148,
    Manzonetto Giulio
    x .gmanzone x
    Dottore Magistrale
    Ph.D. student in Computer Science
    Room 5A09, tel. (+33)(0)1 44 27 69 30 Fo lo manto al caco macaco
    e'l truffo sgarruffo a lo spino del baco
    (Marius, poeta efficace)
    • 01 nov: Alea iacta est: today, I've sent my Ph.D. thesis to the referees. 16 oct: The only four people with who I wouln't like to exchange myself are my referees. 08 oct: The first days of november I must send my Ph.D. Thesis to the referees. I've never been stressed as in this period. 10 sep: I'm in Lausanne to attend the conference CSL 2007. I will held a talk on ''lambda theories of effective lambda models'' the 12th september, and another one titled ''not enough points is enough'' the 13th september. 1 sep: Happy New (psycological) Year! The summer is passed quickly, and I came back in Paris for another exciting year of research. 18 jul: During the academic year 2007/2008 I will be teacher assistant at Paris 7 for the following courses: Intelligence Artificielle (M1), Algorithmique (L3BI), Analyse syntaxique et Compilation (L3) and Suivi projets longs (M1). Summing-up: 101 hours of fun. 16 jul: The following people have accepted to be the referees of my thesis: H.P. Barendregt

    19. Computer Organization And Architecture
    Technical Faculty Institute of computer Science and Applied Mathematics Current activities. Teaching on `Abstract lambda calculus Machines at the
    Computer Organization and Architecture
    Werner Kluge, Prof.(em.)
    Phone: +49-(0)2204-867 512 (private) E-Mail:
    After retiring in 2003, I have found the time to complete a monograph on Abstract Computing Machines which has been published in the Springer EATCS series (ISBN 3-540-21146-2).
    This monograph is on the relationship between basic programming paradigms as they derive from Lambda calculus and the abstract machines featuring the runtime structures and mechanisms that are essential for program execution. It sets out with a brief discussion of an expression-oriented style of programming, addresses the problem of correctly dealing with free variables as a prerequisite for symbolic computations, and gives a brief introduction to Lambda calculus as the underlying theory.
    In its main part, the book is primarily concerned with the description of what are called fully normalizing Lambda-calculus machines. They support the runtime structures and mechanisms necessary to correctly perform substitutions that may involve free variables, and to do symbolic self-optimizations under functions (abstractions), thus treating both functions and variables truly as first class objects.
    These machines are related to various weakly normalizing counterparts which are the work horses for the implementation of functional languages. They rule out substitution and evaluation under abstractions to avoid problems with free variables, which considerably simplifies the machinery but at the same time also sacrifices many of the amenities of symbolic computations.

    20. Mathematician's Professional Homepage, Detail Information
    S. Ghilezan and V. Kuncak Confluence of untyped lambda calculus via simple types, The 5th Italian Conference on Theoretical computer Science,

    General Information



    News and Miscellaneous
    List of publications
    • M.Dezani-Ciancaglini, S. Ghilezan, J. Pantovic, D. Varaca: Security types for dynamic web data Theoretical Computer Science (to appear).
    • H. Herbelin and S. Ghilezan: An approach to call-by-name delimited continuations , The 35th Annual ACM SIGPLAN SIGACT Symposium on Principles of Programming Languages POPL 2008 San Francisco, USA, January 2008.
    • D. Dougherty, S. Ghilezan and P. Lescanne: Characterizing strong normalization in the Curien-Herbelin symmetric lambda calculus: extending the Coppo-Dezani heritage, Theoretical Computer Science (special issue Festschrift Coppo, Dezani, Ronchi, eds S. Berardi, U de' Liquoro) (to appear).
    • S. Ghilezan, J. Pantovic and J. Zunic: Separating Points by Parallel Hyperplanes Characterization Problem, IEEE Transactions of Neural Networks vol. 18 no. 5 (2007) 1356-1363.
    • M.Dezani-Ciancaglini, S. Ghilezan and J. Pantovic:

    21. The Impact Of The Lambda Calculus In Logic And Computer Science
    The Impact of the lambda calculus in Logic and computer Science. Henk Barendregt. Source Bull. Symbolic Logic Volume 3, Number 2 (1997), 181215.
    Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options

    22. Logical Methods In Computer Science
    computeraided verification Real time and hybrid systems close popup Functional programming and lambda calculus close popup

    23. Jean-Jacques Lévy's Publications
    The weak lambda calculus and Programming Languages, with Luc Maranget, FSTTCS 99 foundations of software technology and theoretical computer science,
    • Réductions sûres dans le lambda-calcul, Paris 7, thèse de 3ème cycle, June, 1974. [ Pdf ] (In French)
    • An algebraic interpretation of the lambda-beta-K-calculus; and an application of a labelled lambda-calculus, Proceedings of the Rome Symposium on the Lambda calculus, 1975; also in Theoretical Computer Science 2 (1976), North Holland, pp.97-114. [ Pdf
    • Minimal and Optimal Computations of Recursive Programs, with Gérard Berry, Journal of the ACM, Vol 26, 1, Jan 1979, pp.148-175. [ Pdf ]. Also presented at the Fourth Annual ACM Symposium on Principles of Programming Languages (POPL) 1977.
    • Réductions correctes et optimales dans le lambda-calcul, Paris 7, thèse d'Etat, January, 1978. [ Pdf ] (In French)
    • Le problème du partage dans l'évaluation des lambda-expressions, 1er colloque AFCET-SMF de Mathématiques Appliquées, Palaiseau, 4-8 Sept 1978. (In French)
    • A Survey of Some Syntactic Results in the Lambda-calculus, with Gérard Berry. Proc. Ann. Conf. on Mathematical Foundations of Computer Science, Olomouc, Tchecoslovaquia, Lecture Notes in Computer Science 74, Springer-Verlag (1979).
    • Optimal reductions in the lambda-calculus, To H.B.Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, edited by J.P.Seldin and J.R.Hindley, Academic Press, 1980. [

    24. Homepage
    Infinitary lambda calculus and Discrimination of Berarducci trees. Theoretical computer Science 298(2)275 302, 2003. Tree semantics of lambda calculus
    computer science
    ABOUT ...
    Fer-Jan de Vries
    Department of Computer Science,
    University of Leicester,
    University Road,
    T: +44 (0) 116 252 3903
    E: fdv1 at mcs le ac uk
    A selected annotated bibliography
  • J.R. Kennaway and F.J. de Vries. Infinitary Rewriting. Chapter 12 in Terese, editor, Term Rewriting Systems (Cambridge Tracts in Theoretical Computer Science 55), Cambridge University Press. Page 668-711. 2003. In this chapter we develop a general theory of infinite orthogonal rewriting unifying our earlier work on infinite term rewriting and infinite lambda calculus. Confluence in the infinitary setting is significantly harder than in the finitary case. The technique of transfinite tiling diagrams in the confluence proof is new. Infinitary extensions of confluent finite systems may not be confluent, unless one adds a rule that identifies "meaningless" terms by reducing them to bottom. Then the extensions become confluent and normalising; the sets of their normal forms can give new denotational semantics of the original finite systems. P. Severi and F.J. de Vries.
  • 25. Computer Laboratory - Computer Science Syllabus - Foundations Of Functional Prog
    computer Laboratory computer Science Syllabus Foundations of Functional Programming lambda calculus, combinators and functional programming.
    Computer Laboratory
    Computer Science Syllabus - Foundations of Functional Programming Computer Laboratory Computer Science Syllabus - Foundations of Functional Programming
    Next: Mathematical Methods for Computer Up: Lent Term 2007: Part Previous: Digital Communication I Contents

