-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Boring and Absurd types
--
--
-- - Boring types are isomorphic to ().
-- - Absurd types are isomorphic to Void.
--
--
-- See What does () mean in Haskell -answer by Conor McBride
@package boring
@version 0
-- | Boring and Absurd classes. One approach.
--
-- Different approach would be to have
--
--
-- -- none-one-tons semiring
-- data NOT = None | One | Tons
--
-- type family Cardinality (a :: *) :: NOT
--
-- class Cardinality a ~ None => Absurd a where ...
-- class Cardinality a ~ One => Boring a where ...
--
--
-- This would make possible to define more instances, e.g.
--
--
-- instance (Mult (Cardinality a) (Cardinality b) ~ None) => Absurd (a, b) where ...
--
--
-- Functions
--
-- Function is an exponential:
--
--
-- Cardinality (a -> b) ~ Exponent (Cardinality b) (Cardinality a)
--
--
-- or shortly |a -> b| = |b| ^ |a|. This gives us possible
-- instances:
--
--
-- - |a| = 0 => |a -> b| = m ^ 0 = 1, i.e.
-- Absurd a => Boring (a -> b), or
-- - |b| = 1 => |a -> b| = 1 ^ n = 1, i.e.
-- Boring b => Boring (a -> b).
--
--
-- Both instances are Boring, but we chose to define the latter.
--
-- Note about adding instances
--
-- At this moment this module misses a lot of instances, please make a
-- patch to add more. Especially, if the package is already in the
-- transitive dependency closure.
--
-- E.g. any possibly empty container f has Absurd a
-- => Boring (f a)
module Data.Boring
-- | Boring types which contains one thing, also boring.
-- There is nothing interesting to be gained by comparing one element of
-- the boring type with another, because there is nothing to learn about
-- an element of the boring type by giving it any of your attention.
--
-- Boring Law:
--
--
-- boring == x
--
--
-- Note: This is different class from Default.
-- Default gives you some value, Boring gives
-- you an unique value.
--
-- Also note, that we cannot have instances for e.g. Either, as
-- both (Boring a, Absurd b) => Either a b and
-- (Absurd a, Boring b) => Either a b would be
-- valid instances.
--
-- Another useful trick, is that you can rewrite computations with
-- Boring results, for example foo :: Int -> (),
-- if you are sure that foo is total.
--
--
-- {-# RULES "less expensive" foo = boring #-}
--
--
-- That's particularly useful with equality :~: proofs.
class Boring a
boring :: Boring a => a
-- | The Absurd type is very exciting, because if somebody ever
-- gives you a value belonging to it, you know that you are already dead
-- and in Heaven and that anything you want is yours.
--
-- Similarly as there are many Boring sums, there are many
-- Absurd products, so we don't have Absurd instances for
-- tuples.
class Absurd a
absurd :: Absurd a => a -> b
-- | If Absurd is uninhabited then any Functor that holds
-- only values of type Absurd is holding no values.
vacuous :: (Functor f, Absurd a) => f a -> f b
-- | If an index of Representable f is Absurd, f
-- a is Boring.
boringRep :: (Representable f, Absurd (Rep f)) => f a
-- | If an index of Representable f is Boring,
-- f is isomorphic to Identity.
--
-- See also Settable class in lens.
untainted :: (Representable f, Boring (Rep f)) => f a -> a
instance Data.Boring.Boring ()
instance Data.Boring.Boring b => Data.Boring.Boring (a -> b)
instance Data.Boring.Boring (Data.Proxy.Proxy a)
instance Data.Boring.Boring a => Data.Boring.Boring (Data.Functor.Const.Const a b)
instance Data.Boring.Boring b => Data.Boring.Boring (Data.Tagged.Tagged a b)
instance Data.Boring.Boring a => Data.Boring.Boring (Data.Functor.Identity.Identity a)
instance (Data.Boring.Boring a, Data.Boring.Boring b) => Data.Boring.Boring (a, b)
instance (Data.Boring.Boring a, Data.Boring.Boring b, Data.Boring.Boring c) => Data.Boring.Boring (a, b, c)
instance (Data.Boring.Boring a, Data.Boring.Boring b, Data.Boring.Boring c, Data.Boring.Boring d) => Data.Boring.Boring (a, b, c, d)
instance (Data.Boring.Boring a, Data.Boring.Boring b, Data.Boring.Boring c, Data.Boring.Boring d, Data.Boring.Boring e) => Data.Boring.Boring (a, b, c, d, e)
instance Data.Boring.Absurd a => Data.Boring.Boring [a]
instance Data.Boring.Absurd a => Data.Boring.Boring (GHC.Base.Maybe a)
instance a ~ b => Data.Boring.Boring (a Data.Type.Equality.:~: b)
instance Data.Boring.Absurd Data.Void.Void
instance (Data.Boring.Absurd a, Data.Boring.Absurd b) => Data.Boring.Absurd (Data.Either.Either a b)
instance Data.Boring.Absurd a => Data.Boring.Absurd (Data.List.NonEmpty.NonEmpty a)
instance Data.Boring.Absurd a => Data.Boring.Absurd (Data.Functor.Identity.Identity a)