P'' implementation in under 30 lines of Haskell

pll.hs

data P = R | L | Seq P P | Loop P

data Tape = Tape [Int] Int [Int]

empty :: Tape
empty = Tape (repeat 0) 0 (repeat 0)

left :: Tape -> Tape
left (Tape (l:ls) v rs) = Tape ls l (v:rs)

right :: Tape -> Tape
right (Tape ls v (r:rs)) = Tape (v:ls) r rs

peek :: Tape -> Int
peek (Tape _ v _) = v

edit :: (Int -> Int) -> Tape -> Tape
edit f (Tape ls v rs) = Tape ls (f v) rs

run :: Int -> P -> Tape -> Tape
run n R t = right t
run n L t = left $ edit ((`mod`n) . (+1)) t
run n (Seq p q) t = run n q $ run n p t
run n (Loop  p) t = if peek t == 0
  then t
  else run n (Seq p $ Loop p) t

eval :: P -> Int
eval p = peek $ run 256 p empty