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Re: evaluation-- one or many levels, your thoughts?

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  • Subject: [mg116994] Re: evaluation-- one or many levels, your thoughts?
  • From: Noqsi <noqsiaerospace at>
  • Date: Mon, 7 Mar 2011 05:46:41 -0500 (EST)
  • References: <ikq8gs$7vl$>

On Mar 4, 1:39 am, Richard Fateman <fate... at> wrote:
> How often do you require the behavior that an expression
> is evaluated until it stops changing, rather than evaluated
> "once"?
> Difference in behavior..
> once
> x1=x2
> x2=x3
> x1  evaluates to x2
> "infinite" evaluation until stops changing..
> x1 evaluates to x3.
> Note that with "once" evaluation,
> x=x+1    sets x  to  "x+1"

And, of course you can have that in Mathematica:


Replace[] is a simple "evaluate once" construct. It's not a complex
heuristic "try to figure out what I mean to do" construct, as you seem
to want it to be in other threads.

> not "recursion depth exceeded".
> You may not have a clear idea of the answer to this question, since
> conventionally Mathematica evaluates "as far as possible", and
> you may not, therefore, have an idea of whether your programs
> would still work under the "once" model.
> I invite you to think about this, and whether another model
> might work for you.  I think that the evaluate once model is
> less onerous for the implementor, and might speed up your
> computing.  Given the "once" model, one can easily write
> "evaluate until no change".

I think that for my purposes, invoking FixedPoint[] willy-nilly all
over the place would be a burden, and would make expressions much
harder to read.

> The reverse emulation is
> much harder, as far as I can tell.  The complexity of
> non-evaluation in Mathematica includes, among other operators,
> Hold, Holdform, Defer, HoldAll, HoldFirst, HoldRest, Evaluate,
> Unevaluated, ReleaseHold, HoldComplete, HoldPattern, HoldAllComplete,
> SequenceHold, Update, NHoldAll, NHoldFirst, NHoldRest, With, Extract..

I've been using Mathematica for over 20 years, and I've never needed
the majority of those. Understanding Set[] versus SetDelayed[],
Condition[], and Replace[] cover 99% of the cases where evaluation
needs to be controlled. And to me, they seemed very natural from the
beginning, and still do.

Remember that Mathematica is not fundamentally a "programming
language" based on functions and procedures. It is a term rewriting
system for evaluating mathematical expressions. Now, of course, that
can *emulate* functions, and with a little extra help, procedures too.
But it can also do things unanticipated by the lambda calculus:

x_[whoCalled] ^:= x

While for pure programming, term rewriting isn't the most natural
foundation, it is very natural for manipulating mathematical
expressions, I think. But the user must commit to actually using the
paradigm, and not fighting it (this is true, of course, for *any*
tool). I think you just like to fight. I'd rather get real work done.


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