====================
parses numbers
===================
5
---
(expression (number))

===================
parses variables
===================
x
---
(expression (variable))

===================
parses products
===================
x * x
---
(expression (term
    (variable)
    (times)
    (variable)))

===================
parses sums
===================
x + x
---
(expression
    (variable)
    (plus)
    (variable))

====================
parses complex trees
====================
x * y + z * a
---
(expression
    (term (variable) (times) (variable))
    (plus)
    (term (variable) (times) (variable)))

=================================
handles parenthesized expressions
=================================
x * (y + z)
---
(expression (term
    (variable)
    (times)
    (factor (expression (variable) (plus) (variable)))))