Maintainer  diagramsdiscuss@googlegroups.com 

Safe Haskell  SafeInfered 
The core library of primitives forming the basis of an embedded domainspecific language for describing and rendering diagrams. Normal users of the diagrams library should almost never need to import anything from this package directly; instead, import modules (especially Diagrams.Prelude) from the diagramslib package, which reexports most things of value to users.
For most library code needing access to core internals, it should be sufficient to import this module, which simply reexports useful functionality from other modules in the core library. Library writers needing finergrained access or functionality may occasionally find it useful to directly import one of the constituent core modules.
 type family V a :: *
 data Point v
 origin :: AdditiveGroup v => Point v
 (*.) :: VectorSpace v => Scalar v > Point v > Point v
 withLength :: (InnerSpace v, Floating (Scalar v)) => Scalar v > v > v
 data u :: v
 (<>) :: (HasLinearMap u, HasLinearMap v) => (u > v) > (v > u) > u :: v
 linv :: (u :: v) > v :: u
 lapp :: (VectorSpace v, Scalar u ~ Scalar v, HasLinearMap u) => (u :: v) > u > v
 data Transformation v
 inv :: HasLinearMap v => Transformation v > Transformation v
 transp :: Transformation v > v :: v
 transl :: Transformation v > v
 apply :: HasLinearMap v => Transformation v > v > v
 papply :: HasLinearMap v => Transformation v > Point v > Point v
 fromLinear :: AdditiveGroup v => (v :: v) > (v :: v) > Transformation v
 translation :: HasLinearMap v => v > Transformation v
 translate :: (Transformable t, HasLinearMap (V t)) => V t > t > t
 moveTo :: HasOrigin t => Point (V t) > t > t
 place :: HasOrigin t => t > Point (V t) > t
 scaling :: (HasLinearMap v, Fractional (Scalar v)) => Scalar v > Transformation v
 scale :: (Transformable t, Fractional (Scalar (V t)), Eq (Scalar (V t))) => Scalar (V t) > t > t
 class HasLinearMap (V t) => Transformable t where
 transform :: Transformation (V t) > t > t
 newtype TransInv t = TransInv {
 unTransInv :: t
 data AName
 data Name
 class (Typeable a, Ord a, Show a) => IsName a where
 class Qualifiable q where
 (.>) :: (IsName a1, IsName a2) => a1 > a2 > Name
 data NameMap v
 fromNames :: (InnerSpace v, AdditiveGroup (Scalar v), Ord (Scalar v), Floating (Scalar v), IsName a) => [(a, Point v)] > NameMap v
 fromNamesB :: IsName a => [(a, LocatedEnvelope v)] > NameMap v
 rememberAs :: IsName a => a > LocatedEnvelope v > NameMap v > NameMap v
 lookupN :: IsName n => n > NameMap v > Maybe [LocatedEnvelope v]
 class (Typeable a, Semigroup a) => AttributeClass a
 data Attribute v
 mkAttr :: AttributeClass a => a > Attribute v
 mkTAttr :: (AttributeClass a, Transformable a, V a ~ v) => a > Attribute v
 unwrapAttr :: AttributeClass a => Attribute v > Maybe a
 data Style v
 class HasStyle a where
 applyStyle :: Style (V a) > a > a
 getAttr :: forall a v. AttributeClass a => Style v > Maybe a
 combineAttr :: AttributeClass a => a > Style v > Style v
 applyAttr :: (AttributeClass a, HasStyle d) => a > d > d
 applyTAttr :: (AttributeClass a, Transformable a, V a ~ V d, HasStyle d) => a > d > d
 data Envelope v
 inEnvelope :: (Option (v > Max (Scalar v)) > Option (v > Max (Scalar v))) > Envelope v > Envelope v
 appEnvelope :: Envelope v > Maybe (v > Scalar v)
 onEnvelope :: ((v > Scalar v) > v > Scalar v) > Envelope v > Envelope v
 mkEnvelope :: (v > Scalar v) > Envelope v
 class (InnerSpace (V b), OrderedField (Scalar (V b))) => Enveloped b where
 getEnvelope :: b > Envelope (V b)
 envelopeV :: Enveloped a => V a > a > V a
 envelopeP :: Enveloped a => V a > a > Point (V a)
 boundaryFrom :: (OrderedField (Scalar v), InnerSpace v) => LocatedEnvelope v > v > Point v
 diameter :: Enveloped a => V a > a > Scalar (V a)
 radius :: Enveloped a => V a > a > Scalar (V a)
 data LocatedEnvelope v = LocatedEnvelope (Point v) (TransInv (Envelope v))
 location :: LocatedEnvelope v > Point v
 locateEnvelope :: Point v > Envelope v > LocatedEnvelope v
 class VectorSpace (V t) => HasOrigin t where
