Pattern matching is a powerful tool for symbolic computations. Applications include symbolic integration, term rewriting systems, theorem proving and the manipulation of abstract syntax trees. Given a pattern and an expression, the goal of pattern matching is to find a substitution for all the variables in the pattern such that the pattern becomes the expression. As an example, consider the pattern f(x), where x is a variable, and the expression f(a). Then the substitution that replaces x with a is a match. In practice, functions can also be associative and/or commutative, which makes matching more complicated and can lead to multiple possible matches.

Pattern matching is a powerful tool for symbolic computations, based on the well-defined theory of term rewriting systems. Application domains include algebraic expressions, abstract syntax trees, and XML and JSON data. Unfortunately, no lightweight implementation of pattern matching as general and flexible as Mathematica exists for Python [Pö16], [Hao14], [Sch14], [Jen15]. Therefore, we created the open source module MatchPy which offers similar pattern matching functionality in Python using a novel algorithm which finds matches for large pattern sets more efficiently by exploiting similarities between patterns.

Abstract-Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules.We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems.

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