Diagrams.Core.V

Type family for identifying associated vector spaces.

Documentation

type family V a :: * -> *

Many sorts of objects have an associated vector space in which they "live". The type function V maps from object types to the associated vector space. The resulting vector space has kind * -> * which means it takes another value (a number) and returns a concrete vector. For example V2 has kind * -> * and V2 Double is a vector.

Instances

type V [a]

type V [a] = V a

type V (Option a)

type V (Option a) = V a

type V (Set a)

type V (Set a) = V a

type V (Split m)

type V (Split m) = V m

type V (Deletable m)

type V (Deletable m) = V m

type V (TransInv t)

type V (TransInv t) = V t

type V (a -> b)

type V (a -> b) = V b

type V (a, b)

type V (a, b) = V a

type V (Map k a)

type V (Map k a) = V a

type V (Point v n)

type V (Point v n) = v

type V ((:+:) m n)

type V ((:+:) m n) = V m

type V (Measured n a)

type V (Measured n a) = V a

type V (Transformation v n)

type V (Transformation v n) = v

type V (Style v n)

type V (Style v n) = v

type V (Attribute v n)

type V (Attribute v n) = v

type V (Trace v n)

type V (Trace v n) = v

type V (Envelope v n)

type V (Envelope v n) = v

type V (a, b, c)

type V (a, b, c) = V a

type V (Query v n m)

type V (Query v n m) = v

type V (Prim b v n)

type V (Prim b v n) = v

type V (SubMap b v n m)

type V (SubMap b v n m) = v

type V (Subdiagram b v n m)

type V (Subdiagram b v n m) = v

type V (QDiagram b v n m)

type V (QDiagram b v n m) = v

type family N a :: *

The numerical field for the object, the number type used for calculations.

Instances

type N [a]

type N [a] = N a

type N (Option a)

type N (Option a) = N a

type N (Set a)

type N (Set a) = N a

type N (Split m)

type N (Split m) = N m

type N (Deletable m)

type N (Deletable m) = N m

type N (TransInv t)

type N (TransInv t) = N t

type N (a -> b)

type N (a -> b) = N b

type N (a, b)

type N (a, b) = N a

type N (Map k a)

type N (Map k a) = N a

type N (Point v n)

type N (Point v n) = n

type N ((:+:) m n)

type N ((:+:) m n) = N m

type N (Measured n a)

type N (Measured n a) = N a

type N (Transformation v n)

type N (Transformation v n) = n

type N (Style v n)

type N (Style v n) = n

type N (Attribute v n)

type N (Attribute v n) = n

type N (Trace v n)

type N (Trace v n) = n

type N (Envelope v n)

type N (Envelope v n) = n

type N (a, b, c)

type N (a, b, c) = N a

type N (Query v n m)

type N (Query v n m) = n

type N (Prim b v n)

type N (Prim b v n) = n

type N (SubMap b v n m)

type N (SubMap b v n m) = n

type N (Subdiagram b v n m)

type N (Subdiagram b v n m) = n

type N (QDiagram b v n m)

type N (QDiagram b v n m) = n

type Vn a = V a (N a)

Conveient type alias to retrieve the vector type associated with an object's vector space. This is usually used as Vn a ~ v n where v is the vector space and n is the numerical field.

class (V a ~ v, N a ~ n, Additive v, Num n) => InSpace v n a

InSpace v n a means the type a belongs to the vector space v n, where v is Additive and n is a Num.

Instances

((~) (* -> *) (V a) v, (~) * (N a) n, Additive v, Num n) => InSpace v n a

class (V a ~ V b, N a ~ N b) => SameSpace a b

SameSpace a b means the types a and b belong to the same vector space v n.

Instances

((~) (* -> *) (V a) (V b), (~) * (N a) (N b)) => SameSpace a b