[Haskell-cafe] Haskell purity and printing

This is what I "understand" so far ... Suppose we have these two values: a) \x->x + x b) \x->2 * x Because these to values are equal, all functions definable in Haskell must preserve this. This is why I am not allowed to define a function like h :: (a->b) -> (a->b) h x = x The reasons are very complicated, but it goes something like this: - when one put \x->x+x trough the function h, the compiler might change it to \x -> 2*x - when one put \x->2*x trough the function h, the compiler might change it to \x -> x + x And we all know that \x -> 2*x is not the same as \x->x+x and this is the reason one cannot define h in Haskell