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1. 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, http://en.wikipedia.org/wiki/Lambda_calculus

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; 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

2. Lambda Calculus An online introduction to the lambda calculus by Lloyd Allison, complete with a web form that will evaluate lambda expressions. http://www.csse.monash.edu.au/~lloyd/tildeFP/Lambda/

var REMOTE_HOST="12.68.1243.static.theplanet.com", REMOTE_ADDR="67.18.104.18"; Lambda Calculus (interpreters) LA home FP Lambda Syntax Introduction Also see: Prolog Semantics There are lazy and strict versions of the toy lambda-calculus interpreter. They both share the same input syntax and can be used on the same example lambda-calculus programs, although some programs will not work (i.e. will loop) when using the strict interpreter of course. Introduction to the Lambda-calculus local Syntax - quick guide Lambda-calculus example programs Lazy Interpreter Strict Interpreter main programs Lazy.p Strict.p declarations define values lazy.type.P interpreters proper lazy.exec.P strict.exec.P output lazy.show.P (evaluation is print driven) strict.show.P expressions lazy.eval.p (by-need evaluation) strict.eval.P (strict evaluation) apply functions lazy.apply.P strict.apply.P process declarations lazy.D.P strict.D.P binary operators lazy.O.P unary operators lazy.U.P strict.U.P manipulate environments lazy.env.P strict.env.P form basic values lazy.mkval.P

3. Lambda Calculus Introduction lambda calculus provides the basis for Functional Programming languages. http://www.csse.monash.edu.au/~lloyd/tildeFP/Lambda/Ch/

var REMOTE_HOST="12.68.1243.static.theplanet.com", REMOTE_ADDR="67.18.104.18"; Lambda Calculus LA home FP Lambda (code) Syntax Introduction Also see: PFL Prolog intro Semantics Introduction ... A Functional Programming Language Programming Techniques: Programming Techniques - Recursion Programming Techniques - Circular Programs Programming Techniques - Sieve 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 http://www.allisons.org/ll/ or as otherwise indicated Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering

4. An Introduction To Lambda Calculus And Scheme The Lambdacalculus is a universal model of computation, that is, any computation that can be expressed in a Turing machine can also be expressed in the http://www.jetcafe.org/jim/lambda.html

$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:

5. Page Of Yves Lafont University of Marseille II Linear logic, lambda calculus, proof theory, term rewriting. Lafont invented the theory of interaction nets, an elegant theory of graph rewriting. http://iml.univ-mrs.fr/~lafont/welcome.html

photo by M. Arovas Yves LAFONT professor at Aix-Marseille 2 research at teaching at organizer of Logique et interactions address: office: - phone: - fax: - e-mail: lafont@iml.univ-mrs.fr Discipline mathematics Specialities logic algebra theoretical computer science Papers Recent papers: A folk model structure on omega-cat (with and Krzysztof Worytkiewicz Polygraphic resolutions and homology of monoids pdf ] (with Algebra and geometry of rewriting pdf ] (published in Applied Categorical Structures Other documents: The word problem pdf Homotopy of computation: The Minneapolis Program pdf ] - see also: The folk model structure for omega-categories pdf ] (by Krzysztof Worytkiewicz PhD students: Anne Massol Arnaud Fleury Virgile Mogbil Tom Krantz Sylvain Lippi Pierre Rannou (since 2007) Recent collaborators: Albert Burroni Patrick Dehornoy Yves Guiraud Krzysztof Worytkiewicz Research projects: ANR GDR Meetings: CIRM , 31 March - 4 April 2008) Teaching - Scientific popularization - Various links: see the french version of my home page

6. Lambda Calculus That’s almost a good definition, however, due to the extreme thriftiness of lcalculus, we must impose an even more draconian restriction every LISP lambda http://www.mactech.com/articles/mactech/Vol.07/07.05/LambdaCalculus/

MacTech Network: MacForge.net Computer Memory Register Domains ... Mac Book Shelf The journal of Macintosh technology Magazine In Print About MacTech Home Page Subscribe MacTech CD ... Get a copy of MacTech RISK FREE Entire Web mactech.com Mac Community More... MacTech Central by Category by Company by Product MacTech News MacTech News Previous News MacTech RSS Article Archives Show Indices by Volume by Author Source Code FTP Inside MacTech Writer's Kit Editorial Staff Editorial Calendar Back Issues ... Advertising Contact Us Customer Service MacTech Store Webmaster Feedback ADVERTISEMENT Volume Number: Issue Number: Column Tag: Lisp Listener Lambda Calculus Abe Lincoln Introduction 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:

7. 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 http://users.comlab.ox.ac.uk/luke.ong/teaching/lambda/

