Quoted unit functions don't compose.

[philderbeast]

-- Quoted units without a value specialise to functions we can use to attach
-- units to unitless numeric values.
--
-- >>> [u| m / s^2 |] 9.8
-- [u| 9.8 m / s^2 |]
--
-- >>> [u| m s^-2 |] 9.8
-- [u| 9.8 m / s^2 |]
--
-- >>> [u| m / s / s |] 9.8
-- [u| 9.8 m / s^2 |]
--
-- >>> [u| s^-2 m |] 9.8
-- [u| 9.8 m / s^2 |]
--
-- Composition of these functions doesn't work as I'd expect, applying
-- composed units to the numeric value.
--
-- >>> [u| m |] $ [u| s^-2 |] 9.8
-- [u| [u| 9.8 s^-2 |] m |]
--
-- >>> [u| s^-2 |] $ [u| m |] 9.8
-- [u| [u| 9.8 m |] s^-2 |]
--
-- >>> [u| m |] . [u| s^-2 |] $ 9.8
-- [u| [u| 9.8 s^-2 |] m |]
--
-- >>> [u| s^-2 |] . [u| m |] $ 9.8
-- [u| [u| 9.8 m |] s^-2 |]
--
-- >>> [u| m |] [u| 9.8 s^-2 |]
-- [u| [u| 9.8 s^-2 |] m |]
--
-- >>> [u| s^-2 |] [u| 9.8 m |]
-- [u| [u| 9.8 m |] s^-2 |]
--
-- >>> [u| m |] . [u| s^-1 |] . [u| s^-1 |] $ 9.8
-- [u| [u| [u| 9.8 s^-1 |] s^-1 |] m |]

[philderbeast]

I've left the reproduction in the tutorial for now.

uom-plugin/uom-plugin/doc/Data/UnitsOfMeasure/Tutorial.hs

Lines 249 to 265 in 287dde9

	-- Composition of these functions doesn't work as expected. It doesn't apply
	-- composed units to the numeric value.
	--
	-- >>> [u| m |] $ [u| s^-2 |] 9.8
	-- [u| [u| 9.8 s^-2 |] m |]
	-- >>> [u| s^-2 |] $ [u| m |] 9.8
	-- [u| [u| 9.8 m |] s^-2 |]
	-- >>> [u| m |] . [u| s^-2 |] $ 9.8
	-- [u| [u| 9.8 s^-2 |] m |]
	-- >>> [u| s^-2 |] . [u| m |] $ 9.8
	-- [u| [u| 9.8 m |] s^-2 |]
	-- >>> [u| m |] [u| 9.8 s^-2 |]
	-- [u| [u| 9.8 s^-2 |] m |]
	-- >>> [u| s^-2 |] [u| 9.8 m |]
	-- [u| [u| 9.8 m |] s^-2 |]
	-- >>> [u| m |] . [u| s^-1 |] . [u| s^-1 |] $ 9.8
	-- [u| [u| [u| 9.8 s^-1 |] s^-1 |] m |]

[adamgundry]

This is a very good observation. At the moment we have

[u| m |] :: a -> Quantity a (Base "m")

Instead, I think we should change this to:

[u| m |] :: Quantity a u -> Quantity a (Base "m" *: u)

That is, when the quasiquoter is used in an expression without a number, it produces a function that multiplies a polymorphic value by the given units. Since literals are dimensionless, I think we get this:

[u| m |] 1 == [u| 1 m |] :: Num a => Quantity a (Base "m")
[u| m |] $ [u| s^-2 |] 9.8 == [u| 9.8 m s^-2 |] :: Fractional a => Quantity a [u| m s^-2 |]
[u| m s^-2 |] :: Quantity a u -> Quantity a ([u| m s^ -2 |] *: u)