Remove 'Fractional'/'Whole' type aliases

Not totally happy with the names, and they add another layer of indirection/abstraction in type signatures (which can make compiler error messages more confusing). So leave them out for now, and if needed something like them can be added in the future without triggering a major version bump (as opposed to leaving them in for now and removing/renaming them later, which *would* be a breaking change.)

Note that Quantity.toFractional is no longer required since it can be replaced by 'Quantity.map toFloat'.

README.md

@@ -152,23 +152,11 @@ type Quantity number units
     = Quantity number
 ```
 
-with some convenient type aliases
-
-```elm
--- A fractional number of units, useful for general quantities like length
-type alias Fractional units =
-    Quantity Float units
-
--- A whole number of units, useful for exact values in cents/pixels
-type alias Whole units =
-    Quantity Int units
-```
-
 For example, `Length` is defined as
 
 ```elm
 type alias Length =
-    Fractional Meters
+    Quantity Float Meters
 ```
 
 This means that a `Length` is internally stored as a `Float` number of `Meters`,
@@ -293,26 +281,20 @@ own! See [CustomUnits](doc/CustomUnits.md) for an example.
 
 ### Understanding Quantity Types
 
-The same quantity type can often be expressed in multiple different ways, which is important to understand especially when trying to interpret error messages! Take the `Speed` type alias as an example. It is defined as
-
-```elm
-type alias Speed =
-    Fractional MetersPerSecond
-```
-
-Expanding the `MetersPerSecond` type alias, this is
+The same quantity type can often be expressed in multiple different ways. Take
+the `Speed` type as an example. It is an alias for
 
 ```elm
-Fractional (Rate Meters Seconds)
+Quantity Float MetersPerSecond
 ```
 
-Expanding the `Fractional` type alias then gives
+but expanding the `MetersPerSecond` type alias, this is equivalent to
 