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

8. Zena M. Ariola University of Oregon Programming languages, formal semantics, term rewriting systems, lambda calculus, compilers. http://www.cs.uoregon.edu/~ariola/

Zena M. Ariola, Professor Education BS, 1980, University of Pisa, Italy PhD, 1992, Harvard University Research Areas Programming Languages Term Rewriting Systems lambda-calculus logic Teaching Activities Publications Zena M. Ariola UO Computer Science Homepage

9. Good Math Has Moved To Lamda Calculus (Index). My Favorite Calculus Lambda (part 1) The Genius of Alonzo Church Finally, Modeling lambda calculus Programs are Pr.. http://goodmath.blogspot.com/2006/06/lamda-calculus-index.html

ScienceBlogs : Lamda Calculus (Index) @import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=23588438"); var BL_backlinkURL = "http://www.blogger.com/dyn-js/backlink_count.js";var BL_blogId = "23588438"; Good Math has moved to ScienceBlogs Saturday, June 03, 2006 Lamda Calculus (Index) My Favorite Calculus: Lambda (part 1) The Genius of Alonzo Church: Numbers in Lambda Calculus Booleans and Choice in Lambda Calculus Why oh why Y? ... Finally, Modeling Lambda Calculus: Programs are Proofs! posted by MarkCC at 3:23 PM 0 Comments: Post a Comment Links to this post: See links to this post posted by Create a Link < Home About Finding the fun in good math; Shredding bad math and squashing the crackpots who espouse it. About Me Name: MarkCC View my complete profile Previous Reader poll about topics; and some site maintenanc... Astoundingly Stupid Math: the Bullshit of Homeland... Finally, Modeling Lambda Calculus: Programs are Pr... Friday Random Ten, 6/2 ... PEAR yet again: the theory behind paranormal gibbe... RSS

10. 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. http://www.cs.williams.edu/~kim/

Kim B. Bruce Frederick Latimer Wells Professor of CS, emeritus Department of Computer Science Williams College kim@cs.williams.edu 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 Vita 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

11. To Dissect A Mockingbird: A Graphical Notation For The Lambda Calculus With Anim The lambda calculus, and the closely related theory of combinators, The lambda calculus is based on the more abstract notion of applying a function . http://users.bigpond.net.au/d.keenan/Lambda/index.htm

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 http://users.bigpond.net.au/d.keenan 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.

12. Lambda Calculus And A++: Basic Concepts lambda calculus and A++ Basic Concepts of Lambda Expressions, Lambda Conversions and the Programming Language A++. http://www.lambda-bound.com/book/lambdacalc/

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 Introduction 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 [

13. 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. http://www.dimi.uniud.it/~honsell/

14. Lambda Calculus Reduction Workbench This system implements and visualizes various reduction strategies for the pure untyped lambda calculus. It is intended as a pedagogical tool, http://www.itu.dk/people/sestoft/lamreduce/index.html

Lambda calculus reduction workbench This system implements and visualizes various reduction strategies for the pure untyped lambda calculus. It is intended as a pedagogical tool, and as an experiment in the programming of visual user interfaces using Standard ML and HTML. Start the lambda calculus reducer Here is the implementation source code as a gzipped tar file. There is an old draft report describing the implementation, in Postscript (77 KB) and PDF (645 KB). Syntax Syntactically, a variable is a sequence of letters, digits and underscores, starting with a letter. Variables which stand for abbreviations are displayed with a leading dollar sign `$'. Parentheses may be left out; they are reinserted as follows: Bindings introduce abbreviations for lambda expressions, which must be closed, except for previously defined abbreviations. This example illustrates the use of abbreviations: In fact, there are several predefined abbreviations . The lambda reducer will display the predefined abbreviations if you choose `print abbreviations' and click on `Do it'. Reduction strategies and tracers The following reduction strategies are implemented: call-by-name head spine reduction normal order call-by-value applicative order hybrid reduction The following reduction tracers are available: normalize the expression, and count the number of beta reductions

15. Luke Ong's Home Page Merton College, Oxford Semantics of programming languages, lambda calculus, categorical logic and type theory, game semantics, linear logic. http://web.comlab.ox.ac.uk/oucl/work/luke.ong/

Luke Ong's new OUCL web page oucl work luke.ong Updated April 2004 Home Search SiteMap Feedback ... News

16. Lambda Calculus And Lambda Calculators Several lambdacalculators and many applications of lambda calculus. http://okmij.org/ftp/Computation/lambda-calc.html

previous next contents top Lambda Calculus and Lambda Calculators Negative numbers, subtraction and division in lambda-calculus Basic Lambda Calculus terms Numerals and lists in lambda-calculus: P-numerals The bluff combinator ... Predecessor and lists are not representable in simply typed lambda-calculus Lambda-calculators In Haskell In Scheme As a CPS R5RS Scheme macro As a short, direct-style R5RS Scheme macro 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.

