Copyright	(c) Alice Rixte 2024
License	BSD 3
Maintainer	alice.rixte@u-bordeaux.fr
Stability	unstable
Portability	non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell2010

Data.Act.Act

Contents

Left actions
Right actions
Newtypes for instance derivation

Description

Usage

For both LAct and RAct, the acting type is the second parameter. This is a bit counter intuitive when using LAct, but it allows to use the DerivingVia mechanism to derive instances of LAct and RAct for newtypes that wrap the acting type. For example, you can use ActSelf' as follow to derive instances for LAct and RAct :

{-# LANGUAGE DerivingVia #-}

import Data.Act
import Data.Semigroup

newtype Seconds = Seconds Float
newtype Duration = Duration Seconds
  deriving (Semigroup, Monoid) via (Sum Float)

  deriving (LAct Seconds, RAct Seconds) via (ActSelf' (Sum Float))
  -- derives LAct Second  Duration

  deriving (LAct [Seconds], RAct [Seconds]) via (ActMap (ActSelf' (Sum Float)))
   -- derives LAct [Second] Duration

newtype Durations = Durations [Duration]
  deriving (LAct Seconds, RAct Seconds) via (ActFold [Duration])
  -- derives LAct Second Durations

>>> Duration (Seconds 1) <>$ (Seconds 2)
Seconds 3.0
>>> Duration 2 <>$ Seconds 3
Seconds 5.0
>>> Duration 2 <>$ [Seconds 3, Seconds 4]
[Seconds 5.0,Seconds 6.0]
>>> [Duration 2, Duration 3] <>$ Seconds 4
[Seconds 5.0,Seconds 6.0]
>>> Durations [Duration 2, Duration 3] <>$ Seconds 4
Seconds 9.0

Synopsis

class LAct x s where
- lact :: s -> x -> x
- (<>$) :: s -> x -> x
class (LAct x s, Semigroup s) => LActSg x s
class (LActSg x s, Monoid s) => LActMn x s
type LActGp x s = (LActMn x s, Group s)
class (LAct x s, Semigroup x) => LActDistrib x s
type LActSgMorph x s = (LActSg x s, LActDistrib x s)
class (LAct x s, Monoid x) => LActNeutral x s
type LActMnMorph x s = (LActMn x s, LActSgMorph x s, LActNeutral x s)
class RAct x s where
- ract :: x -> s -> x
- ($<>) :: x -> s -> x
class (RAct x s, Semigroup s) => RActSg x s
class (RActSg x s, Monoid s) => RActMn x s
type RActGp x s = (RActMn x s, Group s)
class (RAct x s, Semigroup x) => RActDistrib x s
type RActSgMorph x s = (RActSg x s, RActDistrib x s)
class (RAct x s, Monoid x) => RActNeutral x s
type RActMnMorph x s = (RActMn x s, RActSgMorph x s, RActNeutral x s)
newtype ActSelf s = ActSelf {
- unactSelf :: s
}
newtype ActSelf' x = ActSelf' {
- unactCoerce :: x
}
newtype ActMap s = ActMap {
- unactMap :: s
}
newtype ActFold s = ActFold {
- unactFold :: s
}
newtype ActFold' s = ActFold' {
- unactFold' :: s
}
newtype ActTrivial x = ActTrivial {
- unactId :: x
}

Left actions

class LAct x s where Source #

A left action of a set s on another set x is a function that maps elements of s to functions on x.

There are no additional laws for this class to satisfy.

One example of useful set action that is not a semigroup action is declared in this file :

 instance (LAct x s, LAct x t) => LAct x (Either s t) where
   Left  s <>$ x = s <>$ x
   Right s <>$ x = s <>$ x

This is often useful when dealing with free monoids :

>>> ActFold [Right (Product (2 :: Int)) , Left (Sum (1 :: Int))] <>$ (2 :: Int)
6
>>> (2 :: Int) $<> ActFold [Right (Product (2 :: Int)) , Left (Sum (1 :: Int))]
5

The order LAct's arguments is counter intuitive : even though we write left actions as s <>$ x, we declare the constraint as LAct x s. The reason for this is to be able to derive instances of LAct while driving the instances by the acting type.

Instances of LAct are driven by the second parameter (the acting type). Concretely, this means you should never write instances of the form

instance LAct SomeType s

where s is a type variable.

Minimal complete definition

lact | (<>$)

Methods

lact :: s -> x -> x infixr 5 Source #

Lifts an element of the set s into a function on the set x

(<>$) :: s -> x -> x infixr 5 Source #

Infix synonym or lact

The acting part is on the right of the operator (symbolized by <>) and the actee on the right (symbolized by $), hence the notation <>$

