rings-0.0.2: Rings, semirings, and dioids.

Safe HaskellSafe
LanguageHaskell2010

Data.Dioid.Signed

Synopsis

Documentation

data Sign Source #

Sign is isomorphic to 'Maybe Ordering' and (Bool,Bool), but has a distinct poset ordering:

Indeterminate >= Positive >= Zero and Indeterminate >= Negative >= Zero

Note that Positive and Negative are not comparable.

  • Positive can be regarded as representing (0, +∞],
  • Negative as representing [−∞, 0),
  • Indeterminate as representing [−∞, +∞] v NaN, and
  • Zero as representing the set {0}.
Instances
Bounded Sign Source # 
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Eq Sign Source # 
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Methods

(==) :: Sign -> Sign -> Bool #

(/=) :: Sign -> Sign -> Bool #

Show Sign Source # 
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Methods

showsPrec :: Int -> Sign -> ShowS #

show :: Sign -> String #

showList :: [Sign] -> ShowS #

Semigroup Sign Source # 
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Methods

(<>) :: Sign -> Sign -> Sign #

sconcat :: NonEmpty Sign -> Sign #

stimes :: Integral b => b -> Sign -> Sign #

Monoid Sign Source # 
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Methods

mempty :: Sign #

mappend :: Sign -> Sign -> Sign #

mconcat :: [Sign] -> Sign #

Prd Sign Source # 
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Methods

(<~) :: Sign -> Sign -> Bool #

(>~) :: Sign -> Sign -> Bool #

(=~) :: Sign -> Sign -> Bool #

(?~) :: Sign -> Sign -> Bool #

pcompare :: Sign -> Sign -> Maybe Ordering #

Min Sign Source # 
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Methods

minimal :: Sign #

Max Sign Source # 
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Methods

maximal :: Sign #

Semiring Sign Source # 
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signOf :: (Eq a, Num a, Prd a) => a -> Sign Source #

newtype Signed Source #

Constructors

Signed 

Fields

Instances
Eq Signed Source # 
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Methods

(==) :: Signed -> Signed -> Bool #

(/=) :: Signed -> Signed -> Bool #

Show Signed Source # 
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Prd Signed Source # 
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newtype Unsigned Source #

Constructors

Unsigned Float 
Instances
Eq Unsigned Source # 
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Show Unsigned Source # 
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Semigroup Unsigned Source # 
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Monoid Unsigned Source # 
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Lattice Unsigned Source # 
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Prd Unsigned Source # 
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Min Unsigned Source # 
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Methods

minimal :: Unsigned #

Max Unsigned Source # 
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Methods

maximal :: Unsigned #

Quantale Unsigned Source # 
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Semiring Unsigned Source # 
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Defined in Data.Dioid.Signed