Safe Haskell	Safe
Language	Haskell2010

Data.Universe

Description

A convenience module that imports the submodules Instances.Base, Instances.Containers, Instances.Extended, and Instances.Trans to provide instances of Universe and Finite for a wide variety of types.

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

class Universe a where #

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:

elem x universe                    -- any inhabitant has a finite index
let pfx = take n universe          -- any finite prefix of universe has unique elements
in length pfx = length (nub pfx)

Minimal complete definition

Nothing

Methods

universe :: [a] #

Instances

Instances details

Universe Bool
Instance details Defined in Data.Universe.Class Methods universe :: [Bool] #
Universe Char
Instance details Defined in Data.Universe.Class Methods universe :: [Char] #
Universe Int
Instance details Defined in Data.Universe.Class Methods universe :: [Int] #
Universe Int8
Instance details Defined in Data.Universe.Class Methods universe :: [Int8] #
Universe Int16
Instance details Defined in Data.Universe.Class Methods universe :: [Int16] #
Universe Int32
Instance details Defined in Data.Universe.Class Methods universe :: [Int32] #
Universe Int64
Instance details Defined in Data.Universe.Class Methods universe :: [Int64] #
Universe Integer
Instance details Defined in Data.Universe.Class Methods universe :: [Integer] #
Universe Natural
Instance details Defined in Data.Universe.Class Methods universe :: [Natural] #
Universe Ordering
Instance details Defined in Data.Universe.Class Methods universe :: [Ordering] #
Universe Word
Instance details Defined in Data.Universe.Class Methods universe :: [Word] #
Universe Word8
Instance details Defined in Data.Universe.Class Methods universe :: [Word8] #
Universe Word16
Instance details Defined in Data.Universe.Class Methods universe :: [Word16] #
Universe Word32
Instance details Defined in Data.Universe.Class Methods universe :: [Word32] #
Universe Word64
Instance details Defined in Data.Universe.Class Methods universe :: [Word64] #
Universe ()
Instance details Defined in Data.Universe.Class Methods universe :: [()] #
Universe Void
Instance details Defined in Data.Universe.Class Methods universe :: [Void] #
Universe All
Instance details Defined in Data.Universe.Class Methods universe :: [All] #
Universe Any
Instance details Defined in Data.Universe.Class Methods universe :: [Any] #
Universe a => Universe [a]
Instance details Defined in Data.Universe.Class Methods universe :: [[a]] #
Universe a => Universe (Maybe a)
Instance details Defined in Data.Universe.Class Methods universe :: [Maybe a] #
RationalUniverse a => Universe (Ratio a)
Instance details Defined in Data.Universe.Class Methods universe :: [Ratio a] #
Universe a => Universe (Solo a)
Instance details Defined in Data.Universe.Class Methods universe :: [Solo a] #
Universe a => Universe (Min a)
Instance details Defined in Data.Universe.Class Methods universe :: [Min a] #
Universe a => Universe (Max a)
Instance details Defined in Data.Universe.Class Methods universe :: [Max a] #
Universe a => Universe (First a)
Instance details Defined in Data.Universe.Class Methods universe :: [First a] #
Universe a => Universe (Last a)
Instance details Defined in Data.Universe.Class Methods universe :: [Last a] #
Universe a => Universe (Identity a)
Instance details Defined in Data.Universe.Class Methods universe :: [Identity a] #
Universe a => Universe (First a)
Instance details Defined in Data.Universe.Class Methods universe :: [First a] #
Universe a => Universe (Last a)
Instance details Defined in Data.Universe.Class Methods universe :: [Last a] #
Universe a => Universe (Dual a)
Instance details Defined in Data.Universe.Class Methods universe :: [Dual a] #
Universe a => Universe (Sum a)
Instance details Defined in Data.Universe.Class Methods universe :: [Sum a] #
Universe a => Universe (Product a)
Instance details Defined in Data.Universe.Class Methods universe :: [Product a] #
Universe a => Universe (NonEmpty a)
Instance details Defined in Data.Universe.Class Methods universe :: [NonEmpty a] #
(Ord a, Universe a) => Universe (Set a)	`>>>` `import qualified Data.Set as Set``>>>` `mapM_ print (universe :: [Set.Set Bool])`fromList [] fromList [False] fromList [True] fromList [False,True]
Instance details Defined in Data.Universe.Class Methods universe :: [Set a] #
(Finite a, Ord a, Universe b) => Universe (a -> b)	`>>>` `mapM_ print (universe :: [Bool -> Bool])`[(False,False),(True,False)] [(False,False),(True,True)] [(False,True),(True,False)] [(False,True),(True,True)]
Instance details Defined in Data.Universe.Class Methods universe :: [a -> b] #
(Universe a, Universe b) => Universe (Either a b)
Instance details Defined in Data.Universe.Class Methods universe :: [Either a b] #
(Universe a, Universe b) => Universe (a, b)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b)] #
Universe (Proxy a)
Instance details Defined in Data.Universe.Class Methods universe :: [Proxy a] #
(Ord k, Finite k, Universe v) => Universe (Map k v)	`>>>` `import qualified Data.Map as Map``>>>` `mapM_ print (universe :: [Map.Map Bool Bool])`fromList [] fromList [(True,False)] fromList [(False,False)] fromList [(True,True)] fromList [(False,False),(True,False)] fromList [(False,True)] fromList [(False,False),(True,True)] fromList [(False,True),(True,False)] fromList [(False,True),(True,True)]
Instance details Defined in Data.Universe.Class Methods universe :: [Map k v] #
(Universe a, Universe b, Universe c) => Universe (a, b, c)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b, c)] #
Universe a => Universe (Const a b)
Instance details Defined in Data.Universe.Class Methods universe :: [Const a b] #
Universe (f a) => Universe (IdentityT f a)
Instance details Defined in Data.Universe.Class Methods universe :: [IdentityT f a] #
(Finite e, Ord e, Universe (m a)) => Universe (ReaderT e m a)
Instance details Defined in Data.Universe.Class Methods universe :: [ReaderT e m a] #
Universe a => Universe (Tagged b a)
Instance details Defined in Data.Universe.Class Methods universe :: [Tagged b a] #
(Universe a, Universe b, Universe c, Universe d) => Universe (a, b, c, d)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b, c, d)] #
(Universe (f a), Universe (g a)) => Universe (Product f g a)
Instance details Defined in Data.Universe.Class Methods universe :: [Product f g a] #
(Universe (f a), Universe (g a)) => Universe (Sum f g a)
Instance details Defined in Data.Universe.Class Methods universe :: [Sum f g a] #
(Universe a, Universe b, Universe c, Universe d, Universe e) => Universe (a, b, c, d, e)
Instance details Defined in Data.Universe.Class Methods universe :: [(a, b, c, d, e)] #
Universe (f (g a)) => Universe (Compose f g a)
Instance details Defined in Data.Universe.Class Methods universe :: [Compose f g a] #

