Copyright	(C) 2018 chessai
License	MIT (see the file LICENSE)
Maintainer	chessai <chessai1996@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell98

Data.Semiring.Generic

Contents

Orphan instances

Description

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

Synopsis

class GSemiring f where
- gzero' :: f a
- gone' :: f a
- gplus' :: f a -> f a -> f a
- gtimes' :: f a -> f a -> f a
- gfromNatural' :: Natural -> f a
gzero :: (Generic a, GSemiring (Rep a)) => a
gone :: (Generic a, GSemiring (Rep a)) => a
gplus :: (Generic a, GSemiring (Rep a)) => a -> a -> a
gtimes :: (Generic a, GSemiring (Rep a)) => a -> a -> a
gfromNatural :: (Generic a, GSemiring (Rep a)) => Natural -> a
class GRing f where
- gnegate' :: f a -> f a
gnegate :: (Generic a, GRing (Rep a)) => a -> a
newtype GenericSemiring a = GenericSemiring a

Documentation

class GSemiring f where Source #

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

Methods

gzero' :: f a Source #

gone' :: f a Source #

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

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

gfromNatural' :: Natural -> f a Source #

Instances

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 #
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 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 #
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 #

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

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

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

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

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

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

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

Instances details

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

gnegate :: (Generic a, GRing (Rep a)) => a -> a Source #

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

gplus a (gnegate a) = zero

newtype GenericSemiring a Source #

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

Constructors

GenericSemiring a

Instances

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 #

Orphan instances

(Ring a, Ring b) => Ring (a, b) Source #
Instance details Methods negate :: (a, b) -> (a, b) Source #
(Semiring a, Semiring b) => Semiring (a, b) Source #
Instance details Methods plus :: (a, b) -> (a, b) -> (a, b) Source # zero :: (a, b) Source # times :: (a, b) -> (a, b) -> (a, b) Source # one :: (a, b) Source # fromNatural :: Natural -> (a, b) Source #
(Ring a, Ring b, Ring c) => Ring (a, b, c) Source #
Instance details Methods negate :: (a, b, c) -> (a, b, c) Source #
(Semiring a, Semiring b, Semiring c) => Semiring (a, b, c) Source #
Instance details Methods plus :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # zero :: (a, b, c) Source # times :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # one :: (a, b, c) Source # fromNatural :: Natural -> (a, b, c) Source #
(Ring a, Ring b, Ring c, Ring d) => Ring (a, b, c, d) Source #
Instance details Methods negate :: (a, b, c, d) -> (a, b, c, d) Source #
(Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a, b, c, d) Source #
Instance details Methods plus :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # zero :: (a, b, c, d) Source # times :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # one :: (a, b, c, d) Source # fromNatural :: Natural -> (a, b, c, d) Source #
(Ring a, Ring b, Ring c, Ring d, Ring e) => Ring (a, b, c, d, e) Source #
Instance details Methods negate :: (a, b, c, d, e) -> (a, b, c, d, e) Source #
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e) => Semiring (a, b, c, d, e) Source #
Instance details Methods plus :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # zero :: (a, b, c, d, e) Source # times :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # one :: (a, b, c, d, e) Source # fromNatural :: Natural -> (a, b, c, d, e) Source #
(Ring a, Ring b, Ring c, Ring d, Ring e, Ring f) => Ring (a, b, c, d, e, f) Source #
Instance details Methods negate :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source #
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f) => Semiring (a, b, c, d, e, f) Source #
Instance details Methods plus :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # zero :: (a, b, c, d, e, f) Source # times :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # one :: (a, b, c, d, e, f) Source # fromNatural :: Natural -> (a, b, c, d, e, f) Source #
(Ring a, Ring b, Ring c, Ring d, Ring e, Ring f, Ring g) => Ring (a, b, c, d, e, f, g) Source #
Instance details Methods negate :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source #
(Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g) => Semiring (a, b, c, d, e, f, g) Source #
Instance details Methods plus :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # zero :: (a, b, c, d, e, f, g) Source # times :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # one :: (a, b, c, d, e, f, g) Source # fromNatural :: Natural -> (a, b, c, d, e, f, g) Source #