#include "share/atspre_staload_libats_ML.hats"
#include "libats/ML/SATS/SHARE/monad.hats"

datatype either(a: t@ype, b: t@ype+) =
  | left of a
  | right of b

fun {a:t@ype}{b:t@ype+} eq_either_either ( x : either(a, INV(b))
                                         , y : either(a, b)
                                         ) : bool

fun {a:t@ype}{b:t@ype+} neq_either_either ( x : either(a, INV(b))
                                          , y : either(a, b)
                                          ) : bool

overload = with eq_either_either

overload != with neq_either_either

fun lefts {a:t@ype}{b:t@ype+}{n:int} (x : list(either(a,b), n)) :
  [ m : int | m <= n ] list(a, m)

fun rights {a:t@ype}{b:t@ype+}{n:int} (x : list(either(a,b), n)) :
  [ m : int | m <= n ] list(b, m)

fun either_ {a:t@ype}{b:t@ype+}{c:t@ype} ( f : a -> c
                                         , g : b -> c
                                         , x : either(a, b)
                                         ) : c

fun is_left {a:t@ype}{b:t@ype+} (x : either(a, b)) : bool

fun is_right {a:t@ype}{b:t@ype+} (x : either(a, b)) : bool

fun from_right {a:t@ype}{b:t@ype+} (x : b, y : either(a, b)) : b

fun from_left {a:t@ype}{b:t@ype+} (x : a, y : either(a, b)) : a