tax-0.2.1.0: Types and combinators for taxes
Safe HaskellNone
LanguageHaskell2010

Data.Tax

Description

This library provides combinators for constructing taxes. It is based on the dollaridoos library.

Synopsis

Overview

The most basic tax is a flat rate tax:

businessTax = flat 0.3

To compute the tax, use getTax:

λ> getTax businessTax (Money 1000000)
$300000.0

Taxes form a semigroup (sum of tax outputs) and monoid:

λ> getTax (flat 0.1 <> flat 0.2) (Money 10)
$3.0
λ> getTax mempty (Money 10)
$0

Progressive taxes can be constructed using the above combinator, which taxes the amount above a given threshold at a flat rate.

individualIncomeTax =
     above (Money 18200 ) (0.19  - 0     )
  <> above (Money 45000 ) (0.325 - 0.19  )
  <> above (Money 120000) (0.37  - 0.325 )
  <> above (Money 180000) (0.45 - 0.37   )

The marginal function provides a shorthand for the above.

individualIncomeTax = marginal
  [ ( Money 18200,  0.19  - 0     )
  , ( Money 45000,  0.325 - 0.19  )
  , ( Money 120000, 0.37  - 0.325 )
  , ( Money 180000, 0.45  - 0.37  ) ]

Taxes can be negative. For example, the lump, above and limit combinators can be used to construct a low-income tax offset that starts at $445 and reduces at a rate of 1.5c per dollar earned over $37000:

lowIncomeTaxOffset =
  limit mempty
  (lump (Money (-445)) <> above (Money 37000) 0.015)

The threshold combinator applies a tax to the full input amount, if it exceeds the threshold.

medicareLevySurcharge =
     threshold (review money 90000 ) 0.0100
  <> threshold (review money 105000) 0.0025
  <> threshold (review money 140000) 0.0025

Some taxes have "shade-in" where the amount above some threshold is taxed at a higher rate to "catch up" to some lower flat rate. The above and lesserOf combinators can be used to construct this tax:

medicareLevy l = lesserOf (above l 0.1) (flat 0.02)

Although some of the combinators deal directory with Money, a Tax can be defined for other types. For example, you can tax a person a certain number of days labour, based on their age.

data Sex = M | F
newtype Years = Years Int
newtype Days = Days Int
data Person = Person Years Sex

corvée :: Tax Person Days
corvée = Tax f
  where
  f (Person (Years age) sex) = Days $ if age >= 18 && age <= maxAge sex then 10 else 0
  maxAge sex = case sex of M -> 45 ; F -> 35

API

newtype Tax a b Source #

A function from an amount or value subject to taxation, to the amount or value of tax due.

Taxes form a semigroup where the tax payable is the sum of tax payable of consituent taxes.

Taxes form a monoid where the identity is a tax of 0%

Taxes are a profunctor, making it trivial to perform simple transformations of the input and/or output (e.g. rounding down to whole dollars).

Constructors

Tax 

Fields

Instances

Instances details
Profunctor Tax Source # 
Instance details

Defined in Data.Tax

Methods

dimap :: (a -> b) -> (c -> d) -> Tax b c -> Tax a d #

lmap :: (a -> b) -> Tax b c -> Tax a c #

rmap :: (b -> c) -> Tax a b -> Tax a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Tax a b -> Tax a c #

(.#) :: forall a b c q. Coercible b a => Tax b c -> q a b -> Tax a c #

Functor (Tax a) Source # 
Instance details

Defined in Data.Tax

Methods

fmap :: (a0 -> b) -> Tax a a0 -> Tax a b #

(<$) :: a0 -> Tax a b -> Tax a a0 #

Monoid b => Monoid (Tax a b) Source # 
Instance details

Defined in Data.Tax

Methods

mempty :: Tax a b #

mappend :: Tax a b -> Tax a b -> Tax a b #

mconcat :: [Tax a b] -> Tax a b #

Semigroup b => Semigroup (Tax a b) Source # 
Instance details

Defined in Data.Tax

Methods

(<>) :: Tax a b -> Tax a b -> Tax a b #

sconcat :: NonEmpty (Tax a b) -> Tax a b #

stimes :: Integral b0 => b0 -> Tax a b -> Tax a b #

type MoneyTax a = Tax (Money a) (Money a) Source #

Convenience synonym for working with Money

lump :: a -> Tax b a Source #

A lump-sum tax; a fixed value (ignores input).

flat :: Num a => a -> Tax (Money a) (Money a) Source #

Construct a flat rate tax with no threshold

threshold :: (Num a, Ord a) => Money a -> a -> Tax (Money a) (Money a) Source #

Tax full amount at flat rate if input >= threshold

threshold' :: (Ord b, Monoid a) => b -> Tax b a -> Tax b a Source #

Levy the tax if input >= threshold, otherwise don't

thresholds :: (Num a, Ord a) => [(Money a, a)] -> Tax (Money a) (Money a) Source #

Convert a [(threshold, rate)] into a flat tax whose rate is the sum of the rates that apply for a given input. The rates are cumulative. For example, if you want to tax people earning >$30,000 20%, and people earning >$50,000 30%, you only tax an extra 10% at 50000:

tax = thresholds [(30000, 0.2), (50000, 0.1)]

above :: (Num a, Ord a) => Money a -> a -> Tax (Money a) (Money a) Source #

Tax the amount exceeding the threshold at a flat rate.

above' :: (Num b, Ord b) => Money b -> Tax (Money b) a -> Tax (Money b) a Source #

Tax the amount exceeding the threshold

marginal :: (Num a, Ord a) => [(Money a, a)] -> Tax (Money a) (Money a) Source #

Convert a [(threshold, rate)] into a progressive tax. The rates are cumulative, i.e. the top marginal rate is the sum of the rates that apply for a given input.

lesserOf :: Ord a => Tax b a -> Tax b a -> Tax b a Source #

Levy the lesser of two taxes

greaterOf :: Ord a => Tax b a -> Tax b a -> Tax b a Source #

Levy the greater of two taxes

limit :: Ord a => a -> Tax b a -> Tax b a Source #

Limit the tax payable to the given amount

This could be used e.g. to limit a compulsory loan repayment to the balance of the loan, or ensure a (negative) tax offset does not become a (positive) tax.

effective :: Fractional a => Money a -> Tax (Money a) (Money a) -> Tax (Money a) (Money a) Source #

Given a tax and an amount construct the effective flat tax rate

Re-exports

module Data.Money

class Semigroup a where #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity
x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit
sconcat (pure x) = x
Multiplication
sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

(<>) :: a -> a -> a infixr 6 #

An associative operation.

