Computer Dictionary of Information Technology

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 observational equivalence, referential transparency.