Theorems, etc with ConTeXt

Theorems, etc with ConTeXt

[Aditya Mahajan]

Hi,

(This post actually belongs to dev-context, but I do not know if 
everyone interested in this reads dev-context, so I am posting it to 
this list).

  I have been looking at what is the best way to do theorems etc with 
ConTeXt. There are ways to handle most of the requirements, but some 
of them are not possible out of the box with ConTeXt. I have searched 
the archives and this questions about theorems and proofs keep on 
coming on and off. I want to see what is the requirements for 
theorems, what all is possible right now, and what needs to be done.

Below I am writing my requirements of theorem. Does anyone have 
anything more to add?

1. They should be numbered, it should be possible to control the 
numbering mechanism, for example way=bysection, bychapter, etc.
> Can be done using enumerations.

2. It should be possible to have two different types of theorems have 
the same number. For example,

\definetheorem[theorem]
\definetheorem[lemma][number=theorem]

should follow the same number as theorems.
> Is possible using enumerations

3. It should be possible to get a list of theorems. It should be 
possible to say which types of theorems go to the list and which do 
not.
> Is possible using enumerations

4. The theorem should have a title. The title should be optional.
> Is partially implemented

5. There should be a mechanism to do end-of-proof marks. The 
end-of-proof marks should also work with itemizations, and formulas.
> Not implemented at all.

6. Anything more...?


Requirement 4 is not completely implemented. With

\defineenumeration[theorem][title=yes] I always have to give a 
title. Normally, while writings theorems, there are only a few 
theorems that have a title. The rest of them do not. Right now, I can 
work around this restriction, by either having two different theorems 
(titledtheorem and nontitledtheorem) or always adding {} at the 
beginning of each theorem. I want the behaviour closer to title=maybe.

I do not understand why \@@startdescription contains
\dowithwargument{\@@startsomedescription{#1}[#2]}

I would prefer it to contain

\dosinglegroupempty{\@@startsomedescription{#1}[#2]}

(well this will of course not work, but I hope the idea is clear)

So that I can do

\defineenumeration[theorem][title=yes]

\starttheorem A silly theorem not worth a title \stoptheorem

as well

\starttheorem {My Fancy Theorem} A fancy theorem that needs to be 
given a title \stoptheorem

I do not think that changing this will break anything. I am not even 
sure why dowithwargument is there. I cannot imagine anyone writing

\startthoerem Title this is a theorem \stoptheorem

instead of

\starttheorem {Title} this is a theorem \stoptheorem


The title also needs some more attributes. Right now, only titlestyle, 
titlecolor and titledistance are there. To be more flexible, you would 
also need something like titleleft, and titleright, which should not 
be too difficult.

The last things, that is the end of proof marker, is right now not 
possible in ConTeXt. There are a lot of things that need to be taken 
care of while having a end-of-proof marker: basically, you need to 
ensure that there is no page break between the proof and the marker. 
Also the marker needs to be moved up or down, depending on how the 
proof ends. At the very least, ConTeXt should have something that 
ensures that the end of proof marker does not go onto a page of its 
own.


Finally, my question is:

Does it make sense to include all these functionality into 
enumerations, or have them in a separate module?


Aditya

Re: Theorems, etc with ConTeXt

[Taco Hoekwater]

Hi Aditya,

Aditya Mahajan wrote:
> 
> 4. The theorem should have a title. The title should be optional.
>> Is partially implemented

I used to work around that by defining a layer on top of the
enumerations that always define the enumeration's settings
on the fly. Quite inefficient, but it worked OK. Support in the
core would be much nicer, though.

> The last things, that is the end of proof marker, is right now not 
> possible in ConTeXt. There are a lot of things that need to be taken 
> care of while having a end-of-proof marker: basically, you need to 
> ensure that there is no page break between the proof and the marker. 
> Also the marker needs to be moved up or down, depending on how the 
> proof ends. At the very least, ConTeXt should have something that 
> ensures that the end of proof marker does not go onto a page of its 
> own.