Examples

Expand
>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
>>> Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]
>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

Examples

Expand

For the following examples, we will assume that we have:

>>> import Data.List.NonEmpty (NonEmpty (..))
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"
>>> sconcat $ Just [1, 2, 3] :| [Nothing, Just [4, 5, 6]]
Just [1,2,3,4,5,6]
>>> sconcat $ Left 1 :| [Right 2, Left 3, Right 4]
Right 2

stimes :: Integral b => b -> a -> a #

Repeat a value n times.

The default definition will raise an exception for a multiplier that is <= 0. This may be overridden with an implementation that is total. For monoids it is preferred to use stimesMonoid.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Examples

Expand
>>> stimes 4 [1]
[1,1,1,1]
>>> stimes 5 (putStr "hi!")
hi!hi!hi!hi!hi!
>>> stimes 3 (Right ":)")
Right ":)"

Instances

Instances details
Semigroup ByteArray

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Semigroup Void

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: Void -> Void -> Void #

sconcat :: NonEmpty Void -> Void #

stimes :: Integral b => b -> Void -> Void #

Semigroup Ordering

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Semigroup ()

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: () -> () -> () #

sconcat :: NonEmpty () -> () #

stimes :: Integral b => b -> () -> () #

Bits a => Semigroup (And a)

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: And a -> And a -> And a #

sconcat :: NonEmpty (And a) -> And a #

stimes :: Integral b => b -> And a -> And a #

FiniteBits a => Semigroup (Iff a)

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: Iff a -> Iff a -> Iff a #

sconcat :: NonEmpty (Iff a) -> Iff a #

stimes :: Integral b => b -> Iff a -> Iff a #

Bits a => Semigroup (Ior a)

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: Ior a -> Ior a -> Ior a #

sconcat :: NonEmpty (Ior a) -> Ior a #

stimes :: Integral b => b -> Ior a -> Ior a #

Bits a => Semigroup (Xor a)

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

(<>) :: Xor a -> Xor a -> Xor a #

sconcat :: NonEmpty (Xor a) -> Xor a #

stimes :: Integral b => b -> Xor a -> Xor a #

Semigroup (FromMaybe b) 
Instance details

Defined in Data.Foldable1

Methods

(<>) :: FromMaybe b -> FromMaybe b -> FromMaybe b #

sconcat :: NonEmpty (FromMaybe b) -> FromMaybe b #

stimes :: Integral b0 => b0 -> FromMaybe b -> FromMaybe b #

Semigroup a => Semigroup (JoinWith a) 
Instance details

Defined in Data.Foldable1

Methods

(<>) :: JoinWith a -> JoinWith a -> JoinWith a #

sconcat :: NonEmpty (JoinWith a) -> JoinWith a #

stimes :: Integral b => b -> JoinWith a -> JoinWith a #

Semigroup (NonEmptyDList a) 
Instance details

Defined in Data.Foldable1

Methods

(<>) :: NonEmptyDList a -> NonEmptyDList a -> NonEmptyDList a #

sconcat :: NonEmpty (NonEmptyDList a) -> NonEmptyDList a #

stimes :: Integral b => b -> NonEmptyDList a -> NonEmptyDList a #

Semigroup (Comparison a)

(<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).

(<>) :: Comparison a -> Comparison a -> Comparison a
Comparison cmp <> Comparison cmp' = Comparison a a' ->
  cmp a a' <> cmp a a'
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Equivalence a)

(<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).

(<>) :: Equivalence a -> Equivalence a -> Equivalence a
Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
  equiv a b && equiv' a b
Instance details

Defined in Data.Functor.Contravariant

Semigroup (Predicate a)

(<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).

(<>) :: Predicate a -> Predicate a -> Predicate a
Predicate pred <> Predicate pred' = Predicate a ->
  pred a && pred' a
Instance details

Defined in Data.Functor.Contravariant

Methods

(<>) :: Predicate a -> Predicate a -> Predicate a #

sconcat :: NonEmpty (Predicate a) -> Predicate a #

stimes :: Integral b => b -> Predicate a -> Predicate a #

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

(<>) :: Identity a -> Identity a -> Identity a #

sconcat :: NonEmpty (Identity a) -> Identity a #

stimes :: Integral b => b -> Identity a -> Identity a #

Semigroup (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: First a -> First a -> First a #

sconcat :: NonEmpty (First a) -> First a #

stimes :: Integral b => b -> First a -> First a #

Semigroup (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a #

sconcat :: NonEmpty (Down a) -> Down a #

stimes :: Integral b => b -> Down a -> Down a #

Semigroup (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a #

sconcat :: NonEmpty (First a) -> First a #

stimes :: Integral b => b -> First a -> First a #

Semigroup (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a #

sconcat :: NonEmpty (Last a) -> Last a #

stimes :: Integral b => b -> Last a -> Last a #

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Max a -> Max a -> Max a #

sconcat :: NonEmpty (Max a) -> Max a #

stimes :: Integral b => b -> Max a -> Max a #

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a #

sconcat :: NonEmpty (Min a) -> Min a #

stimes :: Integral b => b -> Min a -> Min a #

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a #

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a #

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a #

Semigroup a => Semigroup (STM a)

