fun cat nil r = r
  | cat (a::l) r = a :: cat l r

fun rev nil = nil
  | rev (a::l) = cat (rev l) (a::nil)

fun iterev nil r = r
  | iterev (a::l) r = iterev l (a::r)

fun rev' nil f = f nil
  | rev' (a::r) f = rev' r (fn l => a :: f l);

fun addexp (n: int) (IdExp i) = IdExp i
  | addexp n (NumExp i) = NumExp (n+i)
  | addexp n (OpExp (e1,b,e2))=  OpExp (addexp n e1, b, addexp n e2) 
  | addexp n (EseqExp(s,e)) = EseqExp (addstm n s, addexp n e)
and addstm n (CompoundStm(s1,s2)) = CompoundStm(addstm n s1, addstm n s2)
  | addstm n (AssignStm(i,e)) = AssignStm(i, addexp n e)
  | addstm n (PrintStm (el)) = PrintStm (map (addexp n) el)

fun addstm n = 
  let fun f (IdExp i) = IdExp i
        | f(NumExp i) = NumExp (n+i)
        | f (OpExp (e1,b,e2))=  OpExp (f e1, b, f e2) 
        | f (EseqExp(s,e)) = EseqExp (g s, f e)
      and g (CompoundStm(s1,s2)) = CompoundStm(g s1, g s2)
        | g (AssignStm(i,e)) = AssignStm(i, f e)
        | g (PrintStm (el)) = PrintStm (map f el)
   in g
  end