I think a good start is a Scheme equivalent to the BLAS [1].

We could do packed arrays (trigonal, etc.) with storage-classes. The
interface could be made simpler by dispatching against storage classes
(which would then be optimized by the Sufficiently Smart Compiler).
There could then be a fallback option for (pretty slow) general
arithmetic operations.

[1]:
https://web.archive.org/web/20250804020841/https://www.netlib.org/blas/blas.pdf

-- Peter McGoron