Diagrams.Core.Types

The core library of primitives forming the basis of an embedded domain-specific language for describing and rendering diagrams.

Diagrams.Core.Types defines types and classes for primitives, diagrams, and backends.

Diagrams

Annotations

Static annotations

data Annotation

Static annotations which can be placed at a particular node of a diagram tree.

Constructors

Href String

Hyperlink

OpacityGroup Double

Instances

Show Annotation

Methods

showsPrec :: Int -> Annotation -> ShowS

show :: Annotation -> String

showList :: [Annotation] -> ShowS

applyAnnotation :: (Metric v, OrderedField n, Semigroup m) => Annotation -> QDiagram b v n m -> QDiagram b v n m

Apply a static annotation at the root of a diagram.

href :: (Metric v, OrderedField n, Semigroup m) => String -> QDiagram b v n m -> QDiagram b v n m

Make a diagram into a hyperlink. Note that only some backends will honor hyperlink annotations.

opacityGroup :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m

Change the transparency of a Diagram as a group.

groupOpacity :: (Metric v, OrderedField n, Semigroup m) => Double -> QDiagram b v n m -> QDiagram b v n m

Change the transparency of a Diagram as a group.

Dynamic (monoidal) annotations

type UpAnnots b v n m = Deletable (Envelope v n) ::: (Deletable (Trace v n) ::: (Deletable (SubMap b v n m) ::: (Query v n m ::: ())))

Monoidal annotations which travel up the diagram tree, i.e. which are aggregated from component diagrams to the whole:

• envelopes (see Diagrams.Core.Envelope). The envelopes are "deletable" meaning that at any point we can throw away the existing envelope and replace it with a new one; sometimes we want to consider a diagram as having a different envelope unrelated to its "natural" envelope.
• traces (see Diagrams.Core.Trace), also deletable.
• name/subdiagram associations (see Diagrams.Core.Names)
• query functions (see Diagrams.Core.Query)

type DownAnnots v n = (Transformation v n :+: Style v n) ::: (Name ::: ())

Monoidal annotations which travel down the diagram tree, i.e. which accumulate along each path to a leaf (and which can act on the upwards-travelling annotations):

• styles (see Diagrams.Core.Style)
• names (see Diagrams.Core.Names)

transfToAnnot :: Transformation v n -> DownAnnots v n

Inject a transformation into a default downwards annotation value.

transfFromAnnot :: (Additive v, Num n) => DownAnnots v n -> Transformation v n

Extract the (total) transformation from a downwards annotation value.

Basic type definitions

data QDiaLeaf b v n m

A leaf in a QDiagram tree is either a Prim, or a "delayed" QDiagram which expands to a real QDiagram once it learns the "final context" in which it will be rendered. For example, in order to decide how to draw an arrow, we must know the precise transformation applied to it (since the arrow head and tail are scale-invariant).

Constructors

PrimLeaf (Prim b v n)

DelayedLeaf (DownAnnots v n -> n -> n -> QDiagram b v n m)

The QDiagram produced by a DelayedLeaf function must already apply any transformation in the given DownAnnots (that is, the transformation will not be applied by the context).

Instances

Functor (QDiaLeaf b v n)

Methods

fmap :: (a -> b) -> QDiaLeaf b v n a -> QDiaLeaf b v n b

(<$) :: a -> QDiaLeaf b v n b -> QDiaLeaf b v n a

withQDiaLeaf :: (Prim b v n -> r) -> ((DownAnnots v n -> n -> n -> QDiagram b v n m) -> r) -> QDiaLeaf b v n m -> r

newtype QDiagram b v n m

The fundamental diagram type. The type variables are as follows:

• b represents the backend, such as SVG or Cairo. Note that each backend also exports a type synonym B for itself, so the type variable b may also typically be instantiated by B, meaning "use whatever backend is in scope".
• v represents the vector space of the diagram. Typical instantiations include V2 (for a two-dimensional diagram) or V3 (for a three-dimensional diagram).
• n represents the numerical field the diagram uses. Typically this will be a concrete numeric type like Double.
• m is the monoidal type of "query annotations": each point in the diagram has a value of type m associated to it, and these values are combined according to the Monoid instance for m. Most often, m is simply instantiated to Any, associating a simple Bool value to each point indicating whether the point is inside the diagram; Diagram is a synonym for QDiagram with m thus instantiated to Any.

