A program defined using 'Cofree'

cofree.hs

{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE UndecidableInstances #-}

data Program f a = Program {
    annotation :: a
  , running    :: f (Program f a)
  }

deriving instance (Show a, Show (f (Program f a))) => Show (Program f a)

data Instruction r =
    Increment r
  | Decrement r
  | Terminate
  deriving (Functor, Show)

remaining :: Program Instruction Int -> Int
remaining = loop where
  loop (Program a f) = case f of
    Increment p -> succ (loop p)
    Decrement p -> succ (loop p)
    Terminate   -> succ a

increment :: Program Instruction Int -> Program Instruction Int
increment p = Program (remaining p) (Increment p)

decrement :: Program Instruction Int -> Program Instruction Int
decrement p = Program (remaining p) (Decrement p)

terminate :: Program Instruction Int
terminate = Program 0 Terminate

program :: Program Instruction Int
program =
    increment
  . increment
  . decrement
  $ terminate