-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | metric spaces -- -- A MetricSpace is a set together with a notion of distance -- between elements. Distance is computed by a function dist which -- has the following four laws: -- --
    --
  1. non-negative: forall x y. dist x y >= -- 0
    2. --
  2. identity of indiscernibles: forall x y. dist x y -- == 0 <=> x == y
    3. --
  3. symmetry: forall x y. dist x y == dist y -- x
    4. --
  4. triangle inequality: forall x y z. dist x z -- <= dist x y + dist y z
    5. --
-- -- See the Wikipedia article on metric spaces for more details. @package ms @version 0.2.1 -- | A MetricSpace is a set together with a notion of distance -- between elements. Distance is computed by a function dist which -- has the following four laws: -- --
    --
  1. non-negative: forall x y. dist x y >= -- 0
    2. --
  2. identity of indiscernibles: forall x y. dist x y -- == 0 <=> x == y
    3. --
  3. symmetry: forall x y. dist x y == dist y -- x
    4. --
  4. triangle inequality: forall x y z. dist x z -- <= dist x y + dist y z
    5. --
-- -- See the Wikipedia article on metric spaces for more details. module Math.MetricSpace newtype MetricSpace a b MetricSpace :: (a -> a -> b) -> MetricSpace a b [dist] :: MetricSpace a b -> a -> a -> b type ClosedMetricSpace a = MetricSpace a a newtype FlippedMetricSpace b a FlippedMetricSpace :: (MetricSpace a b) -> FlippedMetricSpace b a type ClosedFlippedMetricSpace a = FlippedMetricSpace a a (<->) :: MetricSpace a b -> a -> a -> b _FlippedMetricSpace :: Iso (MetricSpace a b) (MetricSpace x y) (FlippedMetricSpace b a) (FlippedMetricSpace y x) class SwappedMetricSpace m _SwappedMetricSpace :: SwappedMetricSpace m => Iso (m a b) (m x y) (m a b) (m x y) -- | Levenshtein distance between Strings. -- -- 
--   >>> dist levenshtein "foo" "bar"
--   3
--
-- -- 
--   >>> dist levenshtein "hi" "ha"
--   1
--
-- -- 
--   >>> dist levenshtein "ff" "ff"
--   0
--
levenshtein :: Integral b => MetricSpace String b -- | Discrete distance over n-dimensional Vectors. -- -- 
--   >>> dist discrete (V.fromList [3,4]) (V.fromList [3,4])
--   0
--
-- -- 
--   >>> dist discrete (V.fromList [1,49]) (V.fromList [3,-94])
--   1
--
discrete :: (Eq a, Integral b) => MetricSpace (Vector a) b -- | Euclidean distance over n-dimensional Vectors. -- -- 
--   >>> dist euclidean (V.fromList [3,4]) (V.fromList [3,4])
--   0.0
--
-- -- 
--   >>> dist euclidean (V.fromList [1,49]) (V.fromList [3,-94])
--   143.01398533010678
--
euclidean :: RealFloat a => MetricSpace (Vector a) a -- | Taxicab distance over n-dimensional Vectors. -- -- 
--   >>> dist taxicab (V.fromList [3,4]) (V.fromList [3,4])
--   0.0
--
-- -- 
--   >>> dist taxicab (V.fromList [1,49]) (V.fromList [3,-94])
--   145.0
--
taxicab :: RealFloat a => MetricSpace (Vector a) a -- | Hamming distance over n-dimensional Vectors. hamming :: (Eq a, Integral b) => MetricSpace (Vector a) b instance GHC.Base.Functor (Math.MetricSpace.MetricSpace a) instance GHC.Base.Applicative (Math.MetricSpace.MetricSpace a) instance GHC.Base.Monad (Math.MetricSpace.MetricSpace a) instance Data.Semigroup.Semigroup b => Data.Semigroup.Semigroup (Math.MetricSpace.MetricSpace a b) instance GHC.Base.Monoid b => GHC.Base.Monoid (Math.MetricSpace.MetricSpace a b) instance Data.Profunctor.Unsafe.Profunctor Math.MetricSpace.MetricSpace instance Data.Semigroupoid.Semigroupoid Math.MetricSpace.MetricSpace instance Data.Functor.Contravariant.Contravariant (Math.MetricSpace.FlippedMetricSpace b) instance GHC.Base.Monoid b => Data.Functor.Contravariant.Divisible.Divisible (Math.MetricSpace.FlippedMetricSpace b) instance Math.MetricSpace.SwappedMetricSpace Math.MetricSpace.MetricSpace instance Math.MetricSpace.SwappedMetricSpace Math.MetricSpace.FlippedMetricSpace