Eta expansion is a simple syntactic change used to work around the ValueRestriction in Standard ML.

The eta expansion of an expression e is the expression fn z => e z, where z does not occur in e. This only makes sense if e denotes a function, i.e. is of arrow type. Eta expansion delays the evaluation of e until the function is applied, and will re-evaluate e each time the function is applied.

The name "eta expansion" comes from the eta-conversion rule of the lambda calculus. Expansion refers to the directionality of the equivalence being used, namely taking e to fn z => e z rather than fn z => e z to e (eta contraction).