[Edu-sig] "The study of fixed points has been at the foundation of algorithms"

[Scott David Daniels]

Arthur wrote:
  > I have thought of "fixed point"  (in programming) as connected
> to/opposed to "floating point", not as something directly connected to 
> the concept of "f(x)=x"
> 
> The statement above seems to be telling me otherwise.
> Guess I am fishing for some exposition on the statement that the
> "The study of fixed points has been at the foundation of algorithms"

Well, in fact both meanings of "fixed point" are used, seldom by the
same person.  I expect Knuth is in that small group that uses both
meanings regularly (since his basic training was all mathematics).
Look to the "functional programming" people for examination of the
whole idea of fixed points of functions (Bird & Wadler is a standard
F.P. text).


--Scott David Daniels
Scott.Daniels at Acm.Org