Diagrams.Prelude.ThreeD

A module to re-export most of the functionality of the diagrams core and standard library, including 3D types and functions.

Core library

The core definitions of transformations, diagrams, backends, and so on.

module Diagrams.Core

Standard library

Attributes (color, line style, etc.) and styles.

module Diagrams.Attributes

Alignment of diagrams relative to their envelopes.

module Diagrams.Align

Combining multiple diagrams into one.

module Diagrams.Combinators

Giving concrete locations to translation-invariant things.

module Diagrams.Located

Linear and cubic bezier segments.

module Diagrams.Segment

Trails.

module Diagrams.Trail

Parametrization of segments and trails.

module Diagrams.Parametric

Adjusting the length of parameterized objects.

module Diagrams.Parametric.Adjust

Computing tangent and normal vectors of segments and trails.

module Diagrams.Tangent

Trail-like things.

module Diagrams.TrailLike

Paths.

module Diagrams.Path

Cubic splines.

module Diagrams.CubicSpline

Some additional transformation-related functions, like conjugation of transformations.

module Diagrams.Transform

Giving names to subdiagrams and later retrieving subdiagrams by name.

module Diagrams.Names

Envelopes, aka functional bounding regions.

module Diagrams.Envelope

Traces, aka embedded raytracers, for finding points on the boundary of a diagram.

module Diagrams.Trace

A query is a function that maps points in a vector space to values in some monoid; they can be used to annotate the points of a diagram with some values.

module Diagrams.Query

Utilities for working with points.

module Diagrams.Points

Convenience infix operators for working with coordinates.

module Diagrams.Coordinates

things (shapes, transformations, combinators) specific to creating three-dimensional diagrams.

module Diagrams.ThreeD

Tools for making animations.

module Diagrams.Animation

Various utility definitions.

module Diagrams.Util

Convenience re-exports

For representing and operating on colors.

module Data.Colour

A large list of color names.

module Data.Colour.Names

Semigroups and monoids show up all over the place, so things from Data.Semigroup and Data.Monoid often come in handy.

module Data.Semigroup

For computing with vectors.

module Data.VectorSpace

For computing with points and vectors.

module Data.AffineSpace

For working with Active (i.e. animated) things.

module Data.Active

Essential Lens Combinators

(&) :: a -> (a -> b) -> b

Passes the result of the left side to the function on the right side (forward pipe operator).

This is the flipped version of ($), which is more common in languages like F# as (|>) where it is needed for inference. Here it is supplied for notational convenience and given a precedence that allows it to be nested inside uses of ($).

>>> a & f
f a

>>> "hello" & length & succ
6

This combinator is commonly used when applying multiple Lens operations in sequence.

>>> ("hello","world") & _1.element 0 .~ 'j' & _1.element 4 .~ 'y'
("jelly","world")

This reads somewhat similar to:

>>> flip execState ("hello","world") $ do _1.element 0 .= 'j'; _1.element 4 .= 'y'
("jelly","world")

(.~) :: ASetter s t a b -> b -> s -> t

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

 f <$ a ≡ mapped .~ f $ a

>>> (a,b,c,d) & _4 .~ e
(a,b,c,e)

>>> (42,"world") & _1 .~ "hello"
("hello","world")

>>> (a,b) & both .~ c
(c,c)

 (.~) :: Setter s t a b    -> b -> s -> t
 (.~) :: Iso s t a b       -> b -> s -> t
 (.~) :: Lens s t a b      -> b -> s -> t
 (.~) :: Traversal s t a b -> b -> s -> t

(%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t

Modifies the target of a Lens or all of the targets of a Setter or Traversal with a user supplied function.

