purescript data as array of all possible data inhabitants

Question

I got the following data type:

data Icon = IconCircle | IconSquare | IconStar

I need an array of all possible Icon s?:

allPossible :: Array Icon
allPossible = [IconCircle, IconSquare, IconStar]

Is there a shortcut to create this array? eg when there are 20 (or a lot more) possible Icons?

When not:

Is it possible to create a type for allPossible that forces all possible Icons to be included?

My goal is to force that this array is never incomplete.

Answer 1

Yes, there is!

You can derive Generic and then use GenericEnum in combination with GenericBottom to enumerate all constructors:

data Icon = IconCircle | IconSquare | IconStar
derive instance Generic Icon _

allPossible :: Array Icon
allPossible = unfoldr (\a -> Tuple a <$> genericSucc a) genericBottom

And you can even make this completely generic, so it would work for any type, not just for Icon :

allPossible :: forall a rep. 
  Generic a rep =>
  GenericEnum rep => 
  GenericBottom rep => 
  Array a
allPossible = unfoldr (\a -> Tuple a <$> genericSucc a) genericBottom

Of course, this will only work for types that are actually enums - ie every constructor is either parameterless or its parameters have instances of Enum . If the type is not an enum in this sense, this will fail to compile, complaining that it's impossible to construct a GenericEnum instance.

Answer 2

Fyodor's answer is incorrect unfortunately. The last value is omitted because it is mapped on it's non existing successor (ie Nothing).

A working alternative might be:

allPossible :: Array Icon
allPossible = unfoldr (\b -> b >>= next) $ Just genericBottom
  where
    next a = Just $ Tuple a $ genericSucc a