grab: Applicative non-linear consumption

The Grab type

A grab consumes some portion (none, part, or all) of its input bag, and returns a residue consisting of the unconsumed input, some monoidal log (e.g. a list of error messages), and some desideratum (the object of desire) produced from the consumed input, or Nothing if the grab failed.

newtype Grab bag residue log desideratum =
  Grab (
    bag -> (residue, log, Maybe desideratum)
  )

Grabs are useful as parsers for inputs such as JSON objects or lists of form parameters, where the input data is not necessarily given linearly in the same order in which we want to consume it.

Applicative composition

A Simple grab (where the bag and residue are the same type) has an Applicative instance.

instance (bag ~ residue, Monoid log) =>
    Applicative (Grab bag residue log)

For example, we can create two simple list grabs, one that grabs multiples of two, and the other that grabs multiples of three:

twos, threes :: Monoid log =>
    Control.Grab.Simple [Integer] log [Integer]
twos   = partition (Data.List.partition (\x -> mod x 2 == 0))
threes = partition (Data.List.partition (\x -> mod x 3 == 0))

λ> runGrabMaybe ((,) <$> twos @() <*> threes @()) [1..10]
Just ([2,4,6,8,10],[3,9])

Notice that the second part of the resulting tuple contains only the odd multiples of three. Because twos runs first, it consumes 6 before the threes can get it.

Pipeline composition

a / b is a pipeline of two grabs, where the desideratum from a is the bag for b. . > (/) :: Semigroup log > => Grab bag residue log x > -> Grab x _residue log desideratum > -> Grab bag residue log desideratum

λ> runGrabMaybe (twos @() / threes @()) [1..10]
Just [6]

λ> runGrabMaybe ((,) <$> (twos @() / threes @()) <*> threes @()) [1..10]
Just ([6],[3,9])

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• chris_martin, Monoid_Mary

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