Instances

Instances details

LAct () s Source #	Action by morphism of semigroups (resp. monoids) when `Semigroup s` (resp. `Monoid s`)
Instance details Defined in Data.Act.Act Methods lact :: s -> () -> () Source # (<>$) :: s -> () -> () Source #
LAct Bool All Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: All -> Bool -> Bool Source # (<>$) :: All -> Bool -> Bool Source #
LAct Bool Any Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: Any -> Bool -> Bool Source # (<>$) :: Any -> Bool -> Bool Source #
LAct x () Source #	Action by morphism of monoids
Instance details Defined in Data.Act.Act Methods lact :: () -> x -> x Source # (<>$) :: () -> x -> x Source #
Semigroup s => LAct s (ActSelf s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods lact :: ActSelf s -> s -> s Source # (<>$) :: ActSelf s -> s -> s Source #
LAct x s => LAct x (Identity s) Source #	Preserves action properties of `LAct x s`.
Instance details Defined in Data.Act.Act Methods lact :: Identity s -> x -> x Source # (<>$) :: Identity s -> x -> x Source #
LAct x (First x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: First x -> x -> x Source # (<>$) :: First x -> x -> x Source #
LAct x (First x) Source #	Semigroup action
Instance details Defined in Data.Act.Act Methods lact :: First x -> x -> x Source # (<>$) :: First x -> x -> x Source #
RAct x s => LAct x (Dual s) Source #	Preserves action properties of `LAct x s`.
Instance details Defined in Data.Act.Act Methods lact :: Dual s -> x -> x Source # (<>$) :: Dual s -> x -> x Source #
LAct x (Endo x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: Endo x -> x -> x Source # (<>$) :: Endo x -> x -> x Source #
Num x => LAct x (Product x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: Product x -> x -> x Source # (<>$) :: Product x -> x -> x Source #
Num x => LAct x (Sum x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: Sum x -> x -> x Source # (<>$) :: Sum x -> x -> x Source #
(Foldable f, LAct x s) => LAct x (ActFold (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods lact :: ActFold (f s) -> x -> x Source # (<>$) :: ActFold (f s) -> x -> x Source #
(Foldable f, LAct x s) => LAct x (ActFold' (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods lact :: ActFold' (f s) -> x -> x Source # (<>$) :: ActFold' (f s) -> x -> x Source #
(Semigroup s, Coercible x s) => LAct x (ActSelf' s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods lact :: ActSelf' s -> x -> x Source # (<>$) :: ActSelf' s -> x -> x Source #
LAct x (ActTrivial s) Source #	Action by morphism of monoids when `Monoid s` and `Monoid x`
Instance details Defined in Data.Act.Act Methods lact :: ActTrivial s -> x -> x Source # (<>$) :: ActTrivial s -> x -> x Source #
LAct x s => LAct x (Maybe s) Source #	Monoid action when `LAct x s` is a semigroup action.
Instance details Defined in Data.Act.Act Methods lact :: Maybe s -> x -> x Source # (<>$) :: Maybe s -> x -> x Source #
(LAct x s, LAct x t) => LAct x (Either s t) Source #	No additionnal properties. In particular this is _not_ a semigroup action.
Instance details Defined in Data.Act.Act Methods lact :: Either s t -> x -> x Source # (<>$) :: Either s t -> x -> x Source #
LAct x s => LAct (Identity x) (Identity s) Source #	Preserves action properties of `LAct x s`.
Instance details Defined in Data.Act.Act Methods lact :: Identity s -> Identity x -> Identity x Source # (<>$) :: Identity s -> Identity x -> Identity x Source #
Num x => LAct (Product x) (Product x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: Product x -> Product x -> Product x Source # (<>$) :: Product x -> Product x -> Product x Source #
Num x => LAct (Sum x) (Product x) Source #	Action by morphism of monoids
Instance details Defined in Data.Act.Act Methods lact :: Product x -> Sum x -> Sum x Source # (<>$) :: Product x -> Sum x -> Sum x Source #
Num x => LAct (Sum x) (Sum x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods lact :: Sum x -> Sum x -> Sum x Source # (<>$) :: Sum x -> Sum x -> Sum x Source #
(LAct x s, Functor f) => LAct (f x) (ActMap s) Source #	Preserves the semigroup (resp. monoid) property of `LAct x s`, but not the morphism properties, which depend on potential `Semigroup` (resp. `Monoid`) instances of `f x`
Instance details Defined in Data.Act.Act Methods lact :: ActMap s -> f x -> f x Source # (<>$) :: ActMap s -> f x -> f x Source #
(LAct x1 s1, LAct x2 s2) => LAct (x1, x2) (s1, s2) Source #	Same action propety as the weaker properties of `(LAct x1 s1, LAct x2 s2)`
Instance details Defined in Data.Act.Act Methods lact :: (s1, s2) -> (x1, x2) -> (x1, x2) Source # (<>$) :: (s1, s2) -> (x1, x2) -> (x1, x2) Source #

class (LAct x s, Semigroup s) => LActSg x s Source #

A left semigroup action

Instances must satisfy the following law :

 (s <> t) <>$ x == s <>$ (t <>$ x)

Instances

Instances details

Semigroup s => LActSg () s Source #
Instance details Defined in Data.Act.Act
LActSg Bool All Source #
Instance details Defined in Data.Act.Act
LActSg Bool Any Source #
Instance details Defined in Data.Act.Act
LActSg x () Source #
Instance details Defined in Data.Act.Act
Semigroup s => LActSg s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
LActSg x s => LActSg x (Identity s) Source #
Instance details Defined in Data.Act.Act
LActSg x (First x) Source #
Instance details Defined in Data.Act.Act
LActSg x (First x) Source #
Instance details Defined in Data.Act.Act
RActSg x s => LActSg x (Dual s) Source #
Instance details Defined in Data.Act.Act
LActSg x (Endo x) Source #
Instance details Defined in Data.Act.Act
Num x => LActSg x (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => LActSg x (Sum x) Source #
Instance details Defined in Data.Act.Act
LAct x s => LActSg x (ActFold [s]) Source #
Instance details Defined in Data.Act.Act
LAct x s => LActSg x (ActFold' [s]) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Semigroup s) => LActSg x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => LActSg x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
LActSg x s => LActSg x (Maybe s) Source #
Instance details Defined in Data.Act.Act
LActSg x s => LActSg (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => LActSg (Product x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => LActSg (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => LActSg (Sum x) (Sum x) Source #
Instance details Defined in Data.Act.Act
(LActSg x s, Functor f) => LActSg (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
(LActSg x1 s1, LActSg x2 s2) => LActSg (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

class (LActSg x s, Monoid s) => LActMn x s Source #

A left monoid action, also called a left unitary action.