End of proof markers are a pain, and I see no easy solution.

Taco

Re: Theorems, etc with ConTeXt

[Aditya Mahajan]

On Fri, 19 Jan 2007, Taco Hoekwater wrote:

> 
> Hi Aditya,
> 
> Aditya Mahajan wrote:
> > 
> > 4. The theorem should have a title. The title should be optional.
> >> Is partially implemented
> 
> I used to work around that by defining a layer on top of the
> enumerations that always define the enumeration's settings
> on the fly. Quite inefficient, but it worked OK. Support in the
> core would be much nicer, though.

I will try to add this to as a patch to enumerations, and see how it 
works.

> > The last things, that is the end of proof marker, is right now not 
> > possible in ConTeXt. There are a lot of things that need to be taken 
> > care of while having a end-of-proof marker: basically, you need to 
> > ensure that there is no page break between the proof and the marker. 
> > Also the marker needs to be moved up or down, depending on how the 
> > proof ends. At the very least, ConTeXt should have something that 
> > ensures that the end of proof marker does not go onto a page of its 
> > own.
> 
> End of proof markers are a pain, and I see no easy solution.

I saw a proof.tex for plain tex, which ensured that the end of the 
line marker stayed on the same page. No support for correct 
spacing for itemize and formula. The ntheorem package does that, but I 
do not fully understand the algorithm, so it may be harder to port. I 
will try a port of proof.tex if I can find it again.

Aditya

Re: Theorems, etc with ConTeXt

[Oliver Buerschaper]

Hi Aditya, hi Taco,

I would really love to see built-in support for theorems in ConTeXt!

I have been typesetting my diploma thesis (in mathematical physics)  
with ConTeXt and my experience has been that in some areas ConTeXt  
still needs to catch up a bit on LaTeX (especially on the AMS  
packages), although it has definitely come along way already ...

So far I have constructed my theorems etc. as enumerations on an  
adhoc basis and - surprise - noted a few glitches here and there.

1. For some environments I chose style=\it but this resulted in  
italic equation numbers as well. However, these numbers should always  
be typeset upright.

2. There is some odd behaviour concerning the options "right" and  
"stopper" which I mentioned on the list a while ago. I believe this  
is more an issue of descriptions/enumerations  than anything else but  
it would affect any theorem mechanism based on enumerations. Perhaps  
this can be looked into at the same time as you're trying to cook up  
generic theorems.

Have you found out anything about the end of proof markers yet? I  
haven't tried it out but how do the AMS folks handle this issue?  
Unfortunately, I don't have the TeX programming experience (yet) to  
start digging myself ...

Oliver



>> Hi Aditya,
>>
>> Aditya Mahajan wrote:
>>>
>>> 4. The theorem should have a title. The title should be optional.
>>>> Is partially implemented
>>
>> I used to work around that by defining a layer on top of the
>> enumerations that always define the enumeration's settings
>> on the fly. Quite inefficient, but it worked OK. Support in the
>> core would be much nicer, though.
>
> I will try to add this to as a patch to enumerations, and see how it
> works.
>
>>> The last things, that is the end of proof marker, is right now not
>>> possible in ConTeXt. There are a lot of things that need to be taken
>>> care of while having a end-of-proof marker: basically, you need to
>>> ensure that there is no page break between the proof and the marker.
>>> Also the marker needs to be moved up or down, depending on how the
>>> proof ends. At the very least, ConTeXt should have something that
>>> ensures that the end of proof marker does not go onto a page of its
>>> own.
>>
>> End of proof markers are a pain, and I see no easy solution.
>
> I saw a proof.tex for plain tex, which ensured that the end of the
> line marker stayed on the same page. No support for correct
> spacing for itemize and formula. The ntheorem package does that, but I
> do not fully understand the algorithm, so it may be harder to port. I
> will try a port of proof.tex if I can find it again.
>
> Aditya

