Programming with Ellipses

2026-07-10

AI Summary

This work proposes a language extension that introduces the ellipsis ("...") as a first-class syntactic construct in functional programming, enabling its direct use in both patterns and expressions. Traditional list manipulations in functional languages rely on recursive definitions, often resulting in verbose code that can be unintuitive for learners with an imperative background. By leveraging a program translation mechanism based on least general generalization, the proposed notation is automatically desugared into standard functional code. This approach seamlessly integrates iterative intuition with functional expressiveness, significantly simplifying the definition of common list-processing functions while preserving semantic rigor. The extension enhances both the expressivity of the language and its pedagogical accessibility without compromising formal correctness.

Abstract

We present the design of a language extension that allows the use of ellipses ("...") in patterns and expressions, which facilitates function definitions on lists that are more succinct and direct than the standard recursive ones. The semantics of ellipsis notation is defined via a program translation that is based on computing least general generalizations of the expressions on the boundary of ellipses. We show that ellipsis notation applies to a wide spectrum of function definitions. Ellipsis notation can also support the teaching of functional programming, and its inherently iterative nature may make it especially helpful to those with an imperative programming background. Like list comprehensions, ellipsis notation provides an attractive tool for functional languages that adds to their syntactic variety and enriches their expressiveness.

Problem

• ellipsis notation
• functional programming
• list manipulation
• language expressiveness
• program syntax

Innovation

• ellipsis notation
• least general generalization
• program translation
• functional programming
• syntactic extension