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Topic: Lambda abstraction

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	Lambda calculus - Wikipedia, the free encyclopedia
		Lambda calculus can be used to 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, which undecidability could be proved.
		In lambda calculus, every expression stands for a function with a single argument (argument::input of a function); 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_abstraction (2453 words)

	Abstraction (computer science) - Wikipedia, the free encyclopedia
		In functional programming languages, it is common to find abstractions related to functions, such as lambda abstractions (making a term into a function of some variable), higher-order functions (parameters are functions), bracket abstraction (making a term into a function of a variable).
		Data abstraction is the enforcement of a clear separation between the abstract properties of a data type and the concrete details of its implementation.
		Object-oriented languages are commonly claimed to offer data abstraction; however, their inheritance concept tends to put information in the interface that more properly belongs in the implementation; thus, changes to such information ends up impacting client code, leading directly to the fragile base class problem.
	en.wikipedia.org /wiki/Abstraction_(computer_science) (2911 words)

	Typed lambda calculus - Wikipedia, the free encyclopedia
		Typed lambda calculi are foundational programming languages and are the base of typed functional programming languages such as ML and Haskell and, more indirectly, typed imperative programming languages.
		Traditionally, typed lambda calculi were seen as refinements of the untyped lambda calculus.
		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.
	en.wikipedia.org /wiki/Typed_lambda_calculus (571 words)

	Encyclopedia :: encyclopedia : Functional programming (Site not responding. Last check: 2007-11-01)
		Lambda calculus could be considered the first functional programming language, though it was not designed to be executed on a computer.
		Lambda calculus is a model of computation designed by Alonzo Church in the 1930s that provides a very formal way to describe function evaluation.
		Higher-order functions were studied in the lambda calculus theory well before the notion of functional programming existed and are present in the design of a number of functional programming languages, such as Scheme and Haskell.
	www.hallencyclopedia.com /Functional_programming (2123 words)

	from lambda to language
		Lambda abstractions within the body of the named function are translated as named functions with derived names.
		The lct lambda compiler analyses for free variables, so that all bound variables are treated as variables in the language machine and all free variables are treated as symbols in the language machine.
		Lambda abstractions are represented as references l :F :X to the function F with arguments X that can be directly applied, where the function F is the function that represents the definition of the lambda abstraction.
	languagemachine.sourceforge.net /lambda.html (1773 words)

	[No title]
		The usual connection made between the lambda calculus and algebra is to construct the integers using the lambda calculus and then construct algebraic (and other formulas) by Godelizing them.
		LAMBDA A symmetrical situation to currying of arguments is binding a variable over a function.
		When applying a function, each distinct derivative of a lambda variable with a corresponding argument requires that an equation be generated and that derivative variable be eliminated.
	www-swiss.ai.mit.edu /~jaffer/lambda.txt (1465 words)

	[No title]
		Lambda Calculus is a calculus which expresses "computation" via anonymous functions.
		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.
		or as a "lambda abstraction" (a function in which the Greek letter lambda is defined as the abstraction operator).
	www.cs.unm.edu /~bollich/etc/Lambda.html (837 words)

	Joy compared with other functional languages
		Abstraction binds free variables in an expression, and it yields a function which is a first class value.
		Here lambda is taken to be a true function; the universe of models is enlarged to include environments, and variables are interpreted as selector functions mapping environments to values.
		Abstraction is a construction in the object language, the lambda calculus.
	www.latrobe.edu.au /philosophy/phimvt/joy/j08cnt.html (6300 words)