    Foundations of Functional Programming
    Lecturer: Professor A. Mycroft No. of lectures: This course is a prerequisite for Types (Part II). Aims This course aims ( a ) to show how lambda-calculus and related theories can provide a foundation for a large part of practical programming, ( b ) to present students with one particular type analysis algorithm so that they will be better able to appreciate the Part II Types course, and ( c ) to provide a bridge between the Part IA Foundations of Computer Science course and the theory options in Part II. Lectures
    • Introduction. Combinators. Constants and Free Variables. Reduction. Equality. The Church-Rosser theorem. Normal forms. The Lambda calculus. Lambda-terms, alpha and beta conversions. Free and bound variables. Abbreviations in the notation. Pure and applied lambda calculi. Relationship between combinators, lambda calculus and typical programming languages. Eager and Lazy evaluation. Encoding of data: booleans, tuples, lists and trees, numbers. The treatment of recursion: the

    26. CiteULike: Tag Lambda-calculus [72 Articles]
    posted to online lambdacalculus introduction computer-science by robertoalamino on The Impact of the lambda calculus on Logic and computer Science
    Register Log in FAQ
    Tag lambda-calculus [72 articles]
    Recent papers classified by the tag lambda-calculus.
  • Call-by-Push-Value: A Subsuming Paradigm (1999), pp. 228-242. by Paul B Levy posted to lambda-calculus by zednenem on 2007-10-11 04:49:52 as Adequacy for Algebraic Effects Lecture Notes in Computer Science , Vol. 2030 (2001) by Gordon Plotkin , John Power posted to monads lawvere-theories lambda-calculus effects by zednenem on 2007-10-11 04:33:40 as Highlights of the history of the lambda-calculus (1982), pp. 216-225. by Barkley J Rosser posted to lambda-calculus by wadler on 2005-12-09 15:51:38 as along with 9 people and 1 group ds bunge pintman ... Selective strictness and parametricity in structural operational semantics, inequationally Theoretical Computer Science , Vol. 388, No. 1-3. (2007), pp. 290-318. by Janis Voigtl¤nder , Patricia Johann posted to types strict-evaluation shortcut-deforestation seq ... call-by-name by voigt on 2007-12-11 15:51:34 as The anatomy of a loop: a story of scope and control (2005), pp. 2-14. by Olin Shivers posted to functional-programming lambda-calculus scheme by voigt on 2005-10-06 07:22:00 as along with 5 people ryanc robennals pintman ... A step-indexed model of substructural state (2005), pp. 78-91.
  • 27. Full Bibliography
    Normalization by evaluation for typed lambda calculus with coproducts. In Logic in computer Science, pages 303–310. IEEE computer Society Press.
    Next Previous Up
    Full Bibliography
    Alessi, F., Barbanera, F., and Dezani-Ciancaglini, M. (2006). Intersection types and lambda models. Theoretical Computer Science Alessi, F., Dezani-Ciancaglini, M., and Lusin, S. (2004). Intersection types and domain operators. Theoretical Computer Science [Alessi and Lusin, 2002] Alessi, F. and Lusin, S. (2002). Simple easy terms. In van Bakel, S., editor, Intersection Types and Related Systems Electronic Notes in Computer Science . Elsevier. Altenkirch, T., Dybjer, P., Hofmann, M., and Scott, P. (2001). Normalization by evaluation for typed lambda calculus with coproducts. In Logic in Computer Science [Altenkirch and Uustalu, 2004] Altenkirch, T. and Uustalu, T. (2004). Normalization by evaluation for . In Functional and Logic Programming , volume 2998 of Lecture Notes in Computer Science [Anderson, 1960] Journal of Symbolic Logic , 25:388. (Abstract). [Anderson and Belnap, 1975] Entailment. The Logic of Relevance and Necessity, Volume . Princeton University Press, U.S.A.

    28. Summer School In ``Logic In Computer Science''
    It is intended primarily for young researchers in computer Science or in S. RONCHI (Torino, Italy) Fundamentals of lambdacalculus S. BERARDI (Torino,
    [Prev] [Next] [Index] [Thread]
    Summer School in ``Logic in Computer Science''

    29. Computer Science @ UC Davis | Course Descriptions
    The lambda calculus. lambda notation, alphabeta-and eta-reduction, normal order reduction Programming Languages and the lambda calculus
    @import url("../../css/csstyle3.css"); Home Courses Course Descriptions
    Lecture: 3 hours Discussion: 1 hour Prerequisite: Courses ECS 140A ECS 142 Grading: Letter; problem sets (10%), project (30%), midterm (20%), final (40%) Catalog Description:
    Advanced topics in programming languages, including formal syntax and semantics, the relation between formal semantics and verification, and an introduction to the lambda calculus. Additional topics will include language design principles, alternative programming language, in-depth semantic theory and models of language implementation. Expanded Course Description: Lectures provide an introduction to the theoretical side of the study of computer programming languages, including language definition methods and the lambda calculus. The usefulness of advanced language features in appropriate programming applications is also discussed, with examples. The project gives students an opportunity to experiment with defining and prototyping a programming language. The lectures topics include the following, not necessarily listed in chronological order:

    30. Bibliography
    Rewriting with polymorphic extensional lambdacalculus. In, CSL 95. Lecture Notes in computer Science, volume 1092, pp. 215-232. Springer-Verlag, 1996.
    • Di Cosmo (Roberto) Isomorphisms of types: from lambda-calculus to information retrieval and language design Birkhauser, 1995. ISBN-0-8176-3763-X. ( ABSTRACT
    • Di Cosmo (Roberto) et Nora (Dominique) Calmann-Levy, octobre 1998.
    • Special Issue on Type Isomorphisms Mathematical Structures in Computer Science, 2005. To appear.
    • Di Cosmo (Roberto) A brief history of rewriting with extensionality In,: International Summer School on Type Theory and Rewriting Glasgow, septembre 1996. A set of slides on the subject is available as
    • Bruce (Kim), Di Cosmo (Roberto) et Longo (Giuseppe) Provable isomorphisms of types Mathematical Structures in Computer Science , vol. 2, n. 2, 1992, pp. 231-247. ( DVI ABSTRACT
    • Di Cosmo (Roberto) Deciding type isomorphisms in a type assignment framework Journal of Functional Programming , vol. 3, n. 3, 1993, pp. 485-525. Special Issue on ML. ( DVI ABSTRACT
    • Di Cosmo (Roberto) et Kesner (Delia) Simulating expansions without expansions Mathematical Structures in Computer Science , vol. 4, 1994, pp. 1-48. (