 moveOriginTo :: Point (V t) > t > t
 moveOriginBy :: HasOrigin t => V t > t > t
 class Juxtaposable a where
 juxtaposeDefault :: (Enveloped a, HasOrigin a) => V a > a > a > a
 newtype Query v m = Query {}
 data Prim b v where
 Prim :: Renderable t b => t > Prim b (V t)
 nullPrim :: (HasLinearMap v, Monoid (Render b v)) => Prim b v
 data QDiagram b v m
 mkQD :: Prim b v > Envelope v > NameMap v > Query v m > QDiagram b v m
 type Diagram b v = QDiagram b v Any
 prims :: (HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => QDiagram b v m > [(Prim b v, (Split (Transformation v), Style v))]
 envelope :: (OrderedField (Scalar v), InnerSpace v, HasLinearMap v) => QDiagram b v m > Envelope v
 names :: (AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => QDiagram b v m > NameMap v
 query :: (HasLinearMap v, Monoid m) => QDiagram b v m > Query v m
 sample :: (HasLinearMap v, Monoid m) => QDiagram b v m > Point v > m
 value :: Monoid m => m > QDiagram b v Any > QDiagram b v m
 resetValue :: (Eq m, Monoid m) => QDiagram b v m > QDiagram b v Any
 clearValue :: QDiagram b v m > QDiagram b v Any
 named :: forall v b n m. (IsName n, HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => n > QDiagram b v m > QDiagram b v m
 namePoint :: forall v b n m. (IsName n, HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => (QDiagram b v m > LocatedEnvelope v) > n > QDiagram b v m > QDiagram b v m
 withName :: (IsName n, AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => n > (LocatedEnvelope v > QDiagram b v m > QDiagram b v m) > QDiagram b v m > QDiagram b v m
 withNameAll :: (IsName n, AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => n > ([LocatedEnvelope v] > QDiagram b v m > QDiagram b v m) > QDiagram b v m > QDiagram b v m
 withNames :: (IsName n, AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => [n] > ([LocatedEnvelope v] > QDiagram b v m > QDiagram b v m) > QDiagram b v m > QDiagram b v m
 freeze :: forall v b m. (HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => QDiagram b v m > QDiagram b v m
 setEnvelope :: forall b v m. (OrderedField (Scalar v), InnerSpace v, HasLinearMap v, Monoid' m) => Envelope v > QDiagram b v m > QDiagram b v m
 atop :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Monoid' m) => QDiagram b v m > QDiagram b v m > QDiagram b v m
 class (HasLinearMap v, Monoid (Render b v)) => Backend b v where
 data Render b v :: *
 type Result b v :: *
 data Options b v :: *
 withStyle :: b > Style v > Transformation v > Render b v > Render b v
 doRender :: b > Options b v > Render b v > Result b v
 adjustDia :: Monoid' m => b > Options b v > QDiagram b v m > (Options b v, QDiagram b v m)
 renderDia :: (InnerSpace v, OrderedField (Scalar v), Monoid' m) => b > Options b v > QDiagram b v m > Result b v
 class Backend b v => MultiBackend b v where
 renderDias :: b > Options b v > [QDiagram b v m] > Result b v
 class Transformable t => Renderable t b where
 data NullBackend
 type D v = Diagram NullBackend v
 class (HasBasis v, HasTrie (Basis v), VectorSpace v) => HasLinearMap v
 class (Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s
 class (Semigroup m, Monoid m) => Monoid' m
Associated vector spaces
Many sorts of objects have an associated vector space in which
they live. The type function V
maps from objects to their
associated vector space.
Points
data Point v
Point
is a newtype wrapper around vectors that we wish to treat
as points, so we don't get them mixed up. The distinction is
important: translations affect points, but leave vectors
unchanged. Points are instances of the AffineSpace
class from
Data.AffineSpace.
Functor Point  
Typeable1 Point  
Eq v => Eq (Point v)  
Data v => Data (Point v)  
Ord v => Ord (Point v)  
Read v => Read (Point v)  
Show v => Show (Point v)  
AdditiveGroup v => AffineSpace (Point v)  
VectorSpace v => HasOrigin (Point v)  
HasLinearMap v => Transformable (Point v)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (Point v)  
Newtype (Point v) v 
origin :: AdditiveGroup v => Point v
The origin of the vector space v
.
