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Topic: Lambda-calculus

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Lambda calculus - Wikipedia, the free encyclopedia The calculus can be used to cleanly define what a computable function is. The question of whether two lambda calculus expressions are equivalent cannot be solved by a general algorithm, and this was the first question, even before the halting problem, for which undecidability could be proved. In lambda calculus, every expression stands for a function with a single argument; the argument of the function is in turn a function with a single argument, and the value of the function is another function with a single argument. A function of two variables is expressed in lambda calculus as a function of one argument which returns a function of one argument (see currying). en.wikipedia.org /wiki/Lambda_calculus   (2202 words)

Typed lambda calculus - Wikipedia, the free encyclopedia Lambda calculi with dependent types are the base of Intuitionistic Type Theory, the Calculus of Constructions and the Logical Framework (LF), a pure lambda calculus with dependent types. A more modern view is to consider typed lambda calculi as fundamental and to consider the untyped lambda calculus as a special case of a typed lambda calculus with only one type. Based on work by Berardi, Barendregt proposed the Lambda cube to systematize the relations of pure typed lambda calculi (including simply typed lambda calculus, System F, LF and the Calculus of Constructions). en.wikipedia.org /wiki/Typed_lambda_calculus   (518 words)

Knights of the Lambda Calculus - Wikipedia, the free encyclopedia The name refers to the lambda calculus, a mathematical formalism invented by Alonzo Church, with which LISP is intimately connected, and references the Knights Templar. The Knights of the Lambda Calculus is a semi-fictional organization of expert LISP and Scheme hackers. There is no actual organization that goes by the name Knights of the Lambda Calculus; it mostly only exists as a hacker culture in-joke with which to poke fun at conspiracy theories and secret societies. en.wikipedia.org /wiki/Knights_of_the_Lambda-Calculus   (266 words)

Lambda Calculus 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. 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. users.comlab.ox.ac.uk /luke.ong/teaching/lambda   (295 words)

Barendregt: Lambda Calculus The lambda-I calculus corresponds to the combinatory logic with primitive combinators I, B, C, and S. For each lambda term M, we may construct the Bohm tree BT(M) of M. This tree may be infinite. For the lambda-I calculus, consistency of a set of closed equations is equivalent to the inability to prove I = S. For any lambda-theory T, T+eta = T + (I=1) where 1 is the Church numeral lambda x,y. Lambda calculus was originally invented to provide a general theory of functions which could be extended to provide a foundation for mathematics. www.andrew.cmu.edu /~cebrown/notes/barendregt.html   (21701 words)

Lambda Calculus Expressions in the pure lambda calculus are defined according to the following concrete syntax. In practice we enrich the lambda calculus with constants (mostly numeric) and operators (+,- etc.) as we need them. Lambda Calculus and ML There is a very close relationship between scom.hud.ac.uk /scomtlm/cas810/notes/lambda.html   (376 words)

Lambda calculus The lambda calculus was invented by Alonzo Church in the 1930s to study the interaction of functional abstraction and function application from an abstract, purely mathematical point of view. In the lambda calculus, a reduction rule can be performed at any time to any subterm of a lambda term at which the rule is applicable. To code this in the lambda calculus, we can take two terms A and B and produce a function that will apply another function to them. www.cs.unc.edu /~stotts/COMP204/Lambda/overview.html   (1423 words)

Introduction To Lambda Calculus (Tutorial) In lambda calculus a function does not 'return' a result based on its parameters - instead the function and its parameters are 'reduced' to give an answer, which mathematically is equivalent to the question. The Lambda Calculus was developed by Alonzo Church in the 1930s and published in 1941 as 'The Calculi Of Lambda Conversion'. Lambda calculus has the 'Church-Rosser property', so that if two methods of reduction lead to two normal forms, they can differ only by alpha conversion. www.safalra.com /science/lambdacalculus/introduction.html   (375 words)

css-descramble-lambda.txt It is possible to ;; write recursive functions within the lambda calculus, but it is ;; impossible to stop at the base case without relying on knowledge of ;; the underlying language's evaluation order. ;; ;; The lambda calculus, invented by Alonzo Church in the 1930s, is;; a mathematical model of computation based around the operations of ;; "abstraction" (defining functions) and "application" (evaluating ;; them at a point). For example: ;; ;; 0 is (lambda (f) (lambda (x) x)) ;; 1 is (lambda (f) (lambda (x) (f x))), or just (lambda (f) f);; 2 is (lambda (f) (lambda (x) (f (f x)))) ;; 3 is (lambda (f) (lambda (x) (f (f (f x))))) ;; ;;... www.cs.cmu.edu /~dst/DeCSS/Gallery/css-descramble-lambda.txt   (1392 words)

