Why keep reinventing the wheel when there's an ML language family already? Why do people keep giving up these juicy Hindley—Milner-ish type systems and these brief and concise equations for anything? It just doesn't make sense for me.
They are simply explicit. What's so clunky about modular implicits, for example?
Personally, I prefer explicit modules and hate typeclasses, because I can't look at the code and say if this operation is a primitive operator or some dynamically dispatched class method.
Besides, modules are way more powerful, and have a way broader use. They can encapsulate state, types, can be parametric etc.
What? In numeric programming we usually want the opposite, to write a function for specific type, and to make it run fast.
Also, in OCaml you can simply make your computation a parametric module of some algebraic structure, something like
module type Ring = sig
type t
val zero : t
val one : t
val (+) : t -> t -> t
...
end
module Numeric_staff (N : Ring) = struct
...
You also can use classes if you want dynamic dispatch
let (+) x y = x#add yBut previous designs are great for inspiration (like you say, Julia has a lot from them, like sum and product types, subtyping, parametric polymorphism) in the same way it also borrows from Lisp (CLOS). You can probably find in the literature/issues/discussion if you're curious how the language ended up this way, for example:
I have a question on this. I'll note up front that this is not an area of expertise for me.
It seems like knowledge of the types is/could be embedded in the process of currying. Multiple dispatch of a 2-ary function depends on the type of arg1 and arg2. If I call this with just the first arg, then the curried function "has knowledge" of the type of arg1. So now I have a 1-ary function that can do single dispatch on the type of its argument.
This seems possible to me to inductively extend to n-ary functions, since the process of consuming one argument by currying embeds knowledge of the type of that arg in the newly created function of n-1 arity.
Am I way off base here?
f :: (Int -> Double) -> Int -> Double
That would have to dispatch to
f(::Function(::Int, ::Double), ::Int)::Double
Now the dispatch will have to be recursive (it will have to apply to each argument and arguments arguments to evaluate which is more specialized), making finding the most specialized version of a function even more chaotic. I'm trying not to think what dispatching on return types means for the compiler though (and that's not necessary for the auto currying).
And because of the currying, if you apply the first argument you'd have a (g :: Int -> Double) which has the memory of receiving (Int -> Double). But now trying to dispatch on another function with that partial will it dispatch as if it were a normal Int -> Double or will the "knowledge" of receiving a previous argument change which method it will pick?
To be honest I have no idea, it's probably possible but it feels like it would be something very different from Julia.
Excuse me but tuples. You still have to observe them to evaluate them but that's all you need to simulate n-arity in the way you want.
>more dynamic
Well, Hindley—Milner is how you do type-safe stuff with inference that annotates for you. For any generic purposes you just put a typevar with constraints, so I don't see a problem here and can't really get what you gain. MLs are more about proper composition.
But mutability is also a great tool to have, for example for efficient dataframe handling and neural network weights.
>Procedural languages that are inherently distanced from math are used for math for whatever reason.
I think that historically it wasn't easy to make an efficient functional language. Numerical languages all trace back to Fortran after all (which is still alive and well). Nowadays, I think it's mostly because of inertia, and researchers having better things to do than learning a completely different programming language.