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% J Language Summary
% March 23rd, 1992 by Christopher B. Browne
% Ottawa, Ontario
% This file may be freely redistributed.
% Changes/Corrections ought to be sent to Christopher Browne
% at either: cbbrowne@csi.uottawa.ca, or aa454@freenet.carleton.ca
% \lhead, \rhead, \lfoot, \rfoot require fancyheadings.sty
% The LaTeX book describes how the headers can be set/reset, but
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% but there aren't any appropriate commands in LATEX.TEX.  And
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\lhead{J Language Reference} \rhead{Version 6.2}
\lfoot{March 23, 1993} \rfoot{by Christopher B. Browne}

\eject   % As suggested by LJ Dickey

% Short forms for common macros
\def\bs{\backslash}    % Only used once for the prefix/infix operator
\def\df{\dotfill}      % Fill space with dots
\def\na{$\not\exists$} % Unimplemented function - i.e. Does not exist
\def\pc{\df {\sf PC}}  % IBM PC only

\begin{table}[h]
\caption{Vocabulary List}
\begin{center}
\begin{tabular}{||l|c|c|c|r||} \hline \hline
OP        & OP $y$ \df $x$ OP $y$                       &  OP. $y$ \df $x$ OP. $y$          & OP: $y$ \df $x$ OP: $y$       & Page  \\ \hline
=         & $y=y^{t}$ \df $x=y$                         &  Is (Local) \df                   & Is (Global) \df               &  71   \\
$<$       & $\Box y$ \df $<$                            &  $\lfloor x\rfloor$ \df $\min{}$  & $y--$ \df $x \leq y$          &  71   \\
$>$       & Open $\Box$ \df $>$                         &  $\lceil x \rceil$ \df $\max{}$   & $y++$\df $x \geq y$           &  72   \\
\_        & $-y$ \df $\infty$                           &  Indeterminate \df \na            & $\infty$ \df                  &  72   \\
+         & $\bar{y}$ \df $x+y$                         &  Real/Imag \df GCD (Or)           & $2 y$ \df NOR                 &  73   \\
$\star$   & $sgn(y)$ \df $x \times y$                   &  Polar \df LCM (And)              & $y^2$ \df NAND                &  73   \\
$-$       & $-y$ \df $x-y$                              &  Not (1-) \df Less                & $y/2$ \df Match               &  73   \\
\%        & $\frac{1}{y}$ \df $x/y$                     &  Mat $y^{-1}$ \df Mat $x\div y$   & $\sqrt{y}$ \df $\sqrt[x]{y}$  &  74   \\
\^{}      & $e^y$ \df $x^y$                             &  $\ln{x}$ \df $\log_{x}{y}$       & \df $x^{y}(z)$ \df Chain      &  75   \\
\$        & Shape \df Shape                             &  Suite \df                        & Self-Reference \df            &  75   \\
\~{}      & Both \df Cross                              &  Nub \df                          & Nub Sieve \df Not-Equal       &  76   \\
$|$       & $|y|$ \df $y (\hbox{mod} x)$                &  Reverse \df Rotate $y$ by $x$    & $y^{T}$ \df Axis Transpose    &  77   \\
.         & $\det{y}$ \df $x \cdot y$                   &  \df Even                         & \df Odd                       &  78   \\
:         & \df Explicit Def'n                          &  \df Obverse                      & \df Adverse                   &  78   \\
,         & Ravel \df Append                            &  Ravel \df Items                  & Itemize \df Laminate          &  80   \\
;         & Raze \df Link                               &  \df Cut (;.3, ;.\_3 \na)         & Formation \df                 &  81   \\
\#        & Tally \df Copy                              &  $y_{2}$ \df $y${Base}$_{x}$      & Antibase 2 \df Antibase       &  83   \\
!         & $y!$ \df $\left( x \atop y \right)$         &  Customize \df                    & \df Foreign                   &  84   \\
/         & Insert \df Table                            &  Oblique \df Key                  & Grade Up \df Sort             &  84   \\
$\bs$     & Prefix \df Infix                            &  Suffix \df Outfix                & Grade Down \df Sort           &  86   \\
$[$       & Same \df Left                               &  Lev \df                          & Same \df                      &  87   \\
$]$       & Same \df Right                              &  Dex \df                          & Same \df                      &  87   \\
\{        & Catalog \df From                            &  Head \df Take                    & Tail \df                      &  88   \\
\}        & Amend \df                                   &  Behead \df Drop                  & Curtail \df                   &  88   \\
"         & \df Rank                                    &  Do \df Do Left If Error          & \df Format                    &  89   \\
`         & \df Gerund                                  &  \df                              & \df Evoke Gerund              &  91   \\
@         & \df Atop                                    &  \df Agenda                       & \df At                        &  91   \\
\&        & Bond \df Compose                            &  \df Under (Dual)                 & \df Appose                    &  91   \\
?         & Roll \df Deal                               &                                   &                               &  92   \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[h]
\caption{Special vocabulary}
\begin{center}
\begin{tabular}{||c|l||c|l|c||l|r||} \hline \hline
OP & Description & OP & Description & OP & Description & Page \\ \hline
$)$  &  Label \df                           &  a.  &  Alphabet \df                       & A.  & Atomic Permute \df            & 92    \\
b.   &  Boolean \df                         &  c.  &  Characteristic \df \na \df         & C.  & Cycle-Direct \df Permute      & 93    \\
e.   &  Raze In \df Member (In)             &  E.  &  \df Member of Interval             & f.  & Fix              \df          & 95, 96 \\
i.   &  Integers \df Index Of               &  j.  &  Imaginary \df Complex              & NB. & Comment        \df            & 96    \\
o.   &  $\pi \times y$ \df Circular fun.    &  p.  &  Polynomial \df $P_{x}(y)$ \df \na  & r.  & Angle \df Complex             & 96, 97 \\
x.   &  Left Argument \df                   &  y.  &  Right Argument \df                 & 0:  & Zero         \df              & 97    \\
1:   &  One \df                             &  D.  &  $\frac{d^{n}F(x)}{dx^{n}}$ \df     &     &                               & 97 \\
\hline
\end{tabular}
\end{center}
\end{table}


