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In some textbook I have met a statement, that discovery of lambda calculus explained the relation between name and value.

How it did this in a simple example?


I don't remember the context, this is the part of the problem :)

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What is lambda calculus? – Sigur Feb 6 '13 at 0:40
@Sigur: See wikipedia – Hurkyl Feb 6 '13 at 0:41
Any context at all would be helpful! Which textbook was it, what does the surrounding text say, etc., etc.? – Rahul Feb 6 '13 at 1:49

Just guessing since I don't know the context....

One of the problems with conventional notation is what is meant by an expression like "$x^2+1$", if "$x$" is a real variable? Is this supposed to represent a function in the variable $x$? Or is this supposed to represent the real number whose value depends on the value of $x$?

Pretty much every formal treatment of mathematical grammar and syntax I've seen would support the latter interpretation: "$x^2 + 1$" denotes a number. However, the former interpretation is very useful so people keep using it -- and for many purposes the difference is moot anyways so people don't even notice the ambiguity. (of course, this may be a cause of some confusion in beginning students, who haven't adapted properly)

Lambda calculus gives a systematic notation to clarify which interpretation you mean. "$x^2 + 1$" is a number. "$\lambda x.(x^2+1)$" is a function.

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