	Abstraction and Generalization
		Abstraction and generalization are fundamental to mathematics and philosophy and are essential in computer science as well.
		The importance of abstraction is derived from its ability to hide irrelevant details and from the use of names to reference objects.
		In the previous chapter (Abstraction and Generalization), it appears that when an argument is passed to an abstract, it replaces the parameter, that is, it textually replaces the parameter.
	cmpe.emu.edu.tr /aelci/Courses/D-318/D-318-Files/plbook/absgen.htm (5878 words)

	lambda abstraction (Site not responding. Last check: 2007-11-01)
		A lambda abstraction begins with a lower-case lambda (represented as "\" in this document), followed by a variable name (the "bound variable"), a full stop and a lambda expression (the body).
		A lambda abstraction in Lisp is written as the symbol lambda, a list of zero or more variable names and a list of zero or more terms, e.g.
		Lambda expressions in Haskell are written as a backslash, "\", one or more patterns (e.g.
	burks.brighton.ac.uk /burks/foldoc/73/64.htm (148 words)

	Barendregt: Lambda Calculus (Site not responding. Last check: 2007-11-01)
		In a lambda term MN, the occurrence of the subterm M is active and the occurrence of the subterm N is passive.
		Lambda with the eta conversion is the theory Lambda-eta.
		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.
	www.andrew.cmu.edu /~cebrown/notes/barendregt.html (21701 words)

	Lambda Calculus: a Theory of Functions
		lambda abstraction is a linguistic form which directly realizes the abstraction/instantiation process
		we can also view abstraction as a symmetric "opposite" of function application, arising as a means of solving equations directly for functions
		the language of pure lambda calculus includes only variables, abstraction and application; it captures a very general notion of function (including all computable ones)
	www.willamette.edu /~fruehr/talks/ling/clltalk2.html (154 words)

	ARS Based Programming: Fundamental And Without Limits
		ARS is an abstraction from the Lambda Calculus, taking its three basic operations, and giving them a more general meaning.
		ARS is a generalized form of the basic operations of the Lambda Calculus in that respect, that the definition of abstraction retains the full meaning of the word (`give something a name') and that all three operations can be applied anywhere in a program without restrictions.
		An abstraction can be assigned a name, and such an abstraction with its name definition may appear anywhere in a program.
	www.lambda-bound.com (484 words)

	Notes: Lambda Calculus
		Lambda calculus is a formal model of computation.
		function abstraction defining function of one variable "x" with body "lambda y x" which is another function abstraction.
		(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)

	Database Abstraction Layers and Programming Languages \| Lambda the Ultimate
		The author uses an argument I hear all the time: If you use a good abstraction layer, it'll be easy to move from $this_database to $other_database down the road.
		This level of abstraction is already available in any language with modules, classes and other implementation hiding mechanisms.
		So you're still stuck with the basic model of doing a query within the pragmatic limits of the query language, then further processing the results in the programming language, with a sharp line between what can be done easily in each environment.
	lambda-the-ultimate.org /node/view/76 (3048 words)

	CS 152 Homework: Lambda calculus (Site not responding. Last check: 2007-11-01)
		There are three problems on implementing the lambda calculus and three problems on programming with Church numerals.
		A lambda term can be either a variable, a lambda abstraction, an application, or a parenthesized lambda term.
		Ultimately, you will write your function in lambda notation acceptable to the lambda interpreter, but you may find it useful to try to write your initial version in Typed uScheme (or ML or uScheme) to make it easier to debug.
	www.eecs.harvard.edu /~nr/cs152/homework/lambda.html (1295 words)

	[No title]
		Abstraction is an operation in the object language, the lambda calculus.
		The beta rule handles the application of abstractions to arguments, and this requires possibly multiple substitutions of the same argument expression for the multiple occurrences of the same variable.
		One such language is the untyped lambda calculus with variables but without constants, and with abstraction and application as the only constructors.
	www.latrobe.edu.au /philosophy/phimvt/joy/j00rat.html (6933 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'.
		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].
		A clear account of the historical origins and basic properties of the lambda calculus is presented by Curry and Fey in their book [CF58].
	www.aplusplus.net /lcintro.html (259 words)

	gmane.comp.lang.haskell.cafe
		I've never seen the term "lambda abstraction" used in the way it is in the article.
		I've never seen the term > "lambda abstraction" used in the way it is in the article.
		I might say something like: Lambda abstraction takes a function application, such as f x (f applied to x) and "abstracts" away from the symbol or parameter x.
	comments.gmane.org /gmane.comp.lang.haskell.cafe/13063 (501 words)

