Switch to module over ring for duration arithmetic

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The issue names the Semiring instances for Milliseconds and other duration types, and links the modules-over-rings library. Start by locating those instances and reviewing the linked abstraction. The issue proposes replacing them and creating a vector-spaces-over-fields library for division; done means duration arithmetic follows those abstractions without the wrapping shown in the examples.

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描述

status: needs more info

Currently a Semiring Milliseconds instance exists. However, durations are not a semiring: the closure property of the multiplication operation is not honoured because multiplying two durations gives not a duration but a duration squared.

This is incorrect, and causes awkward code where you need to add/remove nonsensical wrappers just so you can multiply or divide. One example is multiplying a duration by a scalar:

twiceAsLong :: Milliseconds -> Milliseconds
twiceAsLong a = a * Milliseconds 2.0 -- nasty wrap

Another example is where you divide two durations when implementing a multiplication between durations and frequencies where the frequency type is in terms of the reciprocal of the frequency, which is a duration:

newtype Freq = Freq Milliseconds

-- | The reciprocal of a frequency is a duration. (Note how 1/ms = kHz.)
reciprocal :: Freq -> Milliseconds
reciprocal (Freq r) = r

-- | Multiplying a duration (ms) by a frequency (1/ms) gives a number.
multiply :: Milliseconds -> Freq -> Number
multiply d f = un Milliseconds (d / reciprocal f) -- nasty unwrap

With the right abstraction, no wrapping and unwrapping would be necessary, because the types would just work out. We should remove the Semiring Milliseconds instance (and the instances for other duration types) and switch to modules over rings instead, which model this correctly. To add division we should make a library for vector spaces over fields.

Modules over rings and vector spaces over fields are generally useful for types that represent quantities, such as durations, distances, and file sizes.

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