    31. The Parametric Lambda Calculus - Mathematical Logic And Formal Languages Journal
    The Parametric lambda calculus. A Metamodel for Computation Series Texts in Theoretical computer Science. An EATCS Series Ronchi Della Rocca, Simona,

    School of computer Science, Carnegie Mellon University. CMUCS-97-151. A Model for a List-oriented Extension of the lambda calculus. Glenn Durfee. May 1997
    Computer Science Department
    School of Computer Science, Carnegie Mellon University
    CMU-CS-97-151 A Model for a List-oriented Extension of the Lambda Calculus Glenn Durfee May 1997 Submitted in partial fulfillment of the requirements for the degree of
    Master of Science (Honors Degree Program)
    Department of Mathematics, Carnegie Mellon University.
    Keywords: Lambda calculus, applicative lists, denotational semantics, domain theory
    This work is intended to provide a semantics for a fragment of a programming language described by Gyorgy Revesz in Lambda-Calculus combinators and Functional Programming), for which no model was known. We begin with a brief presentation of the syntax of the lambda calculus and some relevant extensions. We then describe a class of complete lattices and use them as models for the lambda calculus. We then find specialized sublattices which we use as models for the extensions of the lambda calculus, thus achieving the original goal of finding a semantics for Revesz's language. 33 pages Return to: SCS Technical Report Collection
    School of Computer Science
    This page maintained by

    33. An Introduction To Lambda Calculus And Scheme
    We can use lambdacalculus to describe such a function .. Calculi for Programming Langauges The computer Science and Engineering Handbook,
    $Id: lambda.html,v 1.2 2001/02/01 01:43:43 jim Exp jim $
    An Introduction to Lambda Calculus and Scheme
    Jim Larson
    This talk was given at the JPL Section 312 Programming Lunchtime Seminar.
    Functions and Lambda Notation
    A function accepts input and produces an output. Suppose we have a "chocolate-covering" function that produces the following outputs for the corresponding inputs: peanuts -> chocolate-covered peanuts rasins -> chocolate-covered rasins ants -> chocolate-covered ants We can use Lambda-calculus to describe such a function: Lx.chocolate-covered x This is called a lambda-expression. (Here the "L" is supposed to be a lowercase Greek "lambda" character). If we want to apply the function to an argument, we use the following syntax: (Lx.chocolate-covered x)peanuts -> chocolate-covered peanuts Functions can also be the result of applying a lambda-expression, as with this "covering function maker": Ly.Lx.y-covered x We can use this to create a caramel-covering function: (Ly.Lx.y-covered x)caramel -> Lx.caramel-covered x (Lx.caramel-covered x)peanuts -> caramel-covered peanuts Functions can also be the inputs to other functions, as with this "apply-to-ants" function:

    34. Théorie De La Démonstration
    Thomas Ehrhard and Laurent Regnier. The differential lambdacalculus. Theoretical computer Science, volume 309, issues 1-3, pages 1-41, december 2003. (PS).
    Liste (non exhaustive) d'articles Voir le planning provisoire des soutenances Articles
    • Kanovitch, M. (1992). Horn-programming in linear logic is NP-complete . In Proceedings of the 7th Annual IEEE Symposium on Logic in Computer Science, pp. 200-210. ( P. Baillot and Terui, K., Light types for polynomial time computation in lambda-calculus PS Jean-Marc Andreoli. Focussing and Proof construction Abstract paper.pdf (238KB). (R©serv© par Etienne Miret Andrea Asperti. Light affine logic . In Proc. Symp. Logic in Comp. Sci. (LICS). IEEE, 1998. ( PS A.Asperti, L.Roversi. Intuitionistic Light Affine Logic . ACM Transactions on Computational Logic (TOCL), Volume 3 , Issue 1, January 2002, pp.137 - 175. Y. Lafont, Soft Linear Logic and Polynomial Time , Theoretical Computer Science 318 (special issue on Implicit Computational Complexity) p. 163-180, Elsevier (2004). ( PS Benton, Bierman, de Paiva.

    35. Computer Science Reports
    (199204) Edmund Robinson Notes on the SecondOrder lambda calculus (Now pub. in Proc. of 7th Annual IEEE Symposium on Logic in computer Science

    36. Lambda Calculus Introduction
    lambda calculus provides the basis for Functional Programming languages. Tech., Monash University, was Department of computer Science, Fac. Comp.
    Lambda Calculus
    LA home



    Also see:

    Prolog intro


  • Introduction ...
  • A Functional Programming Language
  • Programming Techniques: The Parser ...
  • Appendix - Misc' Routines
  • Lambda Calculus Example Programs
    The toy Lambda Calculus interpreter can be run through the wwweb. You should read at least the sections down to and including Programming Techniques first. There are very tight limits set on the size and running time of programs that can be run in this way. window on the wide world: The Darwin Awards 4: Intelligent Design Linux free op. sys. OpenOffice free office suite, ver 2.2+ The GIMP ~ free photoshop Firefox web browser list cons nil the [ ] list null predicate hd head (1st) tl tail (rest) L. Allison or as otherwise indicated Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering
  • 37. International Doctoral School In Theoretical Computer Science - Semantic Web Jun
    Theoretical computer Science. The semantics of lambda calculus. speaker Simona Ronchi della Rocca (Dipartimento di Informatica Università di Torino,
    International Doctoral School "Chambéry - Torino"
    In Theoretical Computer Science and In Semantic Web
    21-25, June 2004 Aussois (Savoie - France)
    Home Page
    Scientific Program Poster Session Scientific Committee ... Contacts After the school... Slides S. Web Slides Theoretical C. S. Posters presented Participant list ... Some photos
    June 21st Non-Classical logics
    (Common Topic) speaker: Pierre Lescanne
    (Ecole Normale Supérieure de Lyon, France)
    June 22nd Theoretical Computer Science
    Model Checking

    speaker: Susanne Graf (VERIMAG - Grenoble, France) June 22nd Semantic Web State of the Art speaker: Guus Schreiber (Department of Computer Science, Free University Amsterdam, The Netherlands) June 23rd Theoretical Computer Science Model Checking speaker: Susanne Graf (VERIMAG - Grenoble, France) June 23rd Semantic Web Knowledge representation languages for the semantic Web Knowledge-based retrieval and mining for the Semantic Web speaker: Amedeo Napoli (LORIA, CNRS, Nancy, France) June 24th Theoretical Computer Science The semantics of lambda calculus speaker: Simona Ronchi della Rocca (Dipartimento di Informatica - Università di Torino, Italia)

