Type-level sets in Haskell / Agda

Question

I've seen that in the latest versions of GHC there's support for type-level lists. However, I need to work with type-level sets for an application, and would like to implement a type-level set library based on type-level lists. But I don't know where to start :(

Is there any library supporting type-level sets in Haskell?

Answer 1

You can use HSet property for HList's from HList package:

{-# LANGUAGE FlexibleInstances #-}

import Data.HList

class (HList l, HSet l) => ThisIsSet l where
  -- Here we have @l@ which is @HList@ _and_ @HSet@.
  test :: l

-- This is ok:

instance ThisIsSet HNil where
  test = hNil

-- And this:

instance ThisIsSet (HCons HZero HNil) where
  test = hCons hZero hNil

-- And this (HZero != HSucc HZero):

instance ThisIsSet (HCons HZero (HCons (HSucc HZero) HNil)) where
  test = hCons hZero (hCons (hSucc hZero) hNil)

-- This is an error since HSucc HZero == HSucc HZero:

instance ThisIsSet (HCons (HSucc HZero) (HCons (HSucc HZero) HNil)) where
  test = hCons (hSucc hZero) (hCons (hSucc hZero) hNil)

for working with other types you need to write HEq instances for them.