Thu Jun 16 11:50:59 CEST 2011

intension / extension

Seems the way this is used in CS is due to Church's lambda calculus[1]:

  In developing his theory of lambda calculus, the logician Alonzo
  Church (1941) distinguished equality by intension from equality by

    It is possible, however, to allow two functions to be different on
    the ground that the rule of correspondence is different in meaning
    in the two cases although always yielding the same result when
    applied to any particular argument. When this is done, we shall
    say that we are dealing with functions in intension. The notion of
    difference in meaning between two rules of correspondence is a
    vague one, but in terms of some system of notation, it can be made
    exact in various ways.

In the previous section[2] it is said that:

  The rule that defines a function f:AB as a mapping from a set A to a
  set B is called the intension  of the function f. The extension of f
  is the set of ordered pairs determined by such a rule:

[1] http://www.jfsowa.com/logic/math.htm#Lambda
[2] http://www.jfsowa.com/logic/math.htm#Function