\begin{table}[h]
\caption{Circular/Hyperbolic/Pythagorean Functions}
\begin{center}
\begin{tabular}{||r|l|r|l||} \hline
$k$ & Function  & $k$ & Function \\ \hline
0 & $\frac{1}{1 - y^{2}}$    &     9     & $ \frac{y + \bar{y}}{2}$     \\
1 & $\sin{y}$                &     10    & $ | y | $                    \\
2 & $\cos{y}$                &     11    & $ \frac{y - \bar{y}}{(0,2)} $ \\
3 & $\tan{y}$                &     12    & $ \ln{e^{y}}/(0,1)$          \\
4 & $\frac{1}{1+y^{2}}$      &     \_$k$ & $k o.^{-1} y$                \\
5 & $\sinh{y}$               &     \_1   & $ \arcsin{y} $               \\
6 & $\cosh{y}$               &     \_4   & $ \sqrt{1+y^{2}}$            \\
7 & $\tanh{y}$               &     \_9   & $y$                          \\
8 & $\sqrt{-1-y^{2}}$        &     \_10  & $\bar{y}$                    \\
\hline
\end{tabular}
\end{center}
\end{table}

Where trigonometric arguments are always in radians.\\                   
E.g: {\tt 3 o. 3.1415926 0 7.8539816} $= (\tan{\pi}, \tan{0}, \tan{      
\frac{5} {2} \pi}) = (0, 0, -\infty)$                                    

\begin{table}[h]
\caption{Foreign Conjunctions}
\begin{center}
\begin{tabular}{||r|l||r|l||r|l||}
\hline
Conj.    &    Description            &     Conj.    &      Description          &     Conj.     &     Description           \\ \hline
0!:0     &    Host                   &     2!:55    &    WS Erase Object        &      7!:2     &    Space to Execute       \\
0!:1     &    Host (No Result)       &     3!:0     &    Internal Type          &      8!:0     &    Qry CGA Mode     \pc   \\
0!:2     &    Script                 &     3!:1     &    To   Internal Rep      &      8!:1     &    Set CGA Mode     \pc   \\
0!:3     &    Silent Script          &     3!:2     &    From Internal Rep      &      8!:4     &    Qry Screen Attr  \pc   \\
0!:4     &    Lines                  &     4!:0     &    Name Class             &      8!:5     &    Set Screen Attr  \pc   \\
0!:5     &    Silent Lines           &     4!:1     &    Name List              &      8!:7     &    Refresh Screen   \pc   \\
0!:55    &    Terminate Session      &     4!:55    &    Erase                  &      8!:9     &    Edit             \pc   \\
1!:1     &    File Read              &     4!:56    &    Erase Given Name       &      9!:0     &    Qry Random Link        \\
1!:2     &    File Write             &     5!:0     &    Fix                    &      9!:1     &    Set Random Link        \\
1!:3     &    File Append            &     5!:1     &    Atomic  Rep            &      9!:2     &    Qry Display Reps       \\
1!:4     &    File Size              &     5!:2     &    Display Rep            &      9!:3     &    Set Display Reps       \\
1!:11    &    File Indexed Read      &     5!:3     &    String  Rep            &      9!:4     &    Qry Prompt             \\
1!:12    &    File Indexed Write     &     5!:4     &    Tree    Rep            &      9!:5     &    Set Prompt             \\
1!:55    &    File Erase             &     5!:5     &    Linear  Rep            &      9!:6     &    Qry Box Chars          \\
2!:0     &    WS Name Class          &     6!:0     &    Time Now               &      9!:7     &    Set Box Chars          \\
2!:1     &    WS Name List           &     6!:1     &    Time Since Start       &      9!:8     &    Qry Error Msgs         \\
2!:2     &    WS Save                &     6!:2     &    Time to Execute        &      9!:9     &    Set Error Msgs         \\
2!:3     &    WS PSave               &     6!:3     &    Delay                  &      10!:k    &    (LinkJ) C Function     \\
2!:4     &    WS Copy                &     7!:0     &    Space Now              &      128!:0   &    QR Decomposition       \\
2!:5     &    WS PCopy               &     7!:1     &    Space Since Start      &      128!:1   &    Invert matrix          \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[h]
\caption{Alternative Spellings}
\begin{center}
\begin{tabular}{||c|c|c|c||c|c|c|c||}
\hline \hline
Char   &       &  .     &   :   &   Char &       &  .     &   :    \\ \hline
  @    &  AT.  &  AT1.  &  AT2. &  \#    &  NO.  &  NO1.  &  NO2.  \\
$\bs$  &  BS.  &  BS1.  &  BS2. &  $]$   &  RB.  &  RB1.  &  RB2.  \\
 \^{}  &  CA.  &  CA1.  &  CA2. &  $\}$  &  RC.  &  RC1.  &  RC2.  \\
  `    &  GR.  &  GR1.  &  GR2. &  \$    &  SH.  &  SH1.  &  SH2.  \\
 $[$   &  LB.  &  LB1.  &  LB2. &  $|$   &  ST.  &  ST1.  &  ST2.  \\
 $\{$  &  LC.  &  LC1.  &  LC2. &  \~{}  &  TI.  &  TI1.  &  TI2.  \\
\hline \hline
\end{tabular}
\end{center}
\end{table}
\end{document}