# Lambda Beta (theorical computer science)

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I have to prove thate for all s which is an abstraction we have : lambda x.sx = s And I am completly stuck, I have try a prof by induction on t with s = lambda y.t but I can't prove the induction for the abstraction rule. I think about the fixpoint theorem but I am unable to apply it a useful way.Somebody as an idea ? It will be very helpful. Anyway, thank you to all of you who are going to try to do this prof. Best regards.

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This isn't homework, is it?

Yes it is !

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Well, you aren't supposed to post homework questions here:
Quote:
 From the Math and Physics forum FAQ3a. How should I ask for help on homework problems?Since gamedev.net exists to support the game development community, and is not a homework site, please visit another website that is specifically dedicated to math education and homework specifically. Here are a few nice sites:Math Goodies: Free Interactive Math Lessons, Homework Help, ...That one is very nice, and has a dedicated homework forum.Math.com - World of Math OnlineNice site, but I didn't see a forumAlgebra Homework Help at Algebra.comAAA MathMathforum Discussion Groups - active, ongoing discussions on many topics related to math

I could be completely off, as I don't know too much about lambda calculus yet, it's about 0400 hours and I've had little (read: no) experience doing proofs, but I'll give a hint a shot:
s = λy.t
λx.sx = λx.(λy.t)x = (... β-reduction ...) = (... α-conversion ...) = s

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rule: (Lx.M)N = M[x:=N]
substitute M with sx: (Lx.sx)N = sN

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(Lx.sx)N = sN but from this, I must use the eta rule to have :
Lx.sx = s, the problem is that I am not allowed to use the eta rule ( only Lambda Beta ).

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Homework post, closing thread. See Forum FAQ.

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