Functional programming, object-oriented programming and algebras!

Functional and Object-Oriented (OO) abstractions provide dual views on programming. Functional languages, like ML or Haskell, use algebraic datatypes as the main structuring abstraction. Algebraic datatypes require programmers to think about all the variants in advance, but in return they allow functions to be defined modularly. In Object-Oriented languages, like Java or C#, interfaces are the main abstraction. Interfaces require programmers to think about all the functions in advance, but in return they allow new variants to be defined modularly. This dual view in programming was first observed by Reynolds and later popularized by Wadler via the cunningly named Expression Problem. Wadler's Expression Problem emphasizes an additional question: can we have variants and functions both defined modularly?

Recent years have been prolific in solutions to the Expression Problem for both functional and OO languages. Despite superficially looking quite different, various solutions have in fact a common abstraction behind them: some variant of (F-)Algebras. In this talk I'll give an overview of some of the solutions to the Expression Problem in both Functional and OO languages. Then I will discuss the algebra-related abstractions behind these solutions to relate the different solutions to the Expression Problem. Finally I'll argue that a different programming paradigm arises when we take algebras (instead of algebraic datatypes or interfaces) as a primary structuring abstraction.