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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
extension:

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