17. Perl Contains The Lambda-Calculus Lambda Calculus (pronounced `lambda calculus ) is a model of computation invented by Alonzo Church in 1934. It s analogous to Turing machines, http://perl.plover.com/lambda/

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

18. Lemon Functional language with inductive and coinductive types. Based on simplytyped lambda calculus augmented with sums, products, and mu and nu constructors for least (inductive) and greatest (coinductive) solutions to recursive type equations. http://www.cis.ksu.edu/~bhoward/lemon.html

Lemon A Functional Language with Inductive and Coinductive Types The functional language lemon is based on the simply-typed lambda calculus augmented with sums, products, and the mu and nu constructors for least ( inductive ) and greatest ( coinductive ) solutions to recursive type equations. The term constructors of the language strictly follow the introduction and elimination rules for the corresponding types; in particular, the elimination for mu is iteration and the introduction for nu is coiteration (also called generation ). It includes a small amount of polymorphism and type inference; lambda-bound variables do not need type annotations, but iteration and coiteration need to have their corresponding recursive types specified (this is a problem with the language rather than the implementation). For example, the following program generates the stream of Fibonacci numbers starting with 1,1: Using iteration we may define a function which picks off the first n elements of a stream and returns them as a list: We may combine these terms as follows (currently there is syntactic sugar for natural numbers but not for lists; formatting inserted by hand for clarity):

19. The Unlambda Programming Language Minimalistic functional language based on the lambda calculus but lacking the Lambda operator. Tutorial, reference, GPLed interpreters available. http://www.madore.org/~david/programs/unlambda/

The Unlambda Programming Language Unlambda: Your Functional Programming Language Nightmares Come True Table of contents What's New in Unlambda World? Introduction What is Unlambda? What does Unlambda look like? ... Unlambda distribution (download Unlambda here) Comprehensive Unlambda Archive Network 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. Introduction 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

20. Knights Of The Lambda Calculus Knights of the lambda calculus n. A semimythical organization of wizardly LISP and Scheme hackers. The name refers to a mathematical formalism invented by http://catb.org/jargon/html/K/Knights-of-the-Lambda-Calculus.html

Knights of the Lambda Calculus Prev K Next 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.... Prev Up Next kluge up  Home  knobs

21. 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. http://brunocarle.free.fr

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

22. Lambda Calculus -- From Wolfram MathWorld In the lambda calculus, lambda is defined as the abstraction operator. To H. B. Curry Essays on Combinatory Logic, lambda calculus and Formalism. http://mathworld.wolfram.com/LambdaCalculus.html

Search Site Algebra Applied Mathematics Calculus and Analysis ... General Logic Lambda Calculus A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. In the lambda calculus, is defined as the abstraction operator . Three theorems of lambda calculus are -conversion, -conversion, and -conversion. Lambda-reduction (also called lambda conversion) refers to all three. SEE ALSO: Abstraction Operator Combinator Combinatory Logic Computable Number ... [Pages Linking Here] REFERENCES: Barendregt, H. P. The Lambda Calculus. Amsterdam, Netherlands: North-Holland, 1981. Hankin, C. Lambda Calculi: A Guide for Computer Scientists. Oxford, England: Oxford University Press, 1995. Hindley, J. R. and Seldin, J. P. Introduction to Combinators and -Calculus. Cambridge, England: Cambridge University Press, 1986. Penrose, R. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford, England: Oxford University Press, pp. 66-70, 1989. Lambda-Calculus, Combinators, and Functional Programming. Cambridge, England: Cambridge University Press, 1988. Seldin, J. P. and Hindley, J. R. (Eds.).

23. 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. http://www.cs.vu.nl/

Informatica home 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!

24. John's Combinatory Logic Playground Pictured above you can see on the left the 210 bit binary lambda calculus selfinterpreter, and on the right the 272 bit binary combinatory logic http://www.cwi.nl/~tromp/cl/cl.html

John's Lambda Calculus and Combinatory Logic Playground Pictured above you can see on the left the 210 bit binary lambda calculus self-interpreter, and on the right the 272 bit binary combinatory logic self-interpreter Both are explained in detail in my latest paper available in PostScript and PDF . This design of a minimalistic universal computer was motivated by my desire to come up with a concrete definition of Kolmogorov Complexity , which studies randomness of individual objects. All ideas in the paper have been implemented in the the wonderfully elegant Haskell language, which is basically pure typed lambda calculus with lots of syntactic sugar on top. The implementation also offers a Main module that lets you run the universal binary lambda computer on the command-line argument joined to standard input as a list of bytes: main = do [program] The first example is the half-byte program for identity=^x.x, while the second is the ten-and-a-half-byte program for stutter=^l l(^h^t^n^z z h (^z z h (stutter t)))nil. This online course at Oberlin College provides a very readable introduction to combinators.