    38. J Roger Hindley : Research
    MR1616965 N Ça man, J R Hindley, Combinatory Weak Reduction in lambda calculus, Theoretical computer Science 198 (1998), 239247.
    Swansea University Physical Sciences Mathematics Department J Roger Hindley
    J Roger Hindley : Research
    Fields of Interest
    Mathematical logic; particularly lambda-calculus, combinatory logic and type-theories, with a current bias towards historical aspects. Lambda-calculus and combinatory logic are formal systems, to some extent rivals, used in the construction and study of programming languages which are higher-order (i.e. in which programs may change other programs). These two systems were invented in the 1920s by mathematicians for use in higher-order logic, and came to be applied in programming theory from the 1970s onward, when that theory expanded to cover higher-order computations. In a type-theory, types are labels which may be attached to certain programs to show what other programs they can change. A type-system is a particular set of rules for attaching types; the rules themselves are usually reasonably simple, but such questions as what programs are typable, what set of types a program may receive, and whether a typable computation can continue indefinitely, are not always easy to answer and have occupied many researchers.
    Main Publications
    J R Hindley, J P Seldin

    39. Résumé Of Dr. György E. Révész
    lambdacalculus, Combinators, and Functional Programming, Cambridge Tracts in Theoretical computer Science 4, Cambridge University Press, 1988.
    Résumé of Dr. György E. Révész Education Ph. D. in Mathematics, Eötvös Lóránd University of Budapest, 1968 Areas of specialization Formal Languages and Automata Theory, Semantics of Programming Languages, Compiler Design, Lambda-Calculus and Functional Programming, Numerical Methods, Parallel Computing, Cryptography. Courses taught in the last 5 years Survey of Programming Languages Compiler Design Introductio to Coding Theory Foundations of Cryptography Formal Languages and Automata Theory Switching and Automata Theory Theory of Computation Numerical Methods Data Structures Employment history Visiting Professor, Fall of 2001

    40. Peter Selinger Papers
    A lambda calculus for quantum computation with classical control. With Benoît Valiron. Mathematical Structures in computer Science 16(3)527552, 2006.
    This is a list of Peter Selinger 's papers, along with abstracts and hyperlinks. See also:
    A linear-non-linear model for a computational call-by-value lambda calculus
    Proceedings of the Eleventh International Conference on Foundations of Software Science and Computation Structures (FOSSACS 2008), Budapest

    41. Harry Mairson
    Optimal evaluation An evaluator for lambda calculus (or more broadly speaking, . A simple proof of a theorem of Statman Theoretical computer Science 103
    Harry Mairson
    Ph.D., Computer Science, Stanford University, 1984
    Visiting Professor of Computer Science
    283 MCS / (617) 353-8923
    Research Interests
    Optimal evaluation
    Game semantics and proof structures
    Expressibility and typed lambda calculus ...
    Research Interests
    My research examines the interaction between mathematical logic and computation theory, with application to the design and analysis of functional programming languages, type systems, and database query languages. A primary current research interest is optimal evaluation in lambda calculus and its computational complexity. I also do fundamental research in algorithmics and algorithm analysis. Optimal evaluation: An evaluator for lambda calculus (or more broadly speaking, a functional programming language) is said to be correct and optimal if it returns a normal form whenever there is one (i.e., it never diverges by choosing to evaluate the wrong redex), and never does inessential work (i.e., copying redexes). Recently, several researchers, including Lamping, Gonthier, Abadi, Levy, and Asperti, have constructed optimal evaluators. But are they efficient? I have examined the computational complexity of this problem via the algorithmic analysis of these proposed evaluators. In addition, this work has addressed what reasonable

    42. Mechanically Separated Meat » Blog Archive » The Ballad Of The Lambda Calculus
    The Ballad of the lambda calculus. computer Science can be said to predate even the idea of a computer itself by at least two millennia, in the sense that

    43. To Dissect A Mockingbird: A Graphical Notation For The Lambda Calculus With Anim
    The lambda calculus, and the closely related theory of combinators, .. named after its discoverer the logician and computer scientist Alan Turing.
    To Dissect a Mockingbird:
    A Graphical Notation for the Lambda Calculus with Animated Reduction
    David C Keenan, 27-Aug-1996
    last updated 10-May-2001
    116 Bowman Parade, Bardon QLD 4065, Australia
    Abstract The lambda calculus, and the closely related theory of combinators, are important in the foundations of mathematics, logic and computer science. This paper provides an informal and entertaining introduction by means of an animated graphical notation. Introduction In the 1930s and 40s, around the birth of the "automatic computer", mathematicians wanted to formalise what we mean when we say some result or some function is "effectively computable", whether by machine or human. A "computer", originally, was a person who performed arithmetic calculations. The "effectively" part is included to indicate that we are not concerned with the time any particular computer might take to produce the result, so long as it would get there eventually. They wanted to find the simplest possible system that could be said to compute.
    Several such systems were invented and for the most part looked entirely unlike each other. Remarkably, they were all eventually shown to be equivalent in the sense that any one could be made to behave like the others. Today, the best known of these are the Turing Machine, of the British mathematician Alan Turing (not to be confused with his touring machine, the bicycle of which he was so fond), and the Lambda Calculus, of the American logician Alonzo Church (1941). The Turing machine is reflected in the Von Neumann machine which describes the general form of most computing hardware today. The Lambda calculus is reflected in the programming language Lisp and its relatives which are called "functional" or "applicative" languages.

    44. Gmb://publications
    Proceedings of the Second International Conference on Typed lambda calculus and Applications. In Volume 902 of Lecture Notes in computer Science,
    Quick Links Home Worldwide Search for
    All Microsoft Research Downloads Publications Researcher Pages
    Microsoft Research Home
    About Microsoft Research Research Areas People ... Press Resources
    Being written!
    Contracts for patterns: A comparison. (with Parkinson, Noble and Schulte) UpgradeJ: Incremental typechecking for class upgrades. (with Parkinson and Noble) Submitted. Dec 07. Dynamic Rebinding for Marshalling and Update, via Redex-time and Destruct-time Reduction. (with Hicks, Sewell, Stoyle and Wansborough) Accepted for publication in JFP. 70pp. Separation logic, abstraction and inheritance. (with Parkinson) Accepted to appear in POPL'08. Lost in translation: Formalizing proposed extensions to C# (with Meijer and Torgersen) Proceedings of 22nd OOPSLA. October 2007. [ pdf corrected version (12 Nov 07)] Mutatis Mutandis: Safe and predictable dynamic software updating (Journal Version). (with Stoyle, Hicks, Sewell and Neamtiu) ACM Transactions on Programming Languages and Systems. Volume 29, issue 4, article 22. August 2007. 70pp. pdf (Requires ACM account) Formalizing and extending C# type inference.

    45. Ian Mackie: Publications
    Maribel Fernández and Ian Mackie. Closed Reductions in the lambda calculus. In proceedings of computer Science Logic (CSL99), LNCS 1683, 1999.
    Other Pages
    Home Page Research Publications Software
    Jean Goubault-Larrecq and Ian Mackie. Proof Theory and Automated Deduction volume 6 of Applied Logic Series Kluwer Academic Publishers , Dordrecht. May 1997. Hardbound, ISBN 0-7923-4593-2. (Paperback: November 2001, ISBN 1-4020-0368-4.)
    Books Edited
    Chris Hankin, Ian Mackie and Rajagopal Nagarajan (Eds). Theory and Formal Methods 1994: Proceedings of the Second Imperial College Workshop on Theory and Formal Methods . Imperial College Press, September 1995. ISBN 1-86094-003-X.
    Habilitation, PhD, MSc, BSc (Eng)
    Ian Mackie. English version: Theory and applications of interaction nets: implementations of linear logic and the lambda-calculus Ian Mackie. The Geometry of Implementation . PhD Thesis, Department of Computing, Imperial College of Science, Technology and Medicine, September 1994. Ian Mackie. Lilac: A functional programming language based on Linear Logic . Master's Thesis, Department of Computing, Imperial College of Science, Technology and Medicine, September 1991.