Re: Theorems, etc with ConTeXt

[Aditya Mahajan]

On Mon, 29 Jan 2007, Oliver Buerschaper wrote:

> Hi Aditya, hi Taco,
>
> I would really love to see built-in support for theorems in ConTeXt!
>
> I have been typesetting my diploma thesis (in mathematical physics)
> with ConTeXt and my experience has been that in some areas ConTeXt
> still needs to catch up a bit on LaTeX (especially on the AMS
> packages), although it has definitely come along way already ...
>
> So far I have constructed my theorems etc. as enumerations on an
> adhoc basis and - surprise - noted a few glitches here and there.
>
> 1. For some environments I chose style=\it but this resulted in
> italic equation numbers as well. However, these numbers should always
> be typeset upright.

This was the first thing I noticed when I started with ConTeXt, see
http://archive.contextgarden.net/message/20050526.134831.21522839.en.html 
;)

Now, I use
   \setupformulas[numberstyle=normal]
in my local setup.


> 2. There is some odd behaviour concerning the options "right" and
> "stopper" which I mentioned on the list a while ago. I believe this
> is more an issue of descriptions/enumerations  than anything else but
> it would affect any theorem mechanism based on enumerations. Perhaps
> this can be looked into at the same time as you're trying to cook up
> generic theorems.

I will see if I can do anything about it.

> Have you found out anything about the end of proof markers yet?

Not yet. It is possible to have a simple solution that will work in 
90% of the case. Coming up with something that works for 98% of the 
cases is very hard. I do not understand the working of TeX to do that. 
The idea is to make sure the problem is well defined so that Hans and 
Taco can solve it :)

> I haven't tried it out but how do the AMS folks handle this issue?

The end-of-proof handling in amsthm is not correct. It requires you to 
manually put \qedhere and does not work correctly if the proof ends 
with a equation. Look at ntheorem.sty for the correct behaviour.

> Unfortunately, I don't have the TeX programming experience (yet) to 
> start digging myself ...

Even a description of the expected features and how the output should 
look like will be useful.

This is going to be slow progress due to other time constraints, but I 
should have something working in a month or two.

Aditya


>
>
>>> Hi Aditya,
>>>
>>> Aditya Mahajan wrote:
>>>>
>>>> 4. The theorem should have a title. The title should be optional.
>>>>> Is partially implemented
>>>
>>> I used to work around that by defining a layer on top of the
>>> enumerations that always define the enumeration's settings
>>> on the fly. Quite inefficient, but it worked OK. Support in the
>>> core would be much nicer, though.
>>
>> I will try to add this to as a patch to enumerations, and see how it
>> works.
>>
>>>> The last things, that is the end of proof marker, is right now not
>>>> possible in ConTeXt. There are a lot of things that need to be taken
>>>> care of while having a end-of-proof marker: basically, you need to
>>>> ensure that there is no page break between the proof and the marker.
>>>> Also the marker needs to be moved up or down, depending on how the
>>>> proof ends. At the very least, ConTeXt should have something that
>>>> ensures that the end of proof marker does not go onto a page of its
>>>> own.
>>>
>>> End of proof markers are a pain, and I see no easy solution.
>>
>> I saw a proof.tex for plain tex, which ensured that the end of the
>> line marker stayed on the same page. No support for correct
>> spacing for itemize and formula. The ntheorem package does that, but I
>> do not fully understand the algorithm, so it may be harder to port. I
>> will try a port of proof.tex if I can find it again.
>>
>> Aditya
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>
>
>

-- 
Aditya Mahajan | EECS Systems, University of Michigan
http://www.eecs.umich.edu/~adityam | Ph: 734.262.4008

Re: Theorems, etc with ConTeXt

[Aditya Mahajan]

[-- Attachment #1: Type: TEXT/PLAIN, Size: 2025 bytes --]

On Fri, 19 Jan 2007, Taco Hoekwater wrote:

> Aditya Mahajan wrote:
>>
>> 4. The theorem should have a title. The title should be optional.
>>> Is partially implemented
>
> I used to work around that by defining a layer on top of the
> enumerations that always define the enumeration's settings
> on the fly. Quite inefficient, but it worked OK. Support in the
> core would be much nicer, though.

