MultiInstance

The MultiInstance module provides alternative versions of common typeclasses, augmented with a phantom type parameter x. The purpose of this is to deal with the case where a type has more than one candidate instance for the original, unaugmented class.

Example: Integer sum and product

The canonical example of this predicament is selecting the monoid instance for a type which forms a ring (and thus has at least two strong candidates for selection as the monoid), such as Integer. This therefore gives rise to the Sum and Product newtype wrappers, corresponding to the additive and multiplicative monoids respectively.

The traditional fold-based summation of a list of integers looks like this:

>>> import Data.Foldable (fold)
>>> import Data.Monoid (Sum (..))
>>> getSum (fold [Sum 2, Sum 3, Sum 5]) :: Integer
10

By replacing fold with multi'fold, whose constraint is MultiMonoid rather than Monoid, we can write the same thing without the newtype wrapper:

>>> :set -XFlexibleContexts -XTypeApplications
>>> multi'fold @Addition [2, 3, 5] :: Integer
10

The typeclasses

The current list of "multi-instance" typeclasses:

• MultiSemigroup
• MultiMonoid

The phantom types

The current list of phantom types used for the x type parameter:

• Default
• Conjunction
• Disjunction
• Addition (alias for Disjunction)
• Multiplication (alias for Conjunction)
• And (alias for Conjunction)
• Or (alias for Disjunction)
• Min
• Max
• MinMaybe
• MaxMaybe
• First
• Last
• ArrowComposition
• MultiDual

Semigroup

class MultiSemigroup x a where

Akin to the Semigroup class, but with the addition of the phantom type parameter x which lets you specify which semigroup to use.

For example, the integers form a semigroup via either Addition or Multiplication:

>>> :set -XFlexibleContexts -XTypeApplications
>>> multi'append @Addition 6 7 :: Integer
13
>>> multi'append @Multiplication 6 7 :: Integer
42
>>> multi'stimes @Addition (3 :: Natural) (4 :: Integer)
12
>>> multi'stimes @Multiplication (3 :: Natural) (4 :: Integer)
64

Minimal complete definition

multi'append

Methods

multi'append :: a -> a -> a

An associative operation.

Akin to <>.

multi'sconcat :: NonEmpty a -> a

Reduce a non-empty list with multi'append.

Akin to sconcat.

multi'stimes :: Integral b => b -> a -> a

Repeat a value n times.

Akin to stimes.

Instances

MultiSemigroup x ()

Methods

multi'append :: () -> () -> ()

multi'sconcat :: NonEmpty () -> ()

multi'stimes :: Integral b => b -> () -> ()

Ord a => MultiSemigroup Max a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

Ord a => MultiSemigroup Min a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

MultiSemigroup Multiplication Int

Methods

multi'append :: Int -> Int -> Int

multi'sconcat :: NonEmpty Int -> Int

multi'stimes :: Integral b => b -> Int -> Int

MultiSemigroup Multiplication Integer

Methods

multi'append :: Integer -> Integer -> Integer

multi'sconcat :: NonEmpty Integer -> Integer

multi'stimes :: Integral b => b -> Integer -> Integer

MultiSemigroup Multiplication Natural

Methods

multi'append :: Natural -> Natural -> Natural

multi'sconcat :: NonEmpty Natural -> Natural

multi'stimes :: Integral b => b -> Natural -> Natural

MultiSemigroup Addition Int

Methods

multi'append :: Int -> Int -> Int

multi'sconcat :: NonEmpty Int -> Int

multi'stimes :: Integral b => b -> Int -> Int

MultiSemigroup Addition Integer

Methods

multi'append :: Integer -> Integer -> Integer

multi'sconcat :: NonEmpty Integer -> Integer

multi'stimes :: Integral b => b -> Integer -> Integer

MultiSemigroup Addition Natural

Methods

multi'append :: Natural -> Natural -> Natural

multi'sconcat :: NonEmpty Natural -> Natural

multi'stimes :: Integral b => b -> Natural -> Natural

MultiSemigroup Or Bool

Methods

multi'append :: Bool -> Bool -> Bool

multi'sconcat :: NonEmpty Bool -> Bool

multi'stimes :: Integral b => b -> Bool -> Bool

MultiSemigroup And Bool

Methods

multi'append :: Bool -> Bool -> Bool

multi'sconcat :: NonEmpty Bool -> Bool

multi'stimes :: Integral b => b -> Bool -> Bool

Semigroup a => MultiSemigroup Default a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

