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Re : Unpredictability (was (Re: Unevaluated, Plus and Times (was Re: Mathematica language issues))

About Mathematica language issues and predictability :

i=5

Print[++i * ++i] will always return 42 as Print[++i * i++] will always return 36.
And it's predictable and will always return these values.

In ISO C9x a construction like :

int i=5;

printf("%d",++i * ++i); is unpredictable.
It may return 0 , -45621245 or even 42 !

Such a construction is not forbidden but inpredictable (cf C99 Rationale V5.10).

I think in Mathematica it shoudln't be allowed at all.

Of course who wants to Print[++i * i--] ?

Jean-Michel


Fred Simons wrote:
> The discussion on the behaviour of Unevaluated in cases where it should not 
> be used lasts already for a long time. Though irrelevant there are some 
> interesting aspects in it. The general behaviour of Unevaluated has been 
> explained by Andrzej Kozlowsky. Let me reformulate it very short and 
> therefore inaccurate: when during the evaluation process the expression 
> changes, the arguments that originally were wrapped in Unevaluated are not 
> rewrapped. It is very important to note that changes only due to attributes 
> do not count as an change.
> 
> Examples have been given to demonstrate that Times and Plus behave 
> differently. For example the expression Unevaluated[z]+2. Mathematica looks 
> at z+2. The terms are reordered due to the attribute Orderless so 
> Mathematica arrives at 2+z. That is the end of the evaluation. The change is 
> only due to the attributes so we expect rewrapping of Unevaluated, that is 
> the result 2+Unevaluated[z]. But the outcome is 2+z.
> 
> In my previous mail I tried to explain this behaviour from the fact that the 
> evaluation of expressions with head Plus or Times is slightly different. 
> According to Bobby, that explanation was not very clear, so in this mail I 
> try to do it better.
> 
> There is evidence that as soon as the head Times or Plus of an expression is 
> recognized, Mathematica does some sort of pre-evaluation of the arguments. 
> All numerical arguments are multplied or added and the result is placed 
> befor the other arguments. Only after this pre-evaluation the attributes of 
> Times and Plus are applied and the evaluation continues.
> 
> I will only consider the function Plus. The pre-evaluation of the arguments 
> can be seen from the following function preplus, in which the rules used by 
> Mathematica are 'caught':
> 
> Attributes[preplus]={HoldAllComplete};
> preplus[x___] := Block[{Plus}, plus@@Plus[x]]
> 
> Now we can imitate the evaluation of an expression with head Plus by first 
> doing the pre-evaluation with the function preplus and then apply Plus to 
> the result.
> 
> Here are some examples.
> 
> Evaluation of the expression 2+Unevaluated[z] is done in the following way:
> 
> In[12]:=
> preplus[2,Unevaluated[z]]
> Plus @@ %
> 
> Out[12]=
> plus[2,Unevaluated[z]]
> Out[13]=
> 2+Unevaluated[z]
> 
> The pre-evaluation does not change the arguments, so in the input of Plus 
> the argument z is still wrapped in Unevaluated. Plus do not change the 
> expression so at the end the argument z is wrapped in Unevaluated.
> 
> The expression 1+1+Unevaluated[z] gives a different result:
> 
> In[14]:=
> preplus[1,1,Unevaluated[z]]
> Plus @@ %
> 
> Out[14]=
> plus[2,z]
> Out[15]=
> 2+z
> 
> The pre-evaluation changed the arguments so Unevaluated has completely 
> disappeared in the input of Plus.
> 
> The expression 2+Unevaluated[z+2]:
> 
> In[16]:=
> preplus[2, Unevaluated[z+2]]
> Plus @@ %
> 
> Out[16]=
> plus[2,Unevaluated[z+2]]
> Out[17]=
> 4+z
> 
> Here the pre-evaluation has no effect, so after applying the attributes Flat 
> and Orderless, Plus is called with arguments 2, 2 and z. Plus has no rules 
> for these combination of argument, so it has to return Plus[2,2, 
> Unevaluated[z]]. But then  the evaluation of course continues:
> 
> In[18]:=
> preplus[2, 2, Unevaluated[z]]
> Plus @@ %
> 
> Out[18]=
> plus[4,z]
> Out[19]=
> 4+z
> 
> Pre-evaluation of the arguments gives a new set of arguments, so z is no 
> longer wrapped in Unevaluated, and the outcome is 4+z.
> 
> My conclusion is that the result of all curious examples with head Plus or 
> Times where some of the arguments supplied with Unevaluated can be predicted 
> in the way Andrzej has described when one takes into account the 
> pre-evaluation, as I did in the above examples.
> 
> Fred Simons
> Eindhoven Ubiversity of Technology 
> 

-- 
"They that can give up essential liberty to obtain a little temporary
  safety deserve neither liberty nor safety."     -- B. Franklin, 1759

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jmcollard (2)
12/28/2004 11:38:32 AM
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12/29/2004 1:26:14 AM
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