> I had the impression that even in static languages having tensors with the exact shape as a parameter would stress the compiler, forcing it to compile many versions of every function for every possible size combination, and the output of a function could very well have a non deterministic or multiple possible shapes (for example branching on runtime information).
I was a bit lazy in my original comment - you're right. What I really think should be implemented (and is already starting to in Pytorch and a library named NamedTensor, albeit non-statically) is essentially having "typed axes."
For instance, if I had a sequence of locations in time, I could describe the tensor as:
(3 : DistanceAxis, 32 : TimeAxis, 32 : BatchAxis).
Sure, the number of dimensions could vary and you're right that, if so, the approach implied by my first comment would have a combinatorial explosion. But if I'm contracting a TimeAxis with a BatchAxis accidentally, that can be pretty easily caught before I even have to run the code. But in normal pytorch, such a contraction would succeed - and it would succeed silently.
Julia for example does have an array library that does compile-time shape inference (StaticArrays), but it cannot scale for large arrays (over 100 elements) exactly because it gets too hard for the compiler to keep track, I'm definitely curious about possible solutions.