| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Data.Universe
Description
Synopsis
- class Universe a where
- universe :: [a]
- class Universe a => Finite a where
- universeF :: [a]
- cardinality :: Tagged a Natural
- universeGeneric :: (Generic a, GUniverse (Rep a)) => [a]
- module Data.Universe.Instances.Extended
Documentation
Creating an instance of this class is a declaration that your type is
recursively enumerable (and that universe is that enumeration). In
particular, you promise that any finite inhabitant has a finite index in
universe, and that no inhabitant appears at two different finite indices.
Well-behaved instance should produce elements lazily.
Laws:
elemxuniverse-- any inhabitant has a finite index let pfx =takenuniverse-- any finite prefix of universe has unique elements inlengthpfx =length(nub pfx)
Minimal complete definition
Nothing
Instances
class Universe a => Finite a where #
Creating an instance of this class is a declaration that your universe
eventually ends. Minimal definition: no methods defined. By default,
universeF = universe, but for some types (like Either) the universeF
method may have a more intuitive ordering.
Laws:
elemxuniverseF-- any inhabitant has a finite indexlength(filter(== x)universeF) == 1 -- should terminate (xs ->cardinalityxs ==genericLengthxs)universeF
Note: elemIndex x universe == elemIndex x universeFuniverse
is a permutation of universeF.
>>>elemIndex (Left True :: Either Bool Bool) universeJust 2
>>>elemIndex (Left True :: Either Bool Bool) universeFJust 1
Minimal complete definition
Nothing
Instances
universeGeneric :: (Generic a, GUniverse (Rep a)) => [a] #
>>>data Zero deriving (Show, Generic)>>>universeGeneric :: [Zero][]
>>>data One = One deriving (Show, Generic)>>>universeGeneric :: [One][One]
>>>data Big = B0 Bool Bool | B1 Bool deriving (Show, Generic)>>>universeGeneric :: [Big][B0 False False,B1 False,B0 False True,B1 True,B0 True False,B0 True True]
>>>universeGeneric :: [Maybe Ordering][Nothing,Just LT,Just EQ,Just GT]
>>>take 10 (universeGeneric :: [Either Integer Integer])[Left 0,Right 0,Left 1,Right 1,Left (-1),Right (-1),Left 2,Right 2,Left (-2),Right (-2)]
>>>take 10 (universeGeneric :: [(Integer, Integer, Integer)])[(0,0,0),(0,0,1),(1,0,0),(0,1,0),(1,0,1),(-1,0,0),(0,0,-1),(1,1,0),(-1,0,1),(2,0,0)]