%August 1995, C.G. van der laan, cgl@rc.service.rug.nl
\input blue.tex  
\loadtocmacros
%\tolerance500\hbadness=499\hfuzz=5pt
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\bluetitle Paradigms: It's all in the game

\bluesubtitle Dialogue with \TeX

\blueissue \maps{96}1

\beginscript

\bluehead BLUe's Design VI

Hi folks. 
In {\oldstyle1989} Greene contributed
`Playing in \TeX's mind' to TUG {\oldstyle89}.
Having fun with \TeX{} has been on my mind all the time.
Of late, I thought of tic-tac-too as an exercise in programming
dialogues in \TeX, in a simple and elegant way, with hopefully
some paradigms emerging, suited for educational purposes.
The play is simple but nevertheless entails essential aspects
of having a dialogue with \TeX. 
Below I first strip the play to the essentials and
from there build the user-friendly, but otherwise modest, code.
At the end the \TeX ing peculiarities are summarized. 

\bluehead The play

Tic-tac-too is played by two persons on a board with $3{\times}3$ fields. 
Each player marks a field in turn and the one who has first 
three marks in a row has won. 
\def\data{+\cs o\cs+\rs \cs o\cs+\rs o\cs \cs +}
$$\ruled\btable\data$$

\bluehead Prototyping

The dialogue with \TeX{} goes through the log file, also called transcript.

The board is represented by the defs \cs{1}, \dots\cs{9} row-wise.
Each player owns a  mark called \cs{markplayer} and \cs{markopponent}.
A user is prompted to input a value\Dash 1, 2, ... or 9\Dash
which indicates the field where to put his mark. 
The program keeps track of the kind of mark, via a toggle.
To end the game the user can input 0.

The above resulted in the following bare-to-the-bones
implementation of tic-tac-too.
\beginverbatim
\def\showboard{\immediate\write0{\1\2\3}
               \immediate\write0{\4\5\6}
               \immediate\write0{\7\8\9}}
\def\initialize{\def\1{-}\def\2{-}\def\3{-}
                \def\4{-}\def\5{-}\def\6{-}
                \def\7{-}\def\8{-}\def\9{-}}
\def\play{\initialize \loop\showboard
   \ifx\mark\markplayer
      \let\mark\markopponent\else 
      \let\mark\markplayer\fi
   \immediate\write0{Supply index for \mark:}
   \read0to\index         \expandafter
   \xdef\csname\index\endcsname{\mark}
\ifnum\index>0 \repeat}%end \play
\def\markplayer{+}\def\markopponent{o}
\endlinechar-1 %TB20.18
\play \bye   
!endverbatim
Remarks.
Because of the toggling of the \cs{mark} an \cs{xdef} was needed.

One could code that the player and opponent are both 
taking care of during each traversal of the loop. 
However, apart from that it makes the code longer it is also clumsy, and 
if careless one has to account for multiple exits of the loop.
I assumed states in which the loop is traversed. 
The next steps are not for the faint of heart.

\bluehead Real-life version

Given the above prototype implementation we can refine, 
add more bells-and-whistles. Basically these add-ons are in two directions
\bitem improve the user interface
\bitem let the program do more, such as deciding who has won.
\smallbreak

\bluesubhead Improving the user interface

Explain the conventions adopted, especially what the indices stand for.

Always nice is to allow for personalization, i.e.\ the system prompt asks for
YOU, with your name. 
This entails that the players must be asked to identify themselves and that
the toggling must be extended.

Another feature is that the program prompts the remaining indices to choose from.

And what about robustness? I decided not to implement robustness with respect
to lowercase or uppercase y or n, for example.
I also refrained from checking whether the supplied index is allowed.\ftn
{Not that difficult, actually, 
 because the set of allowed indices is maintained.}

\bluesubhead Let the program do more

The most important aspect is to add intelligence to the program to check
for a winner.

The play restarts automatically 

\bluesubhead The code

The board is represented by the defs
\cs{1}, \cs{2}, \dots \cs{9}, the $3{\times}3$ board row-wise.