The Lambda Calculus Mail Series But in lambda calculus, this definition of natural numbers, is just a nencoding that we have made up, because we think it satisfies the notion of natural numbers, that we want it to satisfy. Lambda calculus was invented long before there were any computers (in the modern sense, as programmable machines), or computer languages. Lambda calculus was created to model the notion of functions that mathematics has. www24.brinkster.com /srineet/lambda\lambda.html   (15635 words)

fanf.hint It is fairly well known that the lambda calculus (and hence SK combinators) can compute anything, but mere computation is no use if you cannot communicate with the world. For example, if I had the appropriate arithmetic operators defined, I could write a factorial function in the lambda calculus like this: Y \f\n((= n 0) 1 (* n (f(- n 1)))) OFL provides a facility for naming expressions so that they can be used more than once without writing them in full. Functions are created from lambda terms which are written in the form `\a(expr)' which is the function taking argument `a' and having value `expr'. www.ioccc.org /1998/fanf.hint   (1937 words)

Lambda Calculus Summary - Lambda Calculus Information Even though Church's original motivation in developing the lambda calculus was to provide a foundation for mathematics by means of creating a special tool for mathematical logic, the results of his work have had considerable application in computer science. The lambda calculus has the power to represent all computable functions, but its uncomplicated syntax and semantics provides a fine basis for the specific context of the study of the semantics of programming language concepts. This was done in the 1930s by Alonzo Church (he of the Church-Turing thesis fame), by his development of the lambda calculus as a theory of functions that provides rules for manipulating functions in a purely syntactic manner. www.bookrags.com /sciences/computerscience/lambda-calculus-wcs.html   (705 words)

Notes: Lambda Calculus Lambda calculus is a formal model of computation. Lambda Calculus as a basis for functional programming languages (lambda x M A) can be reduced by substituting A into M for all free occurrances of x. www.cs.unc.edu /~stotts/COMP204/Lambda   (821 words)

Lambda Calculus Introduction This is a brief introduction to the lambda calculus and the interpreter, including executable example λ-calculus programs and source code; it should be used in conjunction with a book or other material. The toy Lambda Calculus interpreter can be run through the wwweb. There are very tight limits set on the size and running time of programs that can be run in this way. www.csse.monash.edu.au /~lloyd/tildeFP/Lambda/Ch   (95 words)

lambda-calculus This page is not intended to be an introduction to the lambda calculus; there are lots of good books for that. Recursion in the lambda calculus can be done with a fixpoint operator. The lambda calculus is basically function theory, there are only three things available in the pure lambda calculus, these are: frmb.org /lambda-plain.html   (449 words)

No Title Lambda Calculus is intended to capture, in a very simple way, the idea of creating a function and then calling it on an argument. Miraculously, the Lambda Calculus model is both simpler than the Turing machine model and more practical for real computation. Our goals are to develop Lambda Calculus versions of if-then tests, boolean and integer constants, arithmetic operators, and some simple data structures. perl.plover.com /lambda/tpj.html   (3637 words)

lambda calculus - a Whatis.com definition 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. Roger Bishop Jones provides an overview of Lambda calculus, combinatory logic, and type systems. 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). whatis.techtarget.com /definition/0,,sid9_gci341298,00.html   (195 words)

Lambda Calculus Basics 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'. A clear account of the historical origins and basic properties of the lambda calculus is presented by Curry and Fey in their book [CF58]. As a mathematical logical system the Lambda Calculus is covered in detail in [Bar81] and less comprehensively but in a more readable form in [Sto81]. www.aplusplus.net /lcintro.html   (259 words)

Church's lambda calculus Doubtful, since C doesn't lend itself well to working with lambda calculus (the world-view of the two models is too different). http://groups.google.com/groups?sel...ian.ccrwest.org That post has the term "lambda calculus" in it, in reference to a program called loader.c, but I don't understand a lot of that post. If you want to find a treatment of the lambda calculus that uses a programming language rather than mathematical notation, you're better off looking at a functional language like Scheme. www.codecomments.com /message276723.html   (876 words)