Here is my first attempt. I added new keys titleleft, titleright, and 
titlecommand to provide more customization. The solution is not 
pretty, mainly because title was an afterthought, rather than being 
there from the beginning.


% This is the usual visual output

\defineenumeration
   [lemma]
   [        title=yes,
             text=Lemma,
    titledistance=.5em,
     textdistance=1em,
       titlestyle=bold,
        titleleft=(,
       titleright=),
          stopper=.,
         location=hanging,
            style=italic,
   ]

\startlemma {with a title of a certain length}
   \input tufte
\stoplemma

\startlemma
   With no title
   \input tufte
\stoplemma


Basically, works with and without any title.


The list of enumerations does not look good, and I do not know how to 
configure it.


>> The last things, that is the end of proof marker, is right now not
>> possible in ConTeXt. There are a lot of things that need to be taken
>> care of while having a end-of-proof marker: basically, you need to
>> ensure that there is no page break between the proof and the marker.
>> Also the marker needs to be moved up or down, depending on how the
>> proof ends. At the very least, ConTeXt should have something that
>> ensures that the end of proof marker does not go onto a page of its
>> own.
>
> End of proof markers are a pain, and I see no easy solution.

I will try to implement a rudimetary support for end of proof markers, 
something similar to what amsthm does. The right way to do it is too 
complicated for me to understand :-(

The code is attached and suggestions for improvement are welcome.

Aditya

[-- Attachment #2: Type: TEXT/PLAIN, Size: 5312 bytes --]

\unprotect

%D Temporary

\def\c!titleleft{titleleft}
\def\c!titleright{titleright}
\def\c!titlecommand{titlecommand}

%D To be added to syst-ext.tex 

\def\dowithoptargument#1%
  {\def\useoneargument##1{#1{##1}}
   \def\fakeoneargument{#1{}}
   \doifnextcharelse\bgroup{\useoneargument}{\fakeoneargument}}


%D Patch for core-des.tex

\def\@@startdescription[#1][#2]%
  {\def\currentdescription{#1}%
   \doifelse{\descriptionparameter\c!title}\v!yes
     {\dowithoptargument{\@@startsomedescription{#1}[#2]}}
     {\@@startsomedescription{#1}[#2]{}}}

\def\@@description[#1][#2]%
  {\def\currentdescription{#1}%
   \doifelse{\descriptionparameter\c!title}\v!yes
     {\dowithoptargument{\@@somedescription{#1}[#2]}}
     {\@@somedescription{#1}[#2]{}}}