Since: base-4.17.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

(<>) :: STM a -> STM a -> STM a #

sconcat :: NonEmpty (STM a) -> STM a #

stimes :: Integral b => b -> STM a -> STM a #

(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)

Since: base-4.17.0.0

Instance details

Defined in GHC.Generics

Semigroup p => Semigroup (Par1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p #

sconcat :: NonEmpty (Par1 p) -> Par1 p #

stimes :: Integral b => b -> Par1 p -> Par1 p #

Num a => Semigroup (Money a) 
Instance details

Defined in Data.Money

Methods

(<>) :: Money a -> Money a -> Money a #

sconcat :: NonEmpty (Money a) -> Money a #

stimes :: Integral b => b -> Money a -> Money a #

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a #

sconcat :: NonEmpty (IO a) -> IO a #

stimes :: Integral b => b -> IO a -> IO a #

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a #

sconcat :: NonEmpty (Maybe a) -> Maybe a #

stimes :: Integral b => b -> Maybe a -> Maybe a #

Semigroup a => Semigroup (Solo a)

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

(<>) :: Solo a -> Solo a -> Solo a #

sconcat :: NonEmpty (Solo a) -> Solo a #

stimes :: Integral b => b -> Solo a -> Solo a #

Semigroup [a]

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a] #

sconcat :: NonEmpty [a] -> [a] #

stimes :: Integral b => b -> [a] -> [a] #

Semigroup (Either a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b #

sconcat :: NonEmpty (Either a b) -> Either a b #

stimes :: Integral b0 => b0 -> Either a b -> Either a b #

Semigroup a => Semigroup (Op a b)

(<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.

(<>) :: Op a b -> Op a b -> Op a b
Op f <> Op g = Op a -> f a <> g a
Instance details

Defined in Data.Functor.Contravariant

Methods

(<>) :: Op a b -> Op a b -> Op a b #

sconcat :: NonEmpty (Op a b) -> Op a b #

stimes :: Integral b0 => b0 -> Op a b -> Op a b #

Semigroup (Proxy s)

Since: base-4.9.0.0

Instance details

Defined in Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s #

sconcat :: NonEmpty (Proxy s) -> Proxy s #

stimes :: Integral b => b -> Proxy s -> Proxy s #

Semigroup (U1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p #

sconcat :: NonEmpty (U1 p) -> U1 p #

stimes :: Integral b => b -> U1 p -> U1 p #

Semigroup (V1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p #

sconcat :: NonEmpty (V1 p) -> V1 p #

stimes :: Integral b => b -> V1 p -> V1 p #

Semigroup a => Semigroup (ST s a)

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

(<>) :: ST s a -> ST s a -> ST s a #

sconcat :: NonEmpty (ST s a) -> ST s a #

stimes :: Integral b => b -> ST s a -> ST s a #

Semigroup b => Semigroup (Tax a b) Source # 
Instance details

Defined in Data.Tax

Methods

(<>) :: Tax a b -> Tax a b -> Tax a b #

sconcat :: NonEmpty (Tax a b) -> Tax a b #

stimes :: Integral b0 => b0 -> Tax a b -> Tax a b #

(Semigroup a, Semigroup b) => Semigroup (a, b)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b) -> (a, b) -> (a, b) #

sconcat :: NonEmpty (a, b) -> (a, b) #

stimes :: Integral b0 => b0 -> (a, b) -> (a, b) #

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b #

sconcat :: NonEmpty (a -> b) -> a -> b #

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b #

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(<>) :: Const a b -> Const a b -> Const a b #

sconcat :: NonEmpty (Const a b) -> Const a b #

stimes :: Integral b0 => b0 -> Const a b -> Const a b #

(Applicative f, Semigroup a) => Semigroup (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a #

sconcat :: NonEmpty (Ap f a) -> Ap f a #

stimes :: Integral b => b -> Ap f a -> Ap f a #

Semigroup (f p) => Semigroup (Rec1 f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p #

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p #

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p #

(Profunctor p, Arrow p, Semigroup b) => Semigroup (Closure p a b) 
Instance details

Defined in Data.Profunctor.Closed

Methods

(<>) :: Closure p a b -> Closure p a b -> Closure p a b #

sconcat :: NonEmpty (Closure p a b) -> Closure p a b #

stimes :: Integral b0 => b0 -> Closure p a b -> Closure p a b #

ArrowPlus p => Semigroup (Tambara p a b) 
Instance details

Defined in Data.Profunctor.Strong

Methods

(<>) :: Tambara p a b -> Tambara p a b -> Tambara p a b #

sconcat :: NonEmpty (Tambara p a b) -> Tambara p a b #

stimes :: Integral b0 => b0 -> Tambara p a b -> Tambara p a b #

(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) #

sconcat :: NonEmpty (a, b, c) -> (a, b, c) #

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) #

(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a)

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

(<>) :: Product f g a -> Product f g a -> Product f g a #

sconcat :: NonEmpty (Product f g a) -> Product f g a #

stimes :: Integral b => b -> Product f g a -> Product f g a #

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p #

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p #

Semigroup c => Semigroup (K1 i c p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p #

sconcat :: NonEmpty (K1 i c p) -> K1 i c p #

stimes :: Integral b => b -> K1 i c p -> K1 i c p #

Semigroup r => Semigroup (Forget r a b)

Via Semigroup r => (a -> r)

Since: profunctors-5.6.2

Instance details

Defined in Data.Profunctor.Types

Methods

(<>) :: Forget r a b -> Forget r a b -> Forget r a b #

sconcat :: NonEmpty (Forget r a b) -> Forget r a b #

stimes :: Integral b0 => b0 -> Forget r a b -> Forget r a b #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) #

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) #

Semigroup (f (g a)) => Semigroup (Compose f g a)

