extensional equality

(Or extensionality). Functions, f and g are extensionally

equal if and only if

f x = g x for all x.

where "=" means both expressions fail to terminate (under some

given reduction strategy) or they both terminate with the

same basic value.

Two functions may be extensionally equal but not

inter-convertible (neither is reducible to the other). E.g.

x . x+x and x . 2*x. See also observationalequivalence, referential transparency.