Talk:Lambda calculus

Thanks for making this page. I don't understand this topic very well, and I'm wondering if someone could give some examples of l.c. expressions that are worked out step by step to a solution? Thanks a lot. Calamari 16:47, 3 Aug 2005 (GMT)

Sure, I'll just grab some examples from my Lambda Calculus pages. --Safalra 18:08, 3 Aug 2005 (GMT)

That's great. Thank you very much! Calamari 04:51, 4 Aug 2005 (GMT)

If, after looking at the various lambda calculus webpages, you want to get a more-thorough introduction, I think Introduction to Lambda Calculus (53 pages) by Barendregt & Barendsen is hard to beat. It's still available online in a few places (it used to be at citeseer, but no longer?). At the moment, one such place for the 2000 revision seems to be www.cs.chalmers.se/Cs/Research/Logic/TypesSS05/Extra/geuvers.pdf --r.e.s. (Talk) 18:56, 4 Aug 2005 (GMT)

Printed! :D Calamari 16:22, 5 Aug 2005 (GMT)

Can't print it out but currently reading it on the screen. :) Cheers r.e.s.! --User:Keymaker

Fixed-point function

Just how does the fixed-point function let functions access themselves? --Ihope127 00:38, 17 Oct 2005 (GMT)

Call the fixed-point function Y. Then Yfx becomes f(Yf)x which becomes f(f(Yf))x. Here f can either throw away its first parameter, or use it to call itself on some value. Permit me to introduce some high-level syntax to make this easier to understand. Let f=lambda gn.(if n=1 then 1 else n*g(n-1)), then Yf is the factorial function. Consider Yf2. This becomes f(Yf)2 which becomes 2*(Yf)1, which becomes 2*f(Yf)1, which becomes 2*1, which becomes 2. I hope that's not too unclear. --Safalra 09:47, 17 Oct 2005 (GMT)

Now I get it. If you have a function ^tx.stuff, t can be used to mean "this function", if you first apply the fixed-point function to ^tx.stuff. So the "blackhole function" would be ^xy.x (i.e. K) with Y applied to it, so that you would have ^y.x where x is the blackhole function again. --Ihope127 18:26, 3 Nov 2005 (GMT)

History version of Lambda calculus?

Can I write lambda calculus like this?

n̂f̂x̂.f(nfx)

(I often don't sign.)

Strange question. You certainly can write it as you like, but how many people would understand you? --Blashyrkh (talk) 08:16, 3 February 2026 (UTC)

In Isomorphisms: Mathematics in Programming, I saw that this is the earliest form of lambda calculus.

I see, misunderstood you at first. I thought you suggested an alternative notation. Well, this historical fact is rather curious than practical. Diacritics are harder to read, not every output device displays them properly. More common λ, "lambda", \ or ^ are preferrable, imho. --Blashyrkh (talk) 08:27, 3 February 2026 (UTC)

You can write it however you like. Concrete syntax doesn't matter. Corbin (talk) 15:40, 3 February 2026 (UTC)

In fact so.