[arethuza]

A quick Google should point you in the direction of what people use lambda calculus for:

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

One fascinating area for the use of lambda calculus is as a conceptual basis for the implementation of functional programming languages - indeed you could argue that a language is functional iff it can be mapped to the lambda calculus.

Edit: Although it is rather old (like me!) I have fond memories of "The Implementation of Functional Programming Languages" by Simon Peyton Jones:

http://research.microsoft.com/en-us/um/people/simonpj/papers... [PDF]

Another very cool thing is that you can translate expressions in the lambda calculus to SK[I] combinators - which means you can actually implement real programs (including recursion - e.g. using the Y-combinator) as two extremely simple functions - not very efficiently, mind you... :-)

http://en.wikipedia.org/wiki/SKI_combinator_calculus

[chriswarbo]

> indeed you could argue that a language is functional iff it can be mapped to the lambda calculus.

Lambda calculus is a higher-order, applicative functional language. There are other kinds of functional language.

For example, kappa calculus is first-order. Joy is a pure functional programming language which is based around composition instead of application.

[arethuza]

Thanks - it was quite a while ago that I was taught about this kind of stuff and for postgraduate study I ended up going down a AI/engineering route rather than programming languages - I now wish I had done the latter given the resurgence of interest in functional programming :-)