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

Scott David Daniels Scott.Daniels at Acm.Org
Wed Dec 14 18:27:39 CET 2005

Arthur wrote:
> re:  "The study of fixed points has been at the foundation of algorithms"
> I guess what I am asking further is whether the statement is simply 
> referencing the development of  algorithms for solving the mathematical 
> question of the fixed points of a function, in the context of 
> mathematical programming where that particular mathematical problem 
> might happen to present itself- or is there some implication that the 
> problem of  f(x) = x is one that  has more general implications  in 
> algorithmics as  a distinct area of study.
I think the answer is yes (there are such implications), and that those
implications show up in the functional programming world (where they
like to think of everything as constants and pure functions).  The
places it shows up (if I understand correctly) have a lot to do with
compilation and binding functions into environments where the functions
themselves are a part of that environment.  But this is simply a
suspicion, I can't say that I've delved too deeply into this area.
I suspect the other way into this is Category Theory, an area I am
afraid I under-appreciate (though some say it is just because I don't
"get it").

> .. or am I asking a question that is itself too round-about to have an 
> answer of the kind of am looking for? ;)

The above is as much as I can give you.  You may get more from abstract
algebra people.

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

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