diagrams-core-1.4.1.1: Core libraries for diagrams EDSL

Diagrams.Core.V

Description

Type family for identifying associated vector spaces.

Synopsis

Documentation

type family V a :: * -> * Source #

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] Source # type V [a] = V a type V (Option a) Source # type V (Option a) = V a type V (Set a) Source # type V (Set a) = V a type V (Split m) Source # type V (Split m) = V m type V (Deletable m) Source # type V (Deletable m) = V m type V (TransInv t) Source # type V (TransInv t) = V t type V (a -> b) Source # type V (a -> b) = V b type V (a, b) Source # type V (a, b) = V a type V (Map k a) Source # type V (Map k a) = V a type V (Point v n) Source # type V (Point v n) = v type V ((:+:) m n) Source # type V ((:+:) m n) = V m type V (Measured n a) Source # type V (Measured n a) = V a type V (Transformation v n) Source # type V (Transformation v n) = v type V (Style v n) Source # type V (Style v n) = v type V (Attribute v n) Source # type V (Attribute v n) = v type V (Trace v n) Source # type V (Trace v n) = v type V (Envelope v n) Source # type V (Envelope v n) = v type V (a, b, c) Source # type V (a, b, c) = V a type V (Query v n m) Source # type V (Query v n m) = v type V (Prim b v n) Source # type V (Prim b v n) = v type V (SubMap b v n m) Source # type V (SubMap b v n m) = v type V (Subdiagram b v n m) Source # type V (Subdiagram b v n m) = v type V (QDiagram b v n m) Source # type V (QDiagram b v n m) = v

type family N a :: * Source #

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

Instances

 type N [a] Source # type N [a] = N a type N (Option a) Source # type N (Option a) = N a type N (Set a) Source # type N (Set a) = N a type N (Split m) Source # type N (Split m) = N m type N (Deletable m) Source # type N (Deletable m) = N m type N (TransInv t) Source # type N (TransInv t) = N t type N (a -> b) Source # type N (a -> b) = N b type N (a, b) Source # type N (a, b) = N a type N (Map k a) Source # type N (Map k a) = N a type N (Point v n) Source # type N (Point v n) = n type N ((:+:) m n) Source # type N ((:+:) m n) = N m type N (Measured n a) Source # type N (Measured n a) = N a type N (Transformation v n) Source # type N (Transformation v n) = n type N (Style v n) Source # type N (Style v n) = n type N (Attribute v n) Source # type N (Attribute v n) = n type N (Trace v n) Source # type N (Trace v n) = n type N (Envelope v n) Source # type N (Envelope v n) = n type N (a, b, c) Source # type N (a, b, c) = N a type N (Query v n m) Source # type N (Query v n m) = n type N (Prim b v n) Source # type N (Prim b v n) = n type N (SubMap b v n m) Source # type N (SubMap b v n m) = n type N (Subdiagram b v n m) Source # type N (Subdiagram b v n m) = n type N (QDiagram b v n m) Source # type N (QDiagram b v n m) = n

type Vn a = V a (N a) Source #

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.

type InSpace v n a = (V a ~ v, N a ~ n, Additive v, Num n) Source #

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

type SameSpace a b = (V a ~ V b, N a ~ N b) Source #

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