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1. Introduction To Functional Programming - Lambda Calculus
An introduction to lambda calculus and programming in ML. functional programming lambda calculus ml.
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2. 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. [

3. Lambda Calculus - Wikipedia, The Free Encyclopedia
The lambda calculus and the paradigm of functional programming - is still .. The most prominent counterparts to lambda calculus in programming are
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Lambda calculus
From Wikipedia, the free encyclopedia
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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

4. MainFrame: The Lambda-calculus, Combinatory Logic, And Type Systems
The connections between the lambdacalculus and programming languages are diverse and pervasive. Type systems are an important aspect of programming
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.

5. An Introduction To Lambda Calculus And Scheme
The Scheme programming language is essentially the lambdacalculus outlined above, plus . Advantages of a lambda-calculus-based programming language
$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:

6. Lecture About Scheme And Lambda Calculus
This is a presentation that introduces the Scheme programming language, and then uses the learned subset to demonstrate lambda calculus. lambda calculus is
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Lecture about Scheme and Lambda Calculus
This is a presentation that introduces the Scheme programming language , and then uses the learned subset to demonstrate Lambda Calculus. Lambda Calculus is a mathematical model of computation, which only has two primitives and yet is still quite usable and fun.
The Slides
Written, designed and maintained by Shlomi Fish

7. Home Page For Kim B. Bruce
Williams College Semantics and design of programming languages, type theory, object-oriented languages, models of higher-order lambda calculus including subtypes and bounded polymorphism.
Kim B. Bruce
Frederick Latimer Wells Professor of CS, emeritus
Department of Computer Science

Williams College
As of 7/1/2005, I have taken a new position as Professor of Computer Science at Pomona College in Claremont, California.
Click here to go to my new home page.
This page will no longer be updated.
Information is available on:
Programming languages research.
Computer Science Education contributions.
Quick links to:
Contact information

Recent papers

Courses taught
Other Interesting WWWeb sites

My book, Foundations of Object-Oriented Languages: Types and Semantics has now been published by MIT Press.
Recent items
  • The slides and some bonus features from my keynote to SIGCSE 2005 are now available.
  • Unfortunately, the tail end of my paper, "Controversy on How to Teach CS 1: A discussion on the SIGCSE-members mailing list," in the December, 2004, issue of Inroads, the newsletter of SIGCSE, became corrupted at the publishers. The original correct version is available here: Inroads.pdf

8. Peter Selinger Papers
Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation.
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

9. Honsell, Furio
University of Udine lambda calculus; foundations, especially of informatics; type systems for OO languages; logical frameworks and formal verification of proofs, programs, and systems; semantics of programming languages and program logics; mathematical structures for semantics.

10. Tobias Nipkow
Technische Universit¤t M¼nchen Automatic and interactive theorem proving, formal verification, formalizing programming languages, type systems, semantics, rewriting and unification, lambda-calculus.
Theorem Proving Group
Prof. Tobias Nipkow
  • Now soliciting your submission: AFP: The Archive of Formal Proofs
  • Now out: The Isabelle/HOL Tutorial
  • Now out in paperback: Term Rewriting and All That
  • Publications
  • Isabelle
  • Diplomarbeit/SEP der Woche ...
  • Ein IDP!
  • Research Interests
    • Automatic and interactive theorem proving
    • Formal verification
    • Formalizing programming languages
    • Formal foundations of Java
    • Type systems
    • Semantics
    • Rewriting and unification
    • Lambda-calculus
      Verisoft - Verified Software
      TYPES - Mathematical modelling and reasoning using typed logics. ESPRIT Working Group.
      GKLI - PhD programme Logic in Informatics
      InopSys - Calculi for system modelling
      VerifiCard - Theorem proving for JavaCard
      Isar - Intelligible semi-automated reasoning
      Bali - Formalizing Java in Isabelle
      CCL - Construction of Computational Logics. ESPRIT Working Group.
  • 11. Categories And The Lambda Calculus « Programming Musings
    The Knights of the lambda calculus In case you’re wondering, CCC stands for Cartesianclosed category you’ll find a lot of links in John’s post explaining
    programming musings
    random thoughts on programming and programming languages Prolog programming contests Becoming a Haskell developer
    Categories and the Lambda Calculus
    The n-Category Caf© John Baez (of fame), is very interested in the connection between categories and lambda calculus, and has recently posted an article entitled CCCs and the λ-calculus over at the Caf©. Knights of the Lambda Calculus the wizard book , for he has a very funny (and totally unrelated) intro to general relativity called Oz and The Wizard lambda calculus and category theory But the real To Dissect a Mockingbird Raymond Smullyan To Mock a Mockingbird from his book This book needs not title [T]he theory of combinators is an abstract science dealing with objects whose only important property is how they act upon each other. We are free to choose other properties of these objects in any way we like. In his delightful book To mock a mockingbird and he goes on developing a sort of lambda calculus by pictures, or by movies . John Baez gives more details of the math involved in his follow-up post Categorifying CCCs: computation as a process , again at the n-Category Caf©. Too fun and instructive to let it pass, if you ask me.

    12. Luke Ong's Home Page
    Merton College, Oxford Semantics of programming languages, lambda calculus, categorical logic and type theory, game semantics, linear logic.