Diagrams can be combined via their Monoid instance, transformed via their Transformable instance, and assigned attributes via their HasStyle instance.

Note that the Q in QDiagram stands for "Queriable", as distinguished from Diagram, where m is fixed to Any. This is not really a very good name, but it's probably not worth changing it at this point.

Constructors

QD (DUALTree (DownAnnots v n) (UpAnnots b v n m) Annotation (QDiaLeaf b v n m))

Instances

Functor (QDiagram b v n)

Methods

fmap :: (a -> b) -> QDiagram b v n a -> QDiagram b v n b

(<$) :: a -> QDiagram b v n b -> QDiagram b v n a

(Metric v, OrderedField n, Semigroup m) => Semigroup (QDiagram b v n m)

Methods

(<>) :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

sconcat :: NonEmpty (QDiagram b v n m) -> QDiagram b v n m

stimes :: Integral b => b -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => Monoid (QDiagram b v n m)

Diagrams form a monoid since each of their components do: the empty diagram has no primitives, an empty envelope, an empty trace, no named subdiagrams, and a constantly empty query function.

Diagrams compose by aligning their respective local origins. The new diagram has all the primitives and all the names from the two diagrams combined, and query functions are combined pointwise. The first diagram goes on top of the second. "On top of" probably only makes sense in vector spaces of dimension lower than 3, but in theory it could make sense for, say, 3-dimensional diagrams when viewed by 4-dimensional beings.

Methods

mempty :: QDiagram b v n m

mappend :: QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

mconcat :: [QDiagram b v n m] -> QDiagram b v n m

Wrapped (QDiagram b v n m)

Associated Types

type Unwrapped (QDiagram b v n m) :: *

Methods

_Wrapped' :: Iso' (QDiagram b v n m) (Unwrapped (QDiagram b v n m))

(Metric v, OrderedField n, Semigroup m) => HasOrigin (QDiagram b v n m)

Every diagram has an intrinsic "local origin" which is the basis for all combining operations.

Methods

moveOriginTo :: Point (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

(OrderedField n, Metric v, Semigroup m) => Transformable (QDiagram b v n m)

Diagrams can be transformed by transforming each of their components appropriately.

Methods

transform :: Transformation (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => HasStyle (QDiagram b v n m)

Methods

applyStyle :: Style (V (QDiagram b v n m)) (N (QDiagram b v n m)) -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => Qualifiable (QDiagram b v n m)

Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix.

Methods

(.>>) :: IsName a => a -> QDiagram b v n m -> QDiagram b v n m

(Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m)

Methods

getTrace :: QDiagram b v n m -> Trace (V (QDiagram b v n m)) (N (QDiagram b v n m))

(Metric v, OrderedField n, Monoid' m) => Enveloped (QDiagram b v n m)

Methods

getEnvelope :: QDiagram b v n m -> Envelope (V (QDiagram b v n m)) (N (QDiagram b v n m))

(Metric v, OrderedField n, Monoid' m) => Juxtaposable (QDiagram b v n m)

Methods

juxtapose :: Vn (QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m

Rewrapped (QDiagram b v n m) (QDiagram b' v' n' m')

type Unwrapped (QDiagram b v n m)

type Unwrapped (QDiagram b v n m) = DUALTree (DownAnnots v n) (UpAnnots b v n m) Annotation (QDiaLeaf b v n m)

type N (QDiagram b v n m)

type N (QDiagram b v n m) = n

type V (QDiagram b v n m)

type V (QDiagram b v n m) = v

type Diagram b = QDiagram b (V b) (N b) Any

Diagram b is a synonym for QDiagram b (V b) (N b) Any. That is, the default sort of diagram is one where querying at a point simply tells you whether the diagram contains that point or not. Transforming a default diagram into one with a more interesting query can be done via the Functor instance of QDiagram b v n or the value function.

