x . f x -- f
function. Left to right is eta reduction, right to left is
eta abstraction (or eta expansion).
This conversion is only valid if
bottom and x . bottom are
equivalent in all contexts. They are certainly equivalent
when applied to some argument - they both fail to terminate.
If we are allowed to force the evaluation of an expression in
any other way, e.g. using
seq in
Miranda or returning a
function as the overall result of a program, then bottom and
x . bottom will not be equivalent.