    Luke Ong's new OUCL web page

    oucl work
    Updated April 2004 Home Search SiteMap Feedback ... News

    13. Zhenyu Qian
    Universit¤t Bremen Java security, extensions, and semantics; object-oriented, functional, concurrent, logic programming languages; specification languages; compiler construction; program specification, construction and transformation; object-oriented analysis and design; types; lambda-calculus; unification; algebraic semantics; and theorem proving systems.
    Zhenyu Qian

    Research Interests
      Java security, Java extensions, Java semantics, object-oriented, functional, concurrent, logic programming languages, specification languages, compiler construction, program specification, program construction, program transformation, object-oriented analyse and design, types, lambda-calculus, unification, algebraic semantics, theorem proving systems.
    I am now working at the Kestrel Institute . Click here to go to my new homepage. Zhenyu Qian, last update June 23, 2000

    14. Bruno Carle - Java / C++ Developer - Redirect Page
    Some samples of non commercial programming e.g. a lisp like interpreter, lambda calculus interpreter, regular expression tool, and more useless stuff with C++ and Java sources. CV in english, spanish, french and italian languages.
    P lease wait while beeing redirected to the main page...
    F rom this site you can download my resume , and some demos in Java, C++, Javascript and php.
    You may wish to try a plain HTML version of this site

    15. Lambda Calculus Introduction
    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.
    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
  • 16. Luke Ong
    Merton College, Oxford Categorical logic, game semantics, type theory, lambda calculus, semantics of programming languages, and sequentiality.
    Luke Ong
    Professor of Computer Science
    Tutorial Fellow in Computation, Merton College
    Oxford University Computing Laboratory
    Wolfson Building,
    Parks Road,
    Oxford, OX1 3QD,
    Direct: +44 (0)1865 283522
    Department: +44 (0)1865 273838
    Fax: +44 (0)1865 273839
    Work-related information (OUCL)
    Personal Information
    (Personal page,
    content is not the responsibility of OUCL)
    oucl people Updated December 2007 Home Search SiteMap Feedback ... News

    17. Afdeling Informatica, Faculteit Der Exacte Wetenschappen, Vrije Universiteit Ams
    Division of Mathematics and Computer Science. Research interests center around software engineering; parallel and distributed systems, including programming, distributed shared objects, operating systems support, and wide area cluster computing; agent technology; computational intelligence; knowledge representation and reasoning; lambda calculus; programming language semantics; type theory; and proof checking.
    Informatica is overal!
    Informatica gaat over informatie en de manieren waarop je informatie kunt bewerken en verwerken. Daar komt enorm veel bij kijken. Informatica is, jong als het is, dan ook al uitgegroeid tot een breed en interessant vakgebied. De informatica opleidingen aan de Vrije Universiteit bestrijken een groot deel van dat vakgebied: computersystemen, software engineering, formele methoden, kunstmatige intelligentie, bedrijfsinformatica, bedrijfswiskunde, bioinformatica . Wij zijn op zoek naar goede en gemotiveerde studenten voor de bacheloropleidingen informatica, kunstmatige intelligentie en informatiekunde. Welke opleiding het meest geschikt voor je is hangt af van waar je het accent wilt leggen. Verdere specialisatie volgt in de masterfase.
    Wil je meer weten over informatica, kunstmatige intelligentie of informatie, multimedia en management? Kijk op de paginas over onze opleidingen, of ontmoet ons bij een van onze voorlichtingsactiviteiten!

    18. Lambda Calculus And A++: Basic Concepts
    The lambda calculus has stayed alive above all in the context of functional programming. It has gained a major importance in the area of compiler
    Next Page: Lambda Calculus and A++: Contents Up: Back to Entry Page New book on A++ and the Lambda Calculus available! Lambda Calculus A++
    Basic Concepts
    The Lambda Calculus has been created by the American logician Alonzo Church in the 1930's and is documented in his works published in 1941 under the title `The Calculi of Lambda Conversion' Alonzo Church wanted to formulate a mathematical logical system and had no intent to create a programming language. The intrinsic relationship of his system to programming was discovered much later in a time in which programming of computers became an issue. The Lambda Calculus has stayed alive above all in the context of functional programming. It has gained a major importance in the area of compiler construction for functional languages like Haskell, SML, Miranda and others. In this article the importance of the Lambda Calculus is extended to non-functional languages like Java, C, and C++ as well. The article uses A++, a programming language directly derived from the Lambda Calculus, as a vehicle to demonstrate the application of the basic ideas of the Lambda Calculus in a multi-paradigm environment. As a mathematical logical system the Lambda Calculus is covered in detail in [ ] and less comprehensively but in a more readable form in [ ]. A clear account of the historical origins and basic properties of the lambda calculus is presented by Curry and Fey in their book [

    19. Introduction To The Lambda Calculus With Programming Examples
    The calculus (lambda calculus) is a formal mathematical system devised by Alonzo Church to investigate functions, function application and recursion.
    var REMOTE_HOST='(none)', REMOTE_ADDR='';
    LA home








    Also see: Prolog functional programming languages . Lisp was the first of these although only the "pure" Lisp sublanguage can be called a true functional language. Haskell, Miranda and ML are more recent examples. also provides the meta-language for formal definitions in denotational semantics . It has a good claim to be the prototype programming language.
    application abstraction
    A function abstraction is an expression for a function. The identifier is the name of the parameter; it is said to be bound . An unbound identifier is free . The function itself has no name. Application is left associative: f x y=(f x)y. It is convenient, but not essential , to add an option for constants.
    application abstraction
    The clause for constants can be omitted because constants can be defined with what is left but this is inconvenient and does not aid our purpose. (But see [ints] [bool] and [list] The previous grammar forces the use of prefix notation. It costs nothing to extend the grammar to include prefix and infix operators. The gain is purely in convenience not in power or difficulty of implementation.
    Extended Grammar to include Operators.

    20. A++ An Educational Programming Language Based On The Lambda Calculus
    A++ is a programming language helping students quickly and thoroughly understand the essentials and become familiar with powerful programming patterns
    A++ An Educational Programming Language:
    The Language
    A++ is a programming language created for the sole purpose to help people interested in programming to thoroughly understand as quickly and efficiently as possible the essentials of the art of programming . By learning A++ students not only get a deep comprehension of programming very quickly but at the same time they acquire powerful pattern recognition skills that can be applied in most programming languages. A++ , being based on the Lambda Calculus, can be considered to be a hard-core programming language consisting of elements that cannot be further split up or disintegrated whereas other languages have a lot of bells and whistles and many soft features very useful to cope with practical programming problems. Learning the art of programming cannot be accomplished however by becoming familiar with all these nice and handy soft features a programming language has to offer but by learning how to cope with programming problems by continuously applying Abstraction Reference and Synthesis from the beginning to the end.