In addition to the laws of LActSg, instances must satisfy the following law :

 mempty <>$ x == x

Instances

Instances details

Monoid s => LActMn () s Source #
Instance details Defined in Data.Act.Act
LActMn Bool All Source #
Instance details Defined in Data.Act.Act
LActMn Bool Any Source #
Instance details Defined in Data.Act.Act
LActMn x () Source #
Instance details Defined in Data.Act.Act
Monoid s => LActMn s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
LActMn x s => LActMn x (Identity s) Source #
Instance details Defined in Data.Act.Act
LActMn x (First x) Source #
Instance details Defined in Data.Act.Act
RActMn x s => LActMn x (Dual s) Source #
Instance details Defined in Data.Act.Act
LActMn x (Endo x) Source #
Instance details Defined in Data.Act.Act
Num x => LActMn x (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => LActMn x (Sum x) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Monoid s) => LActMn x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
Monoid s => LActMn x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
LActSg x s => LActMn x (Maybe s) Source #
Instance details Defined in Data.Act.Act
LActMn x s => LActMn (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => LActMn (Product x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => LActMn (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => LActMn (Sum x) (Sum x) Source #
Instance details Defined in Data.Act.Act
(LActMn x s, Functor f) => LActMn (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
(LActMn x1 s1, LActMn x2 s2) => LActMn (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

type LActGp x s = (LActMn x s, Group s) Source #

A left action of groups. No additional laws are needed.

class (LAct x s, Semigroup x) => LActDistrib x s Source #

A left distributive action

Instances must satisfy the following law :

 s <>$ (x <> y) == (s <>$ x) <> (s <>$ y)

Instances

Instances details

LActDistrib () s Source #
Instance details Defined in Data.Act.Act
Semigroup x => LActDistrib x () Source #
Instance details Defined in Data.Act.Act
LActDistrib x s => LActDistrib x (Identity s) Source #
Instance details Defined in Data.Act.Act
RActDistrib x s => LActDistrib x (Dual s) Source #
Instance details Defined in Data.Act.Act
Semigroup x => LActDistrib x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
LActDistrib x s => LActDistrib (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => LActDistrib (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
LAct x s => LActDistrib [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(LActDistrib x1 s1, LActDistrib x2 s2) => LActDistrib (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

type LActSgMorph x s = (LActSg x s, LActDistrib x s) Source #

A left action by morphism of semigroups

Whenever the constaints LActSg x s and LActDistrib x s are satisfied, (s <>$) is a morphism of semigroups for any s.

class (LAct x s, Monoid x) => LActNeutral x s Source #

A left action on a monoid that preserves its neutral element.

Instances must satisfy the following law :

 s <>$ mempty == mempty

Instances

Instances details

LActNeutral () s Source #
Instance details Defined in Data.Act.Act
Monoid x => LActNeutral x () Source #
Instance details Defined in Data.Act.Act
LActNeutral x s => LActNeutral x (Identity s) Source #
Instance details Defined in Data.Act.Act
RActNeutral x s => LActNeutral x (Dual s) Source #
Instance details Defined in Data.Act.Act
Monoid x => LActNeutral x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
LActNeutral x s => LActNeutral (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => LActNeutral (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
LAct x s => LActNeutral [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(LActNeutral x1 s1, LActNeutral x2 s2) => LActNeutral (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

type LActMnMorph x s = (LActMn x s, LActSgMorph x s, LActNeutral x s) Source #

A left action by morphism of monoids i.e. such that (s <>$) is a morphism of monoids.

This is equivalent to satisfy the three following properties :

left action by morphism of semigroups (i.e. LActSgMorph x s)
left monoid action (i.e. LActMn x s)
preseving neutral element (i.e. LActNeutral x s)

Right actions

class RAct x s where Source #

A right action of a set s on another set x.

There are no additional laws for this class to satisfy.

Minimal complete definition

ract | ($<>)

Methods

ract :: x -> s -> x infixl 5 Source #

Act on the right of some element of x

($<>) :: x -> s -> x infixl 5 Source #

Infix synonym or ract

The acting part is on the right of the operator (symbolized by <>) and the actee on the left (symbolized by $), hence the notation $<>.