Operations on diagrams

Creating diagrams

mkQD :: Prim b v n -> Envelope v n -> Trace v n -> SubMap b v n m -> Query v n m -> QDiagram b v n m

Create a diagram from a single primitive, along with an envelope, trace, subdiagram map, and query function.

mkQD' :: QDiaLeaf b v n m -> Envelope v n -> Trace v n -> SubMap b v n m -> Query v n m -> QDiagram b v n m

Create a diagram from a generic QDiaLeaf, along with an envelope, trace, subdiagram map, and query function.

pointDiagram :: (Metric v, Fractional n) => Point v n -> QDiagram b v n m

Create a "point diagram", which has no content, no trace, an empty query, and a point envelope.

Extracting information

envelope :: (OrderedField n, Metric v, Monoid' m) => Lens' (QDiagram b v n m) (Envelope v n)

Lens onto the Envelope of a QDiagram.

trace :: (Metric v, OrderedField n, Semigroup m) => Lens' (QDiagram b v n m) (Trace v n)

Lens onto the Trace of a QDiagram.

subMap :: (Metric v, Semigroup m, OrderedField n) => Lens' (QDiagram b v n m) (SubMap b v n m)

Lens onto the SubMap of a QDiagram (i.e. an association from names to subdiagrams).

names :: (Metric v, Semigroup m, OrderedField n) => QDiagram b v n m -> [(Name, [Point v n])]

Get a list of names of subdiagrams and their locations.

query :: Monoid m => QDiagram b v n m -> Query v n m

Get the query function associated with a diagram.

Combining diagrams

For many more ways of combining diagrams, see Diagrams.Combinators and Diagrams.TwoD.Combinators from the diagrams-lib package.

atop :: (OrderedField n, Metric v, Semigroup m) => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m infixl 6

A convenient synonym for mappend on diagrams, designed to be used infix (to help remember which diagram goes on top of which when combining them, namely, the first on top of the second).

Modifying diagrams

Names

nameSub :: (IsName nm, Metric v, OrderedField n, Semigroup m) => (QDiagram b v n m -> Subdiagram b v n m) -> nm -> QDiagram b v n m -> QDiagram b v n m

Attach an atomic name to a certain subdiagram, computed from the given diagram /with the mapping from name to subdiagram included/. The upshot of this knot-tying is that if d' = d # named x, then lookupName x d' == Just d' (instead of Just d).

lookupName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> QDiagram b v n m -> Maybe (Subdiagram b v n m)

Lookup the most recent diagram associated with (some qualification of) the given name.

withName :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> (Subdiagram b v n m -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m

Given a name and a diagram transformation indexed by a subdiagram, perform the transformation using the most recent subdiagram associated with (some qualification of) the name, or perform the identity transformation if the name does not exist.

withNameAll :: (IsName nm, Metric v, Semigroup m, OrderedField n) => nm -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m

Given a name and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the collection of all such subdiagrams associated with (some qualification of) the given name.

withNames :: (IsName nm, Metric v, Semigroup m, OrderedField n) => [nm] -> ([Subdiagram b v n m] -> QDiagram b v n m -> QDiagram b v n m) -> QDiagram b v n m -> QDiagram b v n m

Given a list of names and a diagram transformation indexed by a list of subdiagrams, perform the transformation using the list of most recent subdiagrams associated with (some qualification of) each name. Do nothing (the identity transformation) if any of the names do not exist.

localize :: forall b v n m. (Metric v, OrderedField n, Semigroup m) => QDiagram b v n m -> QDiagram b v n m

"Localize" a diagram by hiding all the names, so they are no longer visible to the outside.

