How do I build a list with a dependently-typed length?

Question

Dipping my toe into the waters of dependent types, I had a crack at the canonical \"list with statically-typed length\" example.

{-# LANGUAGE DataKinds, GADT         


        

Answer 1

In

fromList :: [a] -> SafeList n a

n is universally quantified -- i.e. this signature is claiming that we should be able to build a SafeList of any length from the list. Instead you want to quantify existentially, which can only be done by defining a new data type:

data ASafeList a where
    ASafeList :: SafeList n a -> ASafeList a

Then your signature should be

fromList :: [a] -> ASafeList a

You can use it by pattern matching on ASafeList

useList :: ASafeList a -> ...
useList (ASafeList xs) = ...

and in the body, xs will be a SafeList n a type with an unknown (rigid) n. You will probably have to add more operations to use it in any nontrivial way.