    46. Papers
    E. Tronci, Equational Programming in lambdacalculus, Proceedings IEEE Conference Logic in computer Science, 1991, Amsterdam, IEEE computer Society Press
    Selected Papers
    Giuseppe Della Penna, Benedetto Intrigila, Igor Melatti, Michele Minichino, Ester Ciancamerla, Andrea Parisse, Enrico Tronci, Marisa Venturini Zilli,
    Automatic Verification of a Turbogas Control System with the Murphi Verifier

    Proceedings of: 6th International Workshop Hybrid Systems: Computation and Control (HSCC) April 2003, Prague, Czech Republic, LNCS 2623, Springer-Verlag
    [DITZ 03]
    Giuseppe Della Penna, Benedetto Intrigila, Enrico Tronci, Marisa Venturini Zilli,
    Synchronized regular expressions

    Acta Informatica 39 (2003) 1, 31-70, Springer
    [GHBTCM 02]
    Marco Gribaudo, Andras Horvath, Andrea Bobbio, Enrico Tronci, Ester Ciancamerla, Michele Minichino,
    Model-checking based on Fluid Petri Nets for the temperature control system of the ICARO co-generative plant

    Proceedings of 21th International Conference on: Computer Safety, Reliabiltiy and Security (SAFECOMP 2002), 10-13 September 2002, Catania, Italy, LNCS, Springer Abstract [DITZ 02] Giuseppe Della Penna, Benedetto Intrigila, Enrico Tronci, Marisa Venturini Zilli, Exploiting Transition Locality in the Disk Based Murphi Verifier Proceedings of 4th International Conference on: Formal Methods in Computer Aided Verification (FMCAD 2002), Nov. 2002, Portland, Oregon, USA, LNCS, Springer

    47. Coding Horror: Classic Computer Science Puzzles
    Here s a quick list of the classic computer science puzzles that I remember from .. lambda calculus isn t just a core concept of lisp, it s the smallest
    programming and human factors
    by Jeff Atwood
    September 12, 2007
    Classic Computer Science Puzzles
    Software developers do have a proclivity for puzzles. Perhaps that's why books like To Mock a Mockingbird exist. It's a collection of logic puzzles which is considered an introduction to lambda calculus , one of the core concepts of Lisp Such puzzle questions are de rigueur for many programming interviews , though they're often abused. There is a downside to thinking of programming languages as solutions to arbitrarily difficult abstract mathematical puzzles. That's probably why Lisp has a rich reputation for being powerful but simultaneously dense and impenetrable I prefer to think of programming languages as utilitarian tools for real world problems . They let me accomplish pragmatic (and often prosaic) goals. PHP is about as unsexy a language as you'll ever find, but does that matter when it's the technology driving the current Boardwalk and Park Place of the web world? I'm not a fan of puzzle questions in interviews; I'd rather have potential developers give me a presentation or write a reasonably useful program in the real development environment they'll be using on the job. Solve all the puzzles you want, but the only one we're getting

    48. BRICS Mini-Course: Optimal Graph Reduction: Computation, Continuations, Complexi
    Julia Lawall is a Research Associate in computer Science at Brandeis University. . Optimal reductions in the lambda calculus. JeanJacques Lévy.
    BRICS Contents Lecturers Programme ... References
    Optimal Graph Reduction: Computation, Continuations, Complexity
    A BRICS Mini-Course
    May 25-28, 1999 Lectures by
    Julia Lawall
    Department of Computer Science, Brandeis University, Waltham, Massachusetts 02254 Harry Mairson
    Department of Computer Science, Brandeis University, Waltham, Massachusetts 02254
    Course Contents
    In foundational research some two decades ago, Jean-Jacques Lévy attempted to formalize what an ``optimally efficient'' reduction strategy of the lambda calculus would look like, encompassing correctness (reductions always derive existent normal forms) and optimality (maximal sharing of similar redexes). These dual features can be thought of roughly as a synthesis of the correctness of call-by-name, with the efficiency of call-by-value. Around 1990, John Lamping invented a graph-based implementation that realized Lévy's specification, by introducing a technology for sharing evaluation contexts as well as values. His invention was very similar to Jean-Yves Girard's proofnets for multiplicative-exponential linear logic; subsequently Georges Gonthier showed how a mundane version of Girard's ``geometry of interaction'' could give a semantics to Lamping's graphs. Further, Gonthier's formulation was very similar to that of games for linear logic, with application to full abstraction. In this minicourse, we will introduce optimal graph reduction for lambda calculus, paying particular attention to implementations of sharing. We will discuss as well the semantics of this graph reduction, and how implementations of sharing can be extended to implement graph reduction for languages with explicit control, especially Filinski's symmetric lambda calculus, and Parigot's lambda-mu calculus. Finally, we discuss the inherent complexity of the parallel beta step, the operation that is at the heart of optimal graph reduction.

    49. Dipartim Ento Di Matematica E Informatica - Università Di Catania
    In Proceedings of first international Conference on Typed lambda calculus and Applications TLCA 93 , volume 664 of Lecture Notes in computer Science .
    Notice: Publications (most of the papers antecedent to 1995 are not included in the list below.)
    • F. Barbanera. Combining term-rewriting and type-assignment systems. In Proceedings of the Third Italian Conference on Theoretical Computer Science . World Scientific Publishing Company, 1989.
    • F. Barbanera. Adding algebraic rewriting to the calculus of constructions : Strong normalization preserved. In Proceedings of Conditional and typed Term Rewriting Systems (CTRS '90) , volume 516 of Lecture Notes in Computer Science . Springer-Verlag, 1990.
    • F. Barbanera. Combining term-rewriting and type-assignment systems. International Journal of Foundations of Computer Science
    • F. Alessi and F. Barbanera. Strong conjunction and intersection types. In Proceedings of 16h international symposium on Mathematical Foundation of Computer Science (MFCS '91) , volume 520 of Lecture Notes in Computer Science . Springer Verlag, 1991.
    • F. Alessi and F. Barbanera. Toward a semantics for the quest language. In Proceedings of sixth annual symposium on Logic in Computer Science (LICS'91) . IEEE, 1991.