Other

setEnvelope :: forall b v n m. (OrderedField n, Metric v, Monoid' m) => Envelope v n -> QDiagram b v n m -> QDiagram b v n m

Replace the envelope of a diagram.

setTrace :: forall b v n m. (OrderedField n, Metric v, Semigroup m) => Trace v n -> QDiagram b v n m -> QDiagram b v n m

Replace the trace of a diagram.

Subdiagrams

data Subdiagram b v n m

A Subdiagram represents a diagram embedded within the context of a larger diagram. Essentially, it consists of a diagram paired with any accumulated information from the larger context (transformations, attributes, etc.).

Constructors

Subdiagram (QDiagram b v n m) (DownAnnots v n)

Instances

Functor (Subdiagram b v n)

Methods

fmap :: (a -> b) -> Subdiagram b v n a -> Subdiagram b v n b

(<$) :: a -> Subdiagram b v n b -> Subdiagram b v n a

(Metric v, OrderedField n) => HasOrigin (Subdiagram b v n m)

Methods

moveOriginTo :: Point (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m

Transformable (Subdiagram b v n m)

Methods

transform :: Transformation (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) -> Subdiagram b v n m -> Subdiagram b v n m

(OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m)

Methods

getTrace :: Subdiagram b v n m -> Trace (V (Subdiagram b v n m)) (N (Subdiagram b v n m))

(OrderedField n, Metric v, Monoid' m) => Enveloped (Subdiagram b v n m)

Methods

getEnvelope :: Subdiagram b v n m -> Envelope (V (Subdiagram b v n m)) (N (Subdiagram b v n m))

type N (Subdiagram b v n m)

type N (Subdiagram b v n m) = n

type V (Subdiagram b v n m)

type V (Subdiagram b v n m) = v

mkSubdiagram :: QDiagram b v n m -> Subdiagram b v n m

Turn a diagram into a subdiagram with no accumulated context.

getSub :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> QDiagram b v n m

Turn a subdiagram into a normal diagram, including the enclosing context. Concretely, a subdiagram is a pair of (1) a diagram and (2) a "context" consisting of an extra transformation and attributes. getSub simply applies the transformation and attributes to the diagram to get the corresponding "top-level" diagram.

rawSub :: Subdiagram b v n m -> QDiagram b v n m

Extract the "raw" content of a subdiagram, by throwing away the context.

location :: (Additive v, Num n) => Subdiagram b v n m -> Point v n

Get the location of a subdiagram; that is, the location of its local origin with respect to the vector space of its parent diagram. In other words, the point where its local origin "ended up".

subPoint :: (Metric v, OrderedField n) => Point v n -> Subdiagram b v n m

Create a "point subdiagram", that is, a pointDiagram (with no content and a point envelope) treated as a subdiagram with local origin at the given point. Note this is not the same as mkSubdiagram . pointDiagram, which would result in a subdiagram with local origin at the parent origin, rather than at the given point.

Subdiagram maps

newtype SubMap b v n m

A SubMap is a map associating names to subdiagrams. There can be multiple associations for any given name.

Constructors

SubMap (Map Name [Subdiagram b v n m])

Instances

Action Name (SubMap b v n m)

A name acts on a name map by qualifying every name in it.

Methods

act :: Name -> SubMap b v n m -> SubMap b v n m

Functor (SubMap b v n)

Methods

fmap :: (a -> b) -> SubMap b v n a -> SubMap b v n b

(<$) :: a -> SubMap b v n b -> SubMap b v n a

Semigroup (SubMap b v n m)

Methods

(<>) :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m

sconcat :: NonEmpty (SubMap b v n m) -> SubMap b v n m

stimes :: Integral b => b -> SubMap b v n m -> SubMap b v n m

Monoid (SubMap b v n m)

SubMaps form a monoid with the empty map as the identity, and map union as the binary operation. No information is ever lost: if two maps have the same name in their domain, the resulting map will associate that name to the concatenation of the information associated with that name.

