Data.Monoid.MList

Heterogeneous lists of monoids.

Heterogeneous monoidal lists

The idea of heterogeneous lists has been around for a long time. Here, we adopt heterogeneous lists where the element types are all monoids: this allows us to leave out identity values, so that a heterogeneous list containing only a single non-identity value can be created without incurring constraints due to all the other types, by leaving all the other values out.

type (:::) a l = (Option a, l) infixr 5

(*:) :: a -> l -> a ::: l infixr 5

class MList l where

Type class for heterogeneous monoidal lists, with a single method allowing construction of an empty list.

Minimal complete definition

empty

Methods

empty :: l

The empty heterogeneous list of type l. Of course, empty == mempty, but unlike mempty, empty does not require Monoid constraints on all the elements of l.

Instances

MList ()

Methods

empty :: ()

MList l => MList ((:::) a l)

Methods

empty :: a ::: l

Accessing embedded values

class l :>: a where

The relation l :>: a holds when a is the type of an element in l. For example, (Char ::: Int ::: Bool ::: Nil) :>: Int.

Minimal complete definition

inj, get, alt

Methods

inj :: a -> l

Inject a value into an otherwise empty heterogeneous list.

get :: l -> Option a

Get the value of type a from a heterogeneous list, if there is one.

alt :: (Option a -> Option a) -> l -> l

Alter the value of type a by applying the given function to it.

Instances

(:>:) t a => ((:::) b t) :>: a

Methods

inj :: a -> b ::: t

get :: (b ::: t) -> Option a

alt :: (Option a -> Option a) -> (b ::: t) -> b ::: t

MList t => ((:::) a t) :>: a

Methods

inj :: a -> a ::: t

get :: (a ::: t) -> Option a

alt :: (Option a -> Option a) -> (a ::: t) -> a ::: t

Monoid actions of heterogeneous lists

Monoidal heterogeneous lists may act on one another as you would expect, with each element in the first list acting on each in the second. Unfortunately, coding this up in type class instances is a bit fiddly.

newtype SM m

SM, an abbreviation for "single monoid" (as opposed to a heterogeneous list of monoids), is only used internally to help guide instance selection when defining the action of heterogeneous monoidal lists on each other.

Constructors

SM m

Instances

Show m => Show (SM m)

Methods

showsPrec :: Int -> SM m -> ShowS

show :: SM m -> String

showList :: [SM m] -> ShowS

Action (SM a) ()

Methods

act :: SM a -> () -> ()

(Action a a', Action (SM a) l) => Action (SM a) (Option a', l)

Methods

act :: SM a -> (Option a', l) -> (Option a', l)

Orphan instances

(Action (SM a) l2, Action l1 l2) => Action (a, l1) l2

Methods

act :: (a, l1) -> l2 -> l2