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Module Documentation

Module Data.BooleanAlgebra

Type Classes

class (Lattice a) <= BooleanAlgebra a where
  complement :: a -> a

Type Class Instances

instance booleanBoolean :: BooleanAlgebra Boolean

Values

booleanNegate :: Boolean -> Boolean

not :: forall b. (BooleanAlgebra b) => b -> b

Module Data.BoundedSemilattice

Type Classes

class (JoinSemilattice l) <= LowerSemilattice l where
  bottom :: l

class (MeetSemilattice l) <= UpperSemilattice l where
  top :: l

Type Class Instances

instance lowerSemilatticeBoolean :: LowerSemilattice Boolean

instance upperSemilatticeBoolean :: UpperSemilattice Boolean

Module Data.Group

Type Classes

class (AbelianAddMonoid g, AddGroup g) <= AbelianAddGroup g where

class (AbelianMonoid g, Group g) <= AbelianGroup g where

class (AbelianMultMonoid g, MultGroup g) <= AbelianMultGroup g where

class (AddMonoid g) <= AddGroup g where
  negate :: g -> g
  (-) :: g -> g -> g

class (Monoid g) <= Group g where
  inverse :: g -> g

class (MultMonoid g) <= MultGroup g where
  recip :: g -> g
  (/) :: g -> g -> g

Type Class Instances

instance abelianAddGroup :: AbelianAddGroup Number

instance abelianMultGroup :: AbelianMultGroup Number

instance additiveNumber :: AddGroup Number

instance multiplicativeNumber :: MultGroup Number

Values

numDivide :: Number -> Number -> Number

numMinus :: Number -> Number -> Number

Module Data.Lattice

Type Classes

class (LowerSemilattice l, UpperSemilattice l) <= Lattice l where

Type Class Instances

instance latticeBoolean :: Lattice Boolean

Module Data.Module

Type Classes

class (LeftModule m r, RightModule m r) <= Module m r where

Module Data.Monoid

Type Classes

class (AbelianAddSemigroup m, AddMonoid m) <= AbelianAddMonoid m where

class (AbelianSemigroup m, Monoid m) <= AbelianMonoid m where

class (AbelianMultSemigroup m, MultMonoid m) <= AbelianMultMonoid m where

class (AddSemigroup m) <= AddMonoid m where
  zero :: m

class (Semigroup m) <= Monoid m where
  mempty :: m

class (MultSemigroup m) <= MultMonoid m where
  one :: m

Type Class Instances

instance abelianAddMonoid :: AbelianAddMonoid Number

instance abelianMultMonoid :: AbelianMultMonoid Number

instance additiveNumber :: AddMonoid Number

instance monoidString :: Monoid String

instance multiplicativeNumber :: MultMonoid Number

Module Data.Ring

Type Classes

class (AbelianAddMonoid r, MultMonoid r) <= Rig r where

class (AbelianAddGroup r, MultMonoid r) <= Ring r where

class (AbelianAddGroup r, MultSemigroup r) <= Rng r where

Type Class Instances

instance ringNumber :: Ring Number

Module Data.Semigroup

Type Classes

class (AddSemigroup s) <= AbelianAddSemigroup s where

class (MultSemigroup s) <= AbelianMultSemigroup s where

class (Semigroup s) <= AbelianSemigroup s where

class AddSemigroup s where
  (+) :: s -> s -> s

class MultSemigroup s where
  (*) :: s -> s -> s

class Semigroup s where
  (<>) :: s -> s -> s

Type Class Instances

instance abelianAddSemigroup :: AbelianAddSemigroup Number

instance abelianMultSemigroup :: AbelianMultSemigroup Number

instance additiveNumber :: AddSemigroup Number

instance multiplicativeNumber :: MultSemigroup Number

instance semigroupString :: Semigroup String

Values

numPlus :: Number -> Number -> Number

numTimes :: Number -> Number -> Number

strConcat :: String -> String -> String

Module Data.Semilattice

Type Classes

class JoinSemilattice j where
  (\/) :: j -> j -> j

class MeetSemilattice m where
  (/\) :: m -> m -> m

Type Class Instances

instance joinSemilatticeBoolean :: JoinSemilattice Boolean

instance meetSemilatticeBoolean :: MeetSemilattice Boolean

Values

booleanAnd :: Boolean -> Boolean -> Boolean

booleanOr :: Boolean -> Boolean -> Boolean

Module Data.Module.LeftModule

Type Classes

class (AbelianAddGroup m, Ring r) <= LeftModule m r where
  (*<) :: r -> m -> m

Module Data.Module.RightModule

Type Classes

class (AbelianAddGroup m, Ring r) <= RightModule m r where
  (>*) :: m -> r -> m