Hmm. I had an issue once with numpy shape mismatch errors appearing after 18+ hours of computation. Frustrating, because it could be caught at compile time.
Later, I learned some typelevel programming (in Scala), and by encoding a digital (binary) adder and multiplier at the type level, I showed -- at least to myself -- it was possible to compute and check linear algebra shapes at compile time (without a compiler plugin). It was rather magical and funny to think that I just embedded basic digital logic in such a higher-abstraction world.
It was slow for the inputs I cared about, so I added some optimizations, like an if-statement at the type level, for example, so that it bit-shift for multiplying powers of 2 (multiplication for tensor products). The compile time difference being palpable was a testament to how "some 'ideas' are surprisingly close to others" (err, 'ideas' ~ 'numbers' in this case). There is a connection to the p-adic numbers here, courtesy of dyadics, and some connection to the more-natural "last-mile" problem.
It's not REST, maybe. But I felt it was magical.
Later, I learned some typelevel programming (in Scala), and by encoding a digital (binary) adder and multiplier at the type level, I showed -- at least to myself -- it was possible to compute and check linear algebra shapes at compile time (without a compiler plugin). It was rather magical and funny to think that I just embedded basic digital logic in such a higher-abstraction world.
It was slow for the inputs I cared about, so I added some optimizations, like an if-statement at the type level, for example, so that it bit-shift for multiplying powers of 2 (multiplication for tensor products). The compile time difference being palpable was a testament to how "some 'ideas' are surprisingly close to others" (err, 'ideas' ~ 'numbers' in this case). There is a connection to the p-adic numbers here, courtesy of dyadics, and some connection to the more-natural "last-mile" problem.
It's not REST, maybe. But I felt it was magical.