25. Better Scheme Language designed and largely implemented, now a matter of coding, documenting. Goals high consistency; improve language's functional nature; consistency with lambda calculus; optimize, but not at cost of other goals. http://www.cs.oberlin.edu/~jwalker/bscheme/

Better Scheme A Jeffery Walker Programming Language Project Status: The language is designed and largely implemented, now it is a matter of coding and documenting. A New Vision for Better Scheme Be highly consistent Improve the language's functional nature Consistency with the lambda calculus ... Better Scheme Specification Design: Rationale Problems Reference Implementation References ... jwalker@cs.oberlin.edu

26. Peter Selinger Papers Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional A lambda calculus for quantum computation with classical control http://www.mscs.dal.ca/~selinger/papers.html

Papers This is a list of Peter Selinger 's papers, along with abstracts and hyperlinks. Linear-non-linear model for a computational call-by-value lambda calculus (with B. Valiron Idempotents in dagger categories On a fully abstract model for a quantum linear functional language (with B. Valiron Tree checking for sparse complexes (with M. Caboara and S. Faridi Simplicial cycles and the computation of simplicial trees (with M. Caboara and S. Faridi A lambda calculus for quantum computation with classical control (with B. Valiron Dagger compact closed categories and completely positive maps Towards a semantics for higher-order quantum computation A brief survey of quantum programming languages ... has nonempty products See also: Proceedings of QPL 2006 (editor). Proceedings of QPL 2005 (editor). Proceedings of QPL 2004 (editor). Proceedings of CTCS 2002 (editor, with R. Blute). My compiler for the core join calculus My finite lambda model applet My compiler for the lambda-mu-nu calculus 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

27. Alligator Eggs! This game represents the untyped lambda calculus. A hungry alligator is a lambda abstraction, an old alligator is parentheses, and eggs are variables. http://worrydream.com/AlligatorEggs/

Alligator Eggs! A puzzle game by Bret Victor / May 1, 2007 Japanese translation Materials Step 1 : Print out this PDF onto six or so different colored sheets of paper (Even better, photocopy it onto cardstock.) Step 2 : Print out this PDF onto a couple white sheets of paper. Step 3 : Cut out the pieces! Pieces These are hungry alligators Hungry alligators are hungry . They'll eat anything that's in front of them! But they are also responsible alligators, so they guard their families. These are old alligators Old alligators are not hungry. They've eaten enough. All they do is guard their families. These are eggs Eggs hatch into new families of alligators! Families Here's a small family: A green alligator is guarding her green egg. Here's a slightly bigger family: A green alligator and red alligator are guarding a green egg and a red egg. Or, you could say that the green alligator is guarding the red alligator, and the red alligator is guarding the eggs. Here's a huge family! We've got yellow, green, red alligators guarding this family. They are guarding three things: a green egg, an old alligator, and a red egg. The old alligator is guarding a yellow egg and a green egg. Notice that eggs only use the colors of the alligators guarding them. You can't have a blue egg without there being a blue alligator around to guard it.

28. Luke Ong Merton College, Oxford Categorical logic, game semantics, type theory, lambda calculus, semantics of programming languages, and sequentiality. http://web.comlab.ox.ac.uk/oucl/people/luke.ong.html

Luke Ong Professor of Computer Science Tutorial Fellow in Computation, Merton College Address Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford, OX1 3QD, England. Telephone Direct: +44 (0)1865 283522 Department: +44 (0)1865 273838 Fax: +44 (0)1865 273839 EMail Luke.Ong@comlab.ox.ac.uk WWW 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

29. » Simple Lambda Calculus In Prolog - Ha4 Haskell, Hacking Below I take one of the possible directions to solve this embed a lambda calculus interpreter in Prolog. Look at this common paradigm http://ha4.fajno.net/2007/12/14/simple-lambda-calculus-in-prolog/

30. Stochastic Lambda Calculus And Monads Of Probability Distributions (Abstract) Probability distributions form a monad, and the monadic definition leads to a simple, natural semantics for a stochastic lambda calculus, as well as simple, http://www.eecs.harvard.edu/~nr/pubs/pmonad-abstract.html