Instances

Instances details

RAct () s Source #	Action by morphism of semigroups (resp. monoids) when `Semigroup s` (resp. `Monoid s`)
Instance details Defined in Data.Act.Act Methods ract :: () -> s -> () Source # ($<>) :: () -> s -> () Source #
RAct Bool All Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: Bool -> All -> Bool Source # ($<>) :: Bool -> All -> Bool Source #
RAct Bool Any Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: Bool -> Any -> Bool Source # ($<>) :: Bool -> Any -> Bool Source #
RAct x () Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> () -> x Source # ($<>) :: x -> () -> x Source #
Semigroup s => RAct s (ActSelf s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods ract :: s -> ActSelf s -> s Source # ($<>) :: s -> ActSelf s -> s Source #
RAct x s => RAct x (Identity s) Source #	Preserves action properties of `RAct x s`.
Instance details Defined in Data.Act.Act Methods ract :: x -> Identity s -> x Source # ($<>) :: x -> Identity s -> x Source #
RAct x (Last x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> Last x -> x Source # ($<>) :: x -> Last x -> x Source #
RAct x (Last x) Source #	Semigroup action
Instance details Defined in Data.Act.Act Methods ract :: x -> Last x -> x Source # ($<>) :: x -> Last x -> x Source #
LAct x s => RAct x (Dual s) Source #	Preserves action properties of `LAct x s`.
Instance details Defined in Data.Act.Act Methods ract :: x -> Dual s -> x Source # ($<>) :: x -> Dual s -> x Source #
Num x => RAct x (Product x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> Product x -> x Source # ($<>) :: x -> Product x -> x Source #
Num x => RAct x (Sum x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> Sum x -> x Source # ($<>) :: x -> Sum x -> x Source #
(Foldable f, RAct x s) => RAct x (ActFold (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> ActFold (f s) -> x Source # ($<>) :: x -> ActFold (f s) -> x Source #
(Foldable f, RAct x s) => RAct x (ActFold' (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> ActFold' (f s) -> x Source # ($<>) :: x -> ActFold' (f s) -> x Source #
(Semigroup s, Coercible x s) => RAct x (ActSelf' s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods ract :: x -> ActSelf' s -> x Source # ($<>) :: x -> ActSelf' s -> x Source #
RAct x (ActTrivial s) Source #	Action by morphism of monoids when `Monoid s` and `Monoid x`
Instance details Defined in Data.Act.Act Methods ract :: x -> ActTrivial s -> x Source # ($<>) :: x -> ActTrivial s -> x Source #
RAct x s => RAct x (Maybe s) Source #	Monoid action when `LAct x s` is a semigroup action.
Instance details Defined in Data.Act.Act Methods ract :: x -> Maybe s -> x Source # ($<>) :: x -> Maybe s -> x Source #
(RAct x s, RAct x t) => RAct x (Either s t) Source #	No additionnal properties. In particular this is _not_ a semigroup action.
Instance details Defined in Data.Act.Act Methods ract :: x -> Either s t -> x Source # ($<>) :: x -> Either s t -> x Source #
RAct x s => RAct (Identity x) (Identity s) Source #	Preserves action properties of `LAct x s`.
Instance details Defined in Data.Act.Act Methods ract :: Identity x -> Identity s -> Identity x Source # ($<>) :: Identity x -> Identity s -> Identity x Source #
Num x => RAct (Product x) (Product x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: Product x -> Product x -> Product x Source # ($<>) :: Product x -> Product x -> Product x Source #
Num x => RAct (Sum x) (Product x) Source #	Action by morphism of monoids
Instance details Defined in Data.Act.Act Methods ract :: Sum x -> Product x -> Sum x Source # ($<>) :: Sum x -> Product x -> Sum x Source #
Num x => RAct (Sum x) (Sum x) Source #	Monoid action
Instance details Defined in Data.Act.Act Methods ract :: Sum x -> Sum x -> Sum x Source # ($<>) :: Sum x -> Sum x -> Sum x Source #
(RAct x s, Functor f) => RAct (f x) (ActMap s) Source #	Preserves the semigroup (resp. monoid) property of `LAct x s`, but not the morphism properties, which depend on potential `Semigroup` (resp. `Monoid`) instances of `f x`. When $f = []@, this is an action by morphism of monoids.
Instance details Defined in Data.Act.Act Methods ract :: f x -> ActMap s -> f x Source # ($<>) :: f x -> ActMap s -> f x Source #
(RAct x1 s1, RAct x2 s2) => RAct (x1, x2) (s1, s2) Source #	Same action propety as the weaker properties of `(LAct x1 s1, LAct x2 s2)`
Instance details Defined in Data.Act.Act Methods ract :: (x1, x2) -> (s1, s2) -> (x1, x2) Source # ($<>) :: (x1, x2) -> (s1, s2) -> (x1, x2) Source #

class (RAct x s, Semigroup s) => RActSg x s Source #

A right semigroup action

Instances must satisfy the following law :

 x $<> (s <> t) == (x $<> s) $<> t

Instances

Instances details

Semigroup s => RActSg () s Source #
Instance details Defined in Data.Act.Act
RActSg Bool All Source #
Instance details Defined in Data.Act.Act
RActSg Bool Any Source #
Instance details Defined in Data.Act.Act
RActSg x () Source #
Instance details Defined in Data.Act.Act
Semigroup s => RActSg s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
RActSg x s => RActSg x (Identity s) Source #
Instance details Defined in Data.Act.Act
RActSg x (Last x) Source #
Instance details Defined in Data.Act.Act
RActSg x (Last x) Source #
Instance details Defined in Data.Act.Act
LActSg x s => RActSg x (Dual s) Source #
Instance details Defined in Data.Act.Act
Num x => RActSg x (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => RActSg x (Sum x) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Semigroup s) => RActSg x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => RActSg x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
RActSg x s => RActSg x (Maybe s) Source #
Instance details Defined in Data.Act.Act
RActSg x s => RActSg (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => RActSg (Product x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => RActSg (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => RActSg (Sum x) (Sum x) Source #
Instance details Defined in Data.Act.Act
(RActSg x s, Functor f) => RActSg (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RActSg x1 s1, RActSg x2 s2) => RActSg (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

class (RActSg x s, Monoid s) => RActMn x s Source #

A right monoid action, also called a right unitary action.

