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

TL;DR

This paper introduces a compilation method for Egison's non-linear pattern matching with backtracking, enabling its integration into functional languages like Scheme, and demonstrates improved performance over the original Egison interpreter.

Contribution

It presents a novel translation approach for Egison pattern matching into standard functional language constructs, facilitating broader implementation and efficiency.

Findings

Egison pattern matching embedded in Scheme is faster than the original Egison interpreter.

The proposed method successfully translates Egison pattern matching into Scheme macros.

Benchmark results confirm performance improvements.

Abstract

Pattern matching is an important feature of programming languages for data abstraction. Many pattern-matching extensions have been proposed and implemented for extending the range of data types to which pattern matching is applicable. Among them, the pattern-matching system proposed by Egi and Nishiwaki features practical pattern matching for non-free data types by providing an extensible non-linear pattern-matching facility with backtracking. However, they implemented their proposal only in an interpreter of the Egison programming language, and a method for compiling pattern-matching expressions of Egison was not discussed. This paper proposes a method for translating a program that contains pattern-matching expressions of Egison to a program that contains only the existing syntax constructs of functional programming languages. This method is based on the three key ideas: (i) transformation of a matcher to a function that takes a pattern and a target, and returns lists of triples of a pattern, a matcher, and a target; (ii) compilation of match-all to application of the map function; (iii) transformation of a value pattern to a function that takes an intermediate pattern-matching result and returns a value. This paper shows the proposed method works by showing Scheme macros that provide the users the pattern-matching facility of Egison. This paper also presents benchmark results that show Egison pattern-matching embedded in Gauche Scheme is faster than the original Egison interpreter.