(*.) :: VectorSpace v => Scalar v > Point v > Point v
Scale a point by a scalar.
Vectors
withLength :: (InnerSpace v, Floating (Scalar v)) => Scalar v > v > vSource
Produce a vector with the specified length in the same direction as the given vector.
Transformations
Invertible linear transformations
(v1 :: v2)
is a linear map paired with its inverse.
HasLinearMap v => Monoid (:: v v)  Invertible linear maps from a vector space to itself form a monoid under composition. 
HasLinearMap v => Semigroup (:: v v) 
(<>) :: (HasLinearMap u, HasLinearMap v) => (u > v) > (v > u) > u :: vSource
Create an invertible linear map from two functions which are assumed to be linear inverses.
lapp :: (VectorSpace v, Scalar u ~ Scalar v, HasLinearMap u) => (u :: v) > u > vSource
Apply a linear map to a vector.
General transformations
data Transformation v Source
General (affine) transformations, represented by an invertible linear map, its transpose, and a vector representing a translation component.
By the transpose of a linear map we mean simply the linear map corresponding to the transpose of the map's matrix representation. For example, any scale is its own transpose, since scales are represented by matrices with zeros everywhere except the diagonal. The transpose of a rotation is the same as its inverse.
The reason we need to keep track of transposes is because it turns out that when transforming a shape according to some linear map L, the shape's normal vectors transform according to L's inverse transpose. This is exactly what we need when transforming bounding functions, which are defined in terms of perpendicular (i.e. normal) hyperplanes.
HasLinearMap v => Monoid (Transformation v)  
HasLinearMap v => Semigroup (Transformation v)  Transformations are closed under composition; 
HasLinearMap v => HasOrigin (Transformation v)  
HasLinearMap v => Transformable (Transformation v)  
(HasLinearMap v, ~ * v (V a), Transformable a) => Action (Transformation v) a  Transformations can act on transformable things. 
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
inv :: HasLinearMap v => Transformation v > Transformation vSource
Invert a transformation.
transp :: Transformation v > v :: vSource
Get the transpose of a transformation (ignoring the translation component).
transl :: Transformation v > vSource
Get the translational component of a transformation.
apply :: HasLinearMap v => Transformation v > v > vSource
Apply a transformation to a vector. Note that any translational component of the transformation will not affect the vector, since vectors are invariant under translation.
papply :: HasLinearMap v => Transformation v > Point v > Point vSource
Apply a transformation to a point.
fromLinear :: AdditiveGroup v => (v :: v) > (v :: v) > Transformation vSource
Create a general affine transformation from an invertible linear transformation and its transpose. The translational component is assumed to be zero.
Some specific transformations
translation :: HasLinearMap v => v > Transformation vSource
Create a translation.
translate :: (Transformable t, HasLinearMap (V t)) => V t > t > tSource
Translate by a vector.
moveTo :: HasOrigin t => Point (V t) > t > tSource
Translate the object by the translation that sends the origin to
the given point. Note that this is dual to moveOriginTo
, i.e. we
should have
moveTo (origin .^+ v) === moveOriginTo (origin .^ v)
For types which are also Transformable
, this is essentially the
same as translate
, i.e.
moveTo (origin .^+ v) === translate v
place :: HasOrigin t => t > Point (V t) > tSource
A flipped variant of moveTo
, provided for convenience. Useful
when writing a function which takes a point as an argument, such
as when using withName
and friends.
scaling :: (HasLinearMap v, Fractional (Scalar v)) => Scalar v > Transformation vSource
Create a uniform scaling transformation.
scale :: (Transformable t, Fractional (Scalar (V t)), Eq (Scalar (V t))) => Scalar (V t) > t > tSource
Scale uniformly in every dimension by the given scalar.
The Transformable class
class HasLinearMap (V t) => Transformable t whereSource
Type class for things t
which can be transformed.
transform :: Transformation (V t) > t > tSource
Apply a transformation to an object.
Translational invariance
TransInv
is a wrapper which makes a transformable type
translationally invariant; the translational component of
transformations will no longer affect things wrapped in
TransInv
.
TransInv  

Names
A (qualified) name is a (possibly empty) sequence of atomic names.
Eq Name  
Ord Name  
Show Name  
Typeable Name  
Monoid Name  
Semigroup Name  
Qualifiable Name  Of course, names can be qualified using 
IsName Name  
Action Name a  Names don't act on anything else. 
