# Re: Is a function a relation?

Date: Mon, 22 Jun 2009 22:09:27 -0700 (PDT)

Message-ID: <87d8b6ff-afab-4fe2-bc22-56c49c5f4e5b_at_3g2000yqk.googlegroups.com>

On Jun 22, 11:44 pm, David BL <davi..._at_iinet.net.au> wrote:

> Since Keith popped up recently, I'm interesting in reopening the

*> question of whether a function is a relation (I have a small point to
**> add).
**>
**> I'm interpreting "is a" in the same way as D&D. i.e. the question is
**> equivalent to asking whether every function value is a relation value.
**>
**> D&D use the CIRCLE and ELLIPSE example to illustrate the idea of type
**> inheritance as specialisation by constraint. CIRCLE is a subtype of
**> ELLIPSE because every value of type CIRCLE is also a value of type
**> ELLIPSE.
**>
**> Let E be a variable of type ELLIPSE that happens to hold a value of
**> type CIRCLE. D&D mention that THE_R(E) is not permitted, and it is
**> necessary to instead use THE_R(TREAT_DOWN_AS_CIRCLE(E)). Implicit in
**> this idea is that when an ellipse value happens to also be a circle
**> value, the interpretation of the ellipse as a circle is unambiguous.
**>
**> Consider the binary relation with the following graph
**>
**> { (x,y) | y = x+1 }
**>
**> and the following two functions
**>
**> f(x) = x+1
**> g(y) = y-1
**>
**> It seems to me that assuming D&D's interpretation of "is a", it cannot
**> be said that a function is a relation because TREAT_DOWN_AS_FUNCTION
**> is ambiguous when provided with a relation variable that holds the
**> value f.
*

corresponding to the f(x) and g(y) you gave.

**KHD
**
Received on Tue Jun 23 2009 - 07:09:27 CEST