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a #

sconcat :: NonEmpty (Compose f g a) -> Compose f g a #

stimes :: Integral b => b -> Compose f g a -> Compose f g a #

Semigroup (f (g p)) => Semigroup ((f :.: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p #

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p #

Semigroup (f p) => Semigroup (M1 i c f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p #

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p #

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p #

(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) #

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

class Semigroup a => Monoid a where #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

Right identity
x <> mempty = x
Left identity
mempty <> x = x
Associativity
x <> (y <> z) = (x <> y) <> z (Semigroup law)
Concatenation
mconcat = foldr (<>) mempty

You can alternatively define mconcat instead of mempty, in which case the laws are:

Unit
mconcat (pure x) = x
Multiplication
mconcat (join xss) = mconcat (fmap mconcat xss)
Subclass
mconcat (toList xs) = sconcat xs

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty | mconcat

Methods

mempty :: a #

Identity of mappend

Examples

Expand
>>> "Hello world" <> mempty
"Hello world"
>>> mempty <> [1, 2, 3]
[1,2,3]

mappend :: a -> a -> a #

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a #

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Instances

Instances details
Monoid ByteArray

Since: base-4.17.0.0

Instance details

Defined in Data.Array.Byte

Monoid Ordering

Since: base-2.1

Instance details

Defined in GHC.Base

Monoid ()

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: () #

mappend :: () -> () -> () #

mconcat :: [()] -> () #

FiniteBits a => Monoid (And a)

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: And a #

mappend :: And a -> And a -> And a #

mconcat :: [And a] -> And a #

FiniteBits a => Monoid (Iff a)

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Iff a #

mappend :: Iff a -> Iff a -> Iff a #

mconcat :: [Iff a] -> Iff a #

Bits a => Monoid (Ior a)

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Ior a #

mappend :: Ior a -> Ior a -> Ior a #

mconcat :: [Ior a] -> Ior a #

Bits a => Monoid (Xor a)

Since: base-4.16

Instance details

Defined in Data.Bits

Methods

mempty :: Xor a #

mappend :: Xor a -> Xor a -> Xor a #

mconcat :: [Xor a] -> Xor a #

Monoid (Comparison a)

mempty on comparisons always returns EQ. Without newtypes this equals pure (pure EQ).

mempty :: Comparison a
mempty = Comparison _ _ -> EQ
Instance details

Defined in Data.Functor.Contravariant

Monoid (Equivalence a)

mempty on equivalences always returns True. Without newtypes this equals pure (pure True).

mempty :: Equivalence a
mempty = Equivalence _ _ -> True
Instance details

Defined in Data.Functor.Contravariant

Monoid (Predicate a)

mempty on predicates always returns True. Without newtypes this equals pure True.

mempty :: Predicate a
mempty = _ -> True
Instance details

Defined in Data.Functor.Contravariant

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Methods

mempty :: Identity a #

mappend :: Identity a -> Identity a -> Identity a #

mconcat :: [Identity a] -> Identity a #

Monoid (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: First a #

mappend :: First a -> First a -> First a #

mconcat :: [First a] -> First a #

Monoid (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: Last a #

mappend :: Last a -> Last a -> Last a #

mconcat :: [Last a] -> Last a #

Monoid a => Monoid (Down a)

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

mempty :: Down a #

mappend :: Down a -> Down a -> Down a #

mconcat :: [Down a] -> Down a #

(Ord a, Bounded a) => Monoid (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

mconcat :: [Max a] -> Max a #

(Ord a, Bounded a) => Monoid (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

mconcat :: [Min a] -> Min a #

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Monoid a => Monoid (STM a)

Since: base-4.17.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

mempty :: STM a #

mappend :: STM a -> STM a -> STM a #

mconcat :: [STM a] -> STM a #

(Generic a, Monoid (Rep a ())) => Monoid (Generically a)

Since: base-4.17.0.0

Instance details

Defined in GHC.Generics

Monoid p => Monoid (Par1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Par1 p #

mappend :: Par1 p -> Par1 p -> Par1 p #

mconcat :: [Par1 p] -> Par1 p #

Num a => Monoid (Money a) 
Instance details

Defined in Data.Money

Methods

mempty :: Money a #

mappend :: Money a -> Money a -> Money a #

mconcat :: [Money a] -> Money a #

Monoid a => Monoid (IO a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mempty :: IO a #

mappend :: IO a -> IO a -> IO a #

mconcat :: [IO a] -> IO a #

Semigroup a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

mconcat :: [Maybe a] -> Maybe a #

Monoid a => Monoid (Solo a)

Since: base-4.15

Instance details

Defined in GHC.Base

Methods

mempty :: Solo a #

mappend :: Solo a -> Solo a -> Solo a #

mconcat :: [Solo a] -> Solo a #

Monoid [a]

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: [a] #

mappend :: [a] -> [a] -> [a] #

mconcat :: [[a]] -> [a] #

Monoid a => Monoid (Op a b)

mempty @(Op a b) without newtypes is mempty @(b->a) = _ -> mempty.

mempty :: Op a b
mempty = Op _ -> mempty
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b #

mappend :: Op a b -> Op a b -> Op a b #

mconcat :: [Op a b] -> Op a b #

Monoid (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

mempty :: Proxy s #

mappend :: Proxy s -> Proxy s -> Proxy s #

mconcat :: [Proxy s] -> Proxy s #

Monoid (U1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: U1 p #

mappend :: U1 p -> U1 p -> U1 p #

mconcat :: [U1 p] -> U1 p #

Monoid a => Monoid (ST s a)