    50. Lambda Calculus
    lambda calculus. By André van Meulebrouck, Chatsworth, CA\. “A calculus for the Algebraiclike Manipulation of computer Code”, or “Why Oh Why Oh Y?”
    MacTech Network: Computer Memory Register Domains ... Mac Book Shelf
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    Volume Number: Issue Number: Column Tag: Lisp Listener
    Lambda Calculus
    Abe Lincoln
    Intro to l-calculus
    LISP 101
    What follows will be a crash course in LISP. or even because a list in any position can have a function position and argument positions of its own, and so on, to arbitrary depth. The next thing we need is a way to abstract out common process patterns into descriptions. This is done via lambda, the anonymous function. For instance, (lambda (x) (+ x 1)) is a function that takes in an evaluated argument, binds it with x, and then computes the body of the lambda form with the understanding that any occurrence of parameter x in the body will refer to the value of x bound by the lambda form. In this case, the returned result will be the argument plus one, and the argument will not be side effected. To invoke an anonymous function, we simply invoke it like any other function. We invoked sine like this: (sin 3). Invoking (lambda (x) (+ x 1)) on the argument 3 would look like this:

    51. [0704.2900] The Algebraicity Of The Lambda-calculus
    Title The algebraicity of the lambdacalculus Comments. 10 pages. Subjects. Logic in computer Science (cs.LO). Cite as. arXiv0704.2900v1 cs.LO cs
    Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
    Full-text links: Download:
    Citations p revious n ... ext
    Computer Science > Logic in Computer Science
    Title: The algebraicity of the lambda-calculus
    Authors: Marco Maggesi (Submitted on 22 Apr 2007) Abstract: We propose a new definition for abstract syntax (with binding constructions), and, accordingly, for initial semantics and algebraicity. Our definition is based on the notion of module over a monad and its companion notion of linearity. In our setting, we give a one-line definition of an untyped lambda-calculus. Among untyped lambda-calculi, the initial one, the pure untyped lambda-calculus, appears as defined by two algebraic constructions (abs and the unary application app1), together with two algebraic equations which are essentially the beta and eta rules. Comments: 10 pages Subjects: Logic in Computer Science (cs.LO) Cite as: arXiv:0704.2900v1 [cs.LO]
    Submission history
    From: Marco Maggesi [ view email
    Sun, 22 Apr 2007 18:19:46 GMT (20kb)

    52. Type Theory In Computer Science And Linguistics
    From a computer Science perspective, it is a language in which it is possible to lambda calculus. This is to be handed in on the next lecture (Oct 30)
    Type Theory in Computer Science and Linguistics, a graduate course in Chung-Ang University, Autumn 2003
    (guest professor from Chalmers University of Technology, Sweden)
    Short Description of the course
    From a Computer Science perspective, it is a language in which it is possible to express both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. As a programming language, type theory is similar to typed functional languages such as ML and Haskell, but a major difference is that the evaluation of a well-typed program always terminates. The type system is using dependent types, a concept which makes it possible to identify programs and formal proofs. We can use type theory as a framework in which it is possible to express a whole range of logical formalisms. An important feature of the language is the possibility of using *inductively defined sets*, a concept which is closely related to XML. The lectures will assume a general background in Computer Science. We will explain the theory and show its applications to programming, document structure (like the semanic web) and linguistics.

    53. Publications Of Maribel Fernandez
    lambdacalculus, Type Theory and Natural Language, Special Issue of the Journal of Mathematical Structures in computer Science, volume 15, issue 02.
    Some Recent Publications
    Book: M. Fernandez. Programming Languages and Operational Semantics.
    Texts in Computing, Volume 1. King's College Publications, 2004. ISBN 0-9543006-3-7 Journals:
    • S. Alves, M. Fernandez, M. Florido, I. Mackie. Goedel's System T Revisited . Submitted, 2007. pdf H. Cirstea and M. Fernandez, editors. Rewriting Calculi, Higher-order reductions and Patterns. Special issue of the Journal of Mathematical Structures in Computer Science , to appear. M. Fernandez, M.J. Gabbay. Nominal Rewriting . Information and Computation 205, pages 917-965, 2007. M. Fernandez, I. Mackie, editors. More Developments in Computational Models, 2nd special issue of the Journal of Mathematical Structures in Computer Science , Volume 17(4), August 2007. Cambridge University Press. M. Fernandez, I. Mackie, editors. Developments in Computational Models, Special issue of the Journal of Mathematical Structures in Computer Science , 16(4), August 2006. Cambridge University Press. M. Fernandez, C. Fox, S. Lappin, editors. Lambda-Calculus, Type Theory and Natural Language II, 2nd Special Issue of the Journal of Logic and Computation , Oxford University Press, 2007.

    54. Computer-science - SWiK
    Move computerscience? Moving this page will change its URL and content tagged . (An Implementation of a Dependently Typed lambda calculus)
    SWiK login / register changes) Your tags: or Cancel
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    Barendregt H.P. lambda calculus. Its syntax and semantics. 6 of Handbook of Theoretical computer Science B Formal Methods and Semantics, J. van Leeuwen
    Bar-Ilan University
    Rewrite systems play an important role in various areas of computer science, such as automated deduction, artificial intelligence, program verification, and high-level programming languages. The course will cover some of the important topics related to the use of the theory of rewriting in (1) functional programming and (2) equational reasoning. (1) Rewrite systems (or reduction systems) form a basic model of computation. Computation (= reduction) is performed according to rewrite rules, such as rules for addition and multiplication. A computation may end with a normal form (which is the value of the given expression) or diverge. Typical questions are existence of normal forms, confluence (which implies uniqueness of normal forms), termination (of all reduction paths), normalizing strategies (allowing to compute a normal form when it exists), etc. The most well-known rewrite system is Church's Lambda-calculus. All (partial) recursive functions can be represented as Lambda-expressions, which makes the Lambda-calculus a paradigmatic functional programming language. All recent functional programming languages are based on typed Lambda-calculi. (2) Reasoning with equations includes (a) deriving consequences of a set of equations and (b) finding solutions to a given set of equations.

    56. Lambda Calculus And Lambda Calculators
    Henk Barendregt s ``The impact of the lambdacalculus in logic and computer science (The Bulletin of Symbolic Logic, v3, N2, June 1997) has the following
    previous next contents top
    Lambda Calculus and Lambda Calculators
    Negative numbers, subtraction and division in lambda-calculus
    This article will demonstrate basic arithmetic operations comparison, addition, subtraction, multiplication, and division on non-negative and negative integer numbers. Both the integers and the operations on them are represented as terms in the pure untyped lambda-calculus. The only building blocks are identifiers, abstractions and applications. No constants or delta-rules are used. Reductions follow only the familiar beta-substitution and eta-rules. We also show two approaches of defining a predecessor of a Church numeral. Curiously, none of the arithmetic operations involve the Y combinator; even the division gets by without Y. Addition, multiplication, squaring, and exponentiation are easily expressed in lambda-calculus. We discuss two approaches to their "opposites" subtraction, division, finding of a square root and of a discrete logarithm. The "opposite" operations present quite a challenge. One approach, based on fixpoints, is more elegant but rather impractical. The "dual" approach, which relies on counting, leads to constructive and useful, albeit messy, terms.

