Lambda Beta (theorical computer science)
Author
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.
Well, you aren't supposed to post homework questions here:
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
Quote:From the Math and Physics forum FAQ
3a. 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 Online
Nice site, but I didn't see a forum
Algebra Homework Help at Algebra.com
AAA Math
Mathforum 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
Author
(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 ).
Anyway I thank you very much for your answers and I am really sorry about this break of the rules, I will be more careful next time.
Lx.sx = s, the problem is that I am not allowed to use the eta rule ( only Lambda Beta ).
Anyway I thank you very much for your answers and I am really sorry about this break of the rules, I will be more careful next time.
This topic is closed to new replies.
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