\def\special@@descriptionhandler[#1]#2#3%
  {\strut
   \doifelse{\descriptionparameter\c!number}\v!no
     \!!doneafalse{\doifelse{#1}{-}\!!doneafalse\!!doneatrue}%
   \chardef\descriptioncoupling\zerocount
   \iflocation
     \doifsomething{\descriptionparameter\c!coupling}
       {\processaction % genereert > of <
          [\descriptionparameter\c!couplingway]
          [ \v!local=>\chardef\descriptioncoupling\plusone, % old: default
           \v!global=>\chardef\descriptioncoupling\plustwo]}% new: global crosslinking
   \fi
   \setupnumber % the number is called indirectly
     [\currentdescriptionnumber]
     [\c!sectionnumber=\descriptionparameter\c!sectionnumber]%
   \if!!donea
     \makeprecedingsectionnumber[\currentdescriptionnumber]%
     \prepareprefixnumber{\??dd\currentdescription}\precedingsectionnumber\preparednumber
     \iftrialtypesetting\startlocal\fi
     \getvalue{\e!next\currentdescription}% tricky but we need the preroll
     \iftrialtypesetting\stoplocal\fi
     % \getvalue{\e!next#2#1}%
     \iflocation
       \bgroup
       \letvalue{\??dd\currentdescription\c!sectionnumber}\v!yes
       \protectconversion
       \makeprecedingsectionnumber[\currentdescriptionnumber]%
       \prepareprefixnumber{\??dd\currentdescription}\precedingsectionnumber\preparednumber
       \ifcase\descriptioncoupling \or
         \xdef\@@internalenumber{\doshowdnnumber}%
         \rawreference\s!num{#1:\@@internalenumber}{}%
       \or
         \xdef\@@internalenumber{\countervalue{\??dd\c!coupling\currentdescription}}%
         \rawreference\s!num{\currentdescription:\@@internalenumber}{}%
       \fi
       \egroup
     \fi
    %\makeprecedingsectionnumber[\currentdescriptionnumber]%
    %\prepareprefixnumber{\??dd\currentdescription}\precedingsectionnumber\preparednumber
     \disablepseudocaps   % sorry, uppercase causes troubles
     \doattributes        % \nocase primitive needed
       {\??dd\currentdescription}\c!headstyle\c!headcolor % todo: sub as well
       {\descriptionparameter\c!command
          {\showdntext
%            \domakednnumber % right should be after the title
            \descriptionparameter\c!left
            \strut\doshowdnnumber
           \doif{\descriptionparameter\c!title}\v!yes % new, for david antos
            {\doifsomething{#2}
             {\doattributes{\??dd\currentdescription}\c!titlestyle\c!titlecolor
                {\hskip\descriptionparameter\c!titledistance%
%                   \descriptionparameter\c!titlecommand%
                  {\descriptionparameter\c!titleleft%
                    \begstrut#2\endstrut%
                  \descriptionparameter\c!titleright}}}}%
             % Remaining part of \domakednnumbed
             \descriptionparameter\c!stopper
             \descriptionparameter\c!right
           }}% \c!command is hook for taco
     \doifsomething{\descriptionparameter\c!list} % also for david antos
       {\dowritetolist
          {\descriptionparameter\c!type:\descriptionparameter\c!list}
          {\showdnlisttext\doshowdnnumber}{#2}{\currentdescription}}%
     \iflocation\ifcase\descriptioncoupling \else
       \edef\localconnection{\descriptionparameter\c!coupling:\@@internalenumber}%
       \doifreferencefoundelse\localconnection
         {\in[\localconnection]}\donothing % genereert > of <
     \fi\fi
     \doifnot{#1}{-}{\rawreference\s!num{#1}{\doshowdnnumber}}%
  \else % Why was this strange expansion needed?
     \edef\!!stringa{\showdnpuretext}% nog eens testen binnen \expanded
     \expanded{\doattributes{\??dd\currentdescription}\noexpand\c!headstyle\noexpand\c!headcolor
       {\noexpand\descriptionparameter\noexpand\c!command{\!!stringa}}}%
     \doifnot{#1}{-}{\rawreference\s!num{#1}{}}%
   \fi}
\protect

\starttext

\defineenumeration
  [lemma]
  [             title=yes,
                 text=Lemma,
        titledistance=.5em,
         textdistance=1em,
   %             left=***,
   %            right=**,
   %          command=\framed,
   %     titlecommand=\inframed,
           titlestyle=bold,
            titleleft=(,
           titleright=),
              stopper=.,
             location=hanging,
                style=italic,
  ]

\startlemma[lemma 1] {with a title of a certain length} 
  \input tufte 
\stoplemma

\startlemma[lemma 2]
  With no title 
  \input tufte 
\stoplemma

We have two lemmas, \in Lemma[lemma 1] and \in Lemma[lemma 2].

\stoptext

[-- Attachment #3: Type: text/plain, Size: 139 bytes --]

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Re: Theorems, etc with ConTeXt

[Aditya Mahajan]

Hi Oliver,

On Mon, 29 Jan 2007, Oliver Buerschaper wrote:

> Hi Aditya, hi Taco,
>
> I would really love to see built-in support for theorems in ConTeXt!