Stochastic Lambda Calculus and Monads of Probability Distributions Norman Ramsey and Avi Pfeffer Probability distributions are useful for expressing the meanings of probabilistic languages, which support formal modeling of and reasoning about uncertainty. Probability distributions form a monad, and the monadic definition leads to a simple, natural semantics for a stochastic lambda calculus, as well as simple, clean implementations of common queries. But the monadic implementation of the expectation query can be much less efficient than current best practices in probabilistic modeling. We therefore present a language of measure terms , which can not only denote discrete probability distributions but can also support the best known modeling techniques. We give a translation of stochastic lambda calculus into measure terms. Whether one translates into the probability monad or into measure terms, the results of the translations denote the same probability distribution. Full paper The paper is available as US Letter PostScript US Letter PDF (289K-may be flaky), and

31. Présentation De Laurent Regnier University of Marseilles Linear logic, lambda calculus and abstract machine interpretations. http://iml.univ-mrs.fr/~regnier/

Laurent Regnier Téléphone : bureau +33 4 91 26 96 42 fax +33 4 91 26 96 55 Adresse électronique : regnier à iml point univ-mrs point fr Publications Enseignements (notes de cours, exos, etc.). Responsabilités Professeur à l' Université de la Méditerranée , enseignant au département de mathématiques de la faculté des sciences de Luminy Chercheur à l' Institut de Mathématiques de Luminy , responsable de l'équipe Logique De la Programmation Responsable de la spécialité recherche Mathématiques Discrètes et Fondements de l'Informatique du master Mathématiques et Applications des universités d'Aix-Marseille ; Responsable du groupe de travail Géométrie du calcul au sein du GDR Informatique Mathématique

32. [quant-ph/0307150] A Lambda Calculus For Quantum Computation Abstract The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. http://arxiv.org/abs/quant-ph/0307150

arXiv.org quant-ph Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PostScript PDF Other formats Citations SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted) CiteBase 2 trackbacks p revious ... ext Quantum Physics Title: A Lambda Calculus for Quantum Computation Authors: Andre van Tonder (Submitted on 21 Jul 2003 ( ), last revised 3 Apr 2004 (this version, v5)) Abstract: The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lambda calculus suitable for expressing and reasoning about quantum algorithms. In this paper we develop a quantum lambda calculus as an alternative model of quantum computation, which combines some of the benefits of both the quantum Turing machine and the quantum circuit models. The calculus turns out to be closely related to the linear lambda calculi used in the study of Linear Logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine. Comments: To appear in SIAM Journal on Computing. Minor corrections and improvements. Simulator available at

33. Mathematical Sciences, Richard Statman Carnegie Mellon University Theory of computation, lambda calculus, combinatory logic. http://www.math.cmu.edu/people/fac/statman.html

Faculty Visiting Faculty Staff Graduate Students ... Home Richard Statman Professor Ph.D., Stanford University Office: Wean Hall 7214 Phone: (412) 268-8475 E-mail: statman@cs.cmu.edu Research My principal research interests lie in the theory of computation with special emphasis on symbolic computation. In particular, my current research involves lambda calculus and combinatory algebra. This area underwent extensive development in the first half of this century, and then lay dormant until Dana Scott's fundamental work in the 1970's. Part of what has emerged from Scott's work is that lambda calculus forms the foundation of functional programming at both the semantic and syntactic levels. As a result, the area has been revived by an influx of theoretical problems directly related to design and implementation issues. Selected Publications The omega rule is sigma-zero-three hard (with Benedetto Intrigilia), LICS'04 On the lambda Y calculus, LICS '02 Church's lambda delta calculus, LPR '00 The word problem for combinators, RTA '00

34. 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. http://twelf.plparty.org/wiki/Simply-typed_lambda_calculus

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. Contents What is illustrated by this example? Encoding of syntax Encoding of judgments Static semantics ... edit What is illustrated by this example? There are simpler examples of LF representations (see, e.g., the natural numbers ). However, the STLC is a good first example of a representation that uses higher-order abstract syntax and higher-order judgments . These two representation techniques drastically simplify the process of representing and proving theorems about many programming languages and logics. The idea is that the binding structure of LF is used to represent the binding structure of the object language. At the level of syntax, this gives alpha-equivalence and capture-avoiding substitution "for free" from the representation. At the level of judgements, this gives the properties of a

35. Stewart, Charles Technische Universit¤t Berlin, Theory and Formal Specifications group Proof theoretic semantics, lambda calculus, linear logic, theoretical computer science, philosophy of language. http://www.linearity.org/cas/

36. Notes On Simply Typed Lambda Calculus These notes provide an introduction to lambdacalculi, specifically the simply typed lambda calculus. The first half of the notes gives a fairly thorough http://www.lfcs.inf.ed.ac.uk/reports/98/ECS-LFCS-98-381/

