Re: New version, new bugs
- To: mathgroup at smc.vnet.net
- Subject: [mg42876] Re: New version, new bugs
- From: Maxim <.!dontsendhere at uunet.uu.net>
- Date: Fri, 1 Aug 2003 01:25:48 -0400 (EDT)
- References: <bfdqd8$sfi$1@smc.vnet.net> <bg7vmu$hii$1@smc.vnet.net> <bg9mog$phm$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Jens-Peer Kuska wrote:
> Hi,
>
> > Consider four
> > nearly identical expressions:
> >
> > In[1]:=
> > f[a] + f[b] + 1 /. HoldPattern[Plus][f[_] ..] /; True :> 0
> > f[a] + f[b] + 1 /. HoldPattern[Plus[f[_] ..]] /; True :> 0
> > f[a] + f[b] + 1 /. HoldPattern[Plus][f[_] ..] :> 0 /; True
> > f[a] + f[b] + 1 /. HoldPattern[Plus[f[_] ..]] :> 0 /; True
> >
> > Exactly one of them evaluates to 1. This is something from Who Wants to Be a
> > Millionaire, not a programming language.
>
> If you don't know what you are doing you should not do it.
>
> You first expression f[a]+f[b]+1 is ordered as
>
> 1+f[a]+f[b]
>
> with out the Flat attribute of Plus[] your patterns above match only for
> the
> case f[a]+f[b]+f[c]+f[d]+... and *not* for 1+f[a]+f[b].
>
> In the first two cases, the Condition[Holdpattern[_],_] is not evaluated
> and the
> Flat attribute is not applied, in the third case the
> HoldPattern[Plus][_] prevent the application of the Flat
> attribute ...
>
> If something is "nearly identical" it does not mean that it
> *is* identical.
>
> If you avoid the useless HoldPattern[] nonsense and write
>
> f[a] + f[b] + 1 /. Plus[f[_] ..] /; True :> 0
> f[a] + f[b] + 1 /. Plus[f[_] ..] :> 0 /; True
>
> all works as expected
>
> >
> > Another situation where the result is unpredictable is passing patterns to
> > functions: can you guess what the result of Integrate[x_,x_] will be? And of
> > Integrate[_,_]?
>
> It is semantic nonsens to pass a pattern to a function that expect
> a realisation of a pattern. If you have a function DriveA[car_]
> a call of this function will drive a certain car like
> DriveA[Mercedesbenz] but you can't expect that the function
> can drive all possible cars at the same time when you say
> DriveA[anyCar_]
>
> >
> > Then, of course, there is Mathematica's scoping:
> >
> > In[1]:=
> > Module[
> > {sub,f},
> > sub[a_,b_]:=Module[
> > {aa=a,x},
> > aa-b
> > ];
> > f[x_]=sub[x,x]
> > ]
> >
> > Out[1]=
> > x$-x$38
> >
> > The problem is that the x in aa and the x in b get renamed differently; I am
> > not even trying to figure out if it is a bug, I'm just pointing out how
> > confusing it is (probably it has to do with the fact that assignment in
> > Module initialization doesn't use Set).
>
> It has to do with the fact that you are using lexical scoping and you
> mean
> dynamic scoping
>
> Block[{sub, f}, sub[a_, b_] := Block[{aa = a, x}, aa - b];
> f[x_] = sub[x, x]]
>
> Mathematica does what you say and not that what you mean ...
>
> >
> > Another example:
> >
> > In[1]:=
> > <<discretemath`
> > UndirectedQ[FromAdjacencyMatrix[{{0,1},{0,0}},Type->Directed]]
> > <<numbertheory`
> > UndirectedQ[FromAdjacencyMatrix[{{0,1},{0,0}},Type->Directed]]
> >
> > Out[2]=
> > False
> >
> > Out[4]=
> > True
> >
> > Here the situation is clear: the reason for the two different answers is a
> > name conflict. But it would be nice to at least see a warning message.
>
> If you don't get a error message about symbol shadowing you have
> switched it
> of, but it is still you problem to *say* Mathematica what you mean and
> to
> write
>
> <<discretemath`
> UndirectedQ[FromAdjacencyMatrix[{{0,1},{0,0}},Type->Directed]]
> <<numbertheory`
> discretemat`UndirectedQ[discretemath`FromAdjacencyMatrix[{{0,1},{0,0}},
> discretemath`Type->discretemath`Directed]]
>
> And, yes it is a bug that Mathematica can't read your mind. But AFAIK
> WRI is working on this feature ...
>
> >
> > Finally, whose brilliant idea was it to give the output for ??In and ??Out
> > unsorted?
>
> We must have different Mathematica's because my
>
> DownValues[In]
>
> are sorted. Or did you mean that In/Out should follow the
> Input/Output cell order of the notebook and not the In/Out
> commands send to the Kernel ?
>
> Regards
> Jens
1) Firstly, of course you're wrong if you think that we can just "avoid the
useless HoldPattern[] nonsense and write"
f[a] + f[b] + 1 /. Plus[f[_] ..] /; True :> 0
The Plus in the pattern evaluates, so your rule will also match f[x], not just
sums:
In[1]:=
f[x]/.Plus[f[_]..]/;True:>0
Out[1]=
0
Then you're wrong when you claim that "HoldPattern[Plus][_] prevent the
application of the Flat attribute":
In[1]:=
MatchQ[f[a]+f[b]+1,HoldPattern[Plus][x_,y_]]
MatchQ[f[a]+f[b]+1,HoldPattern[Plus[x_,y_]]]
Out[1]=
True
Out[2]=
True
After all, if it had worked as you described, the pattern in the fourth example
(which does evaluate to 1) wouldn't have matched too.
2) I don't know what you mean by "semantic nonsens", but in any case, I'm not
discussing what the 'correct' answer to Integrate[_,_] or suchlike should be; I
simply claim that if Integrate[_,_] evaluates to _^2/2, then Integrate[x_,x_]
should be evaluated too.
3) Basically you're telling me that Block works so-and-so; yes, thanks for the
information, but what about my example? Consider that
Module[
{sub},
sub[a_,b_]:=Module[
{aa=a,x},
aa-b
];
sub[x,x]
]
gives 0, not x$-x$38. If you're going to argue that both answers are as expected,
I think you're fighting a lost cause.
4) General::shdw is a warning message actually, not an "error message", and I
haven't "switched it of" -- I'm showing the exact output from Mathematica session.
5) When I say ??In, I mean ??In. Mathematica re-sorts some internal list after you
have approximately 20 input lines, and the output looks like this (I'm showing the
first and the last lines):
In[18]:=
??In
In[n] is a global object that is assigned to have a delayed value of the nth input
line.
Attributes[In] = {Listable, Protected}
In[8] = Information["In", LongForm -> True]
In[10] = Information["In", LongForm -> True]
In[12] = Information["In", LongForm -> True]
.............................................
In[2] = Information["In", LongForm -> True]
In[4] = Information["In", LongForm -> True]
In[6] = Information["In", LongForm -> True]
It seems to me that all your statements that aren't insults are simply incorrect.
Maxim Rytin
m.r at prontomail.com