    21. Lambda Calculus Introduction : Programming - Groovyweb Free Downloads And Tutori
    Implementing programming in lambda calculus. Whilst extremely impractical, lamba calculus is Turing complete, and so you can program in it any program you calculus introductio

    22. Foreign Dispatches: An Introduction To The Lambda Calculus
    An Introduction to the lambda calculus. and now for something different. to truly understand what functional programming is all about will likely prove
    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

    23. Lambda Calculus
    Révész, 1988 György E. Révész. lambdacalculus, Combinators, and Functional programming. Cambridge University Press, Cambridge, England, 1988.
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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:

    24. Eugenio Moggi Publications
    HigherOrder Types and Meta-programming for Global Computing, TOSCA WS 2001. ENTCS 62. . Empty types in polymorphic lambda calculus. POPL 1987.
    Dipartimento di Informatica e Scienze dell'Informazione
    Eugenio Moggi Publications
    List of publications by Eugenio Moggi most recent first:
    • Structuring Operational Semantics: Simplification and Computation, Computation, Meaning and Logic - Articles dedicated to Gordon Plotkin , ENTCS vol.172 [ pdf
    • From Partial Lambda-calculus to Monads, Plotkin's Symposium , slides of presentation [ pdf
    • Program Generation and Components, Formal Methods for Components and Objects , Revised Lectures, LNCS tutorial 3167 [ pdf
    • An Abstract Monadic Semantics for Value Recursion, Theoretical Informatics and Applications pdf
    • A Fresh Calculus for Names Management, GPCE 2004, LNCS [ pdf
    • MetaKlaim: A Type Safe Multi-stage Language for Global Computing, Mathematical Structures In Computer Science pdf
    • ML-like Inference for Classifiers, ESOP 2004. LNCS [extended version pdf
    • The Klaim Project: Theory and Practice, Global Computing , Trento Feb 2003. LNCS 2874, [ pdf
    • Mixin Modules and Computational Effects, ICALP pdf
    • An Abstract Monadic Semantics for Value Recursion, FICS pdf ] (please refer to [MS03-sub]
    • A Monadic Multi-stage Metalanguage

    25. Lambda-calculus Combinators And Functional Programming
    lambdacalculus combinators and functional programming. Purchase this Book Purchase this Book. Source, Cambridge Tracts In Theoretical Computer Science

    26. Lambda-calculus - SWiK
    A Brief tutorial on the lambda calculus, functional programming, and LISP. Wednesday, September 12, 2007. Haskell tag/haskell
    SWiK login / register changes) Your tags: or Cancel
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    27. BOOK ANNOUNCEMENT: The Parametric Lambda Calculus
    The first contact between lambdacalculus and real programming languages was in the years 1956-1960, when McCarthy developed the LISP programming language,
    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: network.tin.bug... text.xml.cocoon... ... Perl 5.10 21/12/07 23:57 from

    28. Chapter 8. Boost.Lambda
    The term originates from functional programming and lambda calculus, where a lambda abstraction defines an unnamed function. The primary motivation for the
    Automatic redirection failed, please go to Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at

    29. Harry Mairson
    Optimal evaluation An evaluator for lambda calculus (or more broadly speaking, a functional programming language) is said to be correct and optimal if it
    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

    30. Lambda Calculus - A Definition From
    lambda calculus, considered to be the mathematical basis for programming language, is a calculus developed by Alonzo Church and Stephen Kleene in the 1930s,,sid9_gci341298,00.html
    lambda calculus
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    B C D ... Programming
    lambda calculus
    Lambda calculus, considered to be the mathematical basis for programming language, is a calculus developed by Alonzo Church and Stephen Kleene in the 1930s to express all computable�functions.� In an effort to formalize the concept of computability (also known as constructibility and effective calculability), Church and Kleene developed a powerful language with a simple� syntax and few grammar restrictions. The language deals with the application of a function to its arguments (a function is a set of rules) and expresses any entity as either a variable, the application of one function to another, or as a "lambda abstraction" (a function in which the Greek letter�lambda is defined as the abstraction operator). Lambda calculus, and the closely related theories of combinators and type systems, are important foundations in the study of mathematics, logic, and computer programming language.

    31. New England Programming Languages And Systems Symposium Series (NEPLS): Abstract
    We make Session Types boring by reexpressing them using well understood, standard programming language technology (linear lambda calculus, capabilities,
    S These abstracts are for talks at this event NEPLS is a venue for ongoing research, so the abstract and supplemental material associated with each talk is necessarily temporal. The work presented here may be in a state of flux. In all cases, please consult the authors' Web pages for up-to-date information. Please don't refer to these pages as a definitive source. BAT: The Bit-level Analysis Tool
    Pete Manolios (Northeastern University)
    The Bit-level Analysis Tool (BAT) is a system for verifying bit-level problems arising from hardware, software, and security domains. BAT implements a state-of-the-art decision procedure for solving quantifier-free formulas over the extensional theory of fixed-size bit-vectors and fixed-size bit-vector arrays (memories). Our primary goal in developing BAT is to enable the verification of system-level properties of systems described at the bit-level; an example is the verification of bit-level pipelined machine models. Key features of the BAT system are an expressive strongly-typed modeling and specification language, a fully automatic and efficient memory abstraction algorithm for extensional arrays, and a novel CNF generation algorithm. The BAT system can be used to automatically solve system-level RTL (Register Transfer Level) verification problems that were previously intractable, such as refinement-based verification of RTL-level pipelined machines. Session Types Made Boring
    Alec Heller and Riccardo Pucella (Northeastern University)

