Safe Haskell	Safe
Language	Haskell2010

NumHask.Prelude

Contents

Backend
Algebraic Heirarchy

Description

A prelude for NumHask

Synopsis

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