Re: Behavior of Longest
- To: mathgroup at smc.vnet.net
- Subject: [mg107951] Re: [mg107909] Behavior of Longest
- From: Leonid Shifrin <lshifr at gmail.com>
- Date: Wed, 3 Mar 2010 05:54:35 -0500 (EST)
- References: <201003021254.HAA14195@smc.vnet.net>
Daniel,
My problem is that I assumed that you can match something between one
> element and the whole "level". E.g. in {a,1,2,b} it should be possible to
> match 1,2. In a "regex" like notation you would write something like:
> _Integer{2}.
> However, it looks like in Mathematica you have to match either one element or the
> whole "level". Is this correct?
>
Well, at least that's what I would think. My understanding is that during
the pattern-matching attempts, the pattern matcher normally searches until
the first match is found (this corresponds to Shortest), while Longest
instructs it to search for all matches (much like ReplaceList) and then
choose the one with the longest sequence for the part wrapped in Longest.
But in any case, this should be the match that matches the entire level of
expression, (may be a single element, or a number of them together with
their head), but not some sub-sequence of elements (of course, then we can
extract the subsequence by destructuring). Thus the need for extra
placeholders, like {___,Shortest[__Integer],___}. The placeholders on the
left and on the right effectively allow us to extract the subsequence, but
they seem to be necessary, as well as the outer list.
Regards,
Leonid
>
>
>
> On 02.03.2010 14:32, Leonid Shifrin wrote:
>
> Hi Daniel,
>>
>> I don't think it's a bug. By using the form you did, you gave the
>> pattern-matcher no choice,
>> since there are no other placeholders (in the case of Shortest) to
>> absorb the rest of the elements.
>>
>> In[502]:= {1, 2} /. {___, Longest[x__Integer], ___} :> f[x]
>>
>> Out[502]= f[1, 2]
>>
>> In[504]:= {1, 2} /. {Longest[x__Integer]} :> f[x]
>>
>> Out[504]= f[1, 2]
>>
>> I have an impression that the intended use is in a list, like in your
>> second example or in the following:
>>
>> In[505]:= {1, 2} /. {Shortest[x__Integer]} :> f[x]
>>
>> Out[505]= f[1, 2]
>>
>> In[506]:= {1, 2} /. {___, Shortest[x__Integer], ___} :> f[x]
>>
>> Out[506]= f[1]
>>
>> In[507]:= {1, 2} /. {___, Shortest[x__Integer]} :> f[x]
>>
>> Out[507]= f[2]
>>
>> In the last two cases, there are placeholders to absorb "unused"
>> elements, and thus the pattern-matcher has a freedom it needs for
>> Shortest. In fact, in your first example you really did not apply rules
>> at level 0 (entire expression) - rather, they were applied at level 1,
>> two times: for a sequence <1>, and for a sequence <2>, separately:
>>
>> In[509]:= Replace[{1, 2},
>> Longest[x__Integer] :> (Print["Rule matched"]; f[x]), {0}]
>>
>> Out[509]= {1, 2}
>>
>> In[510]:= Replace[{1, 2},
>> Longest[x__Integer] :> (Print["Rule matched"]; f[x]), {1}]
>>
>> During evaluation of In[510]:= Rule matched
>>
>> During evaluation of In[510]:= Rule matched
>>
>> Out[510]= {f[1], f[2]}
>>
>> Regards,
>> Leonid
>>
>>
>>
>> On Tue, Mar 2, 2010 at 3:54 PM, dh <dh at metrohm.com
>> <mailto:dh at metrohm.com>> wrote:
>>
>> Hello,
>> can somebody give an explanation for the following behavior of Longest
>> (Mathematica version 7.0.1):
>> {1, 2} /. Longest[x__Integer]:>{x} gives {{1}, {2}}
>>
>> the same as Shortest:
>> {1, 2} /. Shortest[x__Integer]:>{x} gives {{1}, {2}}
>>
>> However, it works like expected in the following case:
>> {a, 1, 2, b} /. {x1___, Longest[x__Integer], x2___} :> {x1, {x}, x2}
>> gives: {a, {1, 2}, b}
>>
>> looks like a bug to me.
>>
>> Daniel
>>
>> --
>>
>> Daniel Huber
>> Metrohm Ltd.
>> Oberdorfstr. 68
>> CH-9100 Herisau
>> Tel. +41 71 353 8585, Fax +41 71 353 8907
>> E-Mail:<mailto:dh at metrohm.com <mailto:dh at metrohm.com>>
>>
>> Internet:<http://www.metrohm.com>
>>
>>
>>
>>
>
> --
> Daniel Huber
> Metrohm AG
> International Headquarters
> Oberdorfstr. 68, CH-9101 Herisau / Switzerland
> Phone +41 71 353 8606, Fax +41 71 353 89 01
>
> Mail <mailto:dh at metrohm.com>
> Web <http://www.metrohm.com
>
>
>
- References:
- Behavior of Longest
- From: dh <dh@metrohm.com>
- Behavior of Longest