Copyright	(c) 2015 Maciej Piróg
License	MIT
Maintainer	maciej.adam.pirog@gmail.com
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Data.Monoid.Zero

Contents

Zero monoids
Left zero monoids
Right zero monoids

Description

Typeclasses for monoids with (left, right, or "two-sided") zero elements (aka absorbing elements) and their free implementations. Just like monoids are related to backtracking computations, right zero monoids are related to backtracking computation with Prolog's cut operator (see the module Data.List.Cut).

Synopsis

Zero monoids

class Monoid m => MonoidZero m where Source

Class of zero monoids. Instances should satisfy:

```
mappend zero m = zero
```
```
mappend m zero = zero
```

Methods

zero :: m Source

Instances

MonoidZero () Source
MonoidZero All Source
MonoidZero Any Source
Num n => MonoidZero (Product n) Source
Monoid m => MonoidZero (AdjoinZero m) Source
(MonoidZero a, MonoidZero b) => MonoidZero (a, b) Source
(MonoidZero a, MonoidZero b, MonoidZero c) => MonoidZero (a, b, c) Source
(MonoidZero a, MonoidZero b, MonoidZero c, MonoidZero d) => MonoidZero (a, b, c, d) Source
(MonoidZero a, MonoidZero b, MonoidZero c, MonoidZero d, MonoidZero e) => MonoidZero (a, b, c, d, e) Source

newtype AdjoinZero m Source

A zero monoid freely generated by a monoid.

Constructors

AdjoinZero
Fields adjoinZero :: Maybe m

Instances

Functor AdjoinZero Source
Foldable AdjoinZero Source
Traversable AdjoinZero Source
Eq m => Eq (AdjoinZero m) Source
Ord m => Ord (AdjoinZero m) Source
Show m => Show (AdjoinZero m) Source
Monoid m => Monoid (AdjoinZero m) Source
Monoid m => MonoidRZero (AdjoinZero m) Source
Monoid m => MonoidLZero (AdjoinZero m) Source
Monoid m => MonoidZero (AdjoinZero m) Source

Left zero monoids

class Monoid m => MonoidLZero m where Source

Class of left zero monoids. Instances should satisfy:

```
mappend m lzero = lzero
```

Methods

lzero :: m Source

Instances

MonoidLZero () Source
MonoidLZero All Source
MonoidLZero Any Source
Num n => MonoidLZero (Product n) Source
Monoid m => MonoidLZero (AdjoinLZero m) Source
Monoid m => MonoidLZero (AdjoinZero m) Source
(MonoidLZero a, MonoidLZero b) => MonoidLZero (a, b) Source
(MonoidLZero a, MonoidLZero b, MonoidLZero c) => MonoidLZero (a, b, c) Source
(MonoidLZero a, MonoidLZero b, MonoidLZero c, MonoidLZero d) => MonoidLZero (a, b, c, d) Source
(MonoidLZero a, MonoidLZero b, MonoidLZero c, MonoidLZero d, MonoidLZero e) => MonoidLZero (a, b, c, d, e) Source

newtype AdjoinLZero m Source

A left zero monoid freely generated by a monoid.

Constructors

AdjoinLZero
Fields unAdjoinLZero :: (Bool, m)

Instances

Functor AdjoinLZero Source
Foldable AdjoinLZero Source
Traversable AdjoinLZero Source
Eq m => Eq (AdjoinLZero m) Source
Ord m => Ord (AdjoinLZero m) Source
Show m => Show (AdjoinLZero m) Source
Monoid m => Monoid (AdjoinLZero m) Source
Monoid m => MonoidLZero (AdjoinLZero m) Source

Right zero monoids

class Monoid m => MonoidRZero m where Source

Class of right zero monoids. Instances should satisfy:

```
mappend rzero m = rzero
```

Methods

rzero :: m Source

Instances

MonoidRZero () Source
MonoidRZero All Source
MonoidRZero Any Source
Num n => MonoidRZero (Product n) Source
Monoid m => MonoidRZero (AdjoinRZero m) Source
Monoid m => MonoidRZero (AdjoinZero m) Source
(MonoidRZero a, MonoidRZero b) => MonoidRZero (a, b) Source
(Functor m, Monad m) => MonoidRZero (CutListT m a) Source
(MonoidRZero a, MonoidRZero b, MonoidRZero c) => MonoidRZero (a, b, c) Source
(MonoidRZero a, MonoidRZero b, MonoidRZero c, MonoidRZero d) => MonoidRZero (a, b, c, d) Source
(MonoidRZero a, MonoidRZero b, MonoidRZero c, MonoidRZero d, MonoidRZero e) => MonoidRZero (a, b, c, d, e) Source

newtype AdjoinRZero m Source

A right zero monoid freely generated by a monoid.

Constructors

AdjoinRZero
Fields unAdjoinRZero :: (m, Bool)

Instances

Functor AdjoinRZero Source
Foldable AdjoinRZero Source
Traversable AdjoinRZero Source
Eq m => Eq (AdjoinRZero m) Source
Ord m => Ord (AdjoinRZero m) Source
Show m => Show (AdjoinRZero m) Source
Monoid m => Monoid (AdjoinRZero m) Source
Monoid m => MonoidRZero (AdjoinRZero m) Source