 ```elm
 Quantity Float (Rate Meters Seconds)
 ```
 
-which is the "true" type with no type aliases left to expand.
+and you may see any one of these three forms pop up in error messages.
 
 ## Getting Help
 

doc/CustomUnits.md

@@ -47,14 +47,14 @@ import Quantity
 Quantity.sum [ tiles 5, tiles 2.3, tiles 0.6 ]
 --> tiles 7.9
 
-pixelsPerTile : Fractional (Rate Pixels Tiles)
+pixelsPerTile : Quantity Float (Rate Pixels Tiles)
 pixelsPerTile =
     pixels 24 |> Quantity.per (tiles 1)
 
 tiles 3 |> Quantity.at pixelsPerTile
 --> pixels 72
 
-speed : Fractional (Rate Tiles Seconds)
+speed : Quantity Float (Rate Tiles Seconds)
 speed =
     tiles 12 |> Quantity.per (seconds 1)
 

examples/Eur.elm

@@ -10,7 +10,7 @@ module Eur exposing
     , roundUpToNearestCent
     )
 
-import Quantity exposing (Fractional, Quantity(..), Whole)
+import Quantity exposing (Quantity(..))
 
 
 type Cents
@@ -37,21 +37,21 @@ euros numEuros =
     Quantity (100 * numEuros)
 
 
-inEuros : Fractional Cents -> Float
+inEuros : Quantity Float Cents -> Float
 inEuros (Quantity numCents) =
     numCents / 100
 
 
-roundToNearestCent : Fractional Cents -> Whole Cents
+roundToNearestCent : Quantity Float Cents -> Quantity Int Cents
 roundToNearestCent (Quantity numCents) =
     Quantity (round numCents)
 
 
-roundDownToNearestCent : Fractional Cents -> Whole Cents
+roundDownToNearestCent : Quantity Float Cents -> Quantity Int Cents
 roundDownToNearestCent (Quantity numCents) =
     Quantity (floor numCents)
 
 
-roundUpToNearestCent : Fractional Cents -> Whole Cents
+roundUpToNearestCent : Quantity Float Cents -> Quantity Int Cents
 roundUpToNearestCent (Quantity numCents) =
     Quantity (ceiling numCents)

examples/Usd.elm

@@ -10,7 +10,7 @@ module Usd exposing
     , roundUpToNearestCent
     )
 
-import Quantity exposing (Fractional, Quantity(..), Whole)
+import Quantity exposing (Quantity(..))
 
 
 type Cents
@@ -37,21 +37,21 @@ dollars numDollars =
     Quantity (100 * numDollars)
 
 
-inDollars : Fractional Cents -> Float
+inDollars : Quantity Float Cents -> Float
 inDollars (Quantity numCents) =
     numCents / 100
 
 
-roundToNearestCent : Fractional Cents -> Whole Cents
+roundToNearestCent : Quantity Float Cents -> Quantity Int Cents
 roundToNearestCent (Quantity numCents) =
     Quantity (round numCents)
 
 
-roundDownToNearestCent : Fractional Cents -> Whole Cents
+roundDownToNearestCent : Quantity Float Cents -> Quantity Int Cents
 roundDownToNearestCent (Quantity numCents) =
     Quantity (floor numCents)
 
 
-roundUpToNearestCent : Fractional Cents -> Whole Cents
+roundUpToNearestCent : Quantity Float Cents -> Quantity Int Cents
 roundUpToNearestCent (Quantity numCents) =
     Quantity (ceiling numCents)

src/Acceleration.elm

@@ -11,7 +11,7 @@ module Acceleration exposing
 
 import Duration exposing (Seconds)
 import Length exposing (Meters)
-import Quantity exposing (Fractional, Quantity(..), Rate)
+import Quantity exposing (Quantity(..), Rate)
 import Speed exposing (MetersPerSecond)
 
 
@@ -20,7 +20,7 @@ type alias MetersPerSecondSquared =
 
 
 type alias Acceleration =
-    Fractional MetersPerSecondSquared
+    Quantity Float MetersPerSecondSquared
 
 
 metersPerSecondSquared : Float -> Acceleration

src/Angle.elm

@@ -16,7 +16,7 @@ module Angle exposing
     , turns
     )
 
-import Quantity exposing (Fractional, Quantity(..))
+import Quantity exposing (Quantity(..))
 
 
 {-| Radians are the standard unit of angle.
@@ -28,7 +28,7 @@ type Radians
 {-| An angle is a fractional number of radians.
 -}
 type alias Angle =
-    Fractional Radians
+    Quantity Float Radians
 
 
 radians : Float -> Angle
@@ -91,6 +91,6 @@ atan x =
     Quantity (Basics.atan x)
 
 
-atan2 : Fractional units -> Fractional units -> Angle
+atan2 : Quantity Float units -> Quantity Float units -> Angle
 atan2 (Quantity y) (Quantity x) =
     Quantity (Basics.atan2 y x)

src/Area.elm

@@ -24,15 +24,15 @@ module Area exposing
     )
 
 import Length exposing (Meters)
-import Quantity exposing (Fractional, Quantity(..), Squared, Whole)
+import Quantity exposing (Quantity(..), Squared)
 
 
 type alias SquareMeters =
     Squared Meters
 
 
 type alias Area =
-    Fractional SquareMeters
+    Quantity Float SquareMeters
 
 
 squareMeters : Float -> Area

src/Charge.elm

@@ -9,15 +9,15 @@ module Charge exposing
     , milliampereHours
