# The type-level-sets package

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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.

## Properties

Versions | 0.5, 0.6, 0.6.1, 0.7, 0.7, 0.8.0.0 |
---|---|

Change log | None available |

Dependencies | base (<5), ghc-prim [details] |

License | BSD3 |

Copyright | 2013-16 University of Cambridge |

Author | Dominic Orchard |

Maintainer | Dominic Orchard |

Category | Type System, Data Structures |

Source repository | head: git clone https://github.com/dorchard/type-level-sets |

Uploaded | Fri May 27 11:21:59 UTC 2016 by DominicOrchard |

## Modules

*Data*

[Index]

## Downloads

- type-level-sets-0.7.tar.gz [browse] (Cabal source package)
- Package description (included in the package)

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