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

mempty :: ST s a #

mappend :: ST s a -> ST s a -> ST s a #

mconcat :: [ST s a] -> ST s a #

Monoid b => Monoid (Tax a b) Source # 
Instance details

Defined in Data.Tax

Methods

mempty :: Tax a b #

mappend :: Tax a b -> Tax a b -> Tax a b #

mconcat :: [Tax a b] -> Tax a b #

(Monoid a, Monoid b) => Monoid (a, b)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b) #

mappend :: (a, b) -> (a, b) -> (a, b) #

mconcat :: [(a, b)] -> (a, b) #

Monoid b => Monoid (a -> b)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: a -> b #

mappend :: (a -> b) -> (a -> b) -> a -> b #

mconcat :: [a -> b] -> a -> b #

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b #

mappend :: Const a b -> Const a b -> Const a b #

mconcat :: [Const a b] -> Const a b #

(Applicative f, Monoid a) => Monoid (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mempty :: Ap f a #

mappend :: Ap f a -> Ap f a -> Ap f a #

mconcat :: [Ap f a] -> Ap f a #

Monoid (f p) => Monoid (Rec1 f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Rec1 f p #

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p #

mconcat :: [Rec1 f p] -> Rec1 f p #

(Profunctor p, Arrow p, Semigroup b, Monoid b) => Monoid (Closure p a b) 
Instance details

Defined in Data.Profunctor.Closed

Methods

mempty :: Closure p a b #

mappend :: Closure p a b -> Closure p a b -> Closure p a b #

mconcat :: [Closure p a b] -> Closure p a b #

ArrowPlus p => Monoid (Tambara p a b) 
Instance details

Defined in Data.Profunctor.Strong

Methods

mempty :: Tambara p a b #

mappend :: Tambara p a b -> Tambara p a b -> Tambara p a b #

mconcat :: [Tambara p a b] -> Tambara p a b #

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c) #

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) #

mconcat :: [(a, b, c)] -> (a, b, c) #

(Monoid (f a), Monoid (g a)) => Monoid (Product f g a)

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Product

Methods

mempty :: Product f g a #

mappend :: Product f g a -> Product f g a -> Product f g a #

mconcat :: [Product f g a] -> Product f g a #

(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: (f :*: g) p #

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

mconcat :: [(f :*: g) p] -> (f :*: g) p #

Monoid c => Monoid (K1 i c p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: K1 i c p #

mappend :: K1 i c p -> K1 i c p -> K1 i c p #

mconcat :: [K1 i c p] -> K1 i c p #

Monoid r => Monoid (Forget r a b)

Via Monoid r => (a -> r)

Since: profunctors-5.6.2

Instance details

Defined in Data.Profunctor.Types

Methods

mempty :: Forget r a b #

mappend :: Forget r a b -> Forget r a b -> Forget r a b #

mconcat :: [Forget r a b] -> Forget r a b #

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c, d) #

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

mconcat :: [(a, b, c, d)] -> (a, b, c, d) #

Monoid (f (g a)) => Monoid (Compose f g a)

Since: base-4.16.0.0

Instance details

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a #

mappend :: Compose f g a -> Compose f g a -> Compose f g a #

mconcat :: [Compose f g a] -> Compose f g a #

Monoid (f (g p)) => Monoid ((f :.: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: (f :.: g) p #

mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

mconcat :: [(f :.: g) p] -> (f :.: g) p #

Monoid (f p) => Monoid (M1 i c f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: M1 i c f p #

mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p #

mconcat :: [M1 i c f p] -> M1 i c f p #

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c, d, e) #

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #

class Profunctor (p :: Type -> Type -> Type) where #

Formally, the class Profunctor represents a profunctor from Hask -> Hask.

Intuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.

You can define a Profunctor by either defining dimap or by defining both lmap and rmap.

If you supply dimap, you should ensure that:

dimap id idid

If you supply lmap and rmap, ensure:

lmap idid
rmap idid

If you supply both, you should also ensure:

dimap f g ≡ lmap f . rmap g

These ensure by parametricity:

dimap (f . g) (h . i) ≡ dimap g h . dimap f i
lmap (f . g) ≡ lmap g . lmap f
rmap (f . g) ≡ rmap f . rmap g

Minimal complete definition

dimap | lmap, rmap

Methods

dimap :: (a -> b) -> (c -> d) -> p b c -> p a d #

Map over both arguments at the same time.

dimap f g ≡ lmap f . rmap g

lmap :: (a -> b) -> p b c -> p a c #

Map the first argument contravariantly.

lmap f ≡ dimap f id

rmap :: (b -> c) -> p a b -> p a c #

Map the second argument covariantly.

rmapdimap id

Instances

Instances details
Profunctor Tax Source # 
Instance details

Defined in Data.Tax

Methods

dimap :: (a -> b) -> (c -> d) -> Tax b c -> Tax a d #

lmap :: (a -> b) -> Tax b c -> Tax a c #

rmap :: (b -> c) -> Tax a b -> Tax a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Tax a b -> Tax a c #

(.#) :: forall a b c q. Coercible b a => Tax b c -> q a b -> Tax a c #

Monad m => Profunctor (Kleisli m) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Kleisli m b c -> Kleisli m a d #

lmap :: (a -> b) -> Kleisli m b c -> Kleisli m a c #

rmap :: (b -> c) -> Kleisli m a b -> Kleisli m a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Kleisli m a b -> Kleisli m a c #

(.#) :: forall a b c q. Coercible b a => Kleisli m b c -> q a b -> Kleisli m a c #

Profunctor (CopastroSum p) 
Instance details

Defined in Data.Profunctor.Choice

Methods

dimap :: (a -> b) -> (c -> d) -> CopastroSum p b c -> CopastroSum p a d #

lmap :: (a -> b) -> CopastroSum p b c -> CopastroSum p a c #

rmap :: (b -> c) -> CopastroSum p a b -> CopastroSum p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> CopastroSum p a b -> CopastroSum p a c #

(.#) :: forall a b c q. Coercible b a => CopastroSum p b c -> q a b -> CopastroSum p a c #

