tikz-multinets

A LaTeX package to draw the most general interaction nets: with multiports and multiwires (a.k.a. hyperedges)

An example is worth a thousand codelines

The brute code to this example here.
For some explanation, see below.

Lafont interaction nets.

Lafont interaction nets, presented first in [1], are graphical computation languages in which the minimal step of computation is given by rewriting rules on pairs of cells. This way, a program, having a cell a but missing some cell b can interact with another program which has b, thus modeling interaction. Laffont kept things simple as he was modeling classical computations providing the expressivity of Turing machines.

Since then, interaction nets evolved. One of the evolutions was to bring in concurrency.

In order to do this, cells have been upgraded to multicells: cells with multiple ports, and connection was allowed between mode than just two cells at once by the use of multiwires. This package does exactly this: allows to draw multicells and multiwires.

At the end of the day, multinets are similar to hypergraphs. With the addition of precise connection to vertices by the use of ports.

A brief introduction to the use of the package

Each element of the net is defined separately as you would describe it orally: there are cells like this, others like that. A wire connets that port of that cell to this port of this cell, etc.

To create a cell, give it:

1. a name in order to refer to it later
2. a label: it is the sign shown on the cell.
   If the label is simple (no inline formula), you can skip the name: it will automatically be the same as the label
3. a number of principal ports and of auxiliary ports
4. a position (see below).
5. a direction: U, D, R, L for Up, Down, Right and Left, or an angle in degrees with 0 for Down and going clockwise

\inetmulticell(alpha){$\alpha$}{3}{7}{0,0}[U]

You can then reference its ports using the name of the cell and the type and number of the port:

alpha.pal 2    % second principal port
alpha.pax 7    % seventh auxiliary port

If you want to draw the port for instance, you shall write:

\inetport(alpha.pal 2)

If you want to draw a wire connecting two ports, it's as simple as:

\inetwire(alpha.pal 1)(beta.pax 3)

If there are more than three ports, specify:

\inetmultiwire(alpha.pal 1)(beta.pax 3)(gamma.pal 2)(alpha.pax 2)

That's about it for the cells and wires. Now starts the difficult part: positioning the cells to make the net comprehensible. Following tikz conventions, you can define positions in many ways:

• with cartesian coordinates: {2,3}
• with cartesian coordinates: {2,3}
• with polar coordinates: {50:2cm}
• relative to another element: {a_cell}+{2,3}
• aligned with two existing elements
• horizontally to a_cell, vertically to b_cell: {a_cell -| b_cell}
• vice-versa: {a_cell |- b_cell}
• between two elements at a given proportion: {$(a_cell)!.25!(b_cell)$}
• some combinations of these: {$(a_cell)+(2,4)!.25!(b_cell)$}

This package adds another type of positioning:
    relative to a given port of a given cell. {gamma.pax 3}++{1.7}

1.7 of whatever unit is used in the picture, above the third auxiliary port of cell gamma, where above means "in the direction in which the port points".

While cells are quite straightforward to define (not easy, straightforward) once you've found where to place them, wires require a little more attention if you want them to avoid getting under the cells. The package does not contain automatic calculation of paths. Nevertheless it uses the power of Tikz ... (wire, short wire or very short wire...)

An explanation of the code that produces the nice example above

It's possible to pre-define some cells to be used as a shortcut later. Choose a latex command name, some tikz options, the number of ports:

\newcommand{\selector}
	{\inetmulticellshape[very thick,inner sep=0pt,isosceles triangle apex angle=55]{1}{3}}
\newcommand{\multiplexor}
	{\inetmulticellshape[very thick,inner sep=-3pt,isosceles triangle apex angle=90]{1}{3}}
\newcommand{\decoder}
	{\inetmulticellshape[very thick,inner sep=0pt,isosceles triangle apex angle=55]{1}{1}}

To use later in the code, just add a name, a label, a position and/or a direction:

  \selector(Si1){$S_{i:1}$}{0,0}[U]

If needed, you can add (or overwrite) tikz-style properties to an already predefined cell:

 \multiplexor[arity=7](multiplex){$T_{n+m}$}{0,0}

One can even predefine a cell with a given label:

 \newcommand{\gammacell}
	{\inetmulticelltype[isosceles triangle apex angle=75]{$\gamma$}{1}{2}}

Even easier to use: just add a name, a position (and/or direction):

 \gammacell(gamma){0,0}

\begin{tikzpicture}[show nodes=false]

 \inetmulticell[minimum width=15ex](alpha){$\alpha_i$}{3}{7}{0,0}
 \inetport(alpha.pal 1)
 \inetdotsabove(alpha.pal 2)
 \inetport(alpha.pal 3)
 \inetdotsabove(alpha.pax 4)
%
 \gammacell(gamma1){alpha.pax 7}++1
 \inetwire(gamma1.pal)(alpha.pax 7)
 \gammacell(gammaN){alpha.pax 2}++1
 \inetwire(gammaN.pal)(alpha.pax 2)
%
 \selector(Si1){$S_{i:1}$}{gamma1.pax 1}++{1.7}
 \inetwire(Si1.pal)(gamma1.pax 1)
%
 \selector(SiN){$S_{i:n}$}{gammaN.pax 1}++{1.7}
 \inetwire(SiN.pal)(gammaN.pax 1)
%
 \inetmulticell(rho){$\rho_n$}{3}{1}{0.08,4.5}
 \inetshortwire(rho.pal 1)(Si1.pax 2)
 \inetshortwire(rho.pal 3)(SiN.pax 2)
 \inetdotsabove(rho.pal 2)
%
 \multiplexor[arity=7](multiplex){$T_{n+m}$}{rho.pax 1}++{1}
 \inetwirecoords(multiplex.pal)(rho.pax 1)
 \inetwirefree(multiplex.pax 6)
 \inetabove(multiplex.pax 5){...}
 \inetwirefree(multiplex.pax 4)
 \inetabove(multiplex.pax 2){...}

 \inetnode(n1){gammaN}+{1.2,0}
 \inetnode(nN){n1.e}++{.8}
 \node at ($(n1)!.5!(nN)$){$\ldots$};

 \inetnode(m1){n1 |- multiplex.above above pax}
 \inetnode(mN){nN |-  multiplex.above above pax}+{0,.2}
 \node at ($(m1)!.5!(mN)$) {$\ldots$};
 %\inetnode(mN'){m1.n}+{-.5,.2}
 \inetnode(mN'){mN -| multiplex.pax 3}

 {\inetwiresunder
  \inetwire(alpha.pax 6)<n1.s><m1.n>(multiplex.pax 1);
  \inetwire(alpha.pax 1)<nN.s><mN.s><mN'>(multiplex.pax 3);

  \selector(Si1'){$S_{i:1}$}{-3.4,2.9}[U]
  \inetshortwire(Si1'.pax)(gamma1.pax 2)
  \selector(SiN'){$S_{i:n}$}{Si1'}+{1.4,0}[U]
  \inetshortwire(SiN'.pax)(gammaN.pax 2)
  \node at ($(Si1')!.5!(SiN') + (0,.2)$) (mid1) {\ldots};
 }
%
 \decoder(D1){$D$}{Si1'.pal}++{.6}[U]
 \inetwirefree(D1.pax)
 \decoder(DN){$D$}{SiN' |- D1}[U]
 \inetwirefree(DN.pax)
%
 \multiplexor[inner sep=1pt](multiplex'){$C_{n}$}%
					{mid1 |- multiplex}[U]
%
 \inetveryshortwire(D1.pal)(multiplex'.pax 1)
 \inetdotsabove(multiplex'.pax 2)
 \inetveryshortwire(DN.pal)(multiplex'.pax 3)
%
 \inetcell[shape border uses incircle=false](copy){$C_2$}%
					{$(multiplex'.pal)!.5!(multiplex.pax 7) + (0,.6)$}[U]

 \inetveryshortwire(multiplex.pax 7)(copy.right pax)
 \inetshortwire(multiplex'.pal)(copy.left pax)
%
 \inetwirefree(copy.pal)
\end{tikzpicture}

^ [1]: Lafont, Y. Interaction nets. In Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (New York, NY, USA, 1990), POPL '90, ACM, pp. 95-108.