    32. Quantum Programming Language - Quantiki
    2 Functional quantum programming. 2.1 QPL and cQPL. 2.1.1 Examples. 2.2 Quantum lambda calculus. 3 References. 3.1 Related articles; 3.2 Books
    @import "/wiki/skins/quantiki/mediawiki.css"; @import "/wiki/skins/quantiki/style.css"; Article Discussion ... History
    Quantum Programming Language
    Quantum Programming Language is a programming language, which can be used to write programmes for quantum computer Since every quantum machine has to be controlled by classical device, existing quantum programming languages incorporate classical control structures such as loops and conditional execution and allow to operate on classical and quantum data.
    • Imperative quantum programming
      Imperative quantum programming
      Quantum pseudocode
      Quantum pseudocode proposed by E. Knill is the first formalised language for description of quantum algorithms was introduced and, moreover, it was tightly connected with model of quantum machine called Quantum Random Access Machine (QRAM).
      Quantum Computing Language
      QCL (Quantum Computer Language) is the most advanced implemented quantum programming language. Its syntax resambles syntax of the C programming language and classical data types are similar to data types in C. The basic built-in quantum data type in QCL is qreg (quantum register). It can be interpreted as a an array of qubits (quantum bits).

    33. Computer Science @ UC Davis | Course Descriptions
    programming Languages and the lambda calculus. Currying, functions as first class objects, lazy and eager evaluation; LISP, Scheme, ML
    @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:

    34. » Wikipedia - Lambda Calculus Entry Is Mistaken
    Languages such as Iota and Jot by Chris Barker are universal programming languages and are by any measures far simpler than the lambda calculus.
    @import url(;

    35. CIS 705 -- Programming Languages -- Spring 2007
    In the following, TAPL stands for the book Types and programming Reading Chapter 5 of TAPL; TAPL Chapter 5 Untyped lambda calculus (view/print)
    Instructor Alley Stoughton Office Phone E-mail WWW Home Page Course WWW Page Lectures MWF 1:30-2:20 p.m. N127 Office Hours TU 1:30-2:20 p.m. N214
    Class Sessions
    In the following, TAPL stands for the book Types and Programming Languages , and DAWOC stands for the book Developing Applications With Objective Caml . The OCaml programs referred to below can also be found in the directory ~stough/705 /home/faculty/stough/705 ) on the CIS Linux system.
    • Session 1: Jan 12
      • Reading: Chapter 1 of TAPL Course Syllabus ( view print Tour of course WWW page TAPL Chapter 1: Introduction ( view print
      Session 2: Jan 17
      • Reading: Chapters 1 and 2 of TAPL TAPL Chapter 1: Introduction ( view print TAPL Chapter 2: Mathematical Preliminaries ( view print
      Session 3: Jan 19
      • Reading: Chapter 3 of TAPL TAPL Chapter 2: Mathematical Preliminaries ( view print TAPL Chapter 3: Untyped Arithmetic Expressions (A) ( view print
      Session 4: Jan 22
      • Reading: Chapter 3 of TAPL TAPL Chapter 3: Untyped Arithmetic Expressions (A) ( view print
      Session 5: Jan 24
      • Reading: Chapter 3 of TAPL TAPL Chapter 3: Untyped Arithmetic Expressions (A) ( view print
      Session 6: Jan 26
      • Reading: Chapter 3 of TAPL TAPL Chapter 3: Untyped Arithmetic Expressions (A) ( view print TAPL Chapter 3: Untyped Arithmetic Expressions (B) ( view print
      Session 7: Jan 29
      • Reading: Chapter 3 of TAPL TAPL Chapter 3: Untyped Arithmetic Expressions (B) ( view print
      Session 8: Feb 2

    36. Functional Programming
    It consists of a written exam (75%) mainly on lambda calculus and In functional programming, one of the key concepts is that variables are kept as local
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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

    37. Lambda Calculus And Combinators
    lambda calculus and Combinators. Connections. Related to Functions, functional programming; Prerequisite; Requisite for

    38. Logical Methods In Computer Science
    close popup. Immerman, Neil. Functional programming and lambda calculus Program analysis and type checking Semantics of programming languages close popup

    39. [Some Citations For Lambda Calculus Books From MathSciNet Djr
    Date Mon, 03 May 1999 201715 0700 Newsgroups sci.math,comp.theory Another book is lambda-calculus Combinators and Functional programming by G.Revesz.

    40. CTO : Lambda Calculus
    See logic and functional programming Languages, as well as lambda calculus as a virtual machine the lambda VM. A few bibliographies. Clemens Grelk s.
    CTO CLiki for the TUNES project Home Recent Changes About CLiki Text Formatting ... Create New Page
    Lambda Calculus
    The term for the mathematically formalized theory of abstractions. Well, it's recursive, lexically-scoped theory of functions. And it's not just one theory; there are variations. The usual reference for it is a 1984 book by Barendregt. See logic and functional Programming Languages , as well as lambda calculus as a virtual machine - the Lambda VM A few bibliographies: There are introductory online courses on lambda calculus. Here are a few pointers: See also Epsilon Calculus This page is linked from: Abstraction Basic Computer Science Bisimulation Context ... View source

