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}.