@hackage type-level-sets0.6.1

This package provides type-level sets (no duplicates, sorted to provide a normal form) via Set and type-level finite maps via Map, with value-level counterparts.

Described in the paper "Embedding effect systems in Haskell" by Dominic Orchard and Tomas Petricek http://www.cl.cam.ac.uk/~dao29/publ/haskell14-effects.pdf (Haskell Symposium, 2014). This version now uses Quicksort to normalise the representation.

Here is a brief example for finite maps.:

import Data.Type.Map

foo :: Map '["x" :-> Int, "z" :-> Int, "w" :-> Int]
foo = Ext ((Var :: (Var "x")) :-> 2) $
        Ext ((Var :: (Var "z")) :-> 4) $
          Ext ((Var :: (Var "w")) :-> 5) $
            Empty

bar :: Map '["y" :-> Int, "w" :-> Int]
bar = Ext ((Var :: (Var "y")) :-> 3) $
        Ext ((Var :: (Var "w")) :-> 1) $
          Empty

-- foobar :: Map '["w" :-> Int, "x" :-> Int, "y" :-> Int, "z" :-> Int]
foobar = foo `union` bar

The Set type for foobar here shows the normalised form (sorted with no duplicates). The type signatures is commented out as it can be infered. Running the example we get:

>>> foobar
[(Var :-> 1), (Var :-> 2), (Var :-> 3), (Var :-> 4)]

Thus, we see that the first value paired with the "w" variable is dropped. For sets, here is an example:

import GHC.TypeLits
import Data.Type.Set
type instance Cmp (Natural n) (Natural m) = CmpNat n m

data Natural (a :: Nat) where
  Z :: Natural 0
  S :: Natural n -> Natural (n + 1)

-- foo :: Set '[Natural 0, Natural 1, Natural 3]
foo = asSet $ Ext (S Z) (Ext (S (S (S Z))) (Ext Z Empty))

-- bar :: Set '[Natural 1, Natural 2]
bar = asSet $ Ext (S (S Z)) (Ext (S Z) (Ext (S Z) Empty))

-- foobar :: Set '[Natural 0, Natural 1, Natural 2, Natural 3]
foobar = foo `union` bar

Note the types here are all inferred.