I was trying to work through an example of using Church Pairs in Lambda Calculus, and ended up visiting #scheme @ freenode in hopes of finding some remedial help. This simple goal led to the following encounter (I changed his name to schemer here).

[4:59pm] vovik: can someone explain to me the missing step in this example from the wikipedia article on church numbers: http://gist.github.com/5314?
[5:01pm] schemer: vovik: we write car and cons not fst and pair
[5:02pm] vovik: this is a lambda calculus question, not a scheme question
[5:02pm] schemer: anyway the problem is the wikipeida article doesn't use formal notation
[5:02pm] schemer: scheme notation would be much cleare
[5:02pm] schemer: so let's use that
[5:02pm] schemer: \p.p (\x.\y.x) (\z.z a b)
[5:03pm] vovik: ya i run into this problem occasionally on wikipedia, but i think this is a pretty simple example?
[5:03pm] schemer: --> ((lambda (p) (p (lambda (x) (lambda (y) x)))) (lambda (z) ((z a) b)))
[5:03pm] schemer: ((lambda (z) ((z a) b)) (lambda (x) (lambda (y) x)))
[5:03pm] schemer: (((lambda (x) (lambda (y) x)) a) b)
[5:03pm] schemer: ((lambda (y) a) b)
[5:04pm] schemer: a
[5:05pm] vovik: ok i understand your translation from their notation to scheme's
[5:05pm] vovik: but i don't understand teh transition from ((lambda (p) (p (lambda (x) (lambda (y) x)))) (lambda (z) ((z a) b))) to (lambda (z) ((z a) b)) (lambda (x) (lambda (y) x)))
[5:06pm] schemer: vovik: do you see why pseudcode/informal notation is crap and should die
[5:06pm] schemer: ?
[5:06pm] vovik: ya but i think they're trying to not scare people off with too many parens
[5:06pm] vovik: plus writing out lambda is pretty verbose
[5:06pm] schemer: ((lambda (x) M) N) evaluates to M[x <-- N]
[5:06pm] vovik: what does that mean
[5:07pm] schemer: vovik: that's idiotic
[5:07pm] vovik: of course you'd say that, you're in #scheme
[5:07pm] schemer: ((lambda (x) M) N) evaluates to M with all free occurences of 'x' in there replaced with N
[5:07pm] schemer: vovik: You're an idiot too
[5:07pm] vovik: ...
[5:07pm] schemer: I can't be bothere to teach you basic stuff anymore
[5:07pm] vovik: wow.
[5:08pm] schemer: I tried to help I did not want to argue with you about paranthesis
[5:08pm] vovik: i wasn't arguing, i was simply trying to guess at their motivation for choosing that notation over a more standard one
[5:09pm] vovik: then i pointed out that those parens can be scary for the uninitiated, someone in #scheme is probably accustomed to it and has no problem with them
[5:09pm] vovik: then you just lose it i guess...
[5:10pm] vovik: unbelievable
[5:11pm] schemer: vovik: Can I PM you to apologize?
[5:11pm] vovik: sure...

His apology seemed humble and sincere. What a dramatic range of emotions in a span of ten minutes! And in the end, there was no harm done. In fact, his explanation at 5:07 answered my original question. Thanks!

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