Lambda Calculus and Combinators The lambda calculus was introduced as a notation for representing and studying functions. The lambda calculus is an elegant formulation of the classical idea. M is reduceable to N (M red N) if there is a sequence of alpha, beta, and/or eta reductions from M to N. M is convertable to N (M cnv N) if M = N is a theorem of the lambda calculus. cs.wwc.edu /~aabyan/Logic/lambdaCalculus.html   (608 words)

An Introduction to Lambda Calculus and Scheme The Lambda-calculus is a universal model of computation, that is, any computation that can be expressed in a Turing machine can also be expressed in the lambda calculus. Lambda expressions tend to have fewer free variables and more bound variables than comparable imperative code, since they do not rely as heavily on assignment to express the computation. Lambda expressions can be understood locally - their dependence on their environment is entirely through their free variables. www.jetcafe.org /~jim/lambda.html   (1631 words)

Lambda Calculus Extending the untyped Lambda Calculus by associating a type with each constant and binding results in the formalism described in the text. The Lambda Calculus is a method for investigating and resolving identifier bindings. The form of the expressions in the untyped Lambda Calculus can be found in any elementary programming languages text. ugrad-www.cs.colorado.edu /~csci5535/HW/lamb.html   (375 words)

Infinitary Lambda Calculus - Kennaway, Klop, Sleep, de Vries (ResearchIndex) 8: The Lambda Calculus: Its Syntax and Semantics (context) - Barendregt - 1984 From the viewpoint of infinitary rewriting, the Bohm model of the lambda calculus can be seen as an infinitary term model. In this paper we perform the same task for the lambda calculus. citeseer.ist.psu.edu /351096.html   (519 words)

Lambda calculus plus letrec Since most implementations of non-strict functional languages rely on sharing to avoid repeating computations, we develop a variant of our cyclic lambda calculus that enforces the sharing of computations and show that the two calculi are observationally equivalent. The scoped lambda-graphs are represented by terms defined over lambda calculus extended with the letrec construct. We conclude by presenting a variant of our cyclic lambda calculus, which follows the tradition of the explicit substitution calculi. www.cs.uoregon.edu /~ariola/cycles.html   (357 words)

Lambda tutorial The following is too fun not to mention: David Keenan, To dissect a mockingbird: a graphical notation for the lambda calculus with animated reduction. Here, "var" is the variable bound by the lambda operator, and "body" is the constituent that the lambda operator has scope over. Line 6 (beta reduction): if f has the form ((lambda variable body) argument), it is a lambda form being applied to an argument, so perform lambda conversion. ling.ucsd.edu /~barker/Lambda   (2439 words)

Lambda Calculus An expression in the Lambda Calculus, E, is defined as Also known as Church's Lambda Calculus, we describe here the non pure form which has constants. E defines a set of expressions called lambda expressions. cs.wwc.edu /~aabyan/CII/BOOK/book/node160.html   (163 words)

Computing Papers on Lambda Lambda Calculus uFormal system with three parts Notation for functions Proof system for equations Calculation rules called reduction In particular, we will treat the calculus as a syntactic game, and won t worry about models. argn) uDeclarations and control: Lambda evaluate each of the arguments pass list of argument values to function Example (cond (p1 e1)... computing.breinestorm.net /Lambda   (2190 words)

Lambda Calculus Interpreter I know this isn't user friendly, but if you're learning lambda calculus, you should be able to kill a looping process. This page introduces an interactive interpreter for the lambda calculus. Names can be bound to Lambda expressions, using let = . homepage.mac.com /kimandsally/teacher/LambdaTeacher.html   (446 words)

Lambda Calculus - TunesWiki See logic and functional Programming Languages, as well as lambda calculus as a virtual machine - the Lambda VM. There are introductory online courses on lambda calculus. The usual reference for it is a 1984 book by Barendregt. tunes.org /wiki/Lambda_Calculus   (65 words)

Lambda Calculus for EuLisp V is any Lambda Calculus reference that is a variable, e.g. The command parser, this module parses the input from the user and passes it to the core Lambda Calculus code. To exit the Lambda Calculus interpreter, type: quit software.hixie.ch /utilities/eulisp/lambda-calculus/notes.xml   (974 words)

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