Action Name (NameMap v)  A name acts on a name map by qualifying every name in it. 
Newtype (NameMap v) (Map Name [LocatedEnvelope v])  
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
class Qualifiable q whereSource
Instances of Qualifiable
are things which can be qualified by
prefixing them with a name.
Qualifiable Name  Of course, names can be qualified using 
Qualifiable (NameMap v) 

(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => Qualifiable (QDiagram b v m)  Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix. 
(.>) :: (IsName a1, IsName a2) => a1 > a2 > NameSource
Convenient operator for writing qualified names with atomic
components of different types. Instead of writing toName a1 <>
toName a2 <> toName a3
you can just write a1 .> a2 .> a3
.
A NameMap
is a map associating names to located envelopes,
i.e. envelopes with concrete locations for their base
points. There can be multiple associations for any given name.
Action Name (NameMap v)  A name acts on a name map by qualifying every name in it. 
Show v => Show (NameMap v)  
Monoid (NameMap v) 

Semigroup (NameMap v)  
(AdditiveGroup (Scalar v), Fractional (Scalar v), InnerSpace v) => HasOrigin (NameMap v)  
(AdditiveGroup (Scalar v), InnerSpace v, Floating (Scalar v), HasLinearMap v) => Transformable (NameMap v)  
Qualifiable (NameMap v) 

Newtype (NameMap v) (Map Name [LocatedEnvelope v])  
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
fromNames :: (InnerSpace v, AdditiveGroup (Scalar v), Ord (Scalar v), Floating (Scalar v), IsName a) => [(a, Point v)] > NameMap vSource
Construct a NameMap
from a list of (name, point) pairs.
fromNamesB :: IsName a => [(a, LocatedEnvelope v)] > NameMap vSource
Construct a NameMap
from a list of associations between names
and located envelopes.
rememberAs :: IsName a => a > LocatedEnvelope v > NameMap v > NameMap vSource
Give a name to a located envelope.
lookupN :: IsName n => n > NameMap v > Maybe [LocatedEnvelope v]Source
Look for the given name in a name map, returning a list of located envelopes associated with that name. If no names match the given name exactly, return all the points associated with names of which the given name is a suffix.
Attributes and styles
class (Typeable a, Semigroup a) => AttributeClass a Source
An existential wrapper type to hold attributes. Some attributes are affected by transformations and some are not.
Semigroup (Attribute v)  Attributes form a semigroup, where the semigroup operation simply returns the righthand attribute when the types do not match, and otherwise uses the semigroup operation specific to the (matching) types. 
HasLinearMap v => Transformable (Attribute v) 
mkAttr :: AttributeClass a => a > Attribute vSource
Wrap up an attribute.
mkTAttr :: (AttributeClass a, Transformable a, V a ~ v) => a > Attribute vSource
Wrap up a transformable attribute.
unwrapAttr :: AttributeClass a => Attribute v > Maybe aSource
Unwrap an unknown Attribute
type, performing a dynamic (but
safe) check on the type of the result. If the required type
matches the type of the attribute, the attribute value is
returned wrapped in Just
; if the types do not match, Nothing
is returned.
A Style
is a heterogeneous collection of attributes, containing
at most one attribute of any given type.
Monoid (Style v)  The empty style contains no attributes; composition of styles is a union of attributes; if the two styles have attributes of the same type they are combined according to their semigroup structure. 
Semigroup (Style v)  
HasLinearMap v => Transformable (Style v)  
HasStyle (Style v)  
Action (Style v) m  Styles have no action on other monoids. 
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
Type class for things which have a style.
applyStyle :: Style (V a) > a > aSource
Apply a style by combining it (on the left) with the existing style.
HasStyle a => HasStyle [a]  
(HasStyle a, Ord a) => HasStyle (Set a)  
HasStyle (Style v)  
HasStyle b => HasStyle (a > b)  
(HasStyle a, HasStyle b, ~ * (V a) (V b)) => HasStyle (a, b)  
HasStyle a => HasStyle (Map k a)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => HasStyle (QDiagram b v m) 
getAttr :: forall a v. AttributeClass a => Style v > Maybe aSource
Extract an attribute from a style of a particular type. If the
style contains an attribute of the requested type, it will be
returned wrapped in Just
; otherwise, Nothing
is returned.
combineAttr :: AttributeClass a => a > Style v > Style vSource
Add a new attribute to a style that does not already contain an attribute of this type, or combine it on the left with an existing attribute.
applyAttr :: (AttributeClass a, HasStyle d) => a > d > dSource
Apply an attribute to an instance of HasStyle
(such as a
diagram or a style). If the object already has an attribute of
the same type, the new attribute is combined on the left with the
existing attribute, according to their semigroup structure.
applyTAttr :: (AttributeClass a, Transformable a, V a ~ V d, HasStyle d) => a > d > dSource
Apply a transformable attribute to an instance of HasStyle
(such as a diagram or a style). If the object already has an
attribute of the same type, the new attribute is combined on the
left with the existing attribute, according to their semigroup
structure.
