-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Infinite search in finite time with Hilbert's epsilon
--   
--   Infinite search in finite time with Hilbert's epsilon
@package search
@version 0.2

module Data.Search.LazyBool

-- | Bool with a lazier Ord as suggested <a>here</a>
newtype B
B :: Bool -> B
instance GHC.Read.Read Data.Search.LazyBool.B
instance GHC.Show.Show Data.Search.LazyBool.B
instance GHC.Classes.Eq Data.Search.LazyBool.B
instance GHC.Classes.Ord Data.Search.LazyBool.B

module Data.Search.Intensional

-- | Given a test that is required to execute in finite time for _all_
--   inputs, even infinite ones, <a>Search</a> should productively yield an
--   answer.
--   
--   I currently also assume that comparison of scores can be done in
--   finite time for all scores.
--   
--   This rules out large score sets.
--   
--   <tt><a>Search</a> <a>Bool</a></tt> can be used for predicate searches.
newtype Search a b
Search :: (forall m. Monad m => (b -> m a) -> m b) -> Search a b
[optimumM] :: Search a b -> forall m. Monad m => (b -> m a) -> m b

-- | Find the worst-scoring result of a search with monadic effects.
pessimumM :: Monad m => Search (Down a) b -> (b -> m a) -> m b
optimum :: Search a b -> (b -> a) -> b

-- | Find the worst-scoring result of a search.
pessimum :: Search (Down a) b -> (b -> a) -> b

-- | What is the best score obtained by the search?
optimalScore :: Search a b -> (b -> a) -> a

-- | What is the worst score obtained by the search?
pessimalScore :: Search (Down a) b -> (b -> a) -> a

-- | <a>Search</a> is more powerful than <a>Cont</a>.
--   
--   This provides a canonical monad homomorphism into <a>Cont</a>.
cps :: Search a b -> Cont a b
union :: Ord a => Search a b -> Search a b -> Search a b
pair :: Ord a => b -> b -> Search a b
fromList :: Ord a => [b] -> Search a b

-- | <a>Hilbert's epsilon</a>
class Hilbert a b where epsilon = to <$> gepsilon
epsilon :: Hilbert a b => Search a b
epsilon :: (Hilbert a b, GHilbert a (Rep b), Generic b) => Search a b

-- | search for an optimal answer using Hilbert's epsilon
--   
--   <pre>
--   &gt;&gt;&gt; best (&gt;4) :: Int8
--   5
--   </pre>
best :: Hilbert a b => (b -> a) -> b

-- | What is the worst scoring answer by Hilbert's epsilon?
worst :: Hilbert (Down a) b => (b -> a) -> b
bestScore :: Hilbert a b => (b -> a) -> a
worstScore :: Hilbert (Down a) b => (b -> a) -> a
every :: forall b. Hilbert B b => (b -> Bool) -> Bool

