On 2 Aug 2007, at 1:20 pm, Alexis Hazell wrote:
Category theorists can define monads concisely using the language of their discipline - surely we can settle on a definition of Haskell Monads that would make sense to any programmer who has mastered basic programming concepts?
It all depends on what you mean "make sense to". I can tell my student that (an instance of Monad) is a type constructor applications of which support certain operations that must satisfy certain operations. They can memorise that. But it remains meaningless noise to them. What matters is not what monads *ARE* but what they are *FOR*. Why should anyone care what monads are until they know why monads matter? One of my colleagues here, who has worked in logic for many years, is fond of saying that there are "set theory" people who like to have their feet on the ground and "category theory" people who like to have their heads in the air. There's no dispute that you get a much better view with your head in the air; there is no dispute that the general definitions and understandings of monads have power and utility. Me, I'm a set theory person. I have no trouble with fields, got my head around tensors and Lie groups (or very nearly), and I even know what a fibre bundle is (got an A for that). All of this is *grounded*. But I have repeatedly hit category theory and as repeatedly bounced. Chapter 1? No trouble. Chapter 2? No trouble. Chapter 3? Bounce. If a "category theory" person wants to understand monads, they will be happy with an abstract approach and work down from there. But if a "set theory" person wants to understand monads, they have to start with simple specific cases. The IO monad first. The ST monad. Then perhaps Maybe and []. And then start learning about monad transformers. The understanding of monads as such will grow out of this; by the time they are ready to cope with these compact high level definitions people are talking about they won't need it any more. I don't have any numbers. It would be interesting if someone did a survey. But I suspect that "category theory" people are a minority even among functional programmers. How many O'Caml programmers worry about the definition of monads? So go on arguing about how to define monads for Haskell, but consider your audience.