Data.Semiring.Generic

Description

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

Synopsis

Documentation

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

Methods

gplus' :: f a -> f a -> f a Source #

gtimes' :: f a -> f a -> f a Source #

Instances details

GSemiring (U1 :: Type -> Type) Source #
Instance details Defined in Data.Semiring.Generic Methods gzero' :: U1 a Source # gone' :: U1 a Source # gplus' :: U1 a -> U1 a -> U1 a Source # gtimes' :: U1 a -> U1 a -> U1 a Source # gfromNatural' :: Natural -> U1 a Source #
(GSemiring a, GSemiring b) => GSemiring (a :*: b) Source #
Instance details Defined in Data.Semiring.Generic Methods gzero' :: (a :: b) a0 Source # gone' :: (a :: b) a0 Source # gplus' :: (a :: b) a0 -> (a :: b) a0 -> (a :: b) a0 Source # gtimes' :: (a :: b) a0 -> (a :: b) a0 -> (a :: b) a0 Source # gfromNatural' :: Natural -> (a :*: b) a0 Source #
Semiring a => GSemiring (K1 i a :: Type -> Type) Source #
Instance details Defined in Data.Semiring.Generic Methods gzero' :: K1 i a a0 Source # gone' :: K1 i a a0 Source # gplus' :: K1 i a a0 -> K1 i a a0 -> K1 i a a0 Source # gtimes' :: K1 i a a0 -> K1 i a a0 -> K1 i a a0 Source # gfromNatural' :: Natural -> K1 i a a0 Source #
GSemiring a => GSemiring (M1 i c a) Source #
Instance details Defined in Data.Semiring.Generic Methods gzero' :: M1 i c a a0 Source # gone' :: M1 i c a a0 Source # gplus' :: M1 i c a a0 -> M1 i c a a0 -> M1 i c a a0 Source # gtimes' :: M1 i c a a0 -> M1 i c a a0 -> M1 i c a a0 Source # gfromNatural' :: Natural -> M1 i c a a0 Source #

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

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

gplus :: (Generic a, GSemiring (Rep a)) => a -> a -> a Source #

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

gplus a b = gplus b 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

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

It is only defined for product types.

class GRing f where Source #

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

Methods

gnegate' :: f a -> f a Source #

Instances details

GRing (U1 :: Type -> Type) Source #
Instance details Defined in Data.Semiring.Generic Methods gnegate' :: U1 a -> U1 a Source #
(GRing a, GRing b) => GRing (a :*: b) Source #
Instance details Defined in Data.Semiring.Generic Methods gnegate' :: (a :: b) a0 -> (a :: b) a0 Source #
Ring a => GRing (K1 i a :: Type -> Type) Source #
Instance details Defined in Data.Semiring.Generic Methods gnegate' :: K1 i a a0 -> K1 i a a0 Source #
GRing a => GRing (M1 i c a) Source #
Instance details Defined in Data.Semiring.Generic Methods gnegate' :: M1 i c a a0 -> M1 i c a a0 Source #

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

gplus a (gnegate a) = zero

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

Constructors

Instances details

(Generic a, GSemiring (Rep a)) => Semiring (GenericSemiring a) Source #
Instance details Defined in Data.Semiring.Generic Methods plus :: GenericSemiring a -> GenericSemiring a -> GenericSemiring a Source # zero :: GenericSemiring a Source # times :: GenericSemiring a -> GenericSemiring a -> GenericSemiring a Source # one :: GenericSemiring a Source # fromNatural :: Natural -> GenericSemiring a Source #