MATHEMATICA TUTORIAL

# Manipulating Expressions in External Programs

Mathematica expressions provide a very general way to handle all kinds of data, and you may sometimes want to use such expressions inside your external programs. A language like C, however, offers no direct way to store general Mathematica expressions. It is nevertheless possible to do this by using the loopback links provided by the MathLink library. A loopback link is a local MathLink connection inside your external program, to which you can write expressions that can later be read back.

`...ml = MLLoopbackOpen(stdenv, &errno);`
This puts the expression Power[x, 3] onto the loopback link.
`MLPutFunction(ml, "Power", 2);  MLPutSymbol(ml, "x");  MLPutInteger32(ml, 3);...`
This gets the expression back from the loopback link.
`MLGetFunction(ml, &head, &n);  MLGetSymbol(ml, &sname);  MLGetInteger32(ml, &k);...`
This closes the loopback link again.
`MLClose(ml);`

You can use MLTransferExpression() to take an expression that you get via stdlink from Mathematica, and save it in a local loopback link for later processing.

You can also use MLTransferExpression() to take an expression that you have built up on a local loopback link, and transfer it back to Mathematica via stdlink.

This puts onto a local loopback link.
`...MLPutFunction(ml, "Factorial", 1);  MLPutInteger32(ml, 21);`
This sends the head FactorInteger to Mathematica.
`MLPutFunction(stdlink, "FactorInteger", 1);`
`MLTransferExpression(stdlink, ml);`

You can put any sequence of expressions onto a loopback link. Usually you get the expressions off the link in the same order as you put them on.

And once you have got an expression off the link it is usually no longer saved. But by using MLCreateMark() you can mark a particular position in a sequence of expressions on a link, forcing MathLink to save every expression after the mark so that you can go back to it later.

This puts the integer onto a loopback link.
`...MLPutInteger32(ml, 45);`
`MLPutInteger32(ml, 33);`
And this puts .
`MLPutInteger32(ml, 76);`
This will read from the link. The will no longer be saved.
`MLGetInteger32(ml, &i);`
This creates a mark at the current position on the link.
`mark = MLCreateMark(ml);`
`MLGetInteger32(ml, &i);`
`MLGetInteger32(ml, &i);`
This goes back to the position of the mark.
`MLSeekMark(ml, mark, 0);`
`MLGetInteger32(ml, &i);`
It is important to destroy marks when you have finished with them, so no unnecessary expressions will be saved.
`MLDestroyMark(ml, mark);`

The way the MathLink library is implemented, it is very efficient to open and close loopback links, and to create and destroy marks in them. The only point to remember is that as soon as you create a mark on a particular link, MathLink will save subsequent expressions that are put on that link, and will go on doing this until the mark is destroyed.

Functions for getting pieces of expressions from a link.

 MLTKFUNC composite function—head and arguments MLTKSYM Mathematica symbol MLTKINT integer MLTKREAL floating-point number MLTKSTR character string

Constants returned by MLGetNext().

`switch(MLGetNext(ml)) {`
`    case MLTKFUNC:    MLGetArgCount(ml, &n);     recurse for head    for (i = 0; i < n; i++)          recurse for each argument        ... `
`    case MLTKSYM:    MLGetSymbol(ml, &name);    ... `
`    case MLTKINT:    MLGetInteger32(ml, &i);    ... }`

By using it is straightforward to write programs that can read any expression. The way MathLink works, the head and arguments of a function appear as successive expressions on the link, which you read one after another.

Note that if you know that the head of a function will be a symbol, then you can use instead of . In this case, however, you still need to call to disown the memory used to store the symbol name.