Parsing Overview

All parsing routines are located in mathics.core.parser. See Precedence-Climbing Parser for parsing details.

However, here are the main points:

• The parser is recursive descent

• Because WL has a lot of operators an Operator-precedence parser is used

• The result is an Full-form M-expression, which is a translation of the input string. See Expressions as Trees.

To see a translation of the Full-Form input the flag --full-form can be given to the command-line utilities mathics or mathicsscript.

Here is an example:

$ mathics --full-form

Mathics3 6.0.1
...
Quit by pressing CONTROL-D

In[1]:= 1 + 2 / 3
System`Plus[1, System`Times[2, System`Power[3, -1]]]
Out[1]= 5 / 3

Note that this is different from formatting the output:

In[2]:= (x + 1) / 3
System`Times[System`Plus[Global`x, 1], System`Power[3, -1]]
Out[2]= (x + 1) / 3
In[3]:= (x + 1) / 3 // FullForm
System`FullForm[System`Times[System`Plus[Global`x, 1], System`Power[3, -1]]]
Out[3]= Times[Rational[1, 3], Plus[1, x]]

Some things to notice:

• Parsing fully-qualifies names. So we have System`Times instead of Times, even though the FullForm output shows the simple name.

• Parsing removes parenthesis used for grouping capturing this instead by the function nesting order

Next:

• Precedence-Climbing Parser