Have Object-Oriented Languages Missed a Trick with Class Function and its Subclasses?

TL;DR

This paper explores the potential for object-oriented languages to better classify and utilize functions by introducing class hierarchies for functions, aiming to enhance expressiveness and structure.

Contribution

It proposes new class structures for functions in OO languages and demonstrates their implementation across popular languages through experimental investigation.

Findings

Identifies missing class hierarchies for functions in OO languages

Shows how subclasses of functions can be implemented and used

Highlights potential improvements in language expressiveness

Abstract

Compared to functions in mathematics, functions in programming languages seem to be under classified. Functional programming languages based on the lambda calculus famously treat functions as first-class values. Object-oriented languages have adopted ``lambdas'', notably for call-back routines in event-based programming. Typically a programming language has functions, a function has a type, and some functions act on other functions and/or return functions but there is generally a lack of (i) ``class Function'' in the OO sense of the word class and particularly (ii) subclasses of Function for functions having specific properties. Some such classes are presented here and programmed in some popular programming languages as an experimental investigation into OO languages missing this opportunity.