In addition to the laws of RActSg, instances must satisfy the following law :

 x $<> mempty == x

Instances

Instances details

Monoid s => RActMn () s Source #
Instance details Defined in Data.Act.Act
RActMn Bool All Source #
Instance details Defined in Data.Act.Act
RActMn Bool Any Source #
Instance details Defined in Data.Act.Act
RActMn x () Source #
Instance details Defined in Data.Act.Act
Monoid s => RActMn s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
RActMn x s => RActMn x (Identity s) Source #
Instance details Defined in Data.Act.Act
RActMn x (Last x) Source #
Instance details Defined in Data.Act.Act
LActMn x s => RActMn x (Dual s) Source #
Instance details Defined in Data.Act.Act
Num x => RActMn x (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => RActMn x (Sum x) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Monoid s) => RActMn x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
Monoid s => RActMn x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
RActSg x s => RActMn x (Maybe s) Source #
Instance details Defined in Data.Act.Act
RActMn x s => RActMn (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => RActMn (Product x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => RActMn (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
Num x => RActMn (Sum x) (Sum x) Source #
Instance details Defined in Data.Act.Act
(RActMn x s, Functor f) => RActMn (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RActMn x1 s1, RActMn x2 s2) => RActMn (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

type RActGp x s = (RActMn x s, Group s) Source #

A left action of groups. No additional laws are needed.

class (RAct x s, Semigroup x) => RActDistrib x s Source #

A right distributive action

Instances must satisfy the following law :

 (x <> y) $<> s == (x $<> s) <> (y $<> s)

Instances

Instances details

RActDistrib () s Source #
Instance details Defined in Data.Act.Act
Semigroup x => RActDistrib x () Source #
Instance details Defined in Data.Act.Act
RActDistrib x s => RActDistrib x (Identity s) Source #
Instance details Defined in Data.Act.Act
LActDistrib x s => RActDistrib x (Dual s) Source #
Instance details Defined in Data.Act.Act
Semigroup x => RActDistrib x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
RActDistrib x s => RActDistrib (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => RActDistrib (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
RAct x s => RActDistrib [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RActDistrib x1 s1, RActDistrib x2 s2) => RActDistrib (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

type RActSgMorph x s = (RActSg x s, RActDistrib x s) Source #

A right action by morphism of semigroups

Whenever the constaints RActSg x s and RActDistrib x s are satisfied, ($<> s) is a morphism of semigroups for any s.

class (RAct x s, Monoid x) => RActNeutral x s Source #

A right action on a monoid that preserves its neutral element.

Instances must satisfy the following law :

 x $<> mempty == x

Instances

Instances details

RActNeutral () s Source #
Instance details Defined in Data.Act.Act
Monoid x => RActNeutral x () Source #
Instance details Defined in Data.Act.Act
RActNeutral x s => RActNeutral x (Identity s) Source #
Instance details Defined in Data.Act.Act
LActNeutral x s => RActNeutral x (Dual s) Source #
Instance details Defined in Data.Act.Act
Monoid x => RActNeutral x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
RActNeutral x s => RActNeutral (Identity x) (Identity s) Source #
Instance details Defined in Data.Act.Act
Num x => RActNeutral (Sum x) (Product x) Source #
Instance details Defined in Data.Act.Act
RAct x s => RActNeutral [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RActNeutral x1 s1, RActNeutral x2 s2) => RActNeutral (x1, x2) (s1, s2) Source #
Instance details Defined in Data.Act.Act

type RActMnMorph x s = (RActMn x s, RActSgMorph x s, RActNeutral x s) Source #

A right action by morphism of monoids i.e. such that

($<> s) is a morphism of monoids

Newtypes for instance derivation

newtype ActSelf s Source #

A semigroup always acts on itself by translation.

Notice that whenever there is an instance LAct x s with x different from s, this action is lifted to an ActSelf action.

>>> ActSelf "Hello" <>$ " World !"
"Hello World !"

