Data.Universe

Documentation

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

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.

Methods

universe :: [a]

Instances

Universe Bool

Universe Char

Universe Int

Universe Int8

Universe Int16

Universe Int32

Universe Int64

Universe Integer

Universe Ordering

Universe Word

Universe Word8

Universe Word16

Universe Word32

Universe Word64

Universe ()

Universe All

Universe Any

Universe Void

Universe a => Universe [a]

~ * a Integer => Universe (Ratio a)

Universe a => Universe (Dual a)

Universe a => Universe (Sum a)

Universe a => Universe (Product a)

Universe a => Universe (First a)

Universe a => Universe (Last a)

Universe a => Universe (Maybe a)

Universe a => Universe (Identity a)

(Finite a, Ord a, Universe b) => Universe (a -> b)

(Universe a, Universe b) => Universe (Either a b)

(Universe a, Universe b) => Universe (a, b)

Universe (f a) => Universe (IdentityT f a)

(Representable f, Finite (Key f), Ord (Key f), Universe a) => Universe (Rep f a)

(Universe a, Universe b, Universe c) => Universe (a, b, c)

(Representable f, Finite s, Ord s, Finite (Key f), Ord (Key f), Universe a) => Universe (TracedT s f a)

(Finite e, Ord e, Universe (m a)) => Universe (ReaderT e m a)

Universe (f (g a)) => Universe (Compose f g a)

(Universe (f a), Universe (g a)) => Universe (Product f g a)

(Universe a, Universe b, Universe c, Universe d) => Universe (a, b, c, d)

(Universe a, Universe b, Universe c, Universe d, Universe e) => Universe (a, b, c, d, e)

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.

Methods

universeF :: [a]

Instances

Finite Bool

Finite Char

Finite Int

Finite Int8

Finite Int16

Finite Int32

Finite Int64

Finite Ordering

Finite Word

Finite Word8

Finite Word16

Finite Word32

Finite Word64

Finite ()

Finite All

Finite Any

Finite Void

Finite a => Finite (Dual a)

Finite a => Finite (Sum a)

Finite a => Finite (Product a)

Finite a => Finite (First a)

Finite a => Finite (Last a)

Finite a => Finite (Maybe a)

Finite a => Finite (Identity a)

(Ord a, Finite a, Finite b) => Finite (a -> b)

(Finite a, Finite b) => Finite (Either a b)

(Finite a, Finite b) => Finite (a, b)

Finite (f a) => Finite (IdentityT f a)

(Representable f, Finite (Key f), Ord (Key f), Finite a) => Finite (Rep f a)

(Finite a, Finite b, Finite c) => Finite (a, b, c)

(Representable f, Finite s, Ord s, Finite (Key f), Ord (Key f), Finite a) => Finite (TracedT s f a)

(Finite e, Ord e, Finite (m a)) => Finite (ReaderT e m a)

Finite (f (g a)) => Finite (Compose f g a)

(Finite (f a), Finite (g a)) => Finite (Product f g a)

(Finite a, Finite b, Finite c, Finite d) => Finite (a, b, c, d)

(Finite a, Finite b, Finite c, Finite d, Finite e) => Finite (a, b, c, d, e)