Envelopes
Every diagram comes equipped with an *envelope*.
Intuitively, the envelope for a diagram tells us the
minimum distance we have to go in a given direction to get to a
(hyper)plane entirely containing the diagram on one side of
it. Formally, given a vector v
, it returns a scalar s
such
that
 for every point
u
inside the diagram, if the projection of(u  origin)
ontov
iss' *^ v
, thens' <= s
. 
s
is the smallest such scalar.
This could probably be expressed in terms of a Galois connection; this is left as an exercise for the reader.
There is also a special "empty envelope".
Essentially, envelopes are a functional representation of (a conservative approximation to) convex bounding regions. The idea for this representation came from Sebastian Setzer; see http://byorgey.wordpress.com/2009/10/28/collectingattributes/#comment2030.
Show (Envelope v)  
Ord (Scalar v) => Monoid (Envelope v)  
Ord (Scalar v) => Semigroup (Envelope v)  
(InnerSpace v, AdditiveGroup (Scalar v), Fractional (Scalar v)) => HasOrigin (Envelope v)  The local origin of an envelope is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate. 
(HasLinearMap v, InnerSpace v, Floating (Scalar v), AdditiveGroup (Scalar v)) => Transformable (Envelope v)  
(InnerSpace v, OrderedField (Scalar v)) => Enveloped (Envelope v)  
(InnerSpace v, OrderedField (Scalar v)) => Juxtaposable (Envelope v)  
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
inEnvelope :: (Option (v > Max (Scalar v)) > Option (v > Max (Scalar v))) > Envelope v > Envelope vSource
appEnvelope :: Envelope v > Maybe (v > Scalar v)Source
mkEnvelope :: (v > Scalar v) > Envelope vSource
class (InnerSpace (V b), OrderedField (Scalar (V b))) => Enveloped b whereSource
Enveloped
abstracts over things which have an envelope.
getEnvelope :: b > Envelope (V b)Source
Compute the envelope of an object. For types with an intrinsic
notion of "local origin", the envelope will be based there.
Other types (e.g. Trail
) may have some other default
reference point at which the envelope will be based; their
instances should document what it is.
Enveloped b => Enveloped [b]  
Enveloped b => Enveloped (Set b)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (Point v)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (LocatedEnvelope v)  
(InnerSpace v, OrderedField (Scalar v)) => Enveloped (Envelope v)  
(Enveloped a, Enveloped b, ~ * (V a) (V b)) => Enveloped (a, b)  
Enveloped b => Enveloped (Map k b)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Enveloped (QDiagram b v m) 
envelopeV :: Enveloped a => V a > a > V aSource
Compute the vector from the local origin to a separating hyperplane in the given direction. Returns the zero vector for the empty envelope.
envelopeP :: Enveloped a => V a > a > Point (V a)Source
Compute the point on a separating hyperplane in the given direction. Returns the origin for the empty envelope.
boundaryFrom :: (OrderedField (Scalar v), InnerSpace v) => LocatedEnvelope v > v > Point vSource
boundaryFrom v b
computes the point on the boundary of the
located envelope b
in the direction of v
from the
bounding region's base point. This is most often used to compute
a point on the boundary of a named subdiagram.
diameter :: Enveloped a => V a > a > Scalar (V a)Source
Compute the diameter of a enveloped object along a particular vector. Returns zero for the empty envelope.
radius :: Enveloped a => V a > a > Scalar (V a)Source
Compute the "radius" (1/2 the diameter) of an enveloped object along a particular vector.
data LocatedEnvelope v Source
A LocatedEnvelope
value represents an envelope with its
base point at a particular location.
