Numeric.Algebra.Free.Unital

Documentation

class FreeAlgebra r a => FreeUnitalAlgebra r a where

An associative unital algebra over a semiring, built using a free module

Methods

unit :: r -> a -> r

Instances

FreeUnitalAlgebra () a

(AdditiveMonoid r, Semiring r) => FreeUnitalAlgebra r (Seq a)

(AdditiveMonoid r, Semiring r) => FreeUnitalAlgebra r [a]

(FreeUnitalAlgebra r a, FreeUnitalAlgebra r b) => FreeUnitalAlgebra r (a, b)

(Semiring r, AdditiveMonoid r, Unital r, DecidableZero n, Partitionable n) => FreeUnitalAlgebra r (:^ x n)

(FreeUnitalAlgebra r a, FreeUnitalAlgebra r b, FreeUnitalAlgebra r c) => FreeUnitalAlgebra r (a, b, c)

(FreeUnitalAlgebra r a, FreeUnitalAlgebra r b, FreeUnitalAlgebra r c, FreeUnitalAlgebra r d) => FreeUnitalAlgebra r (a, b, c, d)

(FreeUnitalAlgebra r a, FreeUnitalAlgebra r b, FreeUnitalAlgebra r c, FreeUnitalAlgebra r d, FreeUnitalAlgebra r e) => FreeUnitalAlgebra r (a, b, c, d, e)

(FreeUnitalAlgebra r a, FreeUnitalAlgebra r b) => FreeUnitalAlgebra (a -> r) b

class FreeCoalgebra r c => FreeCounitalCoalgebra r c where

Methods

counit :: (c -> r) -> r

Instances

FreeCounitalCoalgebra () a

Semiring r => FreeCounitalCoalgebra r (Seq a)

Semiring r => FreeCounitalCoalgebra r [a]

(FreeCounitalCoalgebra r a, FreeCounitalCoalgebra r b) => FreeCounitalCoalgebra r (a, b)

(Unital r, FreeUnitalAlgebra r m) => FreeCounitalCoalgebra r (m -> r)

(Semiring r, AdditiveMonoid n) => FreeCounitalCoalgebra r (:^ x n)

(FreeCounitalCoalgebra r a, FreeCounitalCoalgebra r b, FreeCounitalCoalgebra r c) => FreeCounitalCoalgebra r (a, b, c)

(FreeCounitalCoalgebra r a, FreeCounitalCoalgebra r b, FreeCounitalCoalgebra r c, FreeCounitalCoalgebra r d) => FreeCounitalCoalgebra r (a, b, c, d)

(FreeCounitalCoalgebra r a, FreeCounitalCoalgebra r b, FreeCounitalCoalgebra r c, FreeCounitalCoalgebra r d, FreeCounitalCoalgebra r e) => FreeCounitalCoalgebra r (a, b, c, d, e)

(FreeUnitalAlgebra r a, FreeCounitalCoalgebra r c) => FreeCounitalCoalgebra (a -> r) c