Methods

mempty :: SubMap b v n m

mappend :: SubMap b v n m -> SubMap b v n m -> SubMap b v n m

mconcat :: [SubMap b v n m] -> SubMap b v n m

Wrapped (SubMap b v n m)

Associated Types

type Unwrapped (SubMap b v n m) :: *

Methods

_Wrapped' :: Iso' (SubMap b v n m) (Unwrapped (SubMap b v n m))

(OrderedField n, Metric v) => HasOrigin (SubMap b v n m)

Methods

moveOriginTo :: Point (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m

Transformable (SubMap b v n m)

Methods

transform :: Transformation (V (SubMap b v n m)) (N (SubMap b v n m)) -> SubMap b v n m -> SubMap b v n m

Qualifiable (SubMap b v n m)

SubMaps are qualifiable: if ns is a SubMap, then a |> ns is the same SubMap except with every name qualified by a.

Methods

(.>>) :: IsName a => a -> SubMap b v n m -> SubMap b v n m

Rewrapped (SubMap b v n m) (SubMap b' v' n' m')

type Unwrapped (SubMap b v n m)

type Unwrapped (SubMap b v n m) = Map Name [Subdiagram b v n m]

type N (SubMap b v n m)

type N (SubMap b v n m) = n

type V (SubMap b v n m)

type V (SubMap b v n m) = v

fromNames :: IsName a => [(a, Subdiagram b v n m)] -> SubMap b v n m

Construct a SubMap from a list of associations between names and subdiagrams.

rememberAs :: IsName a => a -> QDiagram b v n m -> SubMap b v n m -> SubMap b v n m

Add a name/diagram association to a submap.

lookupSub :: IsName nm => nm -> SubMap b v n m -> Maybe [Subdiagram b v n m]

Look for the given name in a name map, returning a list of subdiagrams associated with that name. If no names match the given name exactly, return all the subdiagrams associated with names of which the given name is a suffix.

Primtives

Ultimately, every diagram is essentially a tree whose leaves are primitives, basic building blocks which can be rendered by backends. However, not every backend must be able to render every type of primitive; the collection of primitives a given backend knows how to render is determined by instances of Renderable.

data Prim b v n where

A value of type Prim b v n is an opaque (existentially quantified) primitive which backend b knows how to render in vector space v.

Constructors

Prim :: (Transformable p, Typeable p, Renderable p b) => p -> Prim b (V p) (N p)

Instances

Transformable (Prim b v n)

The Transformable instance for Prim just pushes calls to transform down through the Prim constructor.

Methods

transform :: Transformation (V (Prim b v n)) (N (Prim b v n)) -> Prim b v n -> Prim b v n

Renderable (Prim b v n) b

The Renderable instance for Prim just pushes calls to render down through the Prim constructor.

Methods

render :: b -> Prim b v n -> Render b (V (Prim b v n)) (N (Prim b v n))

type N (Prim b v n)

type N (Prim b v n) = n

type V (Prim b v n)

type V (Prim b v n) = v

_Prim :: (Typeable p, Renderable p b) => Prism' (Prim b (V p) (N p)) p

Backends

class Backend b v n where

Abstract diagrams are rendered to particular formats by backends. Each backend/vector space combination must be an instance of the Backend class.

A minimal complete definition consists of Render, Result, Options, and renderRTree. However, most backends will want to implement adjustDia as well; the default definition does nothing. Some useful standard definitions are provided in the Diagrams.TwoD.Adjust module from the diagrams-lib package.

Minimal complete definition

renderRTree

Associated Types

data Render b v n :: *

An intermediate representation used for rendering primitives. (Typically, this will be some sort of monad, but it need not be.) The Renderable class guarantees that a backend will be able to convert primitives into this type; how these rendered primitives are combined into an ultimate Result is completely up to the backend.

type Result b v n :: *

The result of running/interpreting a rendering operation.

data Options b v n :: *

Backend-specific rendering options.