    41. Programming Languages; CS6371
    programming with Functions; lambda calculus and ML programming; Logic programming; Unification and backtracking; Search tree; programming in Prolog;
    CS6371: Advanced Programming Languages
    Spr 2007, Tue,Th 4:00-5:15 PM
    Classroom: ECSS 2.306 Click here for Homeworks and Solutions
    Gopal Gupta , ECSS 4.907, 883-4107, Office hours: Wed 2-4PM Teaching Assistant: Ajay Bansal; TA Office Hours and Office: 2-4pm Monday; ECSS 4.404
    This course will deal with Advanced Concepts in Programming Languages. The following are the course learning objectives:
  • Lambda Calculus and functional programming
  • Logic Programming and Prolog
  • Denotational Definition of Programming Languages
  • Fixpoints; Program Verification
  • We will first cover functional programming, followed by logic programming. Then we will switch to studying semantics of programming languages (Operational, Denotational and Axiomatic). We will also study basics of program verification. Good understanding of set theory, discrete mathematics, and data structures is required for this course. In the semantics part, significant amount of time will be devoted to denotational semantics.
    This course will help in considerably improving your understanding of the process of programming and the structure of computation. You will also learn how to
  • 42. Lambda Calculus: Blogs, Photos, Videos And More On Technorati
    Reasoning about program behaviour in programming languages based on the lambdacalculus requires reasoning in a unified way about control,
    Catch the latest action, scores and banter in Sports
    16 posts tagged Lambda Calculus
    Subscribe search in entire post tags only of blogs with any authority a little authority some authority a lot of authority in language all languages Arabic (العربية) Chinese (中文) Dutch (Nederlands) English French (Fran§ais) German (Deutsch) Greek (Ελληνικά) Hebrew (עברית) Italian (Italiano) Japanese (日本語) Korean (한국어) Norwegian (Norsk) Persian (فارسی) Polish (Polski) Portuguese (Portuguªs) Russian (Русский) Spanish (Espa±ol) Swedish (Svenska) Turkish (T¼rk§e) Vietnamese (Tiếng Việt)
  • Natural Deduction for Intuitionistic Non-Commutative Linear Logic node/ 2523 Natural Deduction for Intuitionistic Non-Commutative Linear Logic Natural Deduction for Intuitionistic Non-Commutative Linear Logic, Jeff Polakow and Frank Pfenning. TLCA 1999. Intuitionistic logic captures functional programming in a logical way, as can be seen from the Curry-Howard isomorphism between constructive proofs and functional programs. 45 days ago in Authority: 333
    G¶del, Nagel, minds and machines
  • 43. Lambda Calculus Tutorial
    lambda calculus Tutorial. programming Languages Group 16 The lambda calculus was developed in 1936 by Lorenzo Church, and is a mathematical system for
    Lambda Calculus Tutorial
    Programming Languages Group 16 Cody Robbins [
    Jonathan Dance [
    Jeffrey Lynch [
    Matthew Cherian [
    The lambda calculus was developed in 1936 by Lorenzo Church, and is a mathematical system for defining computable functions (i.e., a model of computation). Church’s lambda calculus is equivalent in power to the Turing machine, although Church and Turing both developed their respective models of computation independently. We attempt to explain to the fundamental principles of the lambda calculus in a clear, concise, and easy to understand fashion. We provide examples and self-tests to facilitate in the conceptualization of the material.
    Table of Contents
  • Introduction Syntax of the Lambda Calculus Evaluation Strategies Reductions ...
  • Download the entire tutorial as a gzipped tar Created April 15, 2002

    44. Scheme Programming
    A practical lambdaCalculator A normal-order evaluator for the untyped lambda-calculus, extended with convenient commands and shortcuts to make programming
    previous next contents top
    Scheme Hash
    XML and Scheme
    Consistent or conformant Scheme implementations of W3C Recommendations: XML Infoset, XPath query language and a small subset of XSL Transformations. An XML document and operations on it can be expressed in Scheme and regarded either as data structures or as code.
    • Tools: SSAX, SXML, SXPath, SXSLT
      • A functional-style framework to parse XML documents
      • SXML specification
      • SXPath SXML query language, XPath implementation
      • SXML traversals and transformations
    • Applications, Examples, Sample Code
      • Authoring of web pages, XML documents and (PDF) papers
      • SXML as a higher-order, more expressive markup language
      • Writing LaTeX/PDF mathematical papers with SXML
      • Joint processing of two immutable SXML documents with update cursors
      • SXML as a normalized database
      • Literate XML/DTD programming
      • Complete examples of stream-wise (SAX) and DOM parsing with SSAX
      • parsing and unparsing of a namespace-rich XML document: DAML/RDF
      • Permissive parsing of perhaps invalid HTML
      • On parent pointers in SXML trees
      • XML pull parsing and SSAX
      • SSAX parsing with limited XML doctype validation and datatype conversion
      • Complete examples of practical (context-sensitive) SXML Transformations
    • SXML Papers and Presentations
    • CDATA #PCDATA , and ANY
    • Evaluating SXML
    • SOAP 1.2 and SXML

    45. FACT! - Multiparadigm Programming With C++ Glossary
    Later, the lambda calculus influenced the design of programming languages including Algol60 and 68 and Pascal (all of which allow procedures to be
    Glossary Algorithmic Skeletons

    Expression Templates

    Functor (Function Object)
    Turing Machine

    Algorithmic Skeletons The Skeletal Parallelism Homepage says: There are many definitions, but the gist of the idea is that useful patterns of parallel computation and interaction can be packaged up as second order constructs (i.e. parameterized by other pieces of code), perhaps presented without reference to explicit parallelism, perhaps not. Implementations and analyses can be shared between instances. Such constructs are skeletons', in that they have structure but lack detail. That's all. The rest is up for investigation and debate.
    Web material:
    Currying Turning an uncurried function into a curried function.
    Every functions with N arguments can be turned into a unary function (a function that takes a single argument) which returns another function with N-1 arguments.

    46. CS 152 Homework: Lambda Calculus
    There are three problems on implementing the lambda calculus and three problems on programming with Church numerals. For problems 13,
    CS152 Assignment: Lambda Calculus
    Due Tuesday, April 3, at 11:59PM.
    Setup and Instructions
    In your cs152 directory create a subdirectory called lambda . You will need to copy the files linterp.sml Lhelp.ui Lhelp.uo Makefile , and basis.lam from directory ~cs152/software/lambda Do all six problems below. There are three problems on implementing the lambda calculus and three problems on programming with Church numerals. For problems 1-3, modify the linterp.sml file. Put your answers for the Church numerals problems, 4-6, in a file called church.lam
    Introduction to the Lambda interpreter
    You will be working with a small, interactive interpreter for the lambda calculus. This section explains what syntax to use and how to interact with the interpreter.
    Concrete syntax
    All toplevel items in the lambda interpreter must be terminated with a semicolon. Comments are C++ style line comments, starting with the string and ending at the next newline. A toplevel item can be a term, a binding, or a use statement.
    A use statement loads a file into the interpreter as if it had been typed in directly. A

