INlambda-calculus, the eta coNversioN rule states x . f x <--> f provided x does Not occur as a free variable iN f aNd f is a 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 iNMiraNda or returNiNg a fuNctioN as the overall result of a program, theN bottom aNd x . bottom will Not be equivaleNt. See also observatioNal equivaleNce, reductioN.
