[slaymaker1907]

Please write a type for the following function:

  def compose(start, *args):
    def helper(x):
      for func in reversed(args):
        x = func(x)
      return start(x)
    return helper

There is no mainstream typed language which can write a fully general type for the vararg compose function. TypeScript is probably the one that comes closest, but last I checked it still was unable to write a sufficiently powerful array type. You can write a type for a version of compose with a fixed number of arguments, but not for one working over an arbitrary number of arguments.

[loup-vaillant]

Vararg functions also have limited use. Especially considering that most of the time, your args will all have the same type, and therefore could just be passed in an array or similar. The one mainstream exception I know of is print functions, and we have* ways to statically check those.

Your toy example, even generalised, has no practical use. If I can write this:

  compose(f, f1, f2, f3)

Then I can write that instead (Haskell):

  f . f3 . f2 . f1

Or this (F#):

  f1 |- f2 |- f3 |- f

And now we’ve reduced the problem to a simple function composition, which is very easy to define (Ocaml):

  let (|-) f g = fun x -> g (f x)
  (|-): (’a -> ’b) -> (’b -> ’c) -> (’a -> ’c)

This generalises to any fold where the programmer would provide the list statically (as they always would for a vararg function): instead of trying to type the whole thing, just define & type the underlying binary operation.

[skrimp]

This still technically reduces the generality of the given function since you are specifying that each function cannot have multiple overloads.

let f be a overload set matching the signatures {a -> b, i -> j} let g be a overload set matching the signatures {b -> c, j -> k}

compose(g, f) could be given a to return c or i to return k

[loup-vaillant]

> This still technically reduces the generality of the given function

My point was that we are almost never hurt by that reduction.

> you are specifying that each function cannot have multiple overloads

Haskell has type classes, and if we restrict ourselves to local type inference it's fairly easy to have C++ style overloads without even that. So no, I'm not specifying such a thing.

[fiddlerwoaroof]

> Vararg functions also have limited use.

This is only because people are using statically typed language that place arbitrary restrictions on such functions and make them harder to use. In dynamically typed languages, vararg functions are widely used and enable patterns that are pretty nice.

[loup-vaillant]

Perhaps. But then I want to know what those patterns are, what are their actual benefits compared to not using them, and most of all I want to know if such benefits outweigh the significant costs that comes with the lack of static analysis¹.

[1] The need to test much more, the need for a better, more accurate documentation, the higher cost of refactoring, even the higher prototyping times (I prototype faster with a REPL that has static typing, because I don't to debug type errors).

[fiddlerwoaroof]

> I prototype faster with a REPL that has static typing, because I don't to debug type errors

On the other hand, because Common Lisp has resumable exceptions and on-the-fly redefinition of just about everything, I prototype significantly faster in CL because I can just let the debugger stay open until I fix the issue and then hit “continue”.

I no longer believe the “static faster for development than dynamic” thesis because I think a lot depends on how the programmer thinks about programming and which tools are available.

[loup-vaillant]

Yeah, I've heard about image based programming, that enables editing your program as you run it. It scares the shit out of me.

See, if I have an unexpected error, that's because I fucked up my program. And because of that, my runtime state is likely screwed as well. So not only do I have to correct my error, I have to correct its consequences before I restart the program. I can't just resume its execution and hope for the best, I need to know that whatever state I keep is not rotten.

On the other hand, that way of doing things is not exclusive to dynamic languages. There's thing things called "dynamically loaded libraries", that you can use even in C. Game programmers routinely recompile & reload specific dlls just so they can correct their mistakes without restarting the whole game. And those who have written in-game editors have a very powerful stop-debug-restart cycle. On top of a statically typed language.

[skrimp]

C++ is an extremely mainstream language that can write a fully general version of compose with variable arguments.

https://godbolt.org/z/h7n8Y7qf1

Like sure, you can't write out a type for the entire overload set. Overload sets don't have types, but functions do. However, I don't think you'd ever actually want to write out the type of the compose function. Instead, I think it would be more reasonable to request that every intermediate function call is type-checked with fully specified types. In C++ this is the case.