This is an infix version of over.

 fmap f ≡ mapped %~ f
 fmapDefault f ≡ traverse %~ f

>>> (a,b,c) & _3 %~ f
(a,b,f c)

>>> (a,b) & both %~ f
(f a,f b)

>>> _2 %~ length $ (1,"hello")
(1,5)

>>> traverse %~ f $ [a,b,c]
[f a,f b,f c]

>>> traverse %~ even $ [1,2,3]
[False,True,False]

>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]

 (%~) :: Setter s t a b    -> (a -> b) -> s -> t
 (%~) :: Iso s t a b       -> (a -> b) -> s -> t
 (%~) :: Lens s t a b      -> (a -> b) -> s -> t
 (%~) :: Traversal s t a b -> (a -> b) -> s -> t

class Functor f => Applicative f where

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

      u *> v = pure (const id) <*> u <*> v
      u <* v = pure const <*> u <*> v

As a consequence of these laws, the Functor instance for f will satisfy

      fmap f x = pure f <*> x

If f is also a Monad, it should satisfy pure = return and (<*>) = ap (which implies that pure and <*> satisfy the applicative functor laws).

Methods

pure :: a -> f a

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b

Sequential application.

(*>) :: f a -> f b -> f b

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a

Sequence actions, discarding the value of the second argument.

Instances

Applicative []

Applicative IO

Applicative Q

Applicative Active

Applicative Maybe

Applicative Result

Applicative Parser

Applicative Id

Applicative ZipList

Applicative STM

Applicative ReadPrec

Applicative ReadP

Applicative RGB

Applicative Identity

Applicative Id

Applicative Tree

Applicative Interval

Applicative Vector

Applicative ReadM

Applicative Parser

Applicative ParserM

Applicative Min

Applicative Max

Applicative First

Applicative Last

Applicative Option

Applicative NonEmpty

Applicative Sum

Applicative ((->) a)

Applicative (Either e)

Monoid a => Applicative ((,) a)

HasTrie a => Applicative (:->: a)

Applicative (ST s)

Applicative (StateL s)

Applicative (StateR s)

Monoid m => Applicative (Const m)

Monad m => Applicative (WrappedMonad m)

Applicative (ST s)

Arrow a => Applicative (ArrowMonad a)

Applicative m => Applicative (IdentityT m)

Applicative (State s)

Applicative (Query v)

Applicative f => Applicative (Backwards f)

Apply f-actions in the reverse order.

Applicative m => Applicative (ListT m)

(Functor m, Monad m) => Applicative (MaybeT m)

Applicative (ReifiedGetter s)

Applicative (ReifiedFold s)

Applicative f => Applicative (Indexing f)

Applicative f => Applicative (Indexing64 f)

Applicative f => Applicative (WrappedApplicative f)

Apply f => Applicative (MaybeApply f)

Applicative (Proxy *)

Applicative f => Applicative (Reverse f)

Derived instance.

Monoid a => Applicative (Constant a)

Arrow a => Applicative (WrappedArrow a b)

Applicative w => Applicative (TracedT m w)

Applicative (Cokleisli w a)

(Functor m, Monad m) => Applicative (ErrorT e m)

(Monad m, Monoid s) => Applicative (Focusing m s)

Applicative (k (May s)) => Applicative (FocusingMay k s)

(Monad m, Monoid r) => Applicative (Effect m r)

Applicative (Indexed i a)

Applicative (ContT r m)

Applicative m => Applicative (ReaderT r m)

(Functor m, Monad m) => Applicative (StateT s m)

(Functor m, Monad m) => Applicative (StateT s m)

(Monoid w, Applicative m) => Applicative (WriterT w m)

(Monoid w, Applicative m) => Applicative (WriterT w m)

(Applicative f, Applicative g) => Applicative (Compose f g)

Applicative (Tagged k s)

(Monad m, Monoid s, Monoid w) => Applicative (FocusingWith w m s)

Applicative (k (s, w)) => Applicative (FocusingPlus w k s)

Applicative (k (f s)) => Applicative (FocusingOn f k s)

Applicative (k (Err e s)) => Applicative (FocusingErr e k s)

(Monoid s, Monoid w, Monad m) => Applicative (EffectRWS w st m s)

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

(*>) :: Applicative f => forall a b. f a -> f b -> f b

Sequence actions, discarding the value of the first argument.

(<*) :: Applicative f => forall a b. f a -> f b -> f a

Sequence actions, discarding the value of the second argument.

(<$>) :: Functor f => (a -> b) -> f a -> f b

An infix synonym for fmap.

(<$) :: Functor f => forall a b. a -> f b -> f a

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

liftA :: Applicative f => (a -> b) -> f a -> f b

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c

Lift a binary function to actions.

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Lift a ternary function to actions.