-- | does there exist an element satisfying the predicate?
--   
--   <pre>
--   &gt;&gt;&gt; exists (&gt;(maxBound::Int8))
--   False
--   </pre>
exists :: forall b. Hilbert B b => (b -> Bool) -> Bool
instance Data.Profunctor.Unsafe.Profunctor Data.Search.Intensional.Search
instance GHC.Base.Functor (Data.Search.Intensional.Search a)
instance Data.Functor.Bind.Class.Apply (Data.Search.Intensional.Search a)
instance GHC.Base.Applicative (Data.Search.Intensional.Search a)
instance GHC.Classes.Ord a => Data.Functor.Alt.Alt (Data.Search.Intensional.Search a)
instance Data.Functor.Bind.Class.Bind (Data.Search.Intensional.Search a)
instance GHC.Base.Monad (Data.Search.Intensional.Search a)
instance Data.Search.Intensional.GHilbert a GHC.Generics.U1
instance (Data.Search.Intensional.GHilbert a f, Data.Search.Intensional.GHilbert a g) => Data.Search.Intensional.GHilbert a (f GHC.Generics.:*: g)
instance (Data.Search.Intensional.GHilbert a f, Data.Search.Intensional.GHilbert a g, GHC.Classes.Ord a) => Data.Search.Intensional.GHilbert a (f GHC.Generics.:+: g)
instance Data.Search.Intensional.Hilbert a b => Data.Search.Intensional.GHilbert a (GHC.Generics.K1 i b)
instance Data.Search.Intensional.GHilbert a f => Data.Search.Intensional.GHilbert a (GHC.Generics.M1 i c f)
instance Data.Search.Intensional.Hilbert x ()
instance Data.Search.Intensional.Hilbert x (Data.Proxy.Proxy a)
instance Data.Search.Intensional.Hilbert x a => Data.Search.Intensional.Hilbert x (Data.Tagged.Tagged s a)
instance (Data.Search.Intensional.Hilbert x a, Data.Search.Intensional.Hilbert x b) => Data.Search.Intensional.Hilbert x (a, b)
instance (Data.Search.Intensional.Hilbert x a, Data.Search.Intensional.Hilbert x b, Data.Search.Intensional.Hilbert x c) => Data.Search.Intensional.Hilbert x (a, b, c)
instance (Data.Search.Intensional.Hilbert x a, Data.Search.Intensional.Hilbert x b, Data.Search.Intensional.Hilbert x c, Data.Search.Intensional.Hilbert x d) => Data.Search.Intensional.Hilbert x (a, b, c, d)
instance (Data.Search.Intensional.Hilbert x a, Data.Search.Intensional.Hilbert x b, Data.Search.Intensional.Hilbert x c, Data.Search.Intensional.Hilbert x d, Data.Search.Intensional.Hilbert x e) => Data.Search.Intensional.Hilbert x (a, b, c, d, e)
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Types.Bool
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x Data.Monoid.Any
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x Data.Monoid.All
instance Data.Search.Intensional.Hilbert x a => Data.Search.Intensional.Hilbert x (Data.Monoid.Product a)
instance Data.Search.Intensional.Hilbert x a => Data.Search.Intensional.Hilbert x (Data.Monoid.Sum a)
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Types.Ordering
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Types.Char
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Int.Int8
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Int.Int16
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Word.Word8
instance GHC.Classes.Ord x => Data.Search.Intensional.Hilbert x GHC.Word.Word16
instance (GHC.Classes.Ord x, Data.Search.Intensional.Hilbert x a) => Data.Search.Intensional.Hilbert x [a]
instance (GHC.Classes.Ord x, Data.Search.Intensional.Hilbert x a) => Data.Search.Intensional.Hilbert x (Control.Applicative.ZipList a)
instance (GHC.Classes.Ord x, Data.Search.Intensional.Hilbert x a) => Data.Search.Intensional.Hilbert x (GHC.Base.Maybe a)
instance (GHC.Classes.Ord x, Data.Search.Intensional.Hilbert x a) => Data.Search.Intensional.Hilbert x (Data.Monoid.First a)
instance (GHC.Classes.Ord x, Data.Search.Intensional.Hilbert x a) => Data.Search.Intensional.Hilbert x (Data.Monoid.Last a)
instance (GHC.Classes.Ord x, Data.Search.Intensional.Hilbert x a, Data.Search.Intensional.Hilbert x b) => Data.Search.Intensional.Hilbert x (Data.Either.Either a b)
instance (GHC.Classes.Ord x, GHC.Classes.Ord a, Data.Search.Intensional.Hilbert x b) => Data.Search.Intensional.Hilbert x (Data.Search.Intensional.Search a b)

module Data.Search

-- | Given a test that is required to execute in finite time for _all_
--   inputs, even infinite ones, <a>Search</a> should productively yield an
--   answer.
--   
--   I currently also assume that comparison of scores can be done in
--   finite time for all scores.
--   
--   This rules out large score sets.
--   
--   <tt><a>Search</a> <a>Bool</a></tt> can be used for predicate searches.
newtype Search a b
Search :: ((b -> a) -> b) -> Search a b
[optimum] :: Search a b -> (b -> a) -> b

-- | Find the worst-scoring result of a search.
pessimum :: Search (Down a) b -> (b -> a) -> b

-- | What is the best score obtained by the search?
optimalScore :: Search a b -> (b -> a) -> a

-- | What is the worst score obtained by the search?
pessimalScore :: Search (Down a) b -> (b -> a) -> a

-- | <a>Search</a> is more powerful than <a>Cont</a>.
--   
--   This provides a canonical monad homomorphism into <a>Cont</a>.
cps :: Search a b -> Cont a b
union :: Ord a => Search a b -> Search a b -> Search a b
pair :: Ord a => b -> b -> Search a b
fromList :: Ord a => [b] -> Search a b

-- | <a>Hilbert's epsilon</a>
class Hilbert a b where epsilon = to <$> gepsilon
epsilon :: Hilbert a b => Search a b
epsilon :: (Hilbert a b, GHilbert a (Rep b), Generic b) => Search a b

-- | search for an optimal answer using Hilbert's epsilon
--   
--   <pre>
--   &gt;&gt;&gt; best (&gt;4) :: Int8
--   5
--   </pre>
best :: Hilbert a b => (b -> a) -> b