People Events Research Home Notes on Simply Typed Lambda Calculus Ralph Loader Abstract: These notes provide an introduction to lambda-calculi, specifically the simply typed lambda calculus. The first half of the notes gives a fairly thorough introduction to fairly traditional and fundamental results about lambda-calculi. The second half gives a detailed, quantitative analysis of the simply typed lambda calculus. ECS-LFCS-98-381 This report is available in the following formats: PDF file Gzipped PDF file PostScript file Gzipped PostScript file ... Next Unless explicitly stated otherwise all material Comments and corrections to: LFCS Webmaster Last modified: Friday 5 May 2006

37. From Lambda To Language But it does show how the language machine relates to the lambda calculus and to The lambda calculus, as is very well known, is a deceptively simple http://languagemachine.sourceforge.net/lambda.html

Gnu FDL - code license Gnu GPL validate HTML from lambda to language introduction This experiment shows that the language machine can operate directly as an evaluator for the lambda calculus . This is of course an academic exercise. As can be seen in the discussion below on the representation of data, the language machine has its own way of doing things. But it does show how the language machine relates to the lambda calculus and to functional languages in general, and that it is in effect a machine for computation and grammar. In particular it shows that rules which implement functional evaluation are a subset of the rules that can usefully be applied by the language machine the lambda calculus The lambda calculus , as is very well known, is a deceptively simple system that is Turing-complete , theoretically capable of computing whatever can be computed. It is not the simplest complete system (see here and here ), but the others are directly related to it, and some are deliberately designed to hurt the contents of your head . The calculus itself is very completely described in the articles linked to above. The notation used here adopts lexical conventions similar to those used in the lmn metalanguage - units of compilation are terminated by a semi-colon, lines of source text are preceded by at least one space, and any other material is treated as comment that may contain markup in a subset of the mediawiki format. The main lambda source files considered in this experiment are

38. Homepage Henk Barendregt Radboud University Nijmegen lambda calculus, type theory and formalising mathematical vernacular. http://www.cs.ru.nl/~henk/

Henk Barendregt Chair Foundations of Mathematics and Computer Science Radboud University, Nijmegen The Netherlands Picture by Amber Beckers (July 2005) Henk Barendregt (1947) holds the chair of Foundations of Mathematics and Computer Science at Nijmegen University, The Netherlands, and is adjunkt professor at Carnegie Mellon University, Pittsburgh Pennsylvania, USA. He studied at Utrecht University mathematical logic, obtaining under his Masters in 1968 and his Ph.D. in 1971, both cum laude and Since 1986 he is professor at Nijmegen University, where he and his group work on Formal Mathematics , a technology based on the idea of AUTOmated verification of MATHematics program of N. G. de Bruijn. For a list of results see the list of Freek Weedijk. Awards Barendregt was elected member of the Academia Europaea Koninklijke Hollandsche Maatschappij der Wetenschappen (1995) and the Royal Dutch Academy of Sciences (1997). In 1998 he obtained a generous seven year grant of the Board of Directors of Nijmegen university. In 2002 he was knighted in the Orde van de Nederlandse Leeuw . Barendregt obtained on February 6, 2003 the NWO Spinoza Award 2002, the highest scientific award in the Netherlands.

39. Church This module allows simple experimentation with the lambda calculus, first developed by Church. It understands the different types of lambda expressions, http://www.alcyone.com/pyos/church/

Table of Contents church Summary This module allows simple experimentation with the lambda calculus, first developed by Church. It understands the different types of lambda expressions, can extract lists of variables (both free and bound) and subterms, and can simplify complicated by expression by means of application. Getting the software The software is available in a tarball here: http://www.alcyone.com/pyos/church/church-latest.tar.gz The official URL for this Web site is http://www.alcyone.com/pyos/church/ Notation Notations for lambda expressions vary slightly, so it is instructive to detail the precise notation used by this module. A variable is expressed with a string of alphanumeric characters, e.g. x or . There are three types of lambda expressions: variable expression A variable expression is simply an expression consisting of a single variable, e.g. x lambda expression where x is a variable and M is an expression. Repeated variables are equivalent to recursed lambda expressions, so is equivalent to application expression An application expression consists of two or more adjacent expressions surrounded by parentheses: (M N) , where M and N are expressions. Applications are left associative, so

40. LtU Classic Archives lambda calculus. Shows how to reduce a subset of Scheme to LC. If you know a little Lisp/Scheme, and ever wondered what (lambda (x) (x x)) might be good for http://lambda-the-ultimate.org/classic/message10113.html