Profunctor (CotambaraSum p) 
Instance details

Defined in Data.Profunctor.Choice

Methods

dimap :: (a -> b) -> (c -> d) -> CotambaraSum p b c -> CotambaraSum p a d #

lmap :: (a -> b) -> CotambaraSum p b c -> CotambaraSum p a c #

rmap :: (b -> c) -> CotambaraSum p a b -> CotambaraSum p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> CotambaraSum p a b -> CotambaraSum p a c #

(.#) :: forall a b c q. Coercible b a => CotambaraSum p b c -> q a b -> CotambaraSum p a c #

Profunctor (PastroSum p) 
Instance details

Defined in Data.Profunctor.Choice

Methods

dimap :: (a -> b) -> (c -> d) -> PastroSum p b c -> PastroSum p a d #

lmap :: (a -> b) -> PastroSum p b c -> PastroSum p a c #

rmap :: (b -> c) -> PastroSum p a b -> PastroSum p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> PastroSum p a b -> PastroSum p a c #

(.#) :: forall a b c q. Coercible b a => PastroSum p b c -> q a b -> PastroSum p a c #

Profunctor p => Profunctor (TambaraSum p) 
Instance details

Defined in Data.Profunctor.Choice

Methods

dimap :: (a -> b) -> (c -> d) -> TambaraSum p b c -> TambaraSum p a d #

lmap :: (a -> b) -> TambaraSum p b c -> TambaraSum p a c #

rmap :: (b -> c) -> TambaraSum p a b -> TambaraSum p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> TambaraSum p a b -> TambaraSum p a c #

(.#) :: forall a b c q. Coercible b a => TambaraSum p b c -> q a b -> TambaraSum p a c #

Profunctor p => Profunctor (Closure p) 
Instance details

Defined in Data.Profunctor.Closed

Methods

dimap :: (a -> b) -> (c -> d) -> Closure p b c -> Closure p a d #

lmap :: (a -> b) -> Closure p b c -> Closure p a c #

rmap :: (b -> c) -> Closure p a b -> Closure p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Closure p a b -> Closure p a c #

(.#) :: forall a b c q. Coercible b a => Closure p b c -> q a b -> Closure p a c #

Profunctor (Environment p) 
Instance details

Defined in Data.Profunctor.Closed

Methods

dimap :: (a -> b) -> (c -> d) -> Environment p b c -> Environment p a d #

lmap :: (a -> b) -> Environment p b c -> Environment p a c #

rmap :: (b -> c) -> Environment p a b -> Environment p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Environment p a b -> Environment p a c #

(.#) :: forall a b c q. Coercible b a => Environment p b c -> q a b -> Environment p a c #

Profunctor p => Profunctor (CofreeMapping p) 
Instance details

Defined in Data.Profunctor.Mapping

Methods

dimap :: (a -> b) -> (c -> d) -> CofreeMapping p b c -> CofreeMapping p a d #

lmap :: (a -> b) -> CofreeMapping p b c -> CofreeMapping p a c #

rmap :: (b -> c) -> CofreeMapping p a b -> CofreeMapping p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> CofreeMapping p a b -> CofreeMapping p a c #

(.#) :: forall a b c q. Coercible b a => CofreeMapping p b c -> q a b -> CofreeMapping p a c #

Profunctor (FreeMapping p) 
Instance details

Defined in Data.Profunctor.Mapping

Methods

dimap :: (a -> b) -> (c -> d) -> FreeMapping p b c -> FreeMapping p a d #

lmap :: (a -> b) -> FreeMapping p b c -> FreeMapping p a c #

rmap :: (b -> c) -> FreeMapping p a b -> FreeMapping p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> FreeMapping p a b -> FreeMapping p a c #

(.#) :: forall a b c q. Coercible b a => FreeMapping p b c -> q a b -> FreeMapping p a c #

Profunctor (Copastro p) 
Instance details

Defined in Data.Profunctor.Strong

Methods

dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d #

lmap :: (a -> b) -> Copastro p b c -> Copastro p a c #

rmap :: (b -> c) -> Copastro p a b -> Copastro p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Copastro p a b -> Copastro p a c #

(.#) :: forall a b c q. Coercible b a => Copastro p b c -> q a b -> Copastro p a c #

Profunctor (Cotambara p) 
Instance details

Defined in Data.Profunctor.Strong

Methods

dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d #

lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c #

rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c #

(.#) :: forall a b c q. Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c #

Profunctor (Pastro p) 
Instance details

Defined in Data.Profunctor.Strong

Methods

dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d #

lmap :: (a -> b) -> Pastro p b c -> Pastro p a c #

rmap :: (b -> c) -> Pastro p a b -> Pastro p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Pastro p a b -> Pastro p a c #

(.#) :: forall a b c q. Coercible b a => Pastro p b c -> q a b -> Pastro p a c #

Profunctor p => Profunctor (Tambara p) 
Instance details

Defined in Data.Profunctor.Strong

Methods

dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d #

lmap :: (a -> b) -> Tambara p b c -> Tambara p a c #

rmap :: (b -> c) -> Tambara p a b -> Tambara p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Tambara p a b -> Tambara p a c #

(.#) :: forall a b c q. Coercible b a => Tambara p b c -> q a b -> Tambara p a c #

Profunctor (Baz t) 
Instance details

Defined in Data.Profunctor.Traversing

Methods

dimap :: (a -> b) -> (c -> d) -> Baz t b c -> Baz t a d #

lmap :: (a -> b) -> Baz t b c -> Baz t a c #

rmap :: (b -> c) -> Baz t a b -> Baz t a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Baz t a b -> Baz t a c #

(.#) :: forall a b c q. Coercible b a => Baz t b c -> q a b -> Baz t a c #

Profunctor (Bazaar a) 
Instance details

Defined in Data.Profunctor.Traversing

Methods

dimap :: (a0 -> b) -> (c -> d) -> Bazaar a b c -> Bazaar a a0 d #

lmap :: (a0 -> b) -> Bazaar a b c -> Bazaar a a0 c #

rmap :: (b -> c) -> Bazaar a a0 b -> Bazaar a a0 c #

(#.) :: forall a0 b c q. Coercible c b => q b c -> Bazaar a a0 b -> Bazaar a a0 c #