The structure of the program is similar to the prototype,
with \cs{play} elaborated and the check \cs{checkforgameend} added.
\beginverbatim
\immediate\write0{Tic-tac-too
          Aug 1995, cgl@rc.service.rug.nl}
\let\ea\expandafter
\newcount\k\newcount\value\newcount\checksum
\newif\ifsol
\newtoks\set %Index set
\def\del#1{\def\lop##1#1##2\pol{\set{##1##2}}
   \ea\lop\the\set\pol}
%
\def\showboard{\immediate\write0{}
\immediate\write0{\1\2\3}
\immediate\write0{\4\5\6}
\immediate\write0{\7\8\9}}
%
%Initialization
\def\initialize{\set{123456789}\solfalse
   \immediate\write0{New names of players? 
       (default \player\space and \opponent)}
   \read0to\yorn
   \if y\yorn 
     \immediate\write0{Name player}
     \read0to\player
     \immediate\write0{Name opponent}
     \read0to\opponent
   \fi\k0
   \loop\advance\k1
       \ea\def\csname\the\k\endcsname{-}
     \ifnum\k<10
   \repeat
   \immediate\write0{Empty board}
}%end initialization
%Test for solution
\def\sol#1#2#3{{\advance\count#1\count#2
  \advance\count#1\count#3
  \ifnum\count#1=\checksum \global\soltrue\fi}}
\def\checkforgameend{%
\sol123\ifsol\message{\who\space  won}\k0 \else
\sol456\ifsol\message{\who\space  won}\k0 \else
\sol789\ifsol\message{\who\space  won}\k0 \else
\sol147\ifsol\message{\who\space  won}\k0 \else
\sol258\ifsol\message{\who\space  won}\k0 \else
\sol369\ifsol\message{\who\space  won}\k0 \else
\sol159\ifsol\message{\who\space  won}\k0 \else
\sol357\ifsol\message{\who\space  won}\k0 \else
\fi\fi\fi\fi\fi\fi\fi\fi}
%Play
\def\play{\initialize\begingroup
\loop\showboard
   \ifx\who\player\value-1 \checksum-3
      \let\who\opponent 
      \let\mark\markopponent  
   \else\value1 \checksum3 
      \let\who\player 
      \let\mark\markplayer 
   \fi
   \immediate\write0{\who, supply index 
                     for \mark:}
   \immediate\write0{Choose from: \the\set. 
         (0 terminates)}
   \read0t\ea o\csname\who\endcsname
   \k\csname\who\endcsname
   \ea\xdef\csname\the\k\endcsname{\mark}
   \count\k\value
   \checkforgameend
\ifnum\k>0 \ea\del\ea{\the\k}
\repeat\endgroup
\immediate\write0{Play another game?}
\read0to\newplayyorn
\if y\newplayyorn\ea\play\fi}%end Play
%
%Defaults
\def\player{Kees} \def\opponent{Ina}
\def\markplayer{+} \def\markopponent{o}
%
\immediate\write0{}
\immediate\write0{Board numbering}
\immediate\write0{123}
\immediate\write0{456}
\immediate\write0{789}
%
\play \bye   
!endverbatim
Remark. In order to get the personalized prompts \cs{Kees}, or \cs{Ina}
the following coding was needed.
\beginverbatim
\read0t\ea o\csname\who\endcsname
!endverbatim
The few lines that follow look unnecessary complex
but are entailed by the above.

\bluehead What more?

It is intrigueing to ponder about adding even more intelligence. 
For example to let the game prompt for obligatory moves, 
or to let the program terminate when draw is inevitable, that is when there
is no possible solution left.
In order to achieve this I chose  to
\bitem maintain the set of possible solutions, instead of checking all possible
       solutions\ftn{This entails that non-feasible candidates are eliminated
           from the set of candidate solutions.}
\bitem update the set of solutions after each move, and
       look for a solution or a draw
\bitem look for obligatory moves.
\smallbreak
With respect to robustness the input can be checked for whether the index
is allowed, casu quo a y(es) or n(o).