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => b -> Options b v n -> QDiagram b v n m -> (Options b v n, Transformation v n, QDiagram b v n m)

adjustDia allows the backend to make adjustments to the final diagram (e.g. to adjust the size based on the options) before rendering it. It returns a modified options record, the transformation applied to the diagram (which can be used to convert attributes whose value is Measure, or transform e.g. screen coordinates back into local diagram coordinates), and the adjusted diagram itself.

See the diagrams-lib package (particularly the Diagrams.TwoD.Adjust module) for some useful implementations.

renderRTree :: b -> Options b v n -> RTree b v n Annotation -> Result b v n

Given some options, take a representation of a diagram as a tree and render it. The RTree has already been simplified and has all measurements converted to Output units.

Instances

Backend NullBackend v n

Associated Types

data Render NullBackend (v :: * -> *) n :: *

type Result NullBackend (v :: * -> *) n :: *

data Options NullBackend (v :: * -> *) n :: *

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => NullBackend -> Options NullBackend v n -> QDiagram NullBackend v n m -> (Options NullBackend v n, Transformation v n, QDiagram NullBackend v n m)

renderRTree :: NullBackend -> Options NullBackend v n -> RTree NullBackend v n Annotation -> Result NullBackend v n

type DTree b v n a = Tree (DNode b v n a)

A DTree is a raw tree representation of a QDiagram, with all the u-annotations removed. It is used as an intermediate type by diagrams-core; backends should not need to make use of it. Instead, backends can make use of RTree, which DTree gets compiled and optimized to.

data DNode b v n a

Constructors

DStyle (Style v n)

DTransform (Transformation v n)

DAnnot a

DDelay

DDelay marks a point where a delayed subtree was expanded. Such subtrees already take all non-frozen transforms above them into account, so when later processing the tree, upon encountering a DDelay node we must drop any accumulated non-frozen transformation.

DPrim (Prim b v n)

DEmpty

type RTree b v n a = Tree (RNode b v n a)

An RTree is a compiled and optimized representation of a QDiagram, which can be used by backends. They have the following invariant which backends may rely upon:

• RPrim nodes never have any children.

data RNode b v n a

Constructors

RStyle (Style v n)

A style node.

RAnnot a

RPrim (Prim b v n)

A primitive.

REmpty

_RStyle :: Prism' (RNode b v n a) (Style v n)

Prism onto a style of an RNode.

_RAnnot :: Prism' (RNode b v n a) a

Prism onto an annotation of an RNode.

_RPrim :: Prism' (RNode b v n a) (Prim b v n)

Prism onto a Prim of an RNode.

_REmpty :: Prism' (RNode b v n a) ()

Prism onto an empty RNode.

Null backend

data NullBackend

A null backend which does no actual rendering. It is provided mainly for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't actually care which one. See D for more explanation and examples.

It is courteous, when defining a new primitive P, to make an instance

instance Renderable P NullBackend where
  render _ _ = mempty

This ensures that the trick with D annotations can be used for diagrams containing your primitive.

Instances

Backend NullBackend v n

Associated Types

data Render NullBackend (v :: * -> *) n :: *

type Result NullBackend (v :: * -> *) n :: *

data Options NullBackend (v :: * -> *) n :: *

Methods

adjustDia :: (Additive v, Monoid' m, Num n) => NullBackend -> Options NullBackend v n -> QDiagram NullBackend v n m -> (Options NullBackend v n, Transformation v n, QDiagram NullBackend v n m)

renderRTree :: NullBackend -> Options NullBackend v n -> RTree NullBackend v n Annotation -> Result NullBackend v n

Semigroup (Render NullBackend v n)

Methods

(<>) :: Render NullBackend v n -> Render NullBackend v n -> Render NullBackend v n

sconcat :: NonEmpty (Render NullBackend v n) -> Render NullBackend v n

stimes :: Integral b => b -> Render NullBackend v n -> Render NullBackend v n

Monoid (Render NullBackend v n)