LocatedEnvelope (Point v) (TransInv (Envelope v)) 
Show v => Show (LocatedEnvelope v)  
VectorSpace v => HasOrigin (LocatedEnvelope v)  
(HasLinearMap v, InnerSpace v, Floating (Scalar v), AdditiveGroup (Scalar v)) => Transformable (LocatedEnvelope v)  
(OrderedField (Scalar v), InnerSpace v) => Enveloped (LocatedEnvelope v)  
Newtype (NameMap v) (Map Name [LocatedEnvelope v]) 
location :: LocatedEnvelope v > Point vSource
Get the location of a located envelope.
locateEnvelope :: Point v > Envelope v > LocatedEnvelope vSource
Create a LocatedEnvelope
value by specifying a location and an
envelope.
Things with local origins
class VectorSpace (V t) => HasOrigin t whereSource
Class of types which have an intrinsic notion of a "local origin", i.e. things which are not invariant under translation, and which allow the origin to be moved.
One might wonder why not just use Transformable
instead of
having a separate class for HasOrigin
; indeed, for types which
are instances of both we should have the identity
moveOriginTo (origin .^+ v) === translate (negateV v)
The reason is that some things (e.g. vectors, Trail
s) are
transformable but are translationally invariant, i.e. have no
origin.
moveOriginTo :: Point (V t) > t > tSource
Move the local origin to another point.
Note that this function is in some sense dual to translate
(for types which are also Transformable
); moving the origin
itself while leaving the object "fixed" is dual to fixing the
origin and translating the diagram.
HasOrigin a => HasOrigin [a]  
(HasOrigin a, Ord a) => HasOrigin (Set a)  
VectorSpace v => HasOrigin (Point v)  
VectorSpace (V t) => HasOrigin (TransInv t)  
HasLinearMap v => HasOrigin (Transformation v)  
VectorSpace v => HasOrigin (LocatedEnvelope v)  
(InnerSpace v, AdditiveGroup (Scalar v), Fractional (Scalar v)) => HasOrigin (Envelope v)  The local origin of an envelope is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate. 
(AdditiveGroup (Scalar v), Fractional (Scalar v), InnerSpace v) => HasOrigin (NameMap v)  
(HasOrigin a, HasOrigin b, ~ * (V a) (V b)) => HasOrigin (a, b)  
HasOrigin a => HasOrigin (Map k a)  
VectorSpace v => HasOrigin (Query v m)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => HasOrigin (QDiagram b v m)  Every diagram has an intrinsic "local origin" which is the basis for all combining operations. 
moveOriginBy :: HasOrigin t => V t > t > tSource
Move the local origin by a relative vector.
Juxtaposable things
class Juxtaposable a whereSource
Class of things which can be placed "next to" other things, for some appropriate notion of "next to".
juxtapose :: V a > a > a > aSource
juxtapose v a1 a2
positions a2
next to a1
in the
direction of v
. In particular, place a2
so that v
points
from the local origin of a1
towards the old local origin of
a2
; a1
's local origin becomes a2
's new local origin. The
result is just a translated version of a2
. (In particular,
this operation does not combine a1
and a2
in any way.)
(Enveloped b, HasOrigin b) => Juxtaposable [b]  
(Enveloped b, HasOrigin b, Ord b) => Juxtaposable (Set b)  
(InnerSpace v, OrderedField (Scalar v)) => Juxtaposable (Envelope v)  
(Enveloped a, HasOrigin a, Enveloped b, HasOrigin b, ~ * (V a) (V b)) => Juxtaposable (a, b)  
(Enveloped b, HasOrigin b) => Juxtaposable (Map k b)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => Juxtaposable (QDiagram b v m) 
juxtaposeDefault :: (Enveloped a, HasOrigin a) => V a > a > a > aSource
Queries
A query is a function that maps points in a vector space to values in some monoid. Queries naturally form a monoid, with two queries being combined pointwise.
The idea for annotating diagrams with monoidal queries came from the graphicsdrawingcombinators package, http://hackage.haskell.org/package/graphicsdrawingcombinators.
Functor (Query v)  
Applicative (Query v)  
Monoid m => Monoid (Query v m)  
Semigroup m => Semigroup (Query v m)  
VectorSpace v => HasOrigin (Query v m)  
HasLinearMap v => Transformable (Query v m)  
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
Primtives
A value of type Prim b v
is an opaque (existentially quantified)
primitive which backend b
knows how to render in vector space v
.
Prim :: Renderable t b => t > Prim b (V t) 
HasLinearMap v => Transformable (Prim b v)  The 
HasLinearMap v => Renderable (Prim b v) b  The 
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
nullPrim :: (HasLinearMap v, Monoid (Render b v)) => Prim b vSource
The null primitive, which every backend can render by doing nothing.