    57. CCCs And The λ-calculus
    The power of the lambda calculus is evident in the textbook developed for MIT s introductory course in computer science, which is available online
    John Baez
    September 28, 2006
    Categorical semantics was born in Lawvere's celebrated 1963 thesis on algebraic theories: Algebraic theories are a simple formalism for reasoning about operations that satisfy equations. For example, since the concept of a "group" involves only some operations (multiplication, inverses...) satisfying equations, this concept can be formalized using an algebraic theory called Th(Grp). The role of semantics enters when we consider "models" of an algebraic theory. Loosely speaking, a model is just one of the things the theory seeks to describe. For example, a "model" of Th(Grp) is just a group. Technically, an algebraic theory T is a category with finite products, and a model is a functor that preserves finite products: from T to the category of sets. The basic idea is simple: if for example T = Th(Grp), then Z maps the abstract concept of "group" to a specific set, the abstract concept of "multiplication" to a specific multiplication on the chosen set, and so on, thus picking out a specific group. Dual to the concept of semantics is the concept of syntax , which deals with symbol manipulation. Just as semantics deals with models, syntax deals with "proofs". For example, starting from Th(Grp) we can prove consequences of the group axioms merely by juggling equations. In the case of algebraic theories, the syntax often goes by the name of

    58. Lecture Notes In Computer Science, 2007(4646 )
    computer Science Logic 21st International Workshop, CSL 2007 . lambda calculus 2 - Classical Program Extraction in the calculus of Constructions
    Sumario Título / Autor(es) Página(s) Computer Science Logic - 21st International Workshop, CSL 2007 . 16th Annual Conference of the EACSL . Lausanne, Switzerland, September 11-15, 2007 . Proceedings / Duparc, Jacques Henzinger, Thomas A Invited Lectures - Full Completeness: Interactive and Geometric Characterizations of the Space of Proofs (Abstract) / Abramsky, Samson Invited Lectures - The Symbolic Approach to Repeated Games (Abstract) / Alfaro, Luca de Invited Lectures - Proofs, Programs and Abstract Complexity / Beckmann, Arnold Invited Lectures - Model-Checking First-Order Logic: Automata and Locality / Dawar, Anuj Invited Lectures - Tightening the Exchange Rates Between Automata / Kupferman, Orna Invited Lectures - Precise Relational Invariants Through Strategy Iteration / Gawlitza, Thomas Seidl, Helmut Logic and Games - Omega-Regular Half-Positional Winning Conditions / Kopczynski, Eryk Logic and Games - Clique-Width and Parity Games / Obdrzálek, Jan Logic and Games - Logical Refinements of Church's Problem / Rabinovich, Alexander

    59. A Certified Type-Preserving Compiler From Lambda Calculus To Assembly Language |
    I present a certified compiler from simplytyped lambda calculus to . for at least as many programs at the world s best computer scientist could.
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    A Certified Type-Preserving Compiler from Lambda Calculus to Assembly Language
    A Certified Type-Preserving Compiler from Lambda Calculus to Assembly Language I present a certified compiler from simply-typed lambda calculus to assembly language. The compiler is certified in the sense that it comes with a machine-checked proof of semantics preservation, performed with the Coq proof assistant. The compiler and the terms of its several intermediate languages are given dependent types that guarantee that only well-typed programs are representable. Thus, type preservation for each compiler pass follows without any significant "proofs" of the usual kind. Semantics preservation is proved based on denotational semantics assigned to the intermediate languages. I demonstrate how working with a type-preserving compiler enables type-directed proof search to discharge automatically large parts of the proof obligations. Software/proof source code and documentation Slides are available from a talk I gave at the Projet Gallium seminar at INRIA Rocquencourt, in

    60. BOOK ANNOUNCEMENT: The Parametric Lambda Calculus
    But the use of lambdacalculus as an abstract paradigm for programming languages started later as the work of three important scientists Strachey,
    var addthis_pub = 'comforteagle'; science.mathematics.frogs Top All Lists Date Thread
    BOOK ANNOUNCEMENT: The Parametric Lambda Calculus
    Subject BOOK ANNOUNCEMENT: The Parametric Lambda Calculus - BOOK ANNOUNCEMENT THE PARAMETRIC LAMBDA CALCULUS - A Metamodel for Computation by Simona Ronchi Della Rocca and Luca Paolini Series : Texts in Theoretical Computer Science. An EATCS Series 2004, XIII, 252 p., Hardcover ISBN: 3-540-20032-0 We are pleased to announce that the book is available. Order informations can be found at,11855,5-40356-72-14202886-0,00.html You can found the table of contents at,11996,0-0-45-117802-0,00.pdf More with this subject... Current Thread Previous by Date: Counterexamples Alessio Guglielmi Previous by Thread: Counterexamples Alessio Guglielmi Indexes: Date Thread Top All Lists Recently Viewed: linux.nfsv4/200... debian.apt.deve... security.risks/... qplus.devel/200... ... Perl 5.10 21/12/07 23:57 from

    61. Advice For Computer Science College Students - Joel On Software
    The moral of the story is that computer science is not the same as software in lambda calculus or linear algebra where you never touch a computer.
    Feb 13-14: Tokyo:
    Shoeisha Developers Summit
    Feb 26-27: New York:
    FutureTest 2008
    Wanted: Software Developer at ZS Associates (Evanston, IL 60201). See this and other great job listings at
    Advice for Computer Science College Students
    By Joel Spolsky
    Sunday, January 02, 2005
    Despite the fact that it was only a year or two ago that I was blubbering about how rich Windows GUI clients were the wave of the future, college students nonetheless do occasionally email me asking for career advice, and since it's recruiting season, I thought I'd write up my standard advice which they can read, laugh at, and ignore. Most college students, fortunately, are brash enough never to bother asking their elders for advice, which, in the field of computer science, is a good thing, because their elders are apt to say goofy, antediluvian things like "the demand for keypunch operators will exceed 100,000,000 by the year 2010" and "lisp careers are really very hot right now." I, too, have no idea what I'm talking about when I give advice to college students. I'm so hopelessly out of date that I can't really figure out AIM and still use (horrors!) this quaint old thing called "email" which was popular in the days when music came on flat round plates called "CDs."

