- class Semiring r => FreeAlgebra r a where
- join :: (a -> a -> r) -> a -> r
- class Semiring r => FreeCoalgebra r c where
- cojoin :: (c -> r) -> c -> c -> r
Documentation
class Semiring r => FreeAlgebra r a whereSource
An associative algebra built with a free module over a semiring
FreeAlgebra () a | |
(FreeAlgebra r a, FreeAlgebra r b) => FreeAlgebra r (a, b) | |
(FreeAlgebra r a, FreeAlgebra r b, FreeAlgebra r c) => FreeAlgebra r (a, b, c) | |
(FreeAlgebra r a, FreeAlgebra r b, FreeAlgebra r c, FreeAlgebra r d) => FreeAlgebra r (a, b, c, d) | |
(FreeAlgebra r a, FreeAlgebra r b, FreeAlgebra r c, FreeAlgebra r d, FreeAlgebra r e) => FreeAlgebra r (a, b, c, d, e) | |
(FreeAlgebra r b, FreeAlgebra r a) => FreeAlgebra (b -> r) a |
class Semiring r => FreeCoalgebra r c whereSource
FreeCoalgebra () c | |
(FreeCoalgebra r a, FreeCoalgebra r b) => FreeCoalgebra r (a, b) | |
FreeAlgebra r m => FreeCoalgebra r (m -> r) | Every coalgebra gives rise to an algebra by vector space duality classically. Sadly, it requires vector space duality, which we cannot use constructively. This is the dual, which relies in the fact that any constructive coalgebra can only inspect a finite number of coefficients. |
(FreeCoalgebra r a, FreeCoalgebra r b, FreeCoalgebra r c) => FreeCoalgebra r (a, b, c) | |
(FreeCoalgebra r a, FreeCoalgebra r b, FreeCoalgebra r c, FreeCoalgebra r d) => FreeCoalgebra r (a, b, c, d) | |
(FreeCoalgebra r a, FreeCoalgebra r b, FreeCoalgebra r c, FreeCoalgebra r d, FreeCoalgebra r e) => FreeCoalgebra r (a, b, c, d, e) | |
(FreeAlgebra r b, FreeCoalgebra r c) => FreeCoalgebra (b -> r) c |