Safe Haskell	Safe
Language	Haskell2010

Data.Universe.Class

Description

Bottoms are ignored for this entire module: only fully-defined inhabitants are considered inhabitants.

Synopsis

class Universe a where
- universe :: [a]
class Universe a => Finite a where
- universeF :: [a]
- cardinality :: Tagged a Natural

Documentation

class Universe a where Source #

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] Source #

default universe :: ( Enum a, Bounded a) => [a] Source #

Instances

Instances details

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

class Universe a => Finite a where Source #

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] Source #

cardinality :: Tagged a Natural Source #

Instances

Instances details

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