# What is the diference between \$lambda x.1\$ and \$1\$?

I know that I can $$(lambda x.1) 0 rhd_beta 1$$. This is the constant 1, but can I contract it automatically? I mean, is $$1$$ the normal form of $$(lambda x.1)$$?

It seems reasonable to do it but when goes to combinators this sense stops, I mean, if I can $$lambda x.1 rhd_beta 1$$, then I would $$lambda xy.y rhd_beta lambda y.y$$ but $$(lambda xy.y) a b rhd_beta b$$ and $$(lambda x.1) a b rhd_beta 1 b$$ so that $$lambda x.1 notequiv_beta 1$$

What rules I’m missing on Lambda cauculus that forbids the contraction $$lambda x.1 rhd_beta 1$$?