open import Pervasives

type M 's 'a = 's -> ('a * 's)

val return : forall 's 'a. 'a -> M 's 'a
let return a = fun s -> (a,s)

val bind : forall 's 'a 'b. M 's 'a -> ('a -> M 's 'b) -> M 's 'b
let bind m f s = let (a,s') = m s in f a s'

let (>>=) = bind
let (>>) m n = m >>= fun _ -> n


val foreach_inc : forall 's 'vars. (nat * nat * nat) -> (nat -> 'vars -> M 's 'vars) ->
                  'vars -> M 's 'vars
let rec foreach_inc (i,stop,by) body vars = 
  if i <= stop
  then (body i vars >>= fun vars -> foreach_inc (i + by,stop,by) body vars)
  else return vars


val foreach_dec : forall 's 'vars. (nat * nat * nat) -> (nat -> 'vars -> M 's 'vars) ->
                  'vars -> M 's 'vars
let rec foreach_dec (i,stop,by) body vars = 
  if i >= stop
  then (body i vars >>= fun vars -> foreach_dec (i - by,stop,by) body vars)
  else return vars