Objective: Improve Type Level Rust in the Rust 2024 Edition

TLDR: Demonstrate unhelpful compile failure errors with TypeNum

backlink to the issue in the main repo: rust-lang/rust#118676

please note: this is a small example

in my real use case, I also have HList (Cons/Nil Russian Doll) of TypeNums, so it's much worse!

Start Quick

clone, change directory, run tests:

gh repo clone bionicles/broadcastable && cd broadcastable && cargo test

once you're inside, you can just run the tests

cargo test

Example of the Issue

Notice how these TypeNums are really hard to read:

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈
error[E0271]: type mismatch resolving `<UInt<UInt<UTerm, B1>, B0> as IsEqual<UInt<UTerm, B1>>>::Output == B1`
 --> tests/ui/compatibility_fail.rs:7:27
  |
7 |     println!("Bound: {}", FailedAlready::bound());
  |                           ^^^^^^^^^^^^^ expected `B0`, found `B1`
  |
  = note: required for `typenum::Less` to implement `CompatibleBounds<UInt<UInt<UTerm, B1>, B0>, UInt<UInt<UTerm, B1>, B1>>`
┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

rustc displays full types even for complex nested types which represent abstractions (i.e. instead of U2 you see UInt<UInt<UTerm, B1>, B0>)

Workarounds Tried

I tried using tnfilt from https://github.com/auxoncorp/tnfilt -- but it clobbers a lot of terminal style content like colors, which causes other issues with Rust compiler error readability in type-level programming
I tried using compile_error! (https://doc.rust-lang.org/std/macro.compile_error.html) in the type Output = ... but unfortunately it always fails to compile which means we can't conditionally trigger compile_error! inside trait impls.
dfdx (https://github.com/coreylowman/dfdx) does implement compile-time shape checking with const generics, however this approach only uses numerical values for the axis bounds, which doesn't align with the principles of Named Arrays (i.e. broadcast by axis names, not axis positions)

Motivations: Benefits of Type Level Linear Algebra

If this issue were fixed, then Rust could have clearly better alternatives to numpy/jax/pytorch/tensorflow etc, because we could detect "shape bugs" at compile time instead of running code and waiting to see if it crashes.

Also, since we could check broadcast alignment compatibility at compile time, the performance could dramatically improve, since the work could be done once and amortized over all the broadcasts during the runtime execution of the program

License: MIT or Apache 2.0, at your option.

See LICENSE_MIT and/or LICENSE_APACHE for details.