Re: Re: Re: Re: New version, new bugs
- To: mathgroup at smc.vnet.net
- Subject: [mg42926] Re: [mg42922] Re: [mg42869] Re: [mg42817] Re: New version, new bugs
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Sat, 2 Aug 2003 12:47:48 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Maxim has pointed out that RuleCondition has the attribute HoldFirst. I
was too careless giving my explanation: what I meant to refer to was
the following difference between Condition and RuleCondition (which I
learned form Allan Hayes)
Hold[a] /. a :> Condition[1 + 1,True]
Hold[1+1]
Hold[a] /. a :> RuleCondition[1 + 1, True]
Hold[2]
On Saturday, August 2, 2003, at 10:12 AM, Andrzej Kozlowski wrote:
> I just noticed an easy way to conclusively demonstrate the cause of the
> "problem" that Maxim Rytin observed.
>
> Note that:
>
>
> f[a] + f[b] + 1 /. HoldPattern[Plus[f[_]..]] /; True :> 0
>
>
> 1 + f[a] + f[b]
>
> does not work (Rytin's example). The FullForm of the input is:
>
> ReplaceAll[Plus[f[a],
> f[b], 1], RuleDelayed[
> Condition[HoldPattern[Plus[Repeated[f[Blank[]]]]], True], 0]]
>
> Now, replace Condition by (the undocumented) RuleCondition, which,
> unlike Condition, evaluates it's first argument and observe that we now
> get:
>
>
> ReplaceAll[Plus[f[a],
> f[b], 1], RuleDelayed[
> RuleCondition[HoldPattern[Plus[Repeated[f[Blank[]]]]], True], 0]]
>
> 1
>
> which works as expected.
>
>
>
>
>
> On Thursday, July 31, 2003, at 07:47 AM, Andrzej Kozlowski wrote:
>
>>
>> On Wednesday, July 30, 2003, at 10:07 AM, Maxim wrote:
>>
>>> I think it should be mentioned that there are some things that
>>> probably
>>> aren't errors but still can be considered as major drawbacks.
>>> 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.
>>>
>>>
>>
>>
>> Pattern matching is of course a very delicate technique, its not at
>> all
>> surprising that "very similar" patterns match different expressions.
>> (Actually the patterns are no longer so similar if you look at their
>> full form).
>> The cases involving HoldPattern[Plus] are obviously nonsense and the
>> fact that they do not work is quite consistent with the description of
>> HoldPattern in the Mathematica book. The only thing about this
>> supposed
>> problem that deserves any comment is the observation that:
>>
>>> f[a] + f[b] + 1 /. HoldPattern[Plus[f[_] ..]] /; True :> 0
>>
>> does not work and
>>
>>> f[a] + f[b] + 1 /. HoldPattern[Plus[f[_] ..]] :> 0 /; True
>>
>> does.
>>
>> This is indeed rather subtle. To see what happens more clearly, let us
>> consider a head h instead of Plus:
>>
>> In[1]:=
>> h[1, f[b], f[c]] /. HoldPattern[h[f[_]..]] /; True :> 0
>>
>> Out[1]=
>> h[1, f[b], f[c]]
>>
>>
>> In[2]:=
>> h[1, f[b], f[c]] /. HoldPattern[h[f[_]..]] :> 0 /; True
>>
>> Out[2]=
>> h[1, f[b], f[c]]
>>
>> We see no difference. Now give h the attribute Flat:
>>
>> SetAttributes[h, {Flat}]
>>
>> In[4]:=
>> h[1, f[b], f[c]] /. HoldPattern[h[f[_]..]] /; True :> 0
>>
>> Out[4]=
>> h[1, f[b], f[c]]
>>
>>
>> In[5]:=
>> h[1, f[b], f[c]] /. HoldPattern[h[f[_]..]] :> 0 /; True
>>
>> Out[5]=
>> h[1,0]
>>
>> You get the difference you observed with Plus.
>> As you can see clearly, in order for the match to take place the Flat
>> property of h needs to be used. This is done in the second case with
>> h[1, f[b], f[c]] being first replaced by h[h[1], h[f[b], f[c]]] and
>> not
>> done in the first case. The reasons are basically to do with the order
>> of pattern matching and evaluation (and are closely related to the so
>> called Trott-Strzebonski method of partial evaluation of expressions).
>> However, this matter, which has been discussed on this list before, is
>> not important here. The important thing here is that the mechanism
>> responsible for this behaviour is both subtle and powerful, although
>> admittedly not very transparent. It may sometimes be confusing but it
>> also underlies lots of very convenient patterns matching constructions
>> many of us use all the time. If you know of a way to achieve all of
>> that in a simple and transparent way I am sure Wolfram Research would
>> be interested. But unlike some of your earlier criticism I can see
>> nothing constructive not in any way valuable in this one. The same, I
>> am afraid, applies to the rest of your posting.
>>
>> Andrzej Kozlowski
>> Yokohama, Japan
>> http://www.mimuw.edu.pl/~akoz/
>> http://platon.c.u-tokyo.ac.jp/andrzej/
>>
>>
>>
> Andrzej Kozlowski
> Yokohama, Japan
> http://www.mimuw.edu.pl/~akoz/
> http://platon.c.u-tokyo.ac.jp/andrzej/
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/