Diagrams
The fundamental diagram type is represented by trees of
primitives with various monoidal annotations. The Q
in
QDiagram
stands for "Queriable", as distinguished from
Diagram
, a synonym for QDiagram
with the query type
specialized to Any
.
Typeable3 QDiagram  
Functor (QDiagram b v)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => Monoid (QDiagram b v m)  Diagrams form a monoid since each of their components do: the empty diagram has no primitives, an empty envelope, no named points, 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, 3dimensional diagrams when viewed by 4dimensional beings. 
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => Semigroup (QDiagram b v m)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => HasOrigin (QDiagram b v m)  Every diagram has an intrinsic "local origin" which is the basis for all combining operations. 
(HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Monoid' m) => Transformable (QDiagram b v m)  Diagrams can be transformed by transforming each of their components appropriately. 
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Enveloped (QDiagram b v m)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => Juxtaposable (QDiagram b v m)  
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => Qualifiable (QDiagram b v m)  Diagrams can be qualified so that all their named points can now be referred to using the qualification prefix. 
(HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => HasStyle (QDiagram b v m)  
Newtype (QDiagram b v m) (UDTree (UpAnnots v m) (DownAnnots v) (Prim b v)) 
mkQD :: Prim b v > Envelope v > NameMap v > Query v m > QDiagram b v mSource
Create a diagram from a single primitive, along with an envelope, name map, and query function.
prims :: (HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => QDiagram b v m > [(Prim b v, (Split (Transformation v), Style v))]Source
Extract a list of primitives from a diagram, together with their associated transformations and styles.
envelope :: (OrderedField (Scalar v), InnerSpace v, HasLinearMap v) => QDiagram b v m > Envelope vSource
Get the envelope of a diagram.
names :: (AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => QDiagram b v m > NameMap vSource
Get the name map of a diagram.
query :: (HasLinearMap v, Monoid m) => QDiagram b v m > Query v mSource
Get the query function associated with a diagram.
sample :: (HasLinearMap v, Monoid m) => QDiagram b v m > Point v > mSource
Sample a diagram's query function at a given point.
clearValue :: QDiagram b v m > QDiagram b v AnySource
Set all the query values of a diagram to False
.
named :: forall v b n m. (IsName n, HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => n > QDiagram b v m > QDiagram b v mSource
Attach an atomic name to (the local origin of) a diagram.
namePoint :: forall v b n m. (IsName n, HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid' m) => (QDiagram b v m > LocatedEnvelope v) > n > QDiagram b v m > QDiagram b v mSource
Attach an atomic name to a certain point and envelope, computed from the given diagram.
withName :: (IsName n, AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => n > (LocatedEnvelope v > QDiagram b v m > QDiagram b v m) > QDiagram b v m > QDiagram b v mSource
Given a name and a diagram transformation indexed by a located envelope, perform the transformation using the most recent located envelope associated with (some qualification of) the name, or perform the identity transformation if the name does not exist.
withNameAll :: (IsName n, AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => n > ([LocatedEnvelope v] > QDiagram b v m > QDiagram b v m) > QDiagram b v m > QDiagram b v mSource
Given a name and a diagram transformation indexed by a list of located envelopes, perform the transformation using the collection of all such located envelopes associated with (some qualification of) the given name.
withNames :: (IsName n, AdditiveGroup (Scalar v), Floating (Scalar v), InnerSpace v, HasLinearMap v) => [n] > ([LocatedEnvelope v] > QDiagram b v m > QDiagram b v m) > QDiagram b v m > QDiagram b v mSource
Given a list of names and a diagram transformation indexed by a list of located envelopes, perform the transformation using the list of most recent envelopes associated with (some qualification of) each name. Do nothing (the identity transformation) if any of the names do not exist.
freeze :: forall v b m. (HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Monoid m) => QDiagram b v m > QDiagram b v mSource
By default, diagram attributes are not affected by
transformations. This means, for example, that lw 0.01 circle
and scale 2 (lw 0.01 circle)
will be drawn with lines of the
same width, and scaleY 3 circle
will be an ellipse drawn with
a uniform line. Once a diagram is frozen, however,
transformations do affect attributes, so, for example, scale 2
(freeze (lw 0.01 circle))
will be drawn with a line twice as
thick as lw 0.01 circle
, and scaleY 3 (freeze circle)
will be
drawn with a "stretched", variablewidth line.
