Data.Agreement

A simple data structure helping us ask questions of the following sort: "does all this data have the same BLANK and if so what is it?"

For example:

doTheseHaveTheSameLength :: [String] -> String
doTheseHaveTheSameLength l = case foldMap (Somebody . length) of
  Somebody n -> "They all have length " <> show n
  Nobody     -> "The lengths differ"
  Anybody    -> "You didn't give me any strings"

This can of course be done with `Maybe (Maybe x)` instead, but doing so runs the risk of getting confused: which is Nothing and which is `Just Nothing`?

Unfortunately, there are two Applicative instances.

One is easy to motivate intrinsically. If we think of Anybody as an empty list, Somebody as a singleton list, and Nobody as a multi-element list, and think of the applicative instance on as corresponding to the cartesian product, then we get an Applicative instance with

Anybody <*> Anybody = Anybody
Anybody <*> Nobody = Nobody

This however cannot possibly correspond to a Monad instance (if the first argument of >>= is Anybody, there's no way of inspecting the second). We thus choose another, which does.

Documentation

data Agreement a

We have the following constructors:

• Somebody is a consistent choice of an element.
• Nobody is an inconsistent choice.
• Anybody is a failure to make any choice.

Constructors

Anybody

Somebody a

Nobody

Instances

Applicative Agreement

Not the only possible instance: see introduction

Defined in Data.Agreement

Methods

pure :: a -> Agreement a

(<*>) :: Agreement (a -> b) -> Agreement a -> Agreement b

liftA2 :: (a -> b -> c) -> Agreement a -> Agreement b -> Agreement c

(*>) :: Agreement a -> Agreement b -> Agreement b

(<*) :: Agreement a -> Agreement b -> Agreement a

Functor Agreement

Defined in Data.Agreement

Methods

fmap :: (a -> b) -> Agreement a -> Agreement b

(<$) :: a -> Agreement b -> Agreement a

Monad Agreement

Defined in Data.Agreement

Methods

(>>=) :: Agreement a -> (a -> Agreement b) -> Agreement b

(>>) :: Agreement a -> Agreement b -> Agreement b

return :: a -> Agreement a

Eq a => Monoid (Agreement a)

Defined in Data.Agreement

Methods

mempty :: Agreement a

mappend :: Agreement a -> Agreement a -> Agreement a

mconcat :: [Agreement a] -> Agreement a

Eq a => Semigroup (Agreement a)

Defined in Data.Agreement

Methods

(<>) :: Agreement a -> Agreement a -> Agreement a

sconcat :: NonEmpty (Agreement a) -> Agreement a

stimes :: Integral b => b -> Agreement a -> Agreement a

Show a => Show (Agreement a)

Defined in Data.Agreement

Methods

showsPrec :: Int -> Agreement a -> ShowS

show :: Agreement a -> String

showList :: [Agreement a] -> ShowS

Eq a => Eq (Agreement a)

Defined in Data.Agreement

Methods

(==) :: Agreement a -> Agreement a -> Bool

(/=) :: Agreement a -> Agreement a -> Bool

Ord a => Ord (Agreement a)

Defined in Data.Agreement

Methods

compare :: Agreement a -> Agreement a -> Ordering

(<) :: Agreement a -> Agreement a -> Bool

(<=) :: Agreement a -> Agreement a -> Bool

(>) :: Agreement a -> Agreement a -> Bool

(>=) :: Agreement a -> Agreement a -> Bool

max :: Agreement a -> Agreement a -> Agreement a

min :: Agreement a -> Agreement a -> Agreement a

getSomebody :: Agreement a -> Maybe a

This picks out consistent choices as Just.