Lambda the Ultimate Lambda Calculus started 11/27/2003; 9:02:07 AM - last post 11/28/2003; 3:51:20 AM Manuel Simoni - Lambda Calculus 11/27/2003; 9:02:07 AM (reads: 10678, responses: 3) Lambda Calculus Shows how to reduce a subset of Scheme to LC. If you know a little Lisp/Scheme, and ever wondered what (lambda (x) (x x)) might be good for, this is for you. From Shiram Krishnamurti's lecture notes Posted to functional by Manuel Simoni on 11/27/03; 9:03:48 AM Manuel Simoni - Re: Lambda Calculus 11/27/2003; 9:12:34 AM (reads: 441, responses: 0) Should be Shriram Krishnamurthi, sorry. Andris Birkmanis - Re: Lambda Calculus 11/28/2003; 3:37:38 AM (reads: 312, responses: 1) Is lazy evaluation covered in some other note? Or the note just assumes we started from the lazy Scheme in the first place? Ehud Lamm - Re: Lambda Calculus 11/28/2003; 3:51:20 AM (reads: 316, responses: 0) I haven't looked at these notes yet, but when I present a similar thing (Scheme -> LC) in my course, I repeatedly mention this fact, especially when I discuss normal order evaluation and again when I present applicative order evaluation. I also conclude by mentioning that the substitution model breaks down in the presence of assignment.

41. A Certified Type-Preserving Compiler From Lambda Calculus To Assembly Language I present a certified compiler from simplytyped lambda calculus to assembly language. The compiler is certified in the sense that it comes with a http://www.cs.berkeley.edu/~adamc/papers/CtpcPLDI07/

A Certified Type-Preserving Compiler from Lambda Calculus to Assembly Language Adam Chlipala . A Certified Type-Preserving Compiler from Lambda Calculus to Assembly Language. Proceedings of ACM SIGPLAN 2007 Conference on Programming Language Design and Implementation (PLDI'07) . June 2007. 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 my PLDI talk in OpenOffice and PDF formats.

42. The Lambda Calculus - Elsevier The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. http://www.elsevier.com/wps/product/cws_home/501727

43. PlanetMath: Lambda Calculus In pure lambda calculus, there are no constants. Instead, there are only lambda abstractions (which are simply specifications of functions), variables, http://planetmath.org/encyclopedia/LambdaCalculus.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About lambda calculus (Definition) Lambda calculus (often referred to as -calculus) was invented in the 1930s by Alonzo Church, as a form of mathematical logic dealing primarly with functions and the application of functions to their arguments . In pure lambda calculus , there are no constants . Instead, there are only lambda abstractions (which are simply specifications of functions), variables , and applications of functions to functions. For instance, Church integers are used as a substitute for actual constants representing integers A lambda abstraction is typically specified using a lambda expression , which might look like the following. The above specifies a function of one argument, that can be reduced by applying the function to its argument (function application is left-associative by default, and parentheses can be used to specify

44. Lambda Calculus But you do not need to know lambda calculus to be impressed by this program! See the file fanf.lambda for more examples of lambda calculus source. http://www.ioccc.org/1998/fanf.hint

45. Into The Wibble [lambda-calculus] This page is all about my lambda computer a program that computes in the lambda calculus. For fun, I also did a Turing machine in lambda calculus (fairly http://frmb.org/lambda.html

Fred's Home Page Main About me csh is bad Debian ... XHPD Lambda calculus intro basic lists recursion ... download This page is all about my lambda computer a program that computes in the lambda calculus. For fun, I also did a Turing machine in lambda calculus (fairly trivial representation). Introduction The lambda calculus is basically function theory, there are only three things available in the pure lambda calculus, these are: Variables a the variable a Applications (a b) a applied to b Abstractions function e with argument x Dispite not being very much here, the expressive power is quite suprising. Using these three simple things, numbers, lists, recursion and much more can be defined. This page is not intended to be an introduction to the lambda calculus; there are lots of good books for that. One excellent one is Barendregt's "The Lambda Calculus : its syntax and semantics". ISBN: 0444875085 (paper-back) and 0444867481 (hard-back). It's rather mathematically extreme though... Acknowledgement: Most of the terms here are from the CO611 (types and computation) course at Kent Uni, kindly taught by Stefan Kahrs and Simon Thompson. The type-theory computing program may happen at some point too.. Here is a picture of the program running.

