diagrams-core-1.3.0.3: 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] = V a type V (Set a) = V a type V (Split m) = V m type V (Deletable m) = V m type V (Option a) = V a type V (TransInv t) = V t type V (a -> b) = V b type V (a, b) = V a type V (Map k a) = V a type V (Point v n) = v type V ((:+:) m n) = V m type V (Measured n a) = V a type V (Transformation v n) = v type V (Style v n) = v type V (Attribute v n) = v type V (Trace v n) = v type V (Envelope v n) = v type V (a, b, c) = V a type V (Query v n m) = v type V (Prim b v n) = v type V (SubMap b v n m) = v type V (Subdiagram b v n m) = v 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] = N a type N (Set a) = N a type N (Split m) = N m type N (Deletable m) = N m type N (Option a) = N a type N (TransInv t) = N t type N (a -> b) = N b type N (a, b) = N a type N (Map k a) = N a type N (Point v n) = n type N ((:+:) m n) = N m type N (Measured n a) = N a type N (Transformation v n) = n type N (Style v n) = n type N (Attribute v n) = n type N (Trace v n) = n type N (Envelope v n) = n type N (a, b, c) = N a type N (Query v n m) = n type N (Prim b v n) = n type N (SubMap b v n m) = n type N (Subdiagram b v n m) = n 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.

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

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 Source

`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