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The Kleene star operator is an important pattern construct for representing apattern that repeats multiple times. Due to its simplicity and usefulness, itis imported into various pattern-matching systems other than regularexpressions. For example, Mathematica has a similar pattern construct calledthe repeated pattern. However, they have the following limitations: (i) Wecannot change the pattern repeated depending on the current repeat count, and(ii) we cannot apply them to arbitrary data structures such as trees and graphsother than lists. This paper proposes the loop patterns that overcome theselimitations. This paper presents numerous working examples and formal semanticsof the loop patterns. The examples in this paper are coded in the Egisonprogramming language, which features the customizable non-linearpattern-matching facility for non-free data types.

Loop Patterns: Extension of Kleene Star Operator for More Expressive Pattern Matching against Arbitrary Data Structures