Unit-safe square roots

f#, functional-programming, math, units-of-measurement

Solution

Allowing nonzero generic constants would make it very easy to break the safety of the type system for units (see Andrew Kennedy's papers). I believe that the answer to your last question is that `sqrt` is indeed magic in some sense in that it shouldn't be possible to define a parametric function with that type signature through normal means. However, it is possible to do what you want (at least in the current version of F#) by taking advantage of boxing and casting:

let sqrt (x : float<'u^2>) =
  let x' = (float x) ** 0.5 (* delete unit and calculate sqrt *)
  ((box x') :?> float<'u>)

Problem

I just wondered how it is possible to write a user-defined square root function (sqrt) in a way that it interacts properly with F#'s unit system. What it should be like: ``` let sqrt (x : float<'u ^ 2>) = let x' = x / 1.0<'u ^ 2> // Delete unit (x ** 0.5) * 1.0<'u> // Reassign unit ``` But this is disallowed due to nonzero constants not being allowed to have generic units. Is there a way to write this function? With the builtin `sqrt` it works fine, so what magic does it perform?

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