.. _symbolic_expressions_chapter:

Symbolic Expressions
====================

Each program variable is assigned a symbolic expression that denotes the current
value of the program variable as a function of any number of symbolic *input
variables*.  Grackle provides builtin functions for creating fresh symbolic variables,
and users can build up expressions by using operations supported by Grackle.  For
example, consider the following code:

::

    x = symbolic('u', 'integer');
    y = symbolic('v', 'integer');
    z = x + y;
    z = z + y;

This code first generates fresh integer variables **u** and **v** and assigns
them to program variables ``x`` and ``y`` respectively.  It then generates the
expression **u + v** and assigns that to the program variable ``z``.  Finally,
it uses the generates the expression **(u + v) + v** by using the current
expressions assigned to ``z`` and ``y``, and then assigns that expression to
``z``.

Grackle supports a variety of mathematical values including logical predicates,
integers, real numbers, and fixed-precision integers.  Input variables for these
types can be created using the :ref:`symbolic_fun` function.  To create more
complex functions, Grackle supports a variety of functions in Matlab have been
implemented in Grackle and extended them to support symbolic expressions.  For
complete documentation about what functions have been implemented in Grackle,
see :ref:`matlab_api_chapter` for the MATLAB API and :ref:`llvm_api_chapter` for
the LLVM API.