Data.Monoid.Null

This module defines the MonoidNull class and some of its instances.

Documentation

class Monoid m => MonoidNull m where

Extension of Monoid that allows testing a value for equality with mempty. The following law must hold:

null x == (x == mempty)

Furthermore, the performance of this method should be constant, i.e., independent of the length of its argument.

Methods

null :: m -> Bool

Instances

MonoidNull Ordering

MonoidNull ()

MonoidNull All

MonoidNull Any

MonoidNull ByteString

MonoidNull ByteString

MonoidNull IntSet

MonoidNull Text

MonoidNull Text

MonoidNull ByteStringUTF8

MonoidNull [x]

MonoidNull a => MonoidNull (Dual a)

(Num a, Eq a) => MonoidNull (Sum a)

(Num a, Eq a) => MonoidNull (Product a)

MonoidNull (First a)

MonoidNull (Last a)

Monoid a => MonoidNull (Maybe a)

MonoidNull (IntMap v)

Ord a => MonoidNull (Set a)

MonoidNull (Seq a)

MonoidNull (Vector a)

MonoidNull (Concat a)

StableFactorialMonoid a => MonoidNull (Measured a)

(MonoidNull a, MonoidNull b) => MonoidNull (a, b)

Ord k => MonoidNull (Map k v)

class MonoidNull m => PositiveMonoid m

Subclass of Monoid for types whose values have no inverse, with the exception of mempty. More formally, the class instances must satisfy the following law:

null (x <> y) == (null x && null y)

Instances

PositiveMonoid Ordering

PositiveMonoid ()

PositiveMonoid All

PositiveMonoid Any

PositiveMonoid ByteString

PositiveMonoid ByteString

PositiveMonoid IntSet

PositiveMonoid Text

PositiveMonoid Text

PositiveMonoid ByteStringUTF8

PositiveMonoid [x]

PositiveMonoid a => PositiveMonoid (Dual a)

PositiveMonoid (First a)

PositiveMonoid (Last a)

Monoid a => PositiveMonoid (Maybe a)

PositiveMonoid (IntMap v)

Ord a => PositiveMonoid (Set a)

PositiveMonoid (Seq a)

PositiveMonoid (Vector a)

PositiveMonoid (Concat a)

StableFactorialMonoid a => PositiveMonoid (Measured a)

Ord k => PositiveMonoid (Map k v)