    47. Marino Miculan
    University of Udine Semantics of programming languages, formal verification of process/program properties, logical frameworks based on typed lambda-calculus.
    Marino Miculan
    Associate professor of Computer Science (INF/01) at the Faculty of Science of the University of Udine Address: Room SN3, Dipartimento di Matematica e Informatica
    - via delle Scienze, 206 - 33100 Udine - Italy.
    Phone: (+39)043255.8486, Fax: (+39)043255.8499, Skype: marinomiculan
    Email: miculan at dimi, uniud, it . (I endorse S/MIME; here is my X.509 certificate

    48. The Unlambda Programming Language
    Minimalistic functional language based on the lambda calculus but lacking the lambda operator. Tutorial, reference, GPLed interpreters available.
    The Unlambda Programming Language
    Unlambda: Your Functional Programming Language Nightmares Come True
    Table of contents
    • What's New in Unlambda World? Introduction
      What's New in Unlambda World?
      (If you don't know what Unlambda is, skip this section and move directly to the introduction below.) [2001/08] This page is being revised in preparation of the Unlambda 3 distribution.
      CyberTabloid Computer Languages Today The Hitch-Hacker's Guide to Programming
      What is Unlambda?
      Unlambda is a programming language. Nothing remarkable there. The originality of Unlambda is that it stands as the unexpected intersection of two marginal families of languages:
      • Obfuscated programming languages, of which the canonical representative is Intercal . This means that the language was deliberately built to make programming painful and difficult (i.e. fun and challenging). Functional programming languages, of which the canonical representative is Scheme (a Lisp dialect). This means that the basic object manipulated by the language (and indeed the

    49. Zena M. Ariola
    University of Oregon programming languages, formal semantics, term rewriting systems, lambda calculus, compilers.
    Zena M. Ariola, Professor Education BS, 1980, University of Pisa, Italy
    PhD, 1992, Harvard University Research Areas Programming Languages
    Term Rewriting Systems
  • Teaching Activities
  • Publications
    Zena M. Ariola UO Computer Science Homepage
  • 50. LCS Publication - MIT-LCS-TR-057
    Publication Title, lambda calculus MODELS OF programming LANGUAGES. Publication Author, Morris, J.H.. Additional Authors

    51. Perl Contains The Lambda-Calculus
    Unlike most popular programming languages, Perl is powerful enough to express the lambda calculus directly, without the need to write a simulator.
    Perl contains the -calculus
    -Calculus (pronounced `lambda calculus') is a model of computation invented by Alonzo Church in 1934. It's analogous to Turing machines, but it's both simpler and more practical. Where the Turing machine is something like a model of assembly language, the -calculus is a model of function application. Like Turing machines, it defines a simplified programming language that you can write real programs in. Writing Turing machine programs is like writing in assembly language, but writing -calculus programs is more like writing in a higher-level language, because it has functions. The two legal operations in the -calculus are to construct a function of one argument with a specified body, and to invoke one of these functions on an argument. What can be in the body of the function? Any legal expression, but expressions are limited to variables, function constructions, and function invocations. What can the argument be? It has to be another function; functions are all you have. With this tiny amount of machinery, we can construct a programming language that can express any computation that any other language can express. Unlike most popular programming languages, Perl is powerful enough to express the

    52. Lambda Calculus
    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
    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

    53. A Certified Type-Preserving Compiler From Lambda Calculus To Assembly Language |
    I present a certified compiler from simplytyped lambda calculus to assembly language . So for me the question is why don t we have certified programming
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    Lambda the Ultimate
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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

    54. Elements Of Programming Linguistics. Part I. The Lambda Calculus And Its Impleme
    The lambda calculus is used as an introduction to programming language concepts, particularly the concepts of functional programming.

    55. Simone Martini
    University of Bologna, Italy Type systems for programming languages, logic in computer science, lambda-calculus.
    home contact teaching publications ... Dipartimento di Scienze dell'Informazione Simone Martini Simone Martini Professor of Computer Science Simone Martini received the Laurea degree in Scienze dell'Informazione and the Dottorato di Ricerca in Informatica (Ph.D. in Computer Science) from He has been a visting scientist at the Systems Research Center of Digital Equipment Corporation, Palo Alto; at Stanford University ; at , Paris; at ; and at University of California at Santa Cruz He is a member of the Executive Boards of the European Association for Computer Science Logic ( EACSL ) and of the Associazione Italiana di Logica e Applicazioni ( AILA His research interests are in the logical foundations of programming languages. He has written papers in lambda-calculus, type theory, linear and resource logics. His is 3.

    56. CiteULike: Tag Lambda-calculus [72 Articles]
    posted to functionalprogramming lambda-calculus scheme by voigt on 2005-10-06 072200 as ** along with 5 people ryanc robennals pintman JeffreyPalmer
    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.
  • 57. Simply-typed Lambda Calculus - The Twelf Project
    The simplytyped lambda calculus is a common example of a simple typed programming language. This article discusses its encoding in Twelf.
    var skin = 'monobook';var stylepath = '/w/skins';
    Simply-typed lambda calculus
    From The Twelf Project
    Jump to: navigation search The simply-typed lambda calculus is a common example of a simple typed programming language. This article discusses its encoding in Twelf. If you're trying to learn Twelf from this example, you may wish to read the discussion starting in Representing the syntax of the STLC in the tutorial Proving metatheorems with Twelf . That introductory guide discusses this representation of the STLC and why it works in more detail. This page summarizes the judgements of the STLC and the corresponding LF code for reference, but does not explain them in detail.

