semiring-num 0.5.0.0 → 0.5.1.1

raw patch · 2 files changed

+44/−10 lines, 2 files

Files

• semiring-num.cabal +1/−1
• src/Data/Semiring.hs +43/−9

@@ -1,5 +1,5 @@ name:                semiring-num-version:             0.5.0.0+version:             0.5.1.1 synopsis:            Basic semiring class and instances description:         Adds a basic semiring class homepage:            https://github.com/oisdk/semiring-num

@@ -15,6 +15,8 @@   ( Semiring(..)   , Add(..)   , Mul(..)+  , add+  , mul   , Max(..)   , Min(..)   ) where@@ -220,27 +222,59 @@   (<.>) = (coerce :: WrapBinary Mul a) (<.>)  ------------------------------------------------------------------------+-- Addition and multiplication folds+------------------------------------------------------------------------++-- | Takes the sum of the elements of a 'Foldable'. Analogous to 'sum'+-- on numbers, or 'or' on 'Bool's.+add :: (Foldable f, Semiring a) => f a -> a+add = getAdd . foldMap Add++-- | Takes the product of the elements of a 'Foldable'. Analogous to+-- 'product' on numbers, or 'and' on 'Bool's.+mul :: (Foldable f, Semiring a) => f a -> a+mul = getMul . foldMap Mul++------------------------------------------------------------------------ -- Ord wrappers ------------------------------------------------------------------------   -- | The "<https://ncatlab.org/nlab/show/tropical+semiring Tropical>" or -- min-plus semiring. It is a semiring where:--- @'<+>'  = 'min'@--- @'zero' = -∞@ (represented by 'Nothing')--- @'<.>'  = '<+>'@ (over the inner value)--- @'one'  = 'zero'@ (over the inner value)+--+-- @'<+>'  = 'min'+--'zero' = -∞ -- represented by 'Nothing'+--'<.>'  = '<+>'+--'one'  = 'zero'@+--+-- Note that we can't use 'Data.Semigroup.Min' from 'Data.Semigroup'+-- because annihilation needs to hold:+--+-- @-∞ '<+>' x = x '<+>' -∞ = -∞@+--+-- Taking -∞ to be 'minBound' would break the above law. Using 'Nothing'+-- to represent it follows the law. newtype Min a = Min   { getMin :: Maybe a   } deriving (Eq, Ord, Read, Show, Generic, Generic1, Functor              ,Foldable) --- | The "<https://ncatlab.org/nlab/show/https://ncatlab.org/nlab/show/max-plus+algebra Arctic>"+-- | The "<https://ncatlab.org/nlab/show/max-plus+algebra Arctic>" -- or max-plus semiring. It is a semiring where:--- @'<+>'  = 'max'@--- @'zero' = ∞@ (represented by 'Nothing')--- @'<.>'  = '<+>'@ (over the inner value)--- @'one'  = 'zero'@ (over the inner value)+--+-- @'<+>'  = 'max'+--'zero' = ∞ -- represented by 'Nothing'+--'<.>'  = '<+>'+--'one'  = 'zero'@+--+-- Note that we can't use 'Data.Semigroup.Max' from 'Data.Semigroup'+-- because annihilation needs to hold:+--+-- @∞ '<+>' x = x '<+>' ∞ = ∞@+--+-- Taking ∞ to be 'maxBound' would break the above law. Using 'Nothing'+-- to represent it follows the law. newtype Max a = Max   { getMax :: Maybe a   } deriving (Eq, Ord, Read, Show, Generic, Generic1, Functor