Modulesemirings-0.7Haskell98

Data.Semiring.Generic

This module provides generic deriving tools for semirings and rings for product-like structures.

classclass GSemiring (f :: Type -> Type) where

Generic Semiring class, used to implement plus, times, zero, and one for product-like types implementing Generic.

Instances4GSemiring

GSemiring U1Defined in semirings-0.7 · Data.Semiring.Generic
Semiring a => GSemiring (K1 i a)Defined in semirings-0.7 · Data.Semiring.Generic
(GSemiring a, GSemiring b) => GSemiring (a :*: b)Defined in semirings-0.7 · Data.Semiring.Generic
GSemiring a => GSemiring (M1 i c a)Defined in semirings-0.7 · Data.Semiring.Generic

valuegzero :: (Generic a, GSemiring (Rep a)) => a

Generically generate a Semiring zero for any product-like type implementing Generic.

It is only defined for product types.

gplus gzero a = a = gplus a gzero

valuegone :: (Generic a, GSemiring (Rep a)) => a

Generically generate a Semiring one for any product-like type implementing Generic.

It is only defined for product types.

gtimes gone a = a = gtimes a gone

valuegplus :: (Generic a, GSemiring (Rep a)) => a -> a -> a

Generically generate a Semiring plus operation for any type implementing Generic. It is only defined for product types.

gplus a b = gplus b a

valuegtimes :: (Generic a, GSemiring (Rep a)) => a -> a -> a

Generically generate a Semiring times operation for any type implementing Generic. It is only defined for product types.

gtimes a (gtimes b c) = gtimes (gtimes a b) c
gtimes a gzero = gzero = gtimes gzero a

valuegfromNatural :: (Generic a, GSemiring (Rep a)) => Natural -> a

Generically generate a Semiring fromNatural for any product-like type implementing Generic.

It is only defined for product types.

classclass GRing (f :: Type -> Type) where

Generic Ring class, used to implement negate for product-like types implementing Generic.

Instances4GRing

GRing U1Defined in semirings-0.7 · Data.Semiring.Generic
Ring a => GRing (K1 i a)Defined in semirings-0.7 · Data.Semiring.Generic
(GRing a, GRing b) => GRing (a :*: b)Defined in semirings-0.7 · Data.Semiring.Generic
GRing a => GRing (M1 i c a)Defined in semirings-0.7 · Data.Semiring.Generic

valuegnegate :: (Generic a, GRing (Rep a)) => a -> a

Generically generate a Ring negate operation for any type implementing Generic. It is only defined for product types.

gplus a (gnegate a) = zero

newtypenewtype GenericSemiring a

An Identity-style wrapper with a Generic interface to be used with '-XDerivingVia'.

Instances1Semiring

(Generic a, GSemiring (Rep a)) => Semiring (GenericSemiring a)Defined in semirings-0.7 · Data.Semiring.Generic