MultiSemigroup Last (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

MultiSemigroup First (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

Ord a => MultiSemigroup MaxMaybe (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

Ord a => MultiSemigroup MinMaybe (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

MultiSemigroup Addition [a]

Methods

multi'append :: [a] -> [a] -> [a]

multi'sconcat :: NonEmpty [a] -> [a]

multi'stimes :: Integral b => b -> [a] -> [a]

MultiSemigroup Addition (NonEmpty a)

Methods

multi'append :: NonEmpty a -> NonEmpty a -> NonEmpty a

multi'sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

multi'stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

MultiSemigroup ArrowComposition (a -> a)

Methods

multi'append :: (a -> a) -> (a -> a) -> a -> a

multi'sconcat :: NonEmpty (a -> a) -> a -> a

multi'stimes :: Integral b => b -> (a -> a) -> a -> a

Monad m => MultiSemigroup ArrowComposition (Kleisli m a a)

Methods

multi'append :: Kleisli m a a -> Kleisli m a a -> Kleisli m a a

multi'sconcat :: NonEmpty (Kleisli m a a) -> Kleisli m a a

multi'stimes :: Integral b => b -> Kleisli m a a -> Kleisli m a a

MultiSemigroup x a => MultiSemigroup (MultiDual x) a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

Monoid

class MultiSemigroup x a => MultiMonoid x a where

Akin to the Monoid class, but with the addition of the phantom type parameter x which lets you specify which monoid to use.

For example, the integers form a monoid via either Addition or Multiplication:

>>> :set -XFlexibleContexts -XTypeApplications
>>> multi'fold @Addition [] :: Integer
0
>>> multi'fold @Addition [2, 3, 5] :: Integer
10
>>> multi'fold @Multiplication [] :: Integer
1
>>> multi'fold @Multiplication [2, 3, 5] :: Integer
30

Minimal complete definition

multi'empty

Methods

multi'empty :: a

Identity of multi'append.

Akin to mempty.

multi'mconcat :: [a] -> a

Fold a list using the monoid.

Akin to mconcat.

Instances

MultiMonoid x ()

Methods

multi'empty :: ()

multi'mconcat :: [()] -> ()

MultiMonoid Multiplication Int

Methods

multi'empty :: Int

multi'mconcat :: [Int] -> Int

MultiMonoid Multiplication Integer

Methods

multi'empty :: Integer

multi'mconcat :: [Integer] -> Integer

MultiMonoid Multiplication Natural

Methods

multi'empty :: Natural

multi'mconcat :: [Natural] -> Natural

MultiMonoid Addition Int

Methods

multi'empty :: Int

multi'mconcat :: [Int] -> Int

MultiMonoid Addition Integer

Methods

multi'empty :: Integer

multi'mconcat :: [Integer] -> Integer

MultiMonoid Addition Natural

Methods

multi'empty :: Natural

multi'mconcat :: [Natural] -> Natural

MultiMonoid Or Bool

Methods

multi'empty :: Bool

multi'mconcat :: [Bool] -> Bool

MultiMonoid And Bool

Methods

multi'empty :: Bool

multi'mconcat :: [Bool] -> Bool

(Semigroup a, Monoid a) => MultiMonoid Default a

Methods

multi'empty :: a

multi'mconcat :: [a] -> a

MultiMonoid Last (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

MultiMonoid First (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

Ord a => MultiMonoid MaxMaybe (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

Ord a => MultiMonoid MinMaybe (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

MultiMonoid Addition [a]

Methods

multi'empty :: [a]

multi'mconcat :: [[a]] -> [a]

MultiMonoid ArrowComposition (a -> a)