Constructors

ActSelf
Fields unactSelf :: s

Instances

Instances details

Semigroup s => LAct s (ActSelf s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods lact :: ActSelf s -> s -> s Source # (<>$) :: ActSelf s -> s -> s Source #
Monoid s => LActMn s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => LActSg s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => RAct s (ActSelf s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods ract :: s -> ActSelf s -> s Source # ($<>) :: s -> ActSelf s -> s Source #
Monoid s => RActMn s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => RActSg s (ActSelf s) Source #
Instance details Defined in Data.Act.Act
Monoid s => LActCyclic s (ActSelf s) Source #
Instance details Defined in Data.Act.Cyclic Methods lorigin' :: s Source # lshift :: s -> ActSelf s Source #
(Eq s, Monoid s) => LActGen s (ActSelf s) Source #
Instance details Defined in Data.Act.Cyclic Methods lgenerators' :: s -> Bool Source # lgeneratorsList' :: [s] Source # lshiftFromGen :: s -> (s, ActSelf s) Source #
Monoid s => RActCyclic s (ActSelf s) Source #
Instance details Defined in Data.Act.Cyclic Methods rorigin' :: s Source # rshift :: s -> ActSelf s Source #
(Eq s, Monoid s) => RActGen s (ActSelf s) Source #
Instance details Defined in Data.Act.Cyclic Methods rgenerators' :: s -> Bool Source # rgeneratorsList' :: [s] Source # rshiftFromGen :: s -> (s, ActSelf s) Source #
Group g => LTorsor g (ActSelf g) Source #
Instance details Defined in Data.Act.Torsor Methods ldiff :: g -> g -> ActSelf g Source # (.-.) :: g -> g -> ActSelf g Source #
Group g => RTorsor g (ActSelf g) Source #
Instance details Defined in Data.Act.Torsor Methods rdiff :: g -> g -> ActSelf g Source # (.~.) :: g -> g -> ActSelf g Source #
Monoid s => Monoid (ActSelf s) Source #
Instance details Defined in Data.Act.Act Methods mempty :: ActSelf s # mappend :: ActSelf s -> ActSelf s -> ActSelf s # mconcat :: [ActSelf s] -> ActSelf s #
Semigroup s => Semigroup (ActSelf s) Source #
Instance details Defined in Data.Act.Act Methods (<>) :: ActSelf s -> ActSelf s -> ActSelf s # sconcat :: NonEmpty (ActSelf s) -> ActSelf s # stimes :: Integral b => b -> ActSelf s -> ActSelf s #
Show s => Show (ActSelf s) Source #
Instance details Defined in Data.Act.Act Methods showsPrec :: Int -> ActSelf s -> ShowS # show :: ActSelf s -> String # showList :: [ActSelf s] -> ShowS #
Eq s => Eq (ActSelf s) Source #
Instance details Defined in Data.Act.Act Methods (==) :: ActSelf s -> ActSelf s -> Bool # (/=) :: ActSelf s -> ActSelf s -> Bool #
Group s => Group (ActSelf s) Source #
Instance details Defined in Data.Act.Act Methods invert :: ActSelf s -> ActSelf s # (~~) :: ActSelf s -> ActSelf s -> ActSelf s # pow :: Integral x => ActSelf s -> x -> ActSelf s #

newtype ActSelf' x Source #

Actions of ActSelf' behave similarly to those of ActSelf, but first try to coerce x to s before using the Semigroup instance. If x can be coerced to s, then we use the ActSelf action.

This is meant to be used in conjunction with the deriving via strategy when defining newtype wrappers. Here is a concrete example, where durations act on time. Here, Seconds is not a semigroup and Duration is a group that acts on time via the derived instance LAct Seconds Duration.

import Data.Semigroup

newtype Seconds = Seconds Float

newtype Duration = Duration Seconds
  deriving (Semigroup, Monoid, Group) via (Sum Float)
  deriving (LAct Seconds) via (ActSelf' (Sum Float))

>>> Duration 2 <>$ Seconds 3
Seconds 5.0

Constructors

ActSelf'
Fields unactCoerce :: x

Instances

Instances details

(Semigroup s, Coercible x s) => LAct x (ActSelf' s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods lact :: ActSelf' s -> x -> x Source # (<>$) :: ActSelf' s -> x -> x Source #
(Coercible x s, Monoid s) => LActMn x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Semigroup s) => LActSg x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
(Semigroup s, Coercible x s) => RAct x (ActSelf' s) Source #	Semigroup action (monoid action when `Monoid s`)
Instance details Defined in Data.Act.Act Methods ract :: x -> ActSelf' s -> x Source # ($<>) :: x -> ActSelf' s -> x Source #
(Coercible x s, Monoid s) => RActMn x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Semigroup s) => RActSg x (ActSelf' s) Source #
Instance details Defined in Data.Act.Act
(Coercible x s, Monoid s) => LActCyclic x (ActSelf' s) Source #
Instance details Defined in Data.Act.Cyclic Methods lorigin' :: x Source # lshift :: x -> ActSelf' s Source #
(Eq x, Coercible x s, Monoid s) => LActGen x (ActSelf' s) Source #
Instance details Defined in Data.Act.Cyclic Methods lgenerators' :: x -> Bool Source # lgeneratorsList' :: [x] Source # lshiftFromGen :: x -> (x, ActSelf' s) Source #
(Coercible x s, Monoid s) => RActCyclic x (ActSelf' s) Source #
Instance details Defined in Data.Act.Cyclic Methods rorigin' :: x Source # rshift :: x -> ActSelf' s Source #
(Eq x, Coercible x s, Monoid s) => RActGen x (ActSelf' s) Source #
Instance details Defined in Data.Act.Cyclic Methods rgenerators' :: x -> Bool Source # rgeneratorsList' :: [x] Source # rshiftFromGen :: x -> (x, ActSelf' s) Source #
(Group g, Coercible x g) => LTorsor x (ActSelf' g) Source #
Instance details Defined in Data.Act.Torsor Methods ldiff :: x -> x -> ActSelf' g Source # (.-.) :: x -> x -> ActSelf' g Source #
(Group g, Coercible x g) => RTorsor x (ActSelf' g) Source #
Instance details Defined in Data.Act.Torsor Methods rdiff :: x -> x -> ActSelf' g Source # (.~.) :: x -> x -> ActSelf' g Source #
Monoid x => Monoid (ActSelf' x) Source #
Instance details Defined in Data.Act.Act Methods mempty :: ActSelf' x # mappend :: ActSelf' x -> ActSelf' x -> ActSelf' x # mconcat :: [ActSelf' x] -> ActSelf' x #
Semigroup x => Semigroup (ActSelf' x) Source #
Instance details Defined in Data.Act.Act Methods (<>) :: ActSelf' x -> ActSelf' x -> ActSelf' x # sconcat :: NonEmpty (ActSelf' x) -> ActSelf' x # stimes :: Integral b => b -> ActSelf' x -> ActSelf' x #
Show x => Show (ActSelf' x) Source #
Instance details Defined in Data.Act.Act Methods showsPrec :: Int -> ActSelf' x -> ShowS # show :: ActSelf' x -> String # showList :: [ActSelf' x] -> ShowS #
Eq x => Eq (ActSelf' x) Source #
Instance details Defined in Data.Act.Act Methods (==) :: ActSelf' x -> ActSelf' x -> Bool # (/=) :: ActSelf' x -> ActSelf' x -> Bool #
Group x => Group (ActSelf' x) Source #
Instance details Defined in Data.Act.Act Methods invert :: ActSelf' x -> ActSelf' x # (~~) :: ActSelf' x -> ActSelf' x -> ActSelf' x # pow :: Integral x0 => ActSelf' x -> x0 -> ActSelf' x #