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:

elem x universeF                       -- any inhabitant has a finite index
length (filter (== x) universeF) == 1  -- should terminate
(xs -> cardinality xs == genericLength xs) universeF

Note: elemIndex x universe == elemIndex x universeF may not hold for all types, though the laws imply that universe is a permutation of universeF.

>>> elemIndex (Left True :: Either Bool Bool) universe
Just 2

>>> elemIndex (Left True :: Either Bool Bool) universeF
Just 1

Minimal complete definition

Nothing

Methods

universeF :: [a] #

cardinality :: Tagged a Natural #

Instances

Instances details

Finite Bool
Instance details Defined in Data.Universe.Class Methods universeF :: [Bool] # cardinality :: Tagged Bool Natural #
Finite Char
Instance details Defined in Data.Universe.Class Methods universeF :: [Char] # cardinality :: Tagged Char Natural #
Finite Int
Instance details Defined in Data.Universe.Class Methods universeF :: [Int] # cardinality :: Tagged Int Natural #
Finite Int8
Instance details Defined in Data.Universe.Class Methods universeF :: [Int8] # cardinality :: Tagged Int8 Natural #
Finite Int16
Instance details Defined in Data.Universe.Class Methods universeF :: [Int16] # cardinality :: Tagged Int16 Natural #
Finite Int32
Instance details Defined in Data.Universe.Class Methods universeF :: [Int32] # cardinality :: Tagged Int32 Natural #
Finite Int64
Instance details Defined in Data.Universe.Class Methods universeF :: [Int64] # cardinality :: Tagged Int64 Natural #
Finite Ordering
Instance details Defined in Data.Universe.Class Methods universeF :: [Ordering] # cardinality :: Tagged Ordering Natural #
Finite Word
Instance details Defined in Data.Universe.Class Methods universeF :: [Word] # cardinality :: Tagged Word Natural #
Finite Word8
Instance details Defined in Data.Universe.Class Methods universeF :: [Word8] # cardinality :: Tagged Word8 Natural #
Finite Word16
Instance details Defined in Data.Universe.Class Methods universeF :: [Word16] # cardinality :: Tagged Word16 Natural #
Finite Word32
Instance details Defined in Data.Universe.Class Methods universeF :: [Word32] # cardinality :: Tagged Word32 Natural #
Finite Word64
Instance details Defined in Data.Universe.Class Methods universeF :: [Word64] # cardinality :: Tagged Word64 Natural #
Finite ()
Instance details Defined in Data.Universe.Class Methods universeF :: [()] # cardinality :: Tagged () Natural #
Finite Void
Instance details Defined in Data.Universe.Class Methods universeF :: [Void] # cardinality :: Tagged Void Natural #
Finite All
Instance details Defined in Data.Universe.Class Methods universeF :: [All] # cardinality :: Tagged All Natural #
Finite Any
Instance details Defined in Data.Universe.Class Methods universeF :: [Any] # cardinality :: Tagged Any Natural #
Finite a => Finite (Maybe a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Maybe a] # cardinality :: Tagged (Maybe a) Natural #
Finite a => Finite (Solo a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Solo a] # cardinality :: Tagged (Solo a) Natural #
Finite a => Finite (Min a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Min a] # cardinality :: Tagged (Min a) Natural #
Finite a => Finite (Max a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Max a] # cardinality :: Tagged (Max a) Natural #
Finite a => Finite (First a)
Instance details Defined in Data.Universe.Class Methods universeF :: [First a] # cardinality :: Tagged (First a) Natural #
Finite a => Finite (Last a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Last a] # cardinality :: Tagged (Last a) Natural #
Finite a => Finite (Identity a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Identity a] # cardinality :: Tagged (Identity a) Natural #
