NumHask.Prelude

A prelude for NumHask

Backend

NumHask imports Protolude as the prelude and replaces much of the Num heirarchy in base. Usage of Semigroup and Monoid has been avoided to retain basic compatability.

module Protolude

(<>) :: Semigroup a => a -> a -> a infixr 6

An associative operation.

(a <> b) <> c = a <> (b <> c)

If a is also a Monoid we further require

(<>) = mappend

class Semigroup a where

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

Since: 4.9.0.0

Methods

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

An associative operation.

(a <> b) <> c = a <> (b <> c)

If a is also a Monoid we further require

(<>) = mappend

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

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

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

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

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

Instances

Semigroup Ordering

Since: 4.9.0.0

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty () -> ()

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

Semigroup Void

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Void -> Void

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

Semigroup Event

Since: 4.10.0.0

Methods

(<>) :: Event -> Event -> Event

sconcat :: NonEmpty Event -> Event

stimes :: Integral b => b -> Event -> Event

Semigroup Lifetime

Since: 4.10.0.0

Methods

(<>) :: Lifetime -> Lifetime -> Lifetime

sconcat :: NonEmpty Lifetime -> Lifetime

stimes :: Integral b => b -> Lifetime -> Lifetime

Semigroup All

Since: 4.9.0.0

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Semigroup Any

Since: 4.9.0.0

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Semigroup IntSet

Methods

(<>) :: IntSet -> IntSet -> IntSet

sconcat :: NonEmpty IntSet -> IntSet

stimes :: Integral b => b -> IntSet -> IntSet

Semigroup Doc

Methods

(<>) :: Doc -> Doc -> Doc

sconcat :: NonEmpty Doc -> Doc

stimes :: Integral b => b -> Doc -> Doc

Semigroup [a]

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Maybe a)

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (IO a)

Since: 4.10.0.0

Methods

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

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

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

Ord a => Semigroup (Min a)

Since: 4.9.0.0

Methods

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

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

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

Ord a => Semigroup (Max a)

Since: 4.9.0.0

Methods

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

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

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

Semigroup (First a)

Since: 4.9.0.0

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: 4.9.0.0

Methods

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

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

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

Monoid m => Semigroup (WrappedMonoid m)

Since: 4.9.0.0

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup a => Semigroup (Option a)

Since: 4.9.0.0

Methods

(<>) :: Option a -> Option a -> Option a

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

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

Semigroup (NonEmpty a)

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Identity a)

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Dual a)

Since: 4.9.0.0

Methods

(<>) :: Dual a -> Dual a -> Dual a

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

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

Semigroup (Endo a)

Since: 4.9.0.0

Methods

(<>) :: Endo a -> Endo a -> Endo a

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

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

Num a => Semigroup (Sum a)

Since: 4.9.0.0

Methods

(<>) :: Sum a -> Sum a -> Sum a

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

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

Num a => Semigroup (Product a)

Since: 4.9.0.0

Methods

(<>) :: Product a -> Product a -> Product a

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

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

Semigroup (First a)

Since: 4.9.0.0

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: 4.9.0.0

Methods

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

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

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

Num a => Semigroup (Colour a)

Methods

(<>) :: Colour a -> Colour a -> Colour a

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

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

Num a => Semigroup (AlphaColour a)

AlphaColour forms a monoid with over and transparent.

Methods

(<>) :: AlphaColour a -> AlphaColour a -> AlphaColour a

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

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

Semigroup (IntMap a)

Methods

(<>) :: IntMap a -> IntMap a -> IntMap a

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

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

Semigroup (Seq a)

Methods

(<>) :: Seq a -> Seq a -> Seq a

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

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

Ord a => Semigroup (Set a)

Methods

(<>) :: Set a -> Set a -> Set a

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

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

Semigroup (Doc a)

Methods

(<>) :: Doc a -> Doc a -> Doc a

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

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

Semigroup b => Semigroup (a -> b)

Since: 4.9.0.0

Methods

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

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

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

Semigroup (Either a b)

Since: 4.9.0.0

Methods

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

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

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

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

Since: 4.9.0.0

Methods

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

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

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

Semigroup (Proxy k s)

Since: 4.9.0.0

Methods

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

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

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

Ord k => Semigroup (Map k v)

Methods

(<>) :: Map k v -> Map k v -> Map k v

sconcat :: NonEmpty (Map k v) -> Map k v

stimes :: Integral b => b -> Map k v -> Map k v

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

Since: 4.9.0.0

Methods

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

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

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

Semigroup a => Semigroup (Const k a b)

Since: 4.9.0.0

Methods

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

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

stimes :: Integral b => b -> Const k a b -> Const k a b

Alternative f => Semigroup (Alt * f a)

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty (Alt * f a) -> Alt * f a

stimes :: Integral b => b -> Alt * f a -> Alt * f a

Semigroup a => Semigroup (Tagged k s a)

Methods

(<>) :: Tagged k s a -> Tagged k s a -> Tagged k s a

sconcat :: NonEmpty (Tagged k s a) -> Tagged k s a

stimes :: Integral b => b -> Tagged k s a -> Tagged k s a

Semigroup a => Semigroup (Constant k a b)

Methods

(<>) :: Constant k a b -> Constant k a b -> Constant k a b

sconcat :: NonEmpty (Constant k a b) -> Constant k a b

stimes :: Integral b => b -> Constant k a b -> Constant k a b

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

Since: 4.9.0.0

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

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

Since: 4.9.0.0

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

Algebraic Heirarchy

Re-defines the numeric tower.

Instances for Int, Integer, Float, Double, Bool and Complex are supplied.

module NumHask.Algebra.Additive

module NumHask.Algebra.Basis

module NumHask.Algebra.Distribution

module NumHask.Algebra.Field

module NumHask.Algebra.Integral

module NumHask.Algebra.Magma

module NumHask.Algebra.Metric

module NumHask.Algebra.Module

module NumHask.Algebra.Multiplicative

module NumHask.Algebra.Ring

module NumHask.Algebra.Singleton