newtype ActMap s Source #

An action on any functor that uses the fmap function. For example :

>>> ActMap (ActSelf "Hello") <>$ [" World !", " !"]
["Hello World !","Hello !"]

Constructors

ActMap
Fields unactMap :: s

Instances

Instances details

Monoid s => Monoid (ActMap s) Source #
Instance details Defined in Data.Act.Act Methods mempty :: ActMap s # mappend :: ActMap s -> ActMap s -> ActMap s # mconcat :: [ActMap s] -> ActMap s #
Semigroup s => Semigroup (ActMap s) Source #
Instance details Defined in Data.Act.Act Methods (<>) :: ActMap s -> ActMap s -> ActMap s # sconcat :: NonEmpty (ActMap s) -> ActMap s # stimes :: Integral b => b -> ActMap s -> ActMap s #
Show s => Show (ActMap s) Source #
Instance details Defined in Data.Act.Act Methods showsPrec :: Int -> ActMap s -> ShowS # show :: ActMap s -> String # showList :: [ActMap s] -> ShowS #
Eq s => Eq (ActMap s) Source #
Instance details Defined in Data.Act.Act Methods (==) :: ActMap s -> ActMap s -> Bool # (/=) :: ActMap s -> ActMap s -> Bool #
Group s => Group (ActMap s) Source #
Instance details Defined in Data.Act.Act Methods invert :: ActMap s -> ActMap s # (~~) :: ActMap s -> ActMap s -> ActMap s # pow :: Integral x => ActMap s -> x -> ActMap s #
(LAct x s, Functor f) => LAct (f x) (ActMap s) Source #	Preserves the semigroup (resp. monoid) property of `LAct x s`, but not the morphism properties, which depend on potential `Semigroup` (resp. `Monoid`) instances of `f x`
Instance details Defined in Data.Act.Act Methods lact :: ActMap s -> f x -> f x Source # (<>$) :: ActMap s -> f x -> f x Source #
LAct x s => LActDistrib [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(LActMn x s, Functor f) => LActMn (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
LAct x s => LActNeutral [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(LActSg x s, Functor f) => LActSg (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RAct x s, Functor f) => RAct (f x) (ActMap s) Source #	Preserves the semigroup (resp. monoid) property of `LAct x s`, but not the morphism properties, which depend on potential `Semigroup` (resp. `Monoid`) instances of `f x`. When $f = []@, this is an action by morphism of monoids.
Instance details Defined in Data.Act.Act Methods ract :: f x -> ActMap s -> f x Source # ($<>) :: f x -> ActMap s -> f x Source #
RAct x s => RActDistrib [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RActMn x s, Functor f) => RActMn (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act
RAct x s => RActNeutral [x] (ActMap s) Source #
Instance details Defined in Data.Act.Act
(RActSg x s, Functor f) => RActSg (f x) (ActMap s) Source #
Instance details Defined in Data.Act.Act

newtype ActFold s Source #

Lifting an a container as an action using foldr (for left actions) or foldl (for right actions). For a strict version, use ActFold'.

A left action (<>$) can be seen as an operator for the foldr function, and a allowing to lift any action to some Foldable container.

> ActFold [Sum (1 :: Int), Sum 2, Sum 3] <>$ (4 :: Int)
  10

Constructors

ActFold
Fields unactFold :: s

Instances

Instances details

(Foldable f, LAct x s) => LAct x (ActFold (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods lact :: ActFold (f s) -> x -> x Source # (<>$) :: ActFold (f s) -> x -> x Source #
LAct x s => LActSg x (ActFold [s]) Source #
Instance details Defined in Data.Act.Act
(Foldable f, RAct x s) => RAct x (ActFold (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> ActFold (f s) -> x Source # ($<>) :: x -> ActFold (f s) -> x Source #
Monoid s => Monoid (ActFold s) Source #
Instance details Defined in Data.Act.Act Methods mempty :: ActFold s # mappend :: ActFold s -> ActFold s -> ActFold s # mconcat :: [ActFold s] -> ActFold s #
Semigroup s => Semigroup (ActFold s) Source #
Instance details Defined in Data.Act.Act Methods (<>) :: ActFold s -> ActFold s -> ActFold s # sconcat :: NonEmpty (ActFold s) -> ActFold s # stimes :: Integral b => b -> ActFold s -> ActFold s #
Show s => Show (ActFold s) Source #
Instance details Defined in Data.Act.Act Methods showsPrec :: Int -> ActFold s -> ShowS # show :: ActFold s -> String # showList :: [ActFold s] -> ShowS #
Eq s => Eq (ActFold s) Source #
Instance details Defined in Data.Act.Act Methods (==) :: ActFold s -> ActFold s -> Bool # (/=) :: ActFold s -> ActFold s -> Bool #
Group s => Group (ActFold s) Source #
Instance details Defined in Data.Act.Act Methods invert :: ActFold s -> ActFold s # (~~) :: ActFold s -> ActFold s -> ActFold s # pow :: Integral x => ActFold s -> x -> ActFold s #

newtype ActFold' s Source #

Lifting an a container as an action using fold'r (for left actions) or foldl' (for right actions). For a lazy version, use ActFold.

