Diagrams.Prelude

A module to re-export most of the functionality of the diagrams core and standard library.

Diagrams library

Exports from this library for working with diagrams.

module Diagrams

Convenience re-exports from other packages

For working with default values. Diagrams also exports with, an alias for def.

module Data.Default.Class

For representing and operating on colors.

module Data.Colour

A large list of color names.

module Data.Colour.Names

Specify your own colours.

module Data.Colour.SRGB

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 Linear.Vector

For computing with points and vectors.

module Linear.Affine

For computing with dot products and norm.

module Linear.Metric

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

module Data.Active

Most of the lens package. The following functions are not exported from lens because they either conflict with diagrams or may conflict with other libraries:

• at
• contains
• .>
• <.>
• index
• indices
• none
• coerce
• indexed
• inside
• levels
• ...
• children
• transform
• outside
• argument
• beside
• singular

module Control.Lens

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

• (<*>) = ap

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, (<*>)

Methods

pure :: a -> f a

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4

Sequential application.

(*>) :: f a -> f b -> f b infixl 4

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4

Sequence actions, discarding the value of the second argument.

Instances

Applicative []

Applicative IO

Applicative Q

Applicative Active

Applicative Duration

Applicative Id

Applicative P

Applicative Identity

Applicative ZipList

Applicative STM

Applicative First

Applicative Last

Applicative ReadPrec

Applicative ReadP

Applicative Maybe

Applicative Id

Applicative Get

Applicative Put

Applicative Get

Applicative RGB

Applicative Tree

Applicative Seq

Applicative Interval

Applicative Vector

Applicative Quaternion

Applicative Plucker

Applicative V4

Applicative V3

Applicative V2

Applicative V1

Applicative V0

Applicative ReadM

Applicative Parser

Applicative ParserM

Applicative ParserResult

Applicative Chunk

Applicative Min

Applicative Max

Applicative First

Applicative Last

Applicative Option

Applicative NonEmpty

Applicative Id

Applicative Box

Applicative Stream

Applicative Angle

Applicative ((->) a)

Applicative (Either e)

Monoid a => Applicative ((,) a)

Representable f => Applicative (Co f)

Applicative (ST s)

Applicative (StateL s)

Applicative (StateR s)

Applicative (ST s)

Monoid m => Applicative (Const m)

Monad m => Applicative (WrappedMonad m)

Arrow a => Applicative (ArrowMonad a)

Applicative (Proxy *)

Applicative (StateL s)

Applicative (StateR s)

Applicative m => Applicative (IdentityT m)

Applicative (State s)

Applicative (Measured n)

Applicative f => Applicative (Point f)

Alternative f => Applicative (Cofree f)

Applicative f => Applicative (Yoneda f)

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 f => Applicative (Reverse f)

Derived instance.

Monoid a => Applicative (Constant a)

Arrow a => Applicative (WrappedArrow a b)

Applicative f => Applicative (Alt * f)

Applicative w => Applicative (TracedT m w)

Applicative (Cokleisli w a)

Applicative (Query v n)

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

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

Applicative (Indexed i a)

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

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

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

Dim k n => Applicative (V k n)

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)

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

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

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

Applicative f => Applicative (Star f a)

Applicative (Costar f a)

Applicative (Tagged k s)

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

(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)

Reifies k s (ReifiedApplicative f) => Applicative (ReflectedApplicative k * f s)

(*>) :: 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 infixl 4

An infix synonym for fmap.

Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

(<$) :: 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.