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

*To*: mathgroup at smc.vnet.net*Subject*: [mg117031] Re: evaluation-- one or many levels, your thoughts?*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Tue, 8 Mar 2011 05:34:57 -0500 (EST)*References*: <ikq8gs$7vl$1@smc.vnet.net> <ikt5i5$5$1@smc.vnet.net> <il2d46$61n$1@smc.vnet.net>

On 07/03/2011 10:47, Richard Fateman wrote: > On 3/5/2011 3:07 AM, David Bailey wrote: > .. > > > e.g. > x1=x2 > x2= Sum[a[i]*v^i,{i,1,1000}] > > x3=x1 is, or should be, fast whether it really assigns literally x2 > or the Sum. It is too fast to measure - I have just tested it! Mathematica seems to be VERY good at tracking which parts of expressions need evaluating. I have often wondered about this, and I wish Wolfram would devote a blog article to lifting the hood a little about this! > > 2. You are mimicking the execution of a program in a language like > FORTRAN, but are doing everything symbolically so as to find bugs, > and relate the computed values to expected mathematical formulas. > The fact that x=x+1 produces, for x, a value of "x+1" means that > x was not properly initialized and you have found a bug in the FORTRAN > program. > If I wanted to do this, I'd probably replace X by a sequence of variables representing the successive values, so we would end up with something like X3=X2+1 I'd certainly not represent the operation x=x+1 by that Mathematica expression! Before you object that this would generate an impossible number of variables, it is worth pointing out that such a simulation would probably also generate some horrendously large expressions, if performed for many cycles. It is interesting that you need to resort to such an obscure example! I think complete evaluation is desirable because there is no clear distinction between programming variables and algebraic variables. If you write x=f[i,j,l,m] (where f stands for a complicated function) you clearly want f to evaluate if i is a loop variable, but not if none of the variables have changed since the expression has been created - in other words, Mathematica would need to track variable changes, whether it performed exhaustive evaluation or not! More generally, I think any CAS system has to contain compromises, particularly when it is also meant to a wider role as a numerical calculator. When I first encountered Mathematica, the exhaustive evaluation paradigm surprised me, but it is clearly implemented in an efficient way, so I am happy with it. Furthermore, there is absolutely no way in which you could change this now, so any discussion seems a little pointless. David Bailey http://www.dbaileyconsultancy.co.uk

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

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