(.#) :: forall a0 b c q. Coercible b a0 => Bazaar a b c -> q a0 b -> Bazaar a a0 c #

Profunctor p => Profunctor (CofreeTraversing p) 
Instance details

Defined in Data.Profunctor.Traversing

Methods

dimap :: (a -> b) -> (c -> d) -> CofreeTraversing p b c -> CofreeTraversing p a d #

lmap :: (a -> b) -> CofreeTraversing p b c -> CofreeTraversing p a c #

rmap :: (b -> c) -> CofreeTraversing p a b -> CofreeTraversing p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> CofreeTraversing p a b -> CofreeTraversing p a c #

(.#) :: forall a b c q. Coercible b a => CofreeTraversing p b c -> q a b -> CofreeTraversing p a c #

Profunctor (FreeTraversing p) 
Instance details

Defined in Data.Profunctor.Traversing

Methods

dimap :: (a -> b) -> (c -> d) -> FreeTraversing p b c -> FreeTraversing p a d #

lmap :: (a -> b) -> FreeTraversing p b c -> FreeTraversing p a c #

rmap :: (b -> c) -> FreeTraversing p a b -> FreeTraversing p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> FreeTraversing p a b -> FreeTraversing p a c #

(.#) :: forall a b c q. Coercible b a => FreeTraversing p b c -> q a b -> FreeTraversing p a c #

Profunctor (Coyoneda p) 
Instance details

Defined in Data.Profunctor.Yoneda

Methods

dimap :: (a -> b) -> (c -> d) -> Coyoneda p b c -> Coyoneda p a d #

lmap :: (a -> b) -> Coyoneda p b c -> Coyoneda p a c #

rmap :: (b -> c) -> Coyoneda p a b -> Coyoneda p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Coyoneda p a b -> Coyoneda p a c #

(.#) :: forall a b c q. Coercible b a => Coyoneda p b c -> q a b -> Coyoneda p a c #

Profunctor (Yoneda p) 
Instance details

Defined in Data.Profunctor.Yoneda

Methods

dimap :: (a -> b) -> (c -> d) -> Yoneda p b c -> Yoneda p a d #

lmap :: (a -> b) -> Yoneda p b c -> Yoneda p a c #

rmap :: (b -> c) -> Yoneda p a b -> Yoneda p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Yoneda p a b -> Yoneda p a c #

(.#) :: forall a b c q. Coercible b a => Yoneda p b c -> q a b -> Yoneda p a c #

Profunctor (Tagged :: Type -> Type -> Type) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Tagged b c -> Tagged a d #

lmap :: (a -> b) -> Tagged b c -> Tagged a c #

rmap :: (b -> c) -> Tagged a b -> Tagged a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Tagged a b -> Tagged a c #

(.#) :: forall a b c q. Coercible b a => Tagged b c -> q a b -> Tagged a c #

Functor w => Profunctor (Cokleisli w) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Cokleisli w b c -> Cokleisli w a d #

lmap :: (a -> b) -> Cokleisli w b c -> Cokleisli w a c #

rmap :: (b -> c) -> Cokleisli w a b -> Cokleisli w a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Cokleisli w a b -> Cokleisli w a c #

(.#) :: forall a b c q. Coercible b a => Cokleisli w b c -> q a b -> Cokleisli w a c #

Functor f => Profunctor (Costar f) 
Instance details

Defined in Data.Profunctor.Types

Methods

dimap :: (a -> b) -> (c -> d) -> Costar f b c -> Costar f a d #

lmap :: (a -> b) -> Costar f b c -> Costar f a c #

rmap :: (b -> c) -> Costar f a b -> Costar f a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Costar f a b -> Costar f a c #

(.#) :: forall a b c q. Coercible b a => Costar f b c -> q a b -> Costar f a c #

Profunctor (Forget r :: Type -> Type -> Type) 
Instance details

Defined in Data.Profunctor.Types

Methods

dimap :: (a -> b) -> (c -> d) -> Forget r b c -> Forget r a d #

lmap :: (a -> b) -> Forget r b c -> Forget r a c #

rmap :: (b -> c) -> Forget r a b -> Forget r a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Forget r a b -> Forget r a c #

(.#) :: forall a b c q. Coercible b a => Forget r b c -> q a b -> Forget r a c #

Functor f => Profunctor (Star f) 
Instance details

Defined in Data.Profunctor.Types

Methods

dimap :: (a -> b) -> (c -> d) -> Star f b c -> Star f a d #

lmap :: (a -> b) -> Star f b c -> Star f a c #

rmap :: (b -> c) -> Star f a b -> Star f a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Star f a b -> Star f a c #

(.#) :: forall a b c q. Coercible b a => Star f b c -> q a b -> Star f a c #

Profunctor (->) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d #

lmap :: (a -> b) -> (b -> c) -> a -> c #

rmap :: (b -> c) -> (a -> b) -> a -> c #

(#.) :: forall a b c q. Coercible c b => q b c -> (a -> b) -> a -> c #

(.#) :: forall a b c q. Coercible b a => (b -> c) -> q a b -> a -> c #

Contravariant f => Profunctor (Clown f :: Type -> Type -> Type) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Clown f b c -> Clown f a d #

lmap :: (a -> b) -> Clown f b c -> Clown f a c #

rmap :: (b -> c) -> Clown f a b -> Clown f a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Clown f a b -> Clown f a c #

(.#) :: forall a b c q. Coercible b a => Clown f b c -> q a b -> Clown f a c #

Functor f => Profunctor (Joker f :: Type -> Type -> Type) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Joker f b c -> Joker f a d #

lmap :: (a -> b) -> Joker f b c -> Joker f a c #

rmap :: (b -> c) -> Joker f a b -> Joker f a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Joker f a b -> Joker f a c #