    62. Theoretical Foundations Of Computer Science
    This course is meant to introduce you to computer science not as the mundane . Implementation of a generalised looping function in the lambdacalculus.
    Theoretical Foundations of Computer Science
    Matthew Belmonte
    The Johns Hopkins University Center for Talented Youth
    TEXTS: This course is meant to introduce you to computer science not as the mundane activity of computer programming, but as a branch of mathematics. If you have studied `computer science' in high school, you're about to experience something rather different. If you've never studied high school computer science, maybe you're better off. The course consists of two interrelated components: automata theory and formal systems, and programming. tSG is the text for the programming component. It contains two types of problems: `exercises', and `problem sets'. You are to work independently through this book; we'll do very little lecturing on programming. You are to complete the following readings and problems by the end of study hall on Tuesday of the second week: READINGS PROBLEMS 1.1, 1.2 all exercises, and all of problem set 1 1.3 all exercises, and all of problem set 2 2.1,2.2,2.3,2.4 all exercises, and all of problem sets 3 and 4 3.1 all exercises, and problem set 5: 1-10, 15, 16 4.1, 4.2 all exercises, and problem set 8: 1, 2 4.3 all exercises

    63. Publications
    HigherOrder Matching in the Linear lambda-calculus with Pairing. In J. Marcinkowski and A. Tarlecki, editors, computer Science Logic, 18th International
    Proceedings, Monograph (Editor)
  • Ph. de Groote, editor. The Curry-Howard Isomorphism , volume 8 of Cahier du centre de Logique
    Ph. de Groote and J.R. Hindley, editors. Typed Lambda Calculi and Applications Lecture Notes in Computer Science , Springer Verlag, 1997.
    Logical Aspects of Computational Linguistics Lecture Notes in Artificial Intelligence , Springer Verlag, 2001.
  • Ph. D. Thesis
  • Ph. de Groote.
  • Articles
  • Logical Frameworks
    Formal Aspects of Computing
    Ph. de Groote. An environment machine for the lambda-mu-calculus. Mathematical Structure in Computer Science
    Ph. de Groote. An algebraic correctness criterion for intuitionistic multiplicative proofnets. Theoretical Computer Science
    Ph. de Groote. On the Strong Normalisation of Intuitionistic Natural Deduction with Permutation-Conversions. Information and Computation
    Ph. de Groote. and F. Lamarche Classical non-associative Lambek calculus. Studia Logica
    Ph. de Groote, S. Pogodalla. On the Expressive Power of Abstract Categorial Grammars: Representing Context-Free Formalisms. Journal of Logic, Language and Information
  • 64. Martin Odersky's Papers
    A Type System for a lambda calculus with Assignment, Kung Chen and Martin Odersky. In Proceedings, Symp. on Theoretical Aspects of computer Software,
    Archive of papers - Martin Odersky
    On Scala and its Foundations:
    On Functional Nets:

    65. Foundational Papers By Henk Barendregt
    Papers and talks on logic and computer science Constructive proofs of the range property in lambda calculus. A collection of contributions in honour of
    Foundational papers by Henk Barendregt (and co-authors)
    Papers and talks on logic and computer science
    Over welke kwestie zijn bijna al uw vakgenoten het oneens met u?
    Towards the range property for the lambda theory H
    Proofs of Correctness To appear in Wiley Encyclopedia of Computer Science and Engineering.
    Bewijzen: Romantisch of Cool
    (with F. Wiedijk) In: Euclides, 81 (4), 2006, 175-179.
    B"ohm's Theorem, Church's Delta, Numeral Systems, and Ershov Morphisms (with R. Statman)
    In: Processes, Terms and Cycles: Steps on the Road to Infinity,
    Essays Dedicated to Jan Willem Klop on the Occasion of His 60th Birthday,
    Eds. A. Middeldorp, V. van Oostrom and F. van Raamsdonk,
    Springer LNCS, vol. 3838, 2005, 40-54.
    The Challenge of Computer Mathematics
    (with F. Wiedijk)
    In Transactions A of the Royal Society, vol. 363, no. 1835, 2351-2375.
    Foundations of Mathematics from the Perspective of Computer Mathematics
    To appear in the Buchberger Festschrift
    Towards an Interactive Mathematical Proof Language
    in: Thirty Five Years of Automath, Ed. F. Kamareddine, Kluwer, 2003, 25-36. (cartoon via advi)
    Autarkic computations in formal proofs
    (with E. Barendsen)

    66. Citebase - Soft Lambda-calculus: A Language For Polynomial Time Computation
    We introduce Soft lambdacalculus as a calculus typable in the computer Science - Computational Complexity computer Science - Logic in computer Science

    67. Gérard Boudol's Home Page
    Termination, deadlock and divergence in the lambdacalculus with multiplicities, with C. Laneve, MFPS 95, Electronic Notes in Theoretical computer Science
    Welcome to my home page. I am a Research Director at INRIA Sophia-Antipolis within the MIMOSA project. My research interests include theory of concurrency (process algebras, verification, ``true concurrency''), lambda-calculus, models of higher-order and mobile distributed systems, semantics of objects, security. I am also interested in programming languages design and semantics, type theories, logics.
    2004, Route des Lucioles
    B.P. 93
    06902 Sophia Antipolis Cedex
    Tel: (33) (0)4 92 38 79 40
    Fax: (33) (0)4 92 38 50 29
    Some Links
    The page Calculi for Mobile Processes provides information and links related to research on the theory of mobile systems. See also Xudong Guan's Mobile Ambients page, and Jonathan Bowen's Concurrent Systems . This is part of the WWW Virtual Library on Computing (other topics may be found here ). I use frequently the DBLP bibliographical database, the Scientific Literature Digital Library (CiteSeer), The Collection of Computer Science Bibliographies , and NCSTRL , the Networked Computer Science Technical Reference Library. To see the home page of the European Association for Theoretical Computer Science, of which I am a member, hit

    68. Foreign Dispatches: An Introduction To The Lambda Calculus
    An Introduction to the lambda calculus. And now for something different. February 18, 2007 in computer Science, Mathematics Permalink
    Foreign Dispatches
    Random Remarks on Current Affairs
    Math Books
    February 18, 2007
    An Introduction to the Lambda Calculus
    And now for something different. Are you a programmer who's made a run in or two with esoteric languages like Haskell, Erlang and OCaml, and do you find yourself confused by closures, maddened by monads and feeling downright cantankerous whenever you hear about currying? If you are, I have a suggestion for you: instead of wasting your time struggling through yet another functional programming tutorial whose writers implicitly assume that you already understand half of the new things they're supposedly trying to teach, you'd be better off giving a close reading to a paper by Henk Barendregt and Erik Barendsen called

    69. Jiri Zlatuska - Biographical Summary
    Courses taught Information Society, Semantics of Program Languages, Types and Proofs, Introduction to Theoretical computer Science, lambdacalculus,
    Jiri Zlatuska Biographical Summary
    Prof. Dr Jiri Zlatuska, CSc. , born September 15, 1957, in Brno, Czechoslovakia, married, 2 children. Academic Qualifications:
    • 1994: Professor of Computer Science (Faculty of Science of Masaryk University);
    • 1990: Associate Professor of Computer Science (Faculty of Science of Masaryk University);
    • 1987: PhD in Theoretical Computer Science; Czechoslovak Academy of Science; theses: ``Functional data modelling'', developing a typed-lambda-calculus-based data model for data modelling encompassing formal tools for data description and data manipulation on several levels of abstraction.
    • 1981: graduated with honors from Computer Science studies at faculty of Science, Masaryk University, awarded RNDr degree upon graduation (theses: ``Program schemata and their applications''; advisor: J. Horejs).
    • 2004 - Dean, Faculty of Informatics at Masaryk University;
    • 1998 - 2004 : Rector of Masaryk University;
    • 1995 - : Full Professor of Computer Science at the Faculty of Informatics at Masaryk University;
    • 1994 : Associate Professor of Computer Science at the Faculty of Informatics at Masaryk University;

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