Finite a => Finite (First a)
Instance details Defined in Data.Universe.Class Methods universeF :: [First a] # cardinality :: Tagged (First a) Natural #
Finite a => Finite (Last a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Last a] # cardinality :: Tagged (Last a) Natural #
Finite a => Finite (Dual a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Dual a] # cardinality :: Tagged (Dual a) Natural #
Finite a => Finite (Sum a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Sum a] # cardinality :: Tagged (Sum a) Natural #
Finite a => Finite (Product a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Product a] # cardinality :: Tagged (Product a) Natural #
(Ord a, Finite a) => Finite (Set a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Set a] # cardinality :: Tagged (Set a) Natural #
(Ord a, Finite a, Finite b) => Finite (a -> b)	`>>>` `mapM_ print (universeF :: [Bool -> Bool])`[(False,False),(True,False)] [(False,False),(True,True)] [(False,True),(True,False)] [(False,True),(True,True)] `>>>` `cardinality :: Tagged (Bool -> Ordering) Natural`Tagged 9 `>>>` `cardinality :: Tagged (Ordering -> Bool) Natural`Tagged 8
Instance details Defined in Data.Universe.Class Methods universeF :: [a -> b] # cardinality :: Tagged (a -> b) Natural #
(Finite a, Finite b) => Finite (Either a b)
Instance details Defined in Data.Universe.Class Methods universeF :: [Either a b] # cardinality :: Tagged (Either a b) Natural #
(Finite a, Finite b) => Finite (a, b)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b)] # cardinality :: Tagged (a, b) Natural #
Finite (Proxy a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Proxy a] # cardinality :: Tagged (Proxy a) Natural #
(Ord k, Finite k, Finite v) => Finite (Map k v)
Instance details Defined in Data.Universe.Class Methods universeF :: [Map k v] # cardinality :: Tagged (Map k v) Natural #
(Finite a, Finite b, Finite c) => Finite (a, b, c)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b, c)] # cardinality :: Tagged (a, b, c) Natural #
Finite a => Finite (Const a b)
Instance details Defined in Data.Universe.Class Methods universeF :: [Const a b] # cardinality :: Tagged (Const a b) Natural #
Finite (f a) => Finite (IdentityT f a)
Instance details Defined in Data.Universe.Class Methods universeF :: [IdentityT f a] # cardinality :: Tagged (IdentityT f a) Natural #
(Finite e, Ord e, Finite (m a)) => Finite (ReaderT e m a)
Instance details Defined in Data.Universe.Class Methods universeF :: [ReaderT e m a] # cardinality :: Tagged (ReaderT e m a) Natural #
Finite a => Finite (Tagged b a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Tagged b a] # cardinality :: Tagged (Tagged b a) Natural #
(Finite a, Finite b, Finite c, Finite d) => Finite (a, b, c, d)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b, c, d)] # cardinality :: Tagged (a, b, c, d) Natural #
(Finite (f a), Finite (g a)) => Finite (Product f g a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Product f g a] # cardinality :: Tagged (Product f g a) Natural #
(Finite (f a), Finite (g a)) => Finite (Sum f g a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Sum f g a] # cardinality :: Tagged (Sum f g a) Natural #
(Finite a, Finite b, Finite c, Finite d, Finite e) => Finite (a, b, c, d, e)
Instance details Defined in Data.Universe.Class Methods universeF :: [(a, b, c, d, e)] # cardinality :: Tagged (a, b, c, d, e) Natural #
Finite (f (g a)) => Finite (Compose f g a)
Instance details Defined in Data.Universe.Class Methods universeF :: [Compose f g a] # cardinality :: Tagged (Compose f g a) Natural #

universeGeneric :: (Generic a, GUniverse (Rep a)) => [a] #

>>> 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)]

module Data.Universe.Instances.Extended