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.