AST, S-Expression, General List: same thing¶
The end-result of scanning and parsing is an S-expression, which is a
Python object of type
Expression. In compiler terminology the
S-expression is also called an abstract syntax tree or AST. The
first leaf of an
Expression is called the “head”.
Expression is to be evaluated, the head should a
Symbol for a Mathics Function or another
evaluated produces a function symbol.
In Mathics, there are only very few different kinds of
Expression nodes, called “atoms” that can appear:
With the exception of the addition of
Filename these are
almost the same atoms described in Basic Internal Architecture
Not listed above but found in the link is “general expressions”: the
thing that glues everything together. In Mathics, I imagine this
The class definitions for these are given in mathics.core.parser.ast.
If you compare the above four AST types with other languages, you’ll find this is pretty sparse. For example, Python’s AST has well over 30 different types.
So what’s the difference? Python specializes AST types for different kinds of programming language constructs, such as for loops, conditional statements, exception blocks, different kinds of expressions, and so on. In WL and Mathics, these are all simply built-in functions.
In the process of Evaluation, described in the next section, more kinds of objects over the above the four may get introduced as the S-expression is rewritten and transformed.
Here is an example of the tranformation from an input string to the AST Form (an S-Expression)
We use the
--full-form option in the
mathics command-line to get this information.
Note that this shows the input before evaluation:
In:= 3 a - b System`Plus[System`Times[3, Global`a], System`Times[-1, Global`b]] Out= 3 a - b In:= 3 5 - 6 System`Plus[System`Times[3, 5], -6] Out= 9