A mini DSL with Type Classes

Frege makes it easy to embed mini DSLs (domain specific languages) into the application. The language construct that we will use to achieve this are type classes.

The Initial Goal

Let’s assume that our DSL models measurements of distance such that ten meters should appear as 10.m and we want to do arithmetic with it like

10.m - 20.cm + 10.mm - 3.cm  == 9780.mm

with m, cm, and mm having the usual meaning in the metric system.

Note	The example is shamelessly stolen from Groovy in Action.

Initial Implementation

The initial implementation idea is to represent measurements with the Int type where the value of 1 represents one millimeter. This gives us arithmetic for free at the expense of not having much type support. We will refine that in a future post.

How can we make 1.mm into a value 1?

In "The power of the dot" we have seen that 1.mm is just the dot notation for XXX.mm 1 where XXX can be the type or a type class of the following value 1. Our actual Int type has no mm function so we are left with using a type class.

The definition of a Millimeter type class for an integral type "a"

class (Integral a) => Millimeter a  where
    mm :: a -> a
    cm :: a -> a
    m  :: a -> a

You can read this definition as follows:

Any type "a" (provided that it is an Integral type like Int or Integer) can be made a type of class Millimeter by defining functions mm, cm, and m that for a given "a" value return a value of type "a" in millimeters.

Note	The "a" is called a type variable. It stands in for a type. Like all variables it must be lowercase.

Now that we have the type class defined, all we need to do is making Int an instance of this class.

Making the Int type an instance of the Millimeter type class

instance Millimeter Int where
    mm i = i
    cm i = i.mm * 10
    m  i = i.cm * 100

And voilà, from now on we can do metrical calculations with ease.

Using the embedded mini-DSL

main args = do
    println $ 10.m - 20.cm + 10.mm - 3.cm  == 9780.mm

Considerations

By making the Int type a member of the class of Millimeter types we have given it a new capability. This was an non-intrusive, incremental change. There was no need for doing any change to existing code. This is important because we can be sure that we haven’t broken anything.

In a future post, we will build on this initial understanding of type classes and do even more sophisticated modeling to cover not only distance but also time and velocity for proper, type-safe modeling of measurements.

A mini DSL with Type Classes