Question

The haskell code below compiles, Ok.

data Point = Point Float Float  
data Radius = Radius Float  
data Shape = Circle Point Radius

Is it possible to write something in line with the code below (Code fails compiling):

data LengthQty = Radius Float | Length Float | Width Float   
data Shape = Circle Point Radius

Idea behind this attempt is that Radius, Length and Width are representing Physical Quantity Length.

Please note that in the second part second line if written like

data Shape = Circle Point LengthQty

Then, it compiles, but in that case the “LengthQty” can be anything like Length, Width or Radius, where only Radius is required.

(1) What is wrong in second part?
(2) How it can be corrected to implement the idea of Physical Quantity Length (LengthQty)?

Answer 1

The reason that your code doesn’t compile is that the right-hand side of a data declaration must be a constructor followed by a list of types, i.e. of the form

data {-type-} = {-constructor-} {-type-} ... {-type-}

In your example, when you define

data LengthQty = Radius Float | Length Float | Width Float 

you have made LengthQty a type whereas Radius, Length and Width are constructors. Therefore when you write

data Shape = Circle Point Radius

the compiler sees something of the form

data {-type-} = {-constructor-} {-type-} {-constructor-}

i.e. it sees a constructor where it is expecting a type, so it throws an error. In the original code, the symbol Radius was used for both a constructor and a type. When the compiler sees

data Shape = Circle Point Radius

it knows that Radius in this context has to be a type, so there is no possibility of confusion with the constructor radius.

With this in mind, you can make your code compile correctly if you just write

data Shape = Circle Point LengthQty

and you can get a particular instance of a circle with

circle :: Shape
circle = Circle (Point 0 0) (Radius 1)