A left action (<>$) can be seen as an operator for the foldr function, and a allowing to lift any action to some Foldable container.

>>> ActFold' [Sum (1 :: Int), Sum 2, Sum 3] <>$ (4 :: Int)
10

Constructors

ActFold'
Fields unactFold' :: s

Instances

Instances details

(Foldable f, LAct x s) => LAct x (ActFold' (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods lact :: ActFold' (f s) -> x -> x Source # (<>$) :: ActFold' (f s) -> x -> x Source #
LAct x s => LActSg x (ActFold' [s]) Source #
Instance details Defined in Data.Act.Act
(Foldable f, RAct x s) => RAct x (ActFold' (f s)) Source #	When used with lists `[]`, this is a monoid action
Instance details Defined in Data.Act.Act Methods ract :: x -> ActFold' (f s) -> x Source # ($<>) :: x -> ActFold' (f s) -> x Source #
Monoid s => Monoid (ActFold' s) Source #
Instance details Defined in Data.Act.Act Methods mempty :: ActFold' s # mappend :: ActFold' s -> ActFold' s -> ActFold' s # mconcat :: [ActFold' s] -> ActFold' s #
Semigroup s => Semigroup (ActFold' s) Source #
Instance details Defined in Data.Act.Act Methods (<>) :: ActFold' s -> ActFold' s -> ActFold' s # sconcat :: NonEmpty (ActFold' s) -> ActFold' s # stimes :: Integral b => b -> ActFold' s -> ActFold' s #
Show s => Show (ActFold' s) Source #
Instance details Defined in Data.Act.Act Methods showsPrec :: Int -> ActFold' s -> ShowS # show :: ActFold' s -> String # showList :: [ActFold' s] -> ShowS #
Eq s => Eq (ActFold' s) Source #
Instance details Defined in Data.Act.Act Methods (==) :: ActFold' s -> ActFold' s -> Bool # (/=) :: ActFold' s -> ActFold' s -> Bool #
Group s => Group (ActFold' s) Source #
Instance details Defined in Data.Act.Act Methods invert :: ActFold' s -> ActFold' s # (~~) :: ActFold' s -> ActFold' s -> ActFold' s # pow :: Integral x => ActFold' s -> x -> ActFold' s #

newtype ActTrivial x Source #

The trivial action where any element of s acts as the identity function on x

>>> ActTrivial "Hello !" <>$ "Hi !"
" Hi !"

Constructors

ActTrivial
Fields unactId :: x

Instances

Instances details

LAct x (ActTrivial s) Source #	Action by morphism of monoids when `Monoid s` and `Monoid x`
Instance details Defined in Data.Act.Act Methods lact :: ActTrivial s -> x -> x Source # (<>$) :: ActTrivial s -> x -> x Source #
Semigroup x => LActDistrib x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Monoid s => LActMn x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Monoid x => LActNeutral x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => LActSg x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
RAct x (ActTrivial s) Source #	Action by morphism of monoids when `Monoid s` and `Monoid x`
Instance details Defined in Data.Act.Act Methods ract :: x -> ActTrivial s -> x Source # ($<>) :: x -> ActTrivial s -> x Source #
Semigroup x => RActDistrib x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Monoid s => RActMn x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Monoid x => RActNeutral x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Semigroup s => RActSg x (ActTrivial s) Source #
Instance details Defined in Data.Act.Act
Monoid x => Monoid (ActTrivial x) Source #
Instance details Defined in Data.Act.Act Methods mempty :: ActTrivial x # mappend :: ActTrivial x -> ActTrivial x -> ActTrivial x # mconcat :: [ActTrivial x] -> ActTrivial x #
Semigroup x => Semigroup (ActTrivial x) Source #
Instance details Defined in Data.Act.Act Methods (<>) :: ActTrivial x -> ActTrivial x -> ActTrivial x # sconcat :: NonEmpty (ActTrivial x) -> ActTrivial x # stimes :: Integral b => b -> ActTrivial x -> ActTrivial x #
Show x => Show (ActTrivial x) Source #
Instance details Defined in Data.Act.Act Methods showsPrec :: Int -> ActTrivial x -> ShowS # show :: ActTrivial x -> String # showList :: [ActTrivial x] -> ShowS #
Eq x => Eq (ActTrivial x) Source #
Instance details Defined in Data.Act.Act Methods (==) :: ActTrivial x -> ActTrivial x -> Bool # (/=) :: ActTrivial x -> ActTrivial x -> Bool #
Group x => Group (ActTrivial x) Source #
Instance details Defined in Data.Act.Act Methods invert :: ActTrivial x -> ActTrivial x # (~~) :: ActTrivial x -> ActTrivial x -> ActTrivial x # pow :: Integral x0 => ActTrivial x -> x0 -> ActTrivial x #