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

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 [20]. 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 patternmatching 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 patternmatching 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.

Functional Programming in Pattern-Match-Oriented Programming Style

“…This section quickly introduces the pattern-matching facility of Egison. The features explained in the former part of this section (section 2.1, section 2.2, and section 2.3) are already discussed in the original paper of Egison [9]. The features explained in the latter part are newly introduced in this paper except for loop patterns that are intensively discussed in the author's previous paper [6].…”

“…Therefore, the time complexities of the above expressions are identical. The patternmatching algorithm inside Egison is discussed in [9] in detail. 2 The Author's paper [8] on Scheme macros that implement our pattern-matching system discusses the performance of a program in pattern-match-oriented style.…”

“…The patternmatching algorithm inside Egison is discussed in [9] in detail. 2 The Author's paper [8] on Scheme macros that implement our pattern-matching system discusses the performance of a program in pattern-match-oriented style. A program in pattern-match-oriented style is currently two times slower when compared with the same program in functional programming style.…”

“…1. Pattern-match-oriented programming requires less local variables; 5 Our previous paper [9] shows benchmark results.…”

“…In Egison [23] whose distinguishing feature is non-linear pattern matching with backtracking [9], we can define map and mapWithBothSides concisely and in a very similar way. In fact, the creator of Egison, an author of this paper, got an idea of the language when he implemented mapWithBothSides for implementing an automated theorem conjecturer.…”