Create a type that is a subset of an other type

Question

How can you create a type that is a subset of an other type? I want a string type that only contains alphanumeric characters.

So I want something like this

type AlphNumString = [AlphaNumChar]
data AlphaNumChar = ???? filter (isAlphaNum) Char ????

Answer 1

The standard way to do this is with so-called "smart constructors".

First, you define a new type that's identical to the old one:

newtype AlphNumString = X String

Next, you write the smart constructor itself:

toAlphNumString :: String -> AlphNumString
toAlphNumString txt = X (filter isAlphNum txt)

Finally, you make it so toAlphNumString is the only way to create an AlphNumString.

module Foo (AlphNumString (), toAlphNumString, ...) where ...

Note that this does not allow you to use an AlphNumString like a normal String; you can't create "subtypes" like that in Haskell. So you'll also need another function

fromAlphNumString :: AlphNumString -> String
fromAlphNumString (X txt) = txt

Answer 2

This concept of types that are "subsets" of other types based on some predicate is called refinement types. For Haskell, this is implemented as LiquidHaskell.

However, I would consider this an ongoing research. In practice, I would go with a newtype and dynamic checks, as MathematicalOrchid describes in their answer.