Talk:Lambda abstraction

"A lambda abstraction is to a functional programming language such as Scheme what pseudo-code is to an imperative programming language."

I thought lambda-calculus is a very sharp mathematical modell of computation - whereas pseudo-code is rather fuzzy.. Can anyone explain this further? Thank you -- Matthias


 * It seems to me that this page contains mostly incorrect information and should probably be just merged with Lambda calculus. AJK 14:23, 7 November 2005 (UTC)


 * This page is confusing, though the subject deserves its own topic seperate from Lambda calculus due to its (related) use in computer programming. Vpoko 22:15, 9 November 2005 (UTC)

This article is inaccurate. Lambda calculus is indeed a mathematical model of computation, completely unrelated to pseudo-code. A "lambda abstraction" (I prefer "lambda expression" because all lambda expressions are also lambda abstractions) is simply an expression with some (zero to many) of the variables in the expression specified as being bound variables which can have other values substituted for them when the lambda expression is applied to arguments. In other words, it "abstracts" over a computation with particular elements that can vary and therefore must be supplied as arguments when reducing the lambda expression to a simpler form (i.e. when using it to compute something). In formal definitions of lambda calculus, a lambda expression always has exactly one bound variable, but it's trivial to extend this to multiple arguments or no arguments. A lambda expression with no free variables is a special type of lambda expression which is usually called a combinator. The sentence at the end, claiming that lambda can stand for "for each", "for some", or "there is" is highly misleading and essentially incorrect; there are typed lambda calculi that have different ways of specifying concepts like this (specifically "for all" (universal quantification) and "there exists" (existential quantification)). I think this article should be removed or merged with another article. -- Mike

I find this to be completely inaccurate. This is a correct definition: http://foldoc.org/foldoc.cgi?lambda+abstraction