Non-linear Pattern Matching with Backtracking for Non-free Data Types

TL;DR

This paper introduces Egison, a new programming language with efficient, extensible, and polymorphic pattern matching designed specifically for complex non-free data types like multisets, graphs, and expressions.

Contribution

It presents a novel pattern matching approach with backtracking for non-linear patterns, fulfilling key practical criteria often unmet by previous languages.

Findings

Implemented and open-sourced Egison language

Demonstrated efficient pattern matching for complex data types

Supports extensibility and polymorphism in pattern matching

Abstract

Non-free data types are data types whose data have no canonical forms. For example, multisets are non-free data types because the multiset $\{a,b,b\}$ has two other equivalent but literally different forms $\{b,a,b\}$ and $\{b,b,a\}$. Pattern matching is known to provide a handy tool set to treat such data types. Although many studies on pattern matching and implementations for practical programming languages have been proposed so far, we observe that none of these studies satisfy all the criteria of practical pattern matching, which are as follows: i) efficiency of the backtracking algorithm for non-linear patterns, ii) extensibility of matching process, and iii) polymorphism in patterns. This paper aims to design a new pattern-matching-oriented programming language that satisfies all the above three criteria. The proposed language features clean Scheme-like syntax and efficient and extensible pattern matching semantics. This programming language is especially useful for the processing of complex non-free data types that not only include multisets and sets but also graphs and symbolic mathematical expressions. We discuss the importance of our criteria of practical pattern matching and how our language design naturally arises from the criteria. The proposed language has been already implemented and open-sourced as the Egison programming language.