\beginverbatim
\immediate\write0{Tic-tac-too
          Aug 1995, cgl@rc.service.rug.nl}
\let\ea\expandafter \let\nx\noexpand
\newcount\k\newcount\kk
\newcount\value\newcount\checksum
\newcount\feasible\newcount\prompt
%Solution lines
\newcount\hi\newcount\hii\newcount\hiii
\newcount\vi\newcount\vii\newcount\viii
\newcount\di\newcount\dii
\newif\ifsol
\newif\ifnotfound
%Index set and deletion from index set
\newtoks\set %Index set
\def\del#1{\def\lop##1#1##2\pol{\set{##1##2}}
   \ea\lop\the\set\pol}
%
\def\showboard{\immediate\write0{}
\immediate\write0{\1\2\3}
\immediate\write0{\4\5\6}
\immediate\write0{\7\8\9}}
%
%Initialization
\def\initialize{\set{123456789}\solfalse
   \hi0 \hii0 \hiii0 \vi0 \vii0\viii0 
   \di0 \dii0 \feasible8 \prompt0
%Cell no associated with solution subsets
\ea\def\csname solset1\endcsname{%
   \ls\hi\ls\vi\ls\di}
\ea\def\csname solset2\endcsname{%
    \ls\hi\ls\vii}
\ea\def\csname solset3\endcsname{%
    \ls\hi\ls\viii\ls\dii}
\ea\def\csname solset4\endcsname{%
    \ls\hii\ls\vi}
\ea\def\csname solset5\endcsname{%
    \ls\hii\ls\vii\ls\di\ls\dii}
\ea\def\csname solset6\endcsname{%
    \ls\hii\ls\viii}
\ea\def\csname solset7\endcsname{%
    \ls\hiii\ls\vi\ls\dii}
\ea\def\csname solset8\endcsname{%
    \ls\hiii\ls\vii}
\ea\def\csname solset9\endcsname{%
    \ls\hiii\ls\viii\ls\di}
   \immediate\write0{New names of players? 
    (default \player\space and \opponent)}
   \read0to\yorn
   \if y\yorn 
     \immediate\write0{Name player}
     \read0to\player
     \immediate\write0{Name opponent}
     \read0to\opponent
   \fi\k0
   \loop\advance\k1
       \ea\def\csname\the\k\endcsname{-}
     \ifnum\k<10
   \repeat
   \immediate\write0{Empty board}
}%end initialization
%
%Test for solution
\def\ls#1{%#1 is a solution counter
  \ifnum#1=0 \advance#1\value
  \else\ifnum\sign#1=\value \advance#1\value
       \else\advance\feasible-1
          \delete#1 %from solution sets
          \ifnum\feasible=0 \showboard
              \message{***Draw***}\k0 
          \fi
       \fi
  \fi
  %Check for solution
  \ifnum#1=\checksum \showboard
       \message{***\who*** won}\k0
  \fi}
%
\def\sign#1{\ifnum#1>0 1\else -1\fi}
\def\solsetk{\csname solset\the\k\endcsname}
%
\def\delete#1{%#1 is a solution counter to be 
              %deleted from all solution sets
{\kk0 
\def\ls##1{\ifx#1##1\else\nx\ls\nx##1\fi}
\loop\advance\kk1
\ifnum\kk<10
\ea\xdef\csname solset\the\kk\endcsname
    {\csname solset\the\kk\endcsname}
\repeat}}%end \delete
%
\def\fifo#1{\ifx#1\ofif\ofif\fi
   \process#1\fifo}
\def\ofif#1\fifo{\fi}
\def\lstry#1{%#1 is a  counter denoting 
             %a solution
   \ifnum#1=0 
   \else\ifnum\sign#1=\value 
            \advance#1\value
        %Check for solution
        \ifnum#1=\checksum \global\prompt\k
        \fi\fi
   \fi}
\def\process#1{\ifnum\prompt=0
  {\k=#1 \let\ls\lstry \solsetk}\fi}
%
\def\readprocess#1{\if#1\csname\who\endcsname 
   \notfoundfalse\fi}
%
\def\readindex{{\let\process\readprocess
   \loop\read0t\ea o\csname\who\endcsname
   %\who value in \set?
   \notfoundtrue\ea\fifo\the\set0\ofif
   \ifnotfound
   \immediate\write0{Please supply index 
                         from \the \set}
   \repeat
   \global\k\csname\who\endcsname}}
%
%Play
\def\play{\initialize\begingroup
\loop\showboard%\show\ the\solset
   \ifx\who\player\value-1 \checksum-3
      \let\who\opponent 
      \let\mark\markopponent  
   \else\value1 \checksum3 
      \let\who\player 
      \let\mark\markplayer 
   \fi 
  %Is there a winning move? 
  %(Prefails obligatory move)
  {\prompt0 \ea\fifo\the\set\ofif 
   \ifnum\prompt>0 \global\prompt0 \fi}
  %The idea is that the player must see it
  %him/herself. Of course the program knows 
  %about the winning move.
  %Obligatory move? (criterion 0<\prompt (<10)  
  \ifnum\prompt>0 \immediate\write0{Sorry \who,
          obligatory move \the\prompt}\k\prompt
  \else
      \immediate\write0{\who, supply index 
                     for \mark:}
      \immediate\write0{Choose from: \the\set. 
         (0 terminates)}
      \readindex
  \fi
  %put mark on board
  \ea\xdef\csname\the\k\endcsname{\mark}         
  %update solutions associated with \k 
  \solsetk                                        
%k=0 is stopping criterion
\ifnum\k>0 \ea\del\ea{\the\k}%
 %Look ahead for obligatory move: 
 %    Can \who gain in next turn?
 \prompt0 \ea\fifo\the\set\ofif
\repeat\endgroup
\immediate\write0{Play another game?}
\read0to\newplayyorn
\if y\newplayyorn\ea\play\fi}%end Play
%
%Defaults
\def\player{Kees} \def\opponent{Ina}
\def\markplayer{+} \def\markopponent{o}
%And off we go
\immediate\write0{}
\immediate\write0{Board numbering}
\immediate\write0{123}
\immediate\write0{456}
\immediate\write0{789}
\immediate\write0{}
\play \bye   
!endverbatim

\bluehead Is this all?

Especially the code in the last section has become complex. Should we make it more complex?
For the moment I stopped.
However, it is tempting to increase the order to {\oldstyle4},
and to extend the play to {\oldstyle3} dimensions.
My case rest.

\bluehead Paradigms

The following functionalites have been encountered and a way how to code
these in \TeX{} have been worked out.
\bitem loop traversal in various states
\bitem global Boolean, \cs{global}\cs{soltrue} 
\bitem maintaining an index set,
       deleting an element from a set
\bitem test for an empty set 
\bitem high-level parameterization, for example 
       a personalized prompt within a state-dependent loop 
\bitem \cs{read} with a {\em reference\/} to a prompt through\\
       |\read0t\ea o\csname\who\endcsname|
\bitem check on what is read is allowed.
\smallbreak
Starting from the bare-to-bones prototype it is quite something to arrive
at a solution, which carries some intelligence and robustness \smiley.
\medskip
Have fun, and all the best. 
\makesignature
\pasteuptoc
\endscript