Expressions are the objects the system manipulates. They represent
mathematical constructs such as numeric values, variables, sums,
fractions, equations, etc. The engine.expressions package contains
the definition of the Expression type and a number of convenience
methods to create a variety of expressions.
Patterns are used to check if an expression is of a given shape
and that it satisfies certain conditions. It is also used to grab
subexpressions to be manipulated. Think of it as a regexp, but for
tree structures. Just like for Expressions, there is a number of
convenience methods for creating patterns in engine.patterns.
A Path represents a position in an expression tree. E.g. "./0/2" means the second child of the zeroth child of the root expression (zero indexed). Internally they are represented by a singly linked list.
Mapped Expressions represent the result of a transformation.
They contain the data of an expression together with information about
the origin of the different parts of that expression. For example,
in the transformation 1 + 2 * 3 -> 1 + 6, the value 6 in the
result expression is obtained by combining the 2 and the 3 from the
initial expression. This can be represented in the mapped expression
with a path mapping (./1/0, ./1/1) -> ./1 (./1/0 being the path
of 2, ./1/1 the path of 3 in the initial expression and ./1 the
path of 6 in the resulting expression).
The Transformation is the data structure which stores the generated solution. It consists of the original and resulting expressions, an explanation of the change in the current step, the skills involved and a list of substeps which are themselves transformations.