    58. Encoding A Dependent-Type Lambda-Calculus In A Logic Programming Language
    Encoding A DependentType lambda-calculus In A Logic programming Language. AUTHOR(S) Amy Felty, INRIA Dale Miller, University of Pennsylvania

    what's this?
    Technical Reports (CIS) Browse this Collection CIS Collections Search CIS Website ... Submit a Paper TITLE:
    Encoding A Dependent-Type lambda-Calculus In A Logic Programming Language AUTHOR(S):
    Amy Felty,
    Dale Miller,
    University of Pennsylvania
    DOCUMENT TYPE: Technical Report Download the Document (PDF format - 504 K) - 01 March 1990
    Tell a colleague
    about it.
    University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-90-18. ABSTRACT:
    logical framework hereditary Harrop formulas with quantification at all non-predicate types, denoted here as hh , is such a meta-logic that has been implemented in both the Isabelle theorem prover and the λProlog logic programming language. Both frameworks provide for specifications of logics in which details involved with free and bound variable occurrences, substitutions, eigenvariables, and the scope of assumptions within object logics are handled correctly and elegantly at the "meta" level. In this paper, we show how LF can be encoded into hh in a direct and natural way by mapping the typing judgments in LF into propositions in the logic of hh . This translation establishes a very strong connection between these two languages: the order of quantification in an LF signature is exactly the order of a set of hh clauses, and the proofs in one system correspond directly to proofs in the other system. Relating these two languages makes it possible to provide implementations of proof checkers and theorem provers for logics specified in LF by using standard logic programming techniques which can be used to implement

    59. Jyte - Lambda Calculus Is At Least A Million Times Less Profound
    (Turing machines are basically being an idealized machine language, while lambda calculus is basically an idealized highlevel programming language.)

    60. Foundational Papers By Henk Barendregt
    lambda Calculi with Types Volume 362 kb Representing ``undefined in lambda calculus. J. Funct. programming 2, no. 3, 367374.
    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)

    61. Lambda Calculus
    See the file fanf.lambda for more examples of lambda calculus source. .. In the tradition of functional programming languages it assumes that memory is

    62. Mechanically Separated Meat » Blog Archive » The Ballad Of The Lambda Calculus
    Unfortunately the lambda calculus is completely alien to anything encountered virtual machines of certain socalled “functional programming” languages,

    63. IngentaConnect Equational Programming In Lambda-calculus Via SL-systems. Part 2
    Equational programming in lambda calculus via SL-systems. Part 2. Author Tronci E.1. Source Theoretical Computer Science, Volume 160, Number 1,
    var tcdacmd="dt";

    64. Programming: To Dissect A Mockingbird: A Graphical Notation For The Lambda Calcu
    To Dissect a Mockingbird A Graphical Notation for the lambda calculus with Animated Reduction (
    register submit help blog ... stats search remember me recover password login sort by other communities To Dissect a Mockingbird: A Graphical Notation for the Lambda Calculus with Animated Reduction ( 2 points posted 4 days ago by [deleted] 5 comments info comments related details you are viewing a single comment's thread jump to the above comments popeix (0 children) [+] popeix 1 point 3 days ago Perty. permalink feedback bookmarklets buttons ... User Agreement
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    65. Arithmetic In Lambda Calculus - Wolfram Demonstration Project
    For further details about the complete description of the operational semantics of the lambda calculus, see J. W. Gray, Mastering Mathematica programming
    Arithmetic in Lambda Calculus
    loadFlash(644, 387, 'ArithmeticInLambdaCalculus'); Lambda calculus was developed by Alonzo Church and Stephen Kleene in 1930 and consists of a single transformation rule (variable substitution) and a single function definition scheme. It is a system capable of universal computation, that is, any computable function that can be computed in any of the standard programming languages can also be done in lambda calculus, though it might be very hard to actually carry out. Only the basic arithmetic operations successor, testing for zero, addition, multiplication, and exponentiation are considered here. The second numeral is not used for successor or testing for zero.
    The central concept in λ calculus is the "expression". A "name" (or "variable") is an identifier that can be any letter. An expression is defined recursively as follows: In order to apply a function to an argument by substituting the argument for a variable in the body of the function and for giving a name to the function determined by a rule, it is necessary to define the following terms: 1) The identity function: (( 2) Self-application: . Applying this to any expression expr results in (expr expr), which may or may not make sense.

    66. Lambda Calculus
    The pure lambda calculus is applicable only to functional programming. A++ is built on ARS which stands for the basic operations of the lambdacalculus
    var topic_urlstring = 'lambda-calculus'; var topic = 'Lambda Calculus'; var subtopic_urlstring= '';
    LYCOS RETRIEVER Retriever Home What is Lycos Retriever? Lambda Calculus built 105 days ago Retriever Science Math Computational Logic
    The pure Lambda Calculus is applicable only to functional programming. A++ ... is built on ARS which stands for the basic operations of the Lambda-Calculus in a generalized form. Guy L. Steele, one of the fathers of the Scheme Programming Language, praises the beauty of ARS in his foreword to [SF93] on page XV and XVI. The following phrase puts everything to a point: Source: Knights of the Lambda Calculus /n./ A semi-mythical organization of wizardly LISP and Scheme hackers. The name refers to a mathematical formalism invented by Alonzo Church, with which LISP is intimately connected. There is no enrollment list and the criteria for induction are unclear, but one well-known LISPer has been known to give out buttons and, in general, the *members* know who they are.... Source:

    67. [quant-ph/9612052] Extending The Lambda Calculus To Express Randomized And Quant
    This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification of classical programming languages. quant-ph
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    Quantum Physics
    Title: Extending the Lambda Calculus to Express Randomized and Quantumized Algorithms
    Authors: Philip Maymin (Harvard University) (Submitted on 31 Dec 1996 (v1), last revised 9 Jan 1997 (this version, v2)) Abstract: This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification of classical programming languages. As an intermediary step, we introduce a formal metalanguage called the lambda-p calculus for the specification of programming languages that allow true random number generation. We demonstrate how selected randomized algorithms can be programmed directly in the lambda-p calculus. We also demonstrate how satisfiability can be solved in the lambda-q calculus. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:quant-ph/9612052v2
    Submission history
    From: Philip Maymin [ view email
    Tue, 31 Dec 1996 19:33:43 GMT (

