The Replace Operator

TL;DR

This paper extends regular expression calculus with a replace operator that encodes various replacement operations, including conditional and contextual replacements, using regular relations and established techniques.

Contribution

It introduces a replace operator into regular expressions, enabling concise encoding of complex replacement rules with conditions and contexts.

Findings

Defines the replace operator within regular expression calculus.

Shows how replacement expressions encode various replacement variations.

Uses established techniques to formalize the replace operator.

Abstract

This paper introduces to the calculus of regular expressions a replace operator, ->, and defines a set of replacement expressions that concisely encode several alternate variations of the operation. The basic case is unconditional obligatory replacement: UPPER -> LOWER Conditional versions of replacement, such as, UPPER -> LOWER || LEFT _ RIGHT constrain the operation by left and right contexts. UPPER, LOWER, LEFT, and RIGHT may be regular expressions of any complexity. Replace expressions denote regular relations. The replace operator is defined in terms of other regular expression operators using techniques introduced by Ronald M. Kaplan and Martin Kay in "Regular Models of Phonological Rule Systems" (Computational Linguistics 20:3 331-378. 1994).