     )
 
-import Quantity exposing (Fractional, Quantity(..))
+import Quantity exposing (Quantity(..))
 
 
 type Coulombs
     = Coulombs
 
 
 type alias Charge =
-    Fractional Coulombs
+    Quantity Float Coulombs
 
 
 coulombs : Float -> Charge

src/Current.elm

@@ -9,15 +9,15 @@ module Current exposing
 
 import Charge exposing (Coulombs)
 import Duration exposing (Seconds)
-import Quantity exposing (Fractional, Quantity(..), Rate)
+import Quantity exposing (Quantity(..), Rate)
 
 
 type alias Amperes =
     Rate Coulombs Seconds
 
 
 type alias Current =
-    Fractional Amperes
+    Quantity Float Amperes
 
 
 amperes : Float -> Current

src/Duration.elm

@@ -18,7 +18,7 @@ module Duration exposing
     , weeks
     )
 
-import Quantity exposing (Fractional, Quantity(..))
+import Quantity exposing (Quantity(..))
 import Time
 
 
@@ -32,7 +32,7 @@ type Seconds
 time (which would generally be represented by a `Posix` value).
 -}
 type alias Duration =
-    Fractional Seconds
+    Quantity Float Seconds
 
 
 {-| Find the elapsed time from a start time to an end time. For example,

src/Energy.elm

@@ -11,15 +11,15 @@ module Energy exposing
     , megajoules
     )
 
-import Quantity exposing (Fractional, Quantity(..))
+import Quantity exposing (Quantity(..))
 
 
 type Joules
     = Joules
 
 
 type alias Energy =
-    Fractional Joules
+    Quantity Float Joules
 
 
 joules : Float -> Energy

src/Force.elm

@@ -13,15 +13,15 @@ module Force exposing
     , pounds
     )
 
-import Quantity exposing (Fractional, Quantity(..))
+import Quantity exposing (Quantity(..))
 
 
 type Newtons
     = Newtons
 
 
 type alias Force =
-    Fractional Newtons
+    Quantity Float Newtons
 
 
 newtons : Float -> Force

src/Length.elm

@@ -28,7 +28,7 @@ module Length exposing
 
 -}
 
-import Quantity exposing (Fractional, Quantity(..))
+import Quantity exposing (Quantity(..))
 
 
 {-| Meters are the standard units of length.
@@ -37,10 +37,10 @@ type Meters
     = Meters
 
 
-{-| A length is a fractional number of meters.
+{-| A length is represented by a number of meters.
 -}
 type alias Length =
-    Fractional Meters
+    Quantity Float Meters
 
 
 meters : Float -> Length

src/Mass.elm

@@ -19,15 +19,15 @@ module Mass exposing
 
 import Acceleration exposing (MetersPerSecondSquared)
 import Force exposing (Newtons)
-import Quantity exposing (Fractional, Quantity(..), Rate)
+import Quantity exposing (Quantity(..), Rate)
 
 
 type alias Kilograms =
     Rate Newtons MetersPerSecondSquared
 
 
 type alias Mass =
-    Fractional Kilograms
+    Quantity Float Kilograms
 
 
 kilograms : Float -> Mass

src/Pixels.elm

@@ -18,7 +18,7 @@ module Pixels exposing
 -}
 
 import Duration exposing (Seconds)
-import Quantity exposing (Fractional, Quantity(..), Rate, Squared, Whole)
+import Quantity exposing (Quantity(..), Rate, Squared)
 
 
 type Pixels
@@ -46,20 +46,12 @@ Note that passing an `Int` will give you a
 
     Quantity Int Pixels
 
-which is equivalent to
-
-    Whole Pixels
-
 while passing a `Float` will give you a
 
     Quantity Float Pixels
 
-which is equivalent to
-
-    Fractional Pixels
-
-If you pass a _literal_ integer like `1920`, the result can be used as either a
-`Fractional` _or_ `Whole` number of pixels.
+If you pass a _literal_ integer like `1920`, the result can be used as either an
+`Int` _or_ `Float` number of pixels.
 
 -}
 pixels : number -> Quantity number Pixels
@@ -72,22 +64,22 @@ inPixels (Quantity numPixels) =
     numPixels
 
 
-pixelsPerSecond : Float -> Fractional PixelsPerSecond
+pixelsPerSecond : Float -> Quantity Float PixelsPerSecond
 pixelsPerSecond numPixelsPerSecond =
     Quantity numPixelsPerSecond
 
 
-inPixelsPerSecond : Fractional PixelsPerSecond -> Float
+inPixelsPerSecond : Quantity Float PixelsPerSecond -> Float
 inPixelsPerSecond (Quantity numPixelsPerSecond) =
     numPixelsPerSecond
 
 
-pixelsPerSecondSquared : Float -> Fractional PixelsPerSecondSquared
+pixelsPerSecondSquared : Float -> Quantity Float PixelsPerSecondSquared
 pixelsPerSecondSquared numPixelsPerSecondSquared =
     Quantity numPixelsPerSecondSquared
 
 
-inPixelsPerSecondSquared : Fractional PixelsPerSecondSquared -> Float
+inPixelsPerSecondSquared : Quantity Float PixelsPerSecondSquared -> Float
 inPixelsPerSecondSquared (Quantity numPixelsPerSecondSquared) =
     numPixelsPerSecondSquared