Pattern matching is used in evaluation of Mathics Expression and therefore in Function resolution. Because this process is both time consuming and involved, it is important to understand how it works. We describe some of this process here.
Based on the
Head of a Mathics Expression, the rules stored the
Definitions object for
Head are examined for matches.
When a rule matches an expression, the rule specifies how sub-expressions get bound to names, and how the expression is transformed. After this happens, the evaluation process is repeated using the replaced expression.
The process repeats until the expression converges and there are no further changes.
The power of the WL then relies in the possibility of defining rules by patterns that can match with many different expressions, and building new expressions based on the variable part of the pattern.
We now describe the Class hierarchy for
Pattern which is defined in
mathics.core.pattern. This is the base class that represents the pattern for an expression.
Two of its subclasses are:
AtomPatternpatterns that match with a given atomic expression, and
ExpressionPatternpatterns matches with non-atomic expressions (i.e., expressions with a head and elements).
There are also have several
Builtin symbols (defined in
represent different pattern constructions like
Alternatives. All of these
Builtin classes are derived from
PatternObject class, which is derived from
Pattern object has three important methods:
does_match()checks if certain expression matches the pattern
get_match_candidates()finds all the potential matches
match()performs what needs to be done when there is a match
The last method,
match(), is the most involved. It has the following function signature:
match(yield_func, expression, vars, evaluation, head=None, element_index=None, element_count=None, fully=True, wrap_oneid=True )
When called, this method binds subexpressions of the expression to
parts of the pattern. For each match,
yield_func(vars, rest) is
vars as a first parameter, and the second parameter
depends on the specific context.