(*   transitive.ml
The function transitive
 accepts truth values for P, Q, and R.
 It returns a list of 4 strings, each
 of which is either "Yes" or "No".
 The first is "Yes" if P -> Q.
  "  second "   "   "  Q -> R.
  "  third  "   "   "  P -> R.
 and the fourth is "Yes" if
  ( (P -> Q) ^ (Q -> R) ) -> (P -> R)
 Note that the fourth is always "Yