type-level-sets

Type-level sets and finite maps (with value-level counterparts)

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

-- Specify how to combine duplicate key-value pairs for Int values
type instance Combine Int Int = Int
instance Combinable Int Int where
    combine x y = x + y

foo :: Map '["x" :-> Int, "z" :-> Bool, "w" :-> Int]
foo = Ext (Var :: (Var "x")) 2
    $ Ext (Var :: (Var "z")) True
    $ 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" :-> Bool]
foobar = foo `union` bar

The Map 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
{w :-> 6, x :-> 2, y :-> 3, z :-> True}

Thus, we see that the values for "w" are added together. 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.