Push and Pull for Linear Haskell

Box

The Linear.Box module exports a data type Box defined like this:

data Box r a where { Box :: a %r -> Box r a }

Here, r is the multiplicity, which is either 1 or Many.

Pushable

If we wanted to "push" a multiplicity from the outside of a list onto all the elements of a list, we could define a function to do so.

pushList :: Box r (List a) %1-> List (Box r a)
pushList (Box (Cons car cdr)) = Cons (Box car) (pushList (Box cdr))
pushList (Box Nil) = Nil

More generally, we can define a Pushable typeclass:

class Pushable f where
  push :: Box r (f a) %1-> f (Box r a)

Deriving Pushable

import TH.Pushable

data List a where
  Cons :: a %1-> List a %1-> List a
  Nil  :: List a

$(derivePushable ''List)