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evaluation-- one or many levels, your thoughts?

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  • Subject: [mg116909] evaluation-- one or many levels, your thoughts?
  • From: Richard Fateman <fateman at>
  • Date: Fri, 4 Mar 2011 03:39:00 -0500 (EST)

How often do you require the behavior that an expression
is evaluated until it stops changing, rather than evaluated

Difference in behavior..


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"

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".  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..

Some languages make do with about 2 constructs, a mechanism to
protect from evaluation (quoting)  and some way of re-evaluating.

Some time ago I wrote a paper on this topic,
but some recent
programming that I was doing suggested to me that Mathematica
was probably doing considerable unnecessary work checking for
something that never happened. (That is, after the 1st evaluation,
nothing ever changed again.)  This is kind of conventional in
ordering programming languages, and that's all I seemed to expect
as I was writing. The choice between 0 ("Hold") and "perhaps many"
  defaults to "perhaps many", which in practice was "just once".


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