Another way of thinking about it is that prefreeze
, we are
transforming the "abstract idea" of a diagram, and the
transformed version is then drawn; when doing a freeze
, we
produce a concrete drawing of the diagram, and it is this visual
representation itself which is acted upon by subsequent
transformations.
setEnvelope :: forall b v m. (OrderedField (Scalar v), InnerSpace v, HasLinearMap v, Monoid' m) => Envelope v > QDiagram b v m > QDiagram b v mSource
Replace the envelope of a diagram.
atop :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Monoid' m) => QDiagram b v m > QDiagram b v m > QDiagram b v mSource
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).
Backends
class (HasLinearMap v, Monoid (Render b v)) => Backend b v whereSource
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 the three associated types and implementations for
withStyle
and doRender
.
The type of rendering operations used by this backend, which
must be a monoid. For example, if Render b v = M ()
for some
monad M
, a monoid instance can be made with mempty = return
()
and mappend = (>>)
.
The result of running/interpreting a rendering operation.
Backendspecific rendering options.
:: b  Backend token (needed only for type inference) 
> Style v  Style to use 
> Transformation v  Transformation to be applied to the style 
> Render b v  Rendering operation to run 
> Render b v  Rendering operation using the style locally 
Perform a rendering operation with a local style.
:: b  Backend token (needed only for type inference) 
> Options b v  Backendspecific collection of rendering options 
> Render b v  Rendering operation to perform 
> Result b v  Output of the rendering operation 
doRender
is used to interpret rendering operations.
adjustDia :: Monoid' m => b > Options b v > QDiagram b v m > (Options b v, QDiagram b v m)Source
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 can also make adjustments to the options
record, usually to fill in incompletely specified size
information. A default implementation is provided which makes
no adjustments. See the diagramslib package for other useful
implementations.
renderDia :: (InnerSpace v, OrderedField (Scalar v), Monoid' m) => b > Options b v > QDiagram b v m > Result b vSource
Render a diagram. This has a default implementation in terms
of adjustDia
, withStyle
, doRender
, and the render
operation from the Renderable
class (first adjustDia
is
used, then withStyle
and render
are used to render each
primitive, the resulting operations are combined with
mconcat
, and the final operation run with doRender
) but
backends may override it if desired.
HasLinearMap v => Backend NullBackend v 
class Backend b v => MultiBackend b v whereSource
A class for backends which support rendering multiple diagrams, e.g. to a multipage pdf or something similar.
renderDias :: b > Options b v > [QDiagram b v m] > Result b vSource
Render multiple diagrams at once.
class Transformable t => Renderable t b whereSource
The Renderable type class connects backends to primitives which they know how to render.
render :: b > t > Render b (V t)Source
Given a token representing the backend and a transformable object, render it in the appropriate rendering context.
(HasLinearMap v, Monoid (Render b v)) => Renderable (NullPrim v) b  
HasLinearMap v => Renderable (Prim b v) b  The 
The null backend
data NullBackend Source
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.
HasLinearMap v => Backend NullBackend v  
Monoid (Render NullBackend v) 
type D v = Diagram NullBackend vSource
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 a radius1 circle (this example requires
diagramslib
):
ghci> width (circle 1) <interactive>:1:8: No instances for (Backend b0 R2, Renderable Diagrams.TwoD.Ellipse.Ellipse b0) arising from a use of `circle' Possible fix: add instance declarations for (Backend b0 R2, Renderable Diagrams.TwoD.Ellipse.Ellipse b0) In the first argument of `width', namely `(circle 1)' In the expression: width (circle 1) In an equation for `it': it = width (circle 1)
GHC complains that it cannot find an instance for "Backend b0
R2
"; what is really going on is that it does not have enough
information to decide which backend to use for the circle (hence
the type variable b0
). This is annoying because we know that
the choice of backend cannot possibly affect the width of the
circle; but there is no way for GHC to know that.
The solution is to annotate circle 1
with the type
,
like so:
D
R2
ghci> width (circle 1 :: D R2) 2.0
Convenience classes
class (HasBasis v, HasTrie (Basis v), VectorSpace v) => HasLinearMap v Source
HasLinearMap
is a poor man's class constraint synonym, just to
help shorten some of the ridiculously long constraint sets.
(HasBasis v, HasTrie (Basis v), VectorSpace v) => HasLinearMap v 
class (Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s Source
When dealing with envelopes we often want scalars to be an ordered field (i.e. support all four arithmetic operations and be totally ordered) so we introduce this class as a convenient shorthand.
(Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s 