Methods

multi'empty :: a -> a

multi'mconcat :: [a -> a] -> a -> a

Monad m => MultiMonoid ArrowComposition (Kleisli m a a)

Methods

multi'empty :: Kleisli m a a

multi'mconcat :: [Kleisli m a a] -> Kleisli m a a

MultiMonoid x a => MultiMonoid (MultiDual x) a

Methods

multi'empty :: a

multi'mconcat :: [a] -> a

Default

data Default

Instances

(Semigroup a, Monoid a) => MultiMonoid Default a

Methods

multi'empty :: a

multi'mconcat :: [a] -> a

Semigroup a => MultiSemigroup Default a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

Conjunction and disjunction

data Conjunction

Instances

MultiMonoid Multiplication Int

Methods

multi'empty :: Int

multi'mconcat :: [Int] -> Int

MultiMonoid Multiplication Integer

Methods

multi'empty :: Integer

multi'mconcat :: [Integer] -> Integer

MultiMonoid Multiplication Natural

Methods

multi'empty :: Natural

multi'mconcat :: [Natural] -> Natural

MultiMonoid And Bool

Methods

multi'empty :: Bool

multi'mconcat :: [Bool] -> Bool

MultiSemigroup Multiplication Int

Methods

multi'append :: Int -> Int -> Int

multi'sconcat :: NonEmpty Int -> Int

multi'stimes :: Integral b => b -> Int -> Int

MultiSemigroup Multiplication Integer

Methods

multi'append :: Integer -> Integer -> Integer

multi'sconcat :: NonEmpty Integer -> Integer

multi'stimes :: Integral b => b -> Integer -> Integer

MultiSemigroup Multiplication Natural

Methods

multi'append :: Natural -> Natural -> Natural

multi'sconcat :: NonEmpty Natural -> Natural

multi'stimes :: Integral b => b -> Natural -> Natural

MultiSemigroup And Bool

Methods

multi'append :: Bool -> Bool -> Bool

multi'sconcat :: NonEmpty Bool -> Bool

multi'stimes :: Integral b => b -> Bool -> Bool

data Disjunction

Instances

MultiMonoid Addition Int

Methods

multi'empty :: Int

multi'mconcat :: [Int] -> Int

MultiMonoid Addition Integer

Methods

multi'empty :: Integer

multi'mconcat :: [Integer] -> Integer

MultiMonoid Addition Natural

Methods

multi'empty :: Natural

multi'mconcat :: [Natural] -> Natural

MultiMonoid Or Bool

Methods

multi'empty :: Bool

multi'mconcat :: [Bool] -> Bool

MultiSemigroup Addition Int

Methods

multi'append :: Int -> Int -> Int

multi'sconcat :: NonEmpty Int -> Int

multi'stimes :: Integral b => b -> Int -> Int

MultiSemigroup Addition Integer

Methods

multi'append :: Integer -> Integer -> Integer

multi'sconcat :: NonEmpty Integer -> Integer

multi'stimes :: Integral b => b -> Integer -> Integer

MultiSemigroup Addition Natural

Methods

multi'append :: Natural -> Natural -> Natural

multi'sconcat :: NonEmpty Natural -> Natural

multi'stimes :: Integral b => b -> Natural -> Natural

MultiSemigroup Or Bool

Methods

multi'append :: Bool -> Bool -> Bool

multi'sconcat :: NonEmpty Bool -> Bool

multi'stimes :: Integral b => b -> Bool -> Bool

MultiMonoid Addition [a]

Methods

multi'empty :: [a]

multi'mconcat :: [[a]] -> [a]

MultiSemigroup Addition [a]

Methods

multi'append :: [a] -> [a] -> [a]

multi'sconcat :: NonEmpty [a] -> [a]

multi'stimes :: Integral b => b -> [a] -> [a]

MultiSemigroup Addition (NonEmpty a)

Methods

multi'append :: NonEmpty a -> NonEmpty a -> NonEmpty a

multi'sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

multi'stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Addition and multiplication

type Addition = Disjunction

type Multiplication = Conjunction

multi'sum :: (Foldable t, MultiMonoid Addition a) => t a -> a

The sum of the numbers in a structure.