	CSc 520 Principles of Programming Languages : (Site not responding. Last check: 2007-11-01)
		In contrast to Turing machines, lambda calculus does not care about any underlying ``hardware'' but rather uses simple syntactic transformation rules to define computations.
		Lambda calculus is the theoretical foundation of functional programming languages.
		or one defined by ourselves, as a lambda abstraction.
	www.cs.arizona.edu /people/collberg/Teaching/520/2005/Html/Html-21/index.html (454 words)

	Functional Programming
		The scope of the variable introduced (or bound) by lambda is the entire body of the lambda-abstraction.
		It is desirable that there be a function which applied to a lambda-abstraction returns the least fixed point of that abstraction.
		The syntax of Scheme is similar to that of the lambda calculus.
	www.cs.jhu.edu /~jason/465/lambdacalc.html (4274 words)

	Chapter 6. Boost.Lambda
		The Boost Lambda Library (BLL in the sequel) is a C++ template library, which implements form of lambda abstractions for C++.
		The term originates from functional programming and lambda calculus, where a lambda abstraction defines an unnamed function.
		The Lambda Library : Lambda Abstraction in C++.
	www.boost.org /doc/html/lambda.html (210 words)

	An Introduction to Lambda Calculus and Scheme
		Lambda expressions can be understood locally - their dependence on their environment is entirely through their free variables.
		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.
		We could produce this program in C as well, using the technique of passing pointers to functions as arguments to other functions.
	www.jetcafe.org /~jim/lambda.html (1631 words)

	LambdaAPI2 design (Site not responding. Last check: 2007-11-01)
		Then action is made of applying (by building the application and reducing its active pair) a decoder with a zero arity and a new index (relatively to the stack of abstraction context).
		The index of the decoder gives the abstraction to which the variable is bound.
		There are three different implementations of Abstraction, used depending on the count of bound variable(s).
	www.xmloperator.net /lambda2/lambdaAPI2Design.html (992 words)

	Lambda Calculus and Lambda Calculators
		An unadorned lambda term that implements division of two signed integers (also represented as lambda terms).
		Definitions of basic lambda terms: Church numerals, combinators, Booleans, etc. These are basic lambda-calculus terms, needed to run more advanced examples.
		is a macro-lambda -- the abstraction of the (meta-) calculator.
	okmij.org /ftp/Computation/lambda-calc.html (1723 words)

	A Brief History of Functional Programming
		e" is for lambda abstraction and "e1 e2" is for lambda application.
		Interestingly, by McCarthy's own account(1978), Lambda Calculus had little impact on the development of LISP other than the lambda notation.
		Its core is based on a typed lambda calculus (the original lambda calculus by Church is untyped).
	www.cs.bc.edu /~gtan/historyOfFP/historyOfFP.html (2297 words)

	Lambda Calculus for EuLisp
		The current implementation hard codes knowledge of abstractions in the application term, but if more types were introduced then a greater level of abstraction could be introduced to remove even that.
		Any command may be prefixed by R= to assign the result of the command to R. Note that the variables used in lambda expressions are in a different namespace to the references.
		In order to fully interpret lambda term expressions, this program uses first a tokeniser, this module, followed by a parser, the next module.
	software.hixie.ch /utilities/eulisp/lambda-calculus/notes.xml (974 words)

	BNF - Syntactic Abstraction - Lambda Calculus
		The following is an s-expr based concrete syntax for the lambda calculus with multiple parameters.
		With this strategy, no reduction is ever applied inside the body of a lambda abstraction.
		Your function will determine the order of evaluation of arguments provided to a lambda function - in such a way that arguments are evaluated left to right.
	www.cs.bgu.ac.il /~elhadad/advpro/2003/hw3.html (899 words)

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