-- | What is the worst scoring answer by Hilbert's epsilon?
worst :: Hilbert (Down a) b => (b -> a) -> b
bestScore :: Hilbert a b => (b -> a) -> a
worstScore :: Hilbert (Down a) b => (b -> a) -> a

-- | Bool with a lazier Ord as suggested <a>here</a>
newtype B
B :: Bool -> B
every :: forall b. Hilbert B b => (b -> Bool) -> Bool

-- | does there exist an element satisfying the predicate?
--   
--   <pre>
--   &gt;&gt;&gt; exists (&gt;(maxBound::Int8))
--   False
--   </pre>
exists :: forall b. Hilbert B b => (b -> Bool) -> Bool
instance Data.Profunctor.Unsafe.Profunctor Data.Search.Search
instance GHC.Base.Functor (Data.Search.Search a)
instance Data.Functor.Bind.Class.Apply (Data.Search.Search a)
instance GHC.Base.Applicative (Data.Search.Search a)
instance GHC.Classes.Ord a => Data.Functor.Alt.Alt (Data.Search.Search a)
instance Data.Functor.Bind.Class.Bind (Data.Search.Search a)
instance GHC.Base.Monad (Data.Search.Search a)
instance Data.Search.GHilbert a GHC.Generics.U1
instance (Data.Search.GHilbert a f, Data.Search.GHilbert a g) => Data.Search.GHilbert a (f GHC.Generics.:*: g)
instance (Data.Search.GHilbert a f, Data.Search.GHilbert a g, GHC.Classes.Ord a) => Data.Search.GHilbert a (f GHC.Generics.:+: g)
instance Data.Search.Hilbert a b => Data.Search.GHilbert a (GHC.Generics.K1 i b)
instance Data.Search.GHilbert a f => Data.Search.GHilbert a (GHC.Generics.M1 i c f)
instance Data.Search.Hilbert x ()
instance Data.Search.Hilbert x (Data.Proxy.Proxy a)
instance Data.Search.Hilbert x a => Data.Search.Hilbert x (Data.Tagged.Tagged s a)
instance (Data.Search.Hilbert x a, Data.Search.Hilbert x b) => Data.Search.Hilbert x (a, b)
instance (Data.Search.Hilbert x a, Data.Search.Hilbert x b, Data.Search.Hilbert x c) => Data.Search.Hilbert x (a, b, c)
instance (Data.Search.Hilbert x a, Data.Search.Hilbert x b, Data.Search.Hilbert x c, Data.Search.Hilbert x d) => Data.Search.Hilbert x (a, b, c, d)
instance (Data.Search.Hilbert x a, Data.Search.Hilbert x b, Data.Search.Hilbert x c, Data.Search.Hilbert x d, Data.Search.Hilbert x e) => Data.Search.Hilbert x (a, b, c, d, e)
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Types.Bool
instance GHC.Classes.Ord x => Data.Search.Hilbert x Data.Monoid.Any
instance GHC.Classes.Ord x => Data.Search.Hilbert x Data.Monoid.All
instance Data.Search.Hilbert x a => Data.Search.Hilbert x (Data.Monoid.Product a)
instance Data.Search.Hilbert x a => Data.Search.Hilbert x (Data.Monoid.Sum a)
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Types.Ordering
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Types.Char
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Int.Int8
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Int.Int16
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Word.Word8
instance GHC.Classes.Ord x => Data.Search.Hilbert x GHC.Word.Word16
instance (GHC.Classes.Ord x, Data.Search.Hilbert x a) => Data.Search.Hilbert x [a]
instance (GHC.Classes.Ord x, Data.Search.Hilbert x a) => Data.Search.Hilbert x (Control.Applicative.ZipList a)
instance (GHC.Classes.Ord x, Data.Search.Hilbert x a) => Data.Search.Hilbert x (GHC.Base.Maybe a)
instance (GHC.Classes.Ord x, Data.Search.Hilbert x a) => Data.Search.Hilbert x (Data.Monoid.First a)
instance (GHC.Classes.Ord x, Data.Search.Hilbert x a) => Data.Search.Hilbert x (Data.Monoid.Last a)
instance (GHC.Classes.Ord x, Data.Search.Hilbert x a, Data.Search.Hilbert x b) => Data.Search.Hilbert x (Data.Either.Either a b)
instance (GHC.Classes.Ord x, GHC.Classes.Ord a, Data.Search.Hilbert x b) => Data.Search.Hilbert x (Data.Search.Search a b)