A System for Typesetting Mathematics


          Brian W. Kernighan and Lorinda L. Cherry



                          _A_B_S_T_R_A_C_T


          This paper describes the design and implemen-
     tation  of  a  system for typesetting mathematics.
     The language has been designed to be easy to learn
     and to use by people (for example, secretaries and
     mathematical typists) who know neither mathematics
     nor  typesetting.   Experience  indicates that the
     language can be learned in an hour or so,  for  it
     has  few  rules and fewer exceptions.  For typical
     expressions, the size and font changes,  position-
     ing, line drawing, and the like necessary to print
     according to mathematical conventions are all done
     automatically.  For example, the input
9        sum from i=0 to infinity x sub i = pi over 2
9     produces

9999                        _i=078_R78oo999_x_i=99277_J9_

9
          The syntax of the language is specified by  a
     small context-free grammar; a compiler-compiler is
     used to  make  a  compiler  that  translates  this
     language into typesetting commands.  Output may be
     produced on either a phototypesetter or on a  ter-
     minal  with forward and reverse half-line motions.
     The system interfaces directly with  text  format-
     ting programs, so mixtures of text and mathematics
     may be handled simply.



          This paper is a revision of  a  paper  origi-
     nally published in CACM, March, 1975.







978
9




                       August 3, 1987





                           - 2 -


_1.  _I_n_t_r_o_d_u_c_t_i_o_n



     ``Mathematics is  known


in  the  trade as _d_i_f_f_i_c_u_l_t,


or _p_e_n_a_l_t_y, _c_o_p_y because  it


is  slower,  more difficult,


and more expensive to set in


type  than any other kind of


copy normally  occurring  in


books and journals.'' [1]



     One   difficulty   with


mathematical   text  is  the


multiplicity of  characters,


sizes,    and   fonts.    An


expression such as



99   _x__->_J_/27lim (tan _x)8sin 2_x9 _= 1


9requires an intimate mixture


of  roman,  italic and greek
7777777777777777777777777777777777777777777777777777778

                                letters, in three sizes, and


                                a  special character or two.


                                (``Requires'' is perhaps the


                                wrong  word, but mathematics


                                has  its  own  typographical


                                conventions  which are quite


                                different  from   those   of


                                ordinary  text.) Typesetting


                                such an expression by tradi-


                                tional  methods  is still an


                                essentially  manual   opera-


                                tion.



                                     A second difficulty  is


                                the  two dimensional charac-


                                ter  of  mathematics,  which


                                the  superscript  and limits


                                in  the  preceding   example


                                showed in its simplest form.




                       August 3, 1987





                           - 3 -


This is carried further by




    _a0_+9999_a1_+9999_a2_+99_a3_+ _. _. _.77_b39____________________777_b29__________________________777_b19________________________________











and still further by