Futhark is really such a great idea. I'm not convinced that dependent types are worth the cognitive overhead in general, but it's definitely worth it to include the length as part of the type information for dynamic arrays, e.g.:
concat(Vec<T, n>, Vec<T, m>) -> Vec<T, n+m>
matmul(Mat<T, n, m>, Mat<T, m, l>) -> Mat<T, n, l>
head(Vec<T, n+1>) -> (T, Vec<T, n>)
Here they are in Futhark:
And here's the pathological case (length cannot be determined at compile time): Other pathological cases include conditionals and loops.The Pyrefly type checker is starting to work on this kind of shape hinting - so far it only works on Torch but I believe the plan is for it to work with other array packages (eg. JAX, NumPy)
https://pyrefly.org/en/docs/tensor-shapes/#how-it-works
See also jaxtyping which, contrary to what its name might imply, covers JAX/PyTorch/NumPy/MLX/TensorFlow arrays and tensors.
https://docs.kidger.site/jaxtyping/
Shape functions and shape analysis are basically mundane infra in almost every ML compiler/language/DSL.
https://mlir.llvm.org/docs/Dialects/ShapeDialect/
I didn't know that, thanks for sharing. It makes sense, but then it also makes me wonder why none of the deep learning libraries (Torch, Jax/NNX, Eigen etc...) make this information available. Instead, ML people all have their own schemes for tracking shape information, like commenting '# (b, n, t)' on every line, or suffixing shapes to variable names - and in my experience it's a common source of bugs.
> Torch, Jax
Both of these "make it available". Just because people don't know how to use/find them doesn't mean they're not "available".
> Eigen
This is not an ML anything, it's a linear algebra library.
> like commenting '# (b, n, t)' on every line, or suffixing shapes to variable names
There's a difference between tracking shapes in the compiler and specifying shapes in the model.
You can do this with templates in C++ and generics in Rust I'm pretty sure. I think the Eigen C++ library supports this. (I have yet to do a linear algebra heavy Rust project, so I can't speak to the options that exist there.)
I'm talking about cases where the array size is not known at compile time. For example, say the user passes in a list of numbers as command line arguments. Then we have
If I want to map these to ints, then I'd like a compile-time guarantee that the resulting array is the same length as argv. Lean and Idris can do this, but AFAIK no commonly used languages can. But unlike general dependent types, these are not hard to wrap one's head around and would save a lot of frustration, in my experience.Yeah, C++ arrays are literally that.
Arrays are not dynamically sized though (handling runtime sizes) and don’t have efficient append/concat. The point of the dependent types is that you can have the type system track that concat creates an M+N length vector, sort preserves length (and adds a sorted guarantee that slice preserves), etc. Sure you can do a lot with templates, but that’s advanced templates not just “C++ arrays” in a throwaway “literally that” way.