I would also like to know this. Fortran itself is column-major, so I would guess the internal layout isn't same for multi-dimensional arrays when compared to row-major C? I'm not sure how LFortran represents arrays internally though.

Lots of scientific code in Fortran has sparse arrays, so a NxN array that only has values on 5 diagonals will store that as 5xN array to save memory allowing you to run a larger problem.

Not naive! The answer is yes and no.

Array layout: yes, for the simple cases this post relies on. In the demo the work arrays are literally calloc'd in a C wrapper and handed straight to the Fortran routine, and it just works. (Column-major vs. C's row-major is still on you to keep straight, of course.) This wouldn't be so easy for fancier Fortran array features — allocatables, assumed-shape (:) dummies, pointer arrays — which in general get a descriptor struct (bounds, strides, etc.) rather than a bare pointer. Flang uses those descriptors much more aggressively, but I don't know how that would manifest at the C-Fortran bridge. Would be interesting to repeat the experiment with Flang (if at all possible) and comparing the pain.

Calling convention: there are well established contracts, much older than the layout story. Fortran passes everything by reference, so a double precision :: x argument is an x* at the ABI level — which is why every argument in the C wrapper is a pointer (&n_, &k0_, ...). Combine that with C-compatible name mangling (a trailing underscore historically, controllable via LFortran/bind(C)) and Bob's your uncle. Nothing here is new, the pipeline is really just leaning on that decades-old interop contract and then letting Enzyme differentiate across the boundary.

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