I have rudimentary support for titled theorems and end of proof 
markers working. It also takes care of your bug-report.

> I have been typesetting my diploma thesis (in mathematical physics)
> with ConTeXt and my experience has been that in some areas ConTeXt
> still needs to catch up a bit on LaTeX (especially on the AMS
> packages), although it has definitely come along way already ...
>
> So far I have constructed my theorems etc. as enumerations on an
> adhoc basis and - surprise - noted a few glitches here and there.
>
> 2. There is some odd behaviour concerning the options "right" and
> "stopper" which I mentioned on the list a while ago. I believe this
> is more an issue of descriptions/enumerations  than anything else but
> it would affect any theorem mechanism based on enumerations. Perhaps
> this can be looked into at the same time as you're trying to cook up
> generic theorems.

I have patched core-des so that stopper is also honored when number=no 
is set.

> Have you found out anything about the end of proof markers yet? I
> haven't tried it out but how do the AMS folks handle this issue?
> Unfortunately, I don't have the TeX programming experience (yet) to
> start digging myself ...

I have a very basic end of proof marker working. Basically, it will 
handle the marker correctly for proofs that end with paragraphs, and 
works hard to avoid a page break when the proof ends with a formula or 
an itemize (in this case, the end of proof marker is in a line of its 
own). The main macro for putting the proof marker on the right is from 
Paul Taylor's qed.sty. If you want to test this, I can send you the 
file offlist. This file is not in a state to be merged into the core 
right now.

Hans, why does core-des.tex define description parameter as:

\def\descriptionparameter#1{\csname\??dd\currentdescription#1\endcsname}

while in some other files, you had

\def\....parameter#1{\executeifdefinedelse{\??..\current....#1}{\executeifdefined{\??..#1}}

which prevents a lot of copying of parameters. Is core-des yet to be 
cleaned up?


Aditya

Re: Theorems, etc with ConTeXt

[Oliver Buerschaper]

Hi Aditya,

> I have rudimentary support for titled theorems and end of proof
> markers working. It also takes care of your bug-report.

That's great news! My fingers are itching to test it ;-)

> I have patched core-des so that stopper is also honored when number=no
> is set.

Does this mean that your patch has already been merged with the  
official release?

> I have a very basic end of proof marker working. Basically, it will
> handle the marker correctly for proofs that end with paragraphs, and
> works hard to avoid a page break when the proof ends with a formula or
> an itemize (in this case, the end of proof marker is in a line of its
> own). The main macro for putting the proof marker on the right is from
> Paul Taylor's qed.sty. If you want to test this, I can send you the
> file offlist. This file is not in a state to be merged into the core
> right now.

Please send it to me ...

Thanks,
Oliver

Re: Theorems, etc with ConTeXt

[Aditya Mahajan]

On Tue, 6 Mar 2007, Oliver Buerschaper wrote:

> Hi Aditya,
>
>> I have rudimentary support for titled theorems and end of proof
>> markers working. It also takes care of your bug-report.
>
> That's great news! My fingers are itching to test it ;-)
>
>> I have patched core-des so that stopper is also honored when number=no
>> is set.
>
> Does this mean that your patch has already been merged with the
> official release?

No, it will be a while before it will be merged in the official 
release. I will make all changes that I want and then ask Hans to look 
at it --- don't want to waste Hans time for including each different 
thing individually.

>> I have a very basic end of proof marker working. Basically, it will
>> handle the marker correctly for proofs that end with paragraphs, and
>> works hard to avoid a page break when the proof ends with a formula or
>> an itemize (in this case, the end of proof marker is in a line of its
>> own). The main macro for putting the proof marker on the right is from
>> Paul Taylor's qed.sty. If you want to test this, I can send you the
>> file offlist. This file is not in a state to be merged into the core
>> right now.
>
> Please send it to me ...

Will do.

Aditya