46. Notes: Lambda Calculus lambda calculus as a basis for functional programming languages More Lambda notes lambda calculus is a formal model of computation. Others include http://www.cs.unc.edu/~stotts/723/Lambda/

Lambda Calculus Lambda Calculus Interpreter Fun to try after you learn the basics of the syntax Notes Lambda Calculus Let's examine some of the theoretical foundations of computation, specifically functional computation. You may wish to read early parts of this paper: Cardelli and Wegner, "On Understanding Types, Data Abstraction, and Polymorphism" Notes we will refer to Encoding Lambda calculus in ML Boolean values and operators ML code: booleans Church numerals ... And More Lambda notes Lambda calculus is a formal model of computation. Others include Turing Machine Post production system (phrase-structure, unrestricted, type-0 grammars) Graph/Net models Petri-nets with inhibitor arcs predicate/transition nets debit-nets under forced anihilation Relational model (resolution/unification, Prolog basis) Theory of recursive functions Basics: variables are lambda-expressions (lexp) lambda abstractions (function definitions) are lexp function applications are lexp For example: variables: a, x, foo, bar lambda abstraction: lambda x 2*x function application: ( (lambda x 2*x) 5 ) specifies value 10 Syntax examples for lambda-expressions x a single variable lambda x x a function abstraction with one argument (x) and the body "x" (x y) function application where function lexp "x" is applied to arg lexp "y" (lambda x x y) function "lambda x x" applied to "y" lambda x (x y) function abstraction with one variable "x" and body "(x y)" which is a function application

47. Lambda Calculus Implementatie Untyped lambda calculus. *) (* *) (* Freek Wiedijk, University of Nijmegen .. lambda.ml ;; *) (* val id a a = fun *) (* val ( ** ) ( a - b) http://www.cs.ru.nl/~freek/notes/lambda.ml

*) (* val ( ** ) : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = *) (* val index : 'a -> 'a list -> int = *) (* val implode : string list -> string = *) (* val lex : string list -> string list = *) (* val parse : string list -> term = *) (* val term : string -> term = *) (* val term_to_string : term -> string = *) (* val alpha : term -> term = *) (* val print_term : term -> unit = *) (* val combinators : (string * term) list = *) (* [("I", term "^x.x"); ("K", term "^xy.x"); ("S", term "^xyz.xz(yz)"); *) (* ("B", term "^xyz.x(yz)"); ("C", term "^xyz.xzy"); ("1", term "^xy.xy") *) (* ("Y", term "^f.(^x.f(xx))^x.f(xx)"); ("T", term "^xy.x"); *) (* ("F", term "^xy.y"); ("J", term "^abcd.ab(adc)")] *) (* val unfold : term -> term = *) (* val lift : int -> int -> term -> term = *) (* val subst : int -> term -> term -> term = *) (* exception Normal *) (* val maybe : ('a -> 'a) -> 'a -> 'a = *) (* val beta : (term -> term) -> term -> term =

48. Pure Lambda Calculus This is a description of the Content Scramble System (CSS) ;; descrambling algorithm in the pure lambda calculus. At the same ;; time it is also a valid http://www.cs.cmu.edu/~dst/DeCSS/Gallery/css-descramble-lambda.txt

< subfunctions ((lambda (reversed-join generalized-filter z4 z8 z1920 zxor) ; < more subfunctions ((lambda (stream->bitstream bitstream->stream xor-bitstreams) ; < more subfunctions ((lambda (test-encryption-flag get-sector-key crypt) ; < subfunctions (lambda (key sector-body) (xor-bitstreams (z* z8 z1920) (unmangle sector-body) (cipher-bitstream key)) )) ;; ================ ;; cipher-bitstream ;; ================ ;; This function returns the pseudo-random bitstream generated ;; by the given key. The random number generator uses two ;; LFSRs, one of 17 bits and the other of 25 bits, initialized ;; from the "key" argument. The outputs of the two LFSRs are ;; added together (with carry) to produce the final result. ;; The 17-bit LFSR's output is negated before the addition. ((lambda (tap-lfsr17 tap-lfsr25 make-bitstream negate-bitstream add-bitstreams) ; < subfunctions (lambda (n stream) (generalized-filter stream n (lambda (s tail) (byte->bitstream (zcar s) tail) ) zcdr z1 ))) ;; =============== ;; byte->bitstream ;; =============== ((lambda (shift) ;

49. 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. http://www.het.brown.edu/people/andre/qlambda/index.html

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 A lambda calculus for quantum computation Quantum computation, categorical semantics and linear logic which develop a linear lambda calculus for expressing quantum algorithms. The code below implements the examples in the first one of these two papers. Instructions 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 quantum.scm quantum-definitions.scm 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. Examples: Simple gate combinations First let's apply a few Hadamard gates in sequence to a single qubit. The QEVAL performs the sum over histories:

50. The Lambda Calculus The lambda calculus was created by Alonzo Church in the 1930s as a construction in abstract logic but has had practical application in the design of http://www.sjsu.edu/faculty/watkins/lambda.htm

applet-magic.com Thayer Watkins Silicon Valley USA The Lambda Calculus The Lambda Calculus was created by Alonzo Church in the 1930s as a construction in abstract logic but has had practical application in the design of program