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

[ bsd3, data-structures, library, type-system ] [ Propose Tags ]

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.

Versions [RSS] [faq] 0.5, 0.6, 0.6.1, 0.7, 0.8.0.0, 0.8.5.0, 0.8.6.0, 0.8.7.0, 0.8.9.0 base (>=4.7.0.0 && <5), ghc-prim [details] BSD-3-Clause 2013-16 University of Cambridge Dominic Orchard Dominic Orchard Type System, Data Structures head: git clone https://github.com/dorchard/type-level-sets by DominicOrchard at 2016-01-05T17:44:56Z NixOS:0.8.9.0 5965 total (61 in the last 30 days) 2.0 (votes: 1) [estimated by Bayesian average] λ λ λ Docs available Last success reported on 2016-11-28  [Index]

• Data
• Type