[Matheus28]

Great implementation of what the parent comment asked. Not only that, but the compiler managed remove all the abstractions.

(very minor nitpick: I'd pick `auto&& x` over `auto x`)

[munificent]

> There is no mainstream typed language which can write a fully general type for the vararg compose function.

True. A more interesting question might be what level of static safety and performance benefits you'd be willing to sacrifice to be able to write functions like this.

Personally, I don't find the kind of code I can't fit into static types particularly appealing, but I find the code navigation, error checking, and optimizations of static types to be priceless.

[tetha]

As I said, there are infinite possible programs that cannot be type checked statically. This is derived from the halting theorem trivially - lambda(p) = if p.halts() then A() else B().

However, the intersection of programs I encounter in practice with the number of programs that can be statically checked is rather large.

[phoneperson]

You are probably thinking of Gödel's incompleteness theorems. I do not think that you can trivially derive it from the halting problem.

[tehnub]

He just did derive it from the halting problem. In words: It's impossible to statically check the type of a function that takes a program P as its input, and returns the integer 1 as its output if P halts, and returns the string "1" if it does not halt. It would require solving the halting problem, which is undecidable.

[phoneperson]

The theorems predate Turing's theorem. As for the halting problem, it is solvable with an oracle, unlike the incompleteness theorems.

[native_samples]

How does that follow? The input type would be vague, e.g. ByteArray or Program or something.

[tehnub]

It's the return type that isn't decidable. You can't statically check, in the arbitrary case, whether the function returns an int or a string.

[native_samples]

No, but that isn't required for a static type system. Most languages would just unify to the top type.

[nybble41]

This is really a fairly trivial exercise in Haskell, provided you pass the arguments as a heterogeneous list—which is semantically equivalent to a variable argument list. Here is my implementation: https://gist.github.com/nybble41/c459c6927a3bad8ec350d227193...

Here I defined a simple `Pipeline` GADT for the argument list, which is just a list of functions with some extra type constraints to ensure that they can be composed. You could do the same thing with a more general type like HList but the type signature for the `compose` function would be much more verbose since you would need to define the relationships between each pair of adjacent function types through explicit constraints involving type families, whereas the `Pipeline` type handles that internally.

Perhaps you don't consider Haskell "mainstream" enough?

[albrewer]

I took a stab at it, there's not enough information to figure out anything more specific:

  from typing import Callable, Any

  def compose(start: Callable[[Any], Any], *args: Callable[[Any], Any] -> Callable[[Any], Any]:
    def helper(x: Any) -> Any:
      for func in reversed(args):
        x = func(x)
      return start(x)
    return helper

[slaymaker1907]

Sure, that's probably as close as you can get, but ideally it would be possible to write a type which guarantees the input functions are compatible as well as knowing what the type is of the returned function.

[iamevn]

I think you can get close implementing it as a macro in typed racket, expanding the type out based on how many arguments you give it. But then it's not a first class function until you expand it.

Found this implementation which also provides pre-expanded forms that are first class functions for specific lengths of arguments docs: https://docs.racket-lang.org/typed-compose/index.html implementation: https://git.marvid.fr/scolobb/typed-compose/src/branch/maste...

[monocasa]

I think you can in rust as long as args is a slice. Rust doesn't have varargs except for c interop. A slice or Vec of function pointers is the idiomatic way to do the same thing.

Something like:

  fn compose<X, T>(start: Box<Fn(T) -> X>, args: Vec<Box<Fn(T) -> T>>) -> Fn(T) -> X {
    move |x: X| {
      let mut x = x;
      for func in args.iter(). reversed() {
        x = func(x);
      }
      start(x)
    }
  }

[slaymaker1907]

This only works if all of the functions return the same type. However, you can write a compose macro which operates as expected.