Always enjoy mattt’s work. Looks like a great library.

Does this handle covariance between different variables? For example, the location of the object your measuring your distance to presumably also has some error in it's position, which may be correlated with your position (if, for example, if it comes from another GPS operating at a similar time).

Certainly a univarient model in the type system could be useful, but it would be extra powerful (and more correct) if it could handle covariance.

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A small note, but GPS is only well-approximated by a circular uncertainty in specific conditions, usually open sky and long-time fixes. The full uncertainty model is much more complicated, hence the profusion of ways to measure error. This becomes important in many of the same situations that would lead you to stop treating the fix as a point location in the first place. To give a concrete example, autonomous vehicles will encounter situations where localization uncertainty is dominated by non-circular multipath effects.

If you go down this road far enough you eventually end up reinventing particle filters and similar.

Arguably Uncertain should be the default, and you should have to annotate a type as certain T when you are really certain. ;)

Is this essentially a programmatic version of fuzzy logic?

https://en.wikipedia.org/wiki/Fuzzy_logic

Monads are really undefeated. This particular application feels to me akin to wavefunction evolution? Density matrices as probability monads over Hilbert space, with unitary evolution as bind, measurement/collapse as pure/return. I guess everything just seems to rhyme under a category theory lens.