Methods

mempty :: Render NullBackend v n

mappend :: Render NullBackend v n -> Render NullBackend v n -> Render NullBackend v n

mconcat :: [Render NullBackend v n] -> Render NullBackend v n

data Render NullBackend

data Render NullBackend = NullBackendRender

data Options NullBackend

data Options NullBackend

type Result NullBackend v n

type Result NullBackend v n = ()

type D v n = QDiagram NullBackend v n Any

The D type is provided for convenience in situations where you must give a diagram a concrete, monomorphic type, but don't care which one. Such situations arise when you pass a diagram to a function which is polymorphic in its input but monomorphic in its output, such as width, height, phantom, or names. Such functions compute some property of the diagram, or use it to accomplish some other purpose, but do not result in the diagram being rendered. If the diagram does not have a monomorphic type, GHC complains that it cannot determine the diagram's type.

For example, here is the error we get if we try to compute the width of an image (this example requires diagrams-lib):

  ghci> width (image (uncheckedImageRef "foo.png" 200 200))
  <interactive>:11:8:
      No instance for (Renderable (DImage n0 External) b0)
        arising from a use of image
      The type variables n0, b0 are ambiguous
      Possible fix: add a type signature that fixes these type variable(s)
      Note: there is a potential instance available:
        instance Fractional n => Renderable (DImage n a) NullBackend
          -- Defined in Image
      Possible fix:
        add an instance declaration for
        (Renderable (DImage n0 External) b0)
      In the first argument of width, namely
        `(image (uncheckedImageRef "foo.png" 200 200))'
      In the expression:
        width (image (uncheckedImageRef "foo.png" 200 200))
      In an equation for it:
          it = width (image (uncheckedImageRef "foo.png" 200 200))
  

GHC complains that there is no instance for Renderable (DImage n0 External) b0; what is really going on is that it does not have enough information to decide what backend to use (hence the uninstantiated n0 and b0). This is annoying because we know that the choice of backend cannot possibly affect the width of the image (it's 200! it's right there in the code!); but there is no way for GHC to know that.

The solution is to annotate the call to image with the type D V2 Double, like so:

  ghci> width (image (uncheckedImageRef "foo.png" 200 200) :: D V2 Double)
  200.00000000000006
  

(It turns out the width wasn't 200 after all...)

As another example, here is the error we get if we try to compute the width of a radius-1 circle:

  ghci> width (circle 1)
  <interactive>:12:1:
      Couldn't match expected type V2 with actual type `V a0'
      The type variable a0 is ambiguous
      Possible fix: add a type signature that fixes these type variable(s)
      In the expression: width (circle 1)
      In an equation for it: it = width (circle 1)
  

There's even more ambiguity here. Whereas image always returns a Diagram, the circle function can produce any TrailLike type, and the width function can consume any Enveloped type, so GHC has no idea what type to pick to go in the middle. However, the solution is the same:

  ghci> width (circle 1 :: D V2 Double)
  1.9999999999999998
  

Number classes

type TypeableFloat n = (Typeable n, RealFloat n)

Constraint for numeric types that are RealFloat and Typeable, which often occur together. This is used to shorten shorten type constraint contexts.

Renderable

class Transformable t => Renderable t b where

The Renderable type class connects backends to primitives which they know how to render.

Minimal complete definition

render

Methods

render :: b -> t -> Render b (V t) (N t)

Given a token representing the backend and a transformable object, render it in the appropriate rendering context.

Instances

Renderable (Prim b v n) b

The Renderable instance for Prim just pushes calls to render down through the Prim constructor.

Methods

render :: b -> Prim b v n -> Render b (V (Prim b v n)) (N (Prim b v n))

Orphan instances

Action Name a => Action Name (Deletable a)

Methods

act :: Name -> Deletable a -> Deletable a

Action Name (Trace v n)

Methods

act :: Name -> Trace v n -> Trace v n

Action Name (Envelope v n)

Methods

act :: Name -> Envelope v n -> Envelope v n

Action Name (Query v n m)

Methods

act :: Name -> Query v n m -> Query v n m