    68. Searching Lambda Calculus
    mathematics, cryptography, functional programming, haskell, formal semantics, lambda calculus, category theory, graph theory, optimality theory, calculus
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    69. Rotten Cotton » Blog Archive » Bootstrapping From The Pure Lambda Calculus
    The lambda calculus serves as the conceptual foundation for a variety of modern functional programming languages including, but not limited to, Lisp,

    70. Lambda Calculus Introduction
    The typed lambda calculus incorporates types, so that a function application can only be made if the argument is the right type. programming languages based
    Lambda Calculus Introduction
    This page is adapted from The Lambda Calculus: Its Syntax and Semantics , by H. P. Barendregt, 1984, primarily sections 2.1, 3.1, 3.2, 6.1, and 6.2. Contents:
    Lambda Terms

    Beta Conversion

    Normal Forms

    Useful Combinators
    Further Reading
    Lambda Terms
  • Outermost parentheses may be omitted. x ...x n n MN N n )N n ) (association to the left) xx
  • An occurence of a variable x is bound free
    Beta Conversion
    M[x:=N]. We also say syntactic sugar Functions in lambda calculus take only one argument, but we can get the effect of multiple-argument functions:
    Normal Forms
    normal form Examples:
  • x is a normal form.
  • A term M has M , then M also has normal form N. However, this does not mean that any
    Useful Combinators
    A combinator I
    S I is the identity function, and K is the function of two arguments that ignores its second argument and returns its first. K can also be thought of as a function of one argument that returns a constant function: K It can be shown that any combinator can be generated from S and K using only function application. As an exercise, verify that I SKK Define truth values as follows: T
    F It may not be immediately obvious why these expressions should represent the truth values, but notice that

    71. Index-411
    The definitive text on the lambda calculus (the theory underlying functional programming) is written by Henk Barendregt there is now a revised edition of
    The purpose of the course is to explore various aspects of functional programming using Haskell. In particular, the course provides an introduction to the lambda calculus, basic type theory, and the role of these in the implementation of functional programming.
    Why is functional programming important ....
    • It promotes the view of programming as a mathematical activity.
      It promotes programming with abstractions (generic code). It is type safe .... the Hindley-Milner polymorphic type checker.
      It allows fast accurate prototyping for complex programs. It has datatypes and monads!
    COURSE OUTLINE: There will be a midterm exam and a final exam. The course will cover the following topics in roughly this order:
    • Introduction to data, maps, and folds in Haskell (3 lectures + assignment)
      Monads, classes, and other topics (3 lectures + assignment) Introduction to the lambda calculus (5 lectures) Introduction to rewriting theory (4 lectures + assignment) Type inference (5 lectures + assignment)
    LECTURE NOTES (as they become available)

    72. J Logic Computation -- Sign In Page
    (1968) lambdacalculus Models of programming Languages. PhD Thesis (Massachusetts Institute of Technology, Cambridge, MA, U.S.A). Newman MHA.
    @import "/resource/css/hw.css"; @import "/resource/css/logcom.css"; Skip Navigation Oxford Journals
    This item requires a subscription* to Journal of Logic and Computation Online. * Please note that articles prior to 1996 are not normally available via a current subscription. In order to view content before this time, access to the Oxford Journals digital archive is required. If you would like to purchase short-term access you must have a personal account. Please sign in below with your personal user name and password or register to obtain a user name and password for free.
    Full Text
    M. H. Newman's Typability Algorithm for Lambda-calculus
    Hindley J Logic Computation.
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    73. CS520: Programming Languages
    There is no programming in this course, but you will appreciate the value of the course Week 5 Simplytyped lambda calculus context-sensitive syntax,
    CS520: Programming Languages
    Fall 2001
    • Instructor: Santiago Pericas-Geertsen Meeting Place: MCS B31 Meeting Time: MWF 10:00-11:00 am Office Hours: WF 11:00-12:00 pm Prerequisites: (CS305 or CS332) and CS320 Overview:
      The course covers the mathematical and formal foundations of modern programming languages. Topics include: syntax and semantics of three paradigm languages, one functional (PCF), one object oriented and one foundational (the lambda calculus); the operational, axiomatic and denotational semantics of programming languages; program verification; topics in the typed and untyped lambda-calculus; topics in type theory (type inference, subtyping, polymorphism). Material presented in class, or assigned for independent reading, will be mostly from the textbook and occasionally from handouts. There is no programming in this course, but you will appreciate the value of the course in proportion to your programming experience and familiarity with different programming paradigms. If you have never programmed before, the material will come across as dry and formal, with little or no practical motivation for it. And I venture to say that the better programmer you are, the easier the course will be for you. Grading:
      • Homework assignments, about 40% of final grade

    74. Powell's Books - Programming Language Pragmatics By
    x Provides an accessible introduction to the formal foundations of compilation (automata theory), functional programming (lambda calculus),

    75. A Lambda Calculus For Quantum Computation
    which develop a linear lambda calculus for expressing quantum algorithms. The code below implements the examples in the first one of these two papers.
    A lambda calculus for quantum computation
    Scheme simulator
    This page provides a simulator for a functional language based on Scheme for expressing and simulating quantum algorithms. Example code implementing some simple quantum algorithms is provided. For the theory, see my papers which develop a linear lambda calculus for expressing quantum algorithms. The code below implements the examples in the first one of these two papers.
    The code should work in any Scheme adhering to the R5RS standard. It has been tested in PLT's DrScheme and Petite Chez Scheme, both of which are freely available. Instructions are as follows for DrScheme:
    • Install DrScheme . When asked during installation, choose the "Pretty Big" language level. Save the two files wherever you like, but they should be in the same directory. Launch DrScheme, load the file quantum.scm, and click on the "execute" button to run the algorithms.
    Simple gate combinations
    First let's apply a few Hadamard gates in sequence to a single qubit. The QEVAL performs the sum over histories:

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