(.#) :: forall a b c q. Coercible b a => Joker f b c -> q a b -> Joker f a c #

Profunctor p => Profunctor (Codensity p) 
Instance details

Defined in Data.Profunctor.Ran

Methods

dimap :: (a -> b) -> (c -> d) -> Codensity p b c -> Codensity p a d #

lmap :: (a -> b) -> Codensity p b c -> Codensity p a c #

rmap :: (b -> c) -> Codensity p a b -> Codensity p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Codensity p a b -> Codensity p a c #

(.#) :: forall a b c q. Coercible b a => Codensity p b c -> q a b -> Codensity p a c #

Arrow p => Profunctor (WrappedArrow p) 
Instance details

Defined in Data.Profunctor.Types

Methods

dimap :: (a -> b) -> (c -> d) -> WrappedArrow p b c -> WrappedArrow p a d #

lmap :: (a -> b) -> WrappedArrow p b c -> WrappedArrow p a c #

rmap :: (b -> c) -> WrappedArrow p a b -> WrappedArrow p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> WrappedArrow p a b -> WrappedArrow p a c #

(.#) :: forall a b c q. Coercible b a => WrappedArrow p b c -> q a b -> WrappedArrow p a c #

(Profunctor p, Profunctor q) => Profunctor (Product p q) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Product p q b c -> Product p q a d #

lmap :: (a -> b) -> Product p q b c -> Product p q a c #

rmap :: (b -> c) -> Product p q a b -> Product p q a c #

(#.) :: forall a b c q0. Coercible c b => q0 b c -> Product p q a b -> Product p q a c #

(.#) :: forall a b c q0. Coercible b a => Product p q b c -> q0 a b -> Product p q a c #

(Profunctor p, Profunctor q) => Profunctor (Sum p q) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Sum p q b c -> Sum p q a d #

lmap :: (a -> b) -> Sum p q b c -> Sum p q a c #

rmap :: (b -> c) -> Sum p q a b -> Sum p q a c #

(#.) :: forall a b c q0. Coercible c b => q0 b c -> Sum p q a b -> Sum p q a c #

(.#) :: forall a b c q0. Coercible b a => Sum p q b c -> q0 a b -> Sum p q a c #

(Functor f, Profunctor p) => Profunctor (Tannen f p) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Tannen f p b c -> Tannen f p a d #

lmap :: (a -> b) -> Tannen f p b c -> Tannen f p a c #

rmap :: (b -> c) -> Tannen f p a b -> Tannen f p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Tannen f p a b -> Tannen f p a c #

(.#) :: forall a b c q. Coercible b a => Tannen f p b c -> q a b -> Tannen f p a c #

(Functor f, Profunctor p) => Profunctor (Cayley f p) 
Instance details

Defined in Data.Profunctor.Cayley

Methods

dimap :: (a -> b) -> (c -> d) -> Cayley f p b c -> Cayley f p a d #

lmap :: (a -> b) -> Cayley f p b c -> Cayley f p a c #

rmap :: (b -> c) -> Cayley f p a b -> Cayley f p a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Cayley f p a b -> Cayley f p a c #

(.#) :: forall a b c q. Coercible b a => Cayley f p b c -> q a b -> Cayley f p a c #

(Profunctor p, Profunctor q) => Profunctor (Procompose p q) 
Instance details

Defined in Data.Profunctor.Composition

Methods

dimap :: (a -> b) -> (c -> d) -> Procompose p q b c -> Procompose p q a d #

lmap :: (a -> b) -> Procompose p q b c -> Procompose p q a c #

rmap :: (b -> c) -> Procompose p q a b -> Procompose p q a c #

(#.) :: forall a b c q0. Coercible c b => q0 b c -> Procompose p q a b -> Procompose p q a c #

(.#) :: forall a b c q0. Coercible b a => Procompose p q b c -> q0 a b -> Procompose p q a c #

(Profunctor p, Profunctor q) => Profunctor (Rift p q) 
Instance details

Defined in Data.Profunctor.Composition

Methods

dimap :: (a -> b) -> (c -> d) -> Rift p q b c -> Rift p q a d #

lmap :: (a -> b) -> Rift p q b c -> Rift p q a c #

rmap :: (b -> c) -> Rift p q a b -> Rift p q a c #

(#.) :: forall a b c q0. Coercible c b => q0 b c -> Rift p q a b -> Rift p q a c #

(.#) :: forall a b c q0. Coercible b a => Rift p q b c -> q0 a b -> Rift p q a c #

(Profunctor p, Profunctor q) => Profunctor (Ran p q) 
Instance details

Defined in Data.Profunctor.Ran

Methods

dimap :: (a -> b) -> (c -> d) -> Ran p q b c -> Ran p q a d #

lmap :: (a -> b) -> Ran p q b c -> Ran p q a c #

rmap :: (b -> c) -> Ran p q a b -> Ran p q a c #

(#.) :: forall a b c q0. Coercible c b => q0 b c -> Ran p q a b -> Ran p q a c #

(.#) :: forall a b c q0. Coercible b a => Ran p q b c -> q0 a b -> Ran p q a c #

(Profunctor p, Functor f, Functor g) => Profunctor (Biff p f g) 
Instance details

Defined in Data.Profunctor.Unsafe

Methods

dimap :: (a -> b) -> (c -> d) -> Biff p f g b c -> Biff p f g a d #

lmap :: (a -> b) -> Biff p f g b c -> Biff p f g a c #

rmap :: (b -> c) -> Biff p f g a b -> Biff p f g a c #

(#.) :: forall a b c q. Coercible c b => q b c -> Biff p f g a b -> Biff p f g a c #

(.#) :: forall a b c q. Coercible b a => Biff p f g b c -> q a b -> Biff p f g a c #