[hcoop/debian/mlton.git] / doc / guide / src / EtaExpansion.adoc

EtaExpansion
============

Eta expansion is a simple syntactic change used to work around the
<:ValueRestriction:> in <:StandardML: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
<:LambdaCalculus: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).
Commit	Line	Data
7f918cf1 CE	1	EtaExpansion
	2	============
	3
	4	Eta expansion is a simple syntactic change used to work around the
	5	<:ValueRestriction:> in <:StandardML:Standard ML>.
	6
	7	The eta expansion of an expression `e` is the expression
	8	`fn z => e z`, where `z` does not occur in `e`. This only
	9	makes sense if `e` denotes a function, i.e. is of arrow type. Eta
	10	expansion delays the evaluation of `e` until the function is
	11	applied, and will re-evaluate `e` each time the function is
	12	applied.
	13
	14	The name "eta expansion" comes from the eta-conversion rule of the
	15	<:LambdaCalculus:lambda calculus>. Expansion refers to the
	16	directionality of the equivalence being used, namely taking `e` to
	17	`fn z => e z` rather than `fn z => e z` to `e` (eta
	18	contraction).