Data.Dioid

Documentation

type Ordered = Additive

type PredioidLaw a = (Prd a, (Ordered - Semigroup) a, (Multiplicative - Semigroup) a)

type DioidLaw a = (Prd a, (Ordered - Monoid) a, (Multiplicative - Monoid) a)

class (Presemiring a, PredioidLaw a) => Predioid a

Right pre-dioids and dioids.

A right-dioid is a semiring with a right-canonical pre-order relation relative to +:

a Prd b <==> b == a + c
a Prd (a + b) == True

Consequently Prd is both reflexive and transitive:

a Prd a == True
a Prd b && b Prd c ==> a Prd c == True

Finally Prd is an order relation:

(a =~ b) <==> (a == b)

See Property

Instances

Predioid Bool

Defined in Data.Dioid

Predioid Natural

Defined in Data.Dioid

Predioid Word

Defined in Data.Dioid

Predioid Word8

Defined in Data.Dioid

Predioid Word16

Defined in Data.Dioid

Predioid Word32

Defined in Data.Dioid

Predioid Word64

Defined in Data.Dioid

Predioid ()

Defined in Data.Dioid

Predioid IntSet

Defined in Data.Dioid

(Prd a, (Additive - Semigroup) a) => Predioid [a]

Defined in Data.Dioid

(Prd a, Predioid a) => Predioid (Maybe a)

Defined in Data.Dioid

Predioid (Ratio Natural)

Defined in Data.Dioid

(Prd a, Ord a, (Additive - Semigroup) a) => Predioid (Min a)

Defined in Data.Dioid

(Prd a, Ord a, (Multiplicative - Semigroup) a) => Predioid (Max a)

Defined in Data.Dioid

(Prd a, Predioid a) => Predioid (IntMap a)

Defined in Data.Dioid

Ord a => Predioid (Set a)

Defined in Data.Dioid

(Prd a, Prd b, Predioid a, Predioid b) => Predioid (Either a b)

Defined in Data.Dioid

(Ord k, Prd a, Predioid a) => Predioid (Map k a)

Defined in Data.Dioid

class (Semiring a, Predioid a) => Dioid a

Instances

Dioid Bool

Defined in Data.Dioid

Dioid Natural

Defined in Data.Dioid

Dioid Word

Defined in Data.Dioid

Dioid Word8

Defined in Data.Dioid

Dioid Word16

Defined in Data.Dioid

Dioid Word32

Defined in Data.Dioid

Dioid Word64

Defined in Data.Dioid

Dioid ()

Defined in Data.Dioid

(Prd a, (Additive - Monoid) a) => Dioid [a]

Defined in Data.Dioid

(Prd a, Dioid a) => Dioid (Maybe a)

Defined in Data.Dioid

Dioid (Ratio Natural)

Defined in Data.Dioid

(Ord a, Maximal a, (Additive - Monoid) (Min a), (Additive - Monoid) a) => Dioid (Min a)

Defined in Data.Dioid

(Ord a, Minimal a, (Additive - Monoid) (Max a), (Multiplicative - Monoid) a) => Dioid (Max a)

Defined in Data.Dioid

(Prd a, Dioid a) => Dioid (IntMap a)

Defined in Data.Dioid

(Ord k, (Multiplicative - Monoid) k, Prd a, Dioid a) => Dioid (Map k a)

Defined in Data.Dioid

minPlus :: (Additive - Monoid) a => Maximal a => Ord a => Functor f => Functor g => Foldable f => Foldable g => f (g a) -> a

Evaluate a min-plus dioid expression.

>>> minPlus [[1..4 :: Int], [0..2 :: Int]]
3

maxPlus :: (Additive - Monoid) a => Minimal a => Ord a => Functor f => Functor g => Foldable f => Foldable g => f (g a) -> a

Evaluate a max-plus dioid expression.

>>> maxPlus [[1..4 :: Int], [0..2 :: Int]]
10

minTimes :: (Multiplicative - Monoid) a => Maximal a => Ord a => Functor f => Functor g => Foldable f => Foldable g => f (g a) -> a

Evaluate a min-times dioid expression.

>>> minTimes [[1..4 :: Int], [0..2 :: Int]]
0

maxTimes :: (Multiplicative - Monoid) a => Minimal a => Ord a => Functor f => Functor g => Foldable f => Foldable g => f (g a) -> a

Evaluate a max-times dioid expression.

>>> maxTimes [[1..4 :: Int], [0..2 :: Int]]
24

Orphan instances

(Ord a, (Additive - Semigroup) a) => Presemiring (Min a)

(Ord a, (Multiplicative - Semigroup) a) => Presemiring (Max a)

(Ord a, Maximal a, (Additive - Monoid) (Min a), (Additive - Monoid) a) => Semiring (Min a)

(Ord a, Minimal a, (Additive - Monoid) (Max a), (Multiplicative - Monoid) a) => Semiring (Max a)