jonathanfishbein1 / numeric-typeclasses / Monoid

Monoid typeclass definition and its instances for basic types.

Definition


type alias Monoid a =
{ semigroup : Semigroup a
, identity : a
, concat : List a -> a 
}

Explicit typeclass which implements monoid operations for type a.

Construction utilities

identityAndConcat : a -> (List a -> a) -> Monoid a

Construct an instance by specifying identity value and a concatenation operation.

semigroupAndIdentity : Semigroup a -> a -> Monoid a

Construct an instance by specifying a semigroup instance and an identity value.

appendable : appendable -> Monoid appendable

Construct an instance for any type which satisfies Elm's appendable magic constraint, by providing an identity value.

Instance transformation utilities

map : (a -> b) -> (b -> a) -> Monoid a -> Monoid b

Map over the owner type of an instance to produce a new instance.

You need to provide both a covariant and a contravariant mapping (i.e., (a -> b) and (b -> a)).

Instances

string : Monoid String

Instance for strings under the appending operation.

maybeFirst : Monoid (Maybe a)

Instance for maybe, which chooses the first Just value.

list : Monoid (List a)

Instance for list under concatenation.

cmd : Monoid (Platform.Cmd.Cmd msg)

Instance for commands under the batch operation.

sub : Monoid (Platform.Sub.Sub msg)

Instance for subscriptions under the batch operation.

task : Monoid a -> Monoid (Task x a)

Instance for tasks, which sequentially executes them and groups the results.

composition : Monoid (a -> a)

Instance for a -> a function

setDifference : Monoid (Set comparable)

Instance for set under the difference operation.

setUnion : Monoid (Set comparable)

Instance for set under the union operation.

all : Monoid Basics.Bool

Instance for all

any : Monoid Basics.Bool

Instance for any

exclusiveOr : Monoid Basics.Bool

Instance for exclusiveOr

intProduct : Monoid Basics.Int

Instance for integers under the multiplication operation.

intSum : Monoid Basics.Int

Instance for integers under the sum operation.

modularArithmetic : Basics.Int -> Monoid Basics.Int

Instance for modularArithmetic

numberProduct : Monoid number

Construct an instance for any type which satisfies Elm's number magic constraint. Implements multiplication.

numberSum : Monoid number

Construct an instance for any type which satisfies Elm's number magic constraint. Implements sum.

unit : Monoid ()

Instance for trivial monoid