Separate MultMonoid interface from MultGroup

This commit is contained in:
Kiana Sheibani 2022-08-04 15:18:12 -04:00
parent 7916e10aef
commit 95a13ffd91
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
2 changed files with 28 additions and 20 deletions

View file

@ -140,18 +140,18 @@ export
Num a => Mult (Matrix m n a) (Vector n a) (Vector m a) where
mat *. v with (viewShape mat)
_ | Shape [m,n] = fromFunction [m]
(\[i] => foldMap @{%search} @{Additive}
(\j => mat !! [i,j] * v !! j) range)
(\[i] => sum $ map (\j => mat!![i,j] * v!!j) range)
export
Num a => Mult (Matrix m n a) (Matrix n p a) (Matrix m p a) where
m1 *. m2 with (viewShape m1, viewShape m2)
_ | (Shape [m,n], Shape [n,p]) = fromFunction [m,p]
(\[i,j] => foldMap @{%search} @{Additive}
(\k => m1 !! [i,k] * m2 !! [k,j]) range)
(\[i,j] => sum $ map (\k => m1!![i,k] * m2!![k,j]) range)
export
{n : _} -> Num a => MultGroup (Matrix' n a) where
{n : _} -> Num a => MultMonoid (Matrix' n a) where
identity = repeatDiag 1 0
inverse = ?matrixInverse
export
{n : _} -> Neg a => Fractional a => MultGroup (Matrix' n a) where

View file

@ -21,28 +21,36 @@ Mult' : Type -> Type
Mult' a = Mult a a a
||| An interface for monoids using the `*.` operator.
|||
||| An instance of this interface must satisfy:
||| * `x *. identity == x`
||| * `identity *. x == x`
public export
interface Mult' a => MultMonoid a where
identity : a
||| An interface for groups using the `*.` operator.
|||
||| An instance of this interface must satisfy:
||| * `x *. neutral == x`
||| * `neutral *. x == x`
||| * `x *. inverse x == neutral`
||| * `inverse x *. x == neutral`
||| * `x *. inverse x == identity`
||| * `inverse x *. x == identity`
public export
interface Mult' a => MultGroup a where
identity : a
interface MultMonoid a => MultGroup a where
inverse : a -> a
||| Multiplication forms a semigroup
public export
[MultSemigroup] Mult' a => Semigroup a where
(<+>) = (*.)
namespace Semigroup
||| Multiplication forms a semigroup
public export
[Mult] Mult' a => Semigroup a where
(<+>) = (*.)
||| Multiplication with an identity element forms a monoid
public export
[MultMonoid] MultGroup a => Monoid a using MultSemigroup where
neutral = identity
namespace Monoid
||| Multiplication with an identity element forms a monoid
public export
[Mult] MultMonoid a => Monoid a using Semigroup.Mult where
neutral = identity
||| Raise a multiplicative value (e.g. a matrix or a transformation) to a natural