Equivalent to multi'fold @Addition.

Akin to sum.

multi'product :: (Foldable t, MultiMonoid Multiplication a) => t a -> a

The product of the numbers of a structure.

Equivalent to multi'fold @Multiplication.

Akin to product.

Boolean and and or

type And = Conjunction

type Or = Disjunction

multi'and :: (Foldable t, MultiMonoid And a) => t a -> a

The conjunction of a container of Bools.

Equivalent to multi'fold @And.

Akin to and.

multi'or :: (Foldable t, MultiMonoid Or a) => t a -> a

The disjunction of a container of Bools.

Equivalent to multi'fold @Or.

Akin to or.

multi'any :: (Foldable t, MultiMonoid Or b) => (a -> b) -> t a -> b

Determines whether any element of the structure satisfies the predicate.

Equivalent to multi'foldMap @Or.

Akin to any.

multi'all :: Foldable t => (a -> Bool) -> t a -> Bool

Determines whether all elements of the structure satisfy the predicate.

Equivalent to multi'foldMap @And.

Akin to all.

Min and max

data Min

Instances

Ord a => MultiSemigroup Min a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

data Max

Instances

Ord a => MultiSemigroup Max a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

data MinMaybe

Instances

Ord a => MultiMonoid MinMaybe (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

Ord a => MultiSemigroup MinMaybe (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

data MaxMaybe

Instances

Ord a => MultiMonoid MaxMaybe (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

Ord a => MultiSemigroup MaxMaybe (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

First and last

data First

Instances

MultiMonoid First (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

MultiSemigroup First (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

data Last

Instances

MultiMonoid Last (Maybe a)

Methods

multi'empty :: Maybe a

multi'mconcat :: [Maybe a] -> Maybe a

MultiSemigroup Last (Maybe a)

Methods

multi'append :: Maybe a -> Maybe a -> Maybe a

multi'sconcat :: NonEmpty (Maybe a) -> Maybe a

multi'stimes :: Integral b => b -> Maybe a -> Maybe a

Arrow composition

data ArrowComposition

Instances

MultiMonoid ArrowComposition (a -> a)

Methods

multi'empty :: a -> a

multi'mconcat :: [a -> a] -> a -> a

MultiSemigroup ArrowComposition (a -> a)

Methods

multi'append :: (a -> a) -> (a -> a) -> a -> a

multi'sconcat :: NonEmpty (a -> a) -> a -> a

multi'stimes :: Integral b => b -> (a -> a) -> a -> a

Monad m => MultiMonoid ArrowComposition (Kleisli m a a)

Methods

multi'empty :: Kleisli m a a

multi'mconcat :: [Kleisli m a a] -> Kleisli m a a

Monad m => MultiSemigroup ArrowComposition (Kleisli m a a)

Methods

multi'append :: Kleisli m a a -> Kleisli m a a -> Kleisli m a a

multi'sconcat :: NonEmpty (Kleisli m a a) -> Kleisli m a a

multi'stimes :: Integral b => b -> Kleisli m a a -> Kleisli m a a

Dual

data MultiDual a

Instances

MultiMonoid x a => MultiMonoid (MultiDual x) a

Methods

multi'empty :: a

multi'mconcat :: [a] -> a

MultiSemigroup x a => MultiSemigroup (MultiDual x) a

Methods

multi'append :: a -> a -> a

multi'sconcat :: NonEmpty a -> a

multi'stimes :: Integral b => b -> a -> a

Monoidal folds

multi'fold :: forall x t m. (MultiMonoid x m, Foldable t) => t m -> m

Combine the elements of a structure using a monoid.

Akin to fold.

multi'foldMap :: forall x t m a. (MultiMonoid x m, Foldable t) => (a -> m) -> t a -> m

Map each element of the structure to a monoid, and combine the results.

Akin to foldMap.

Looking for elements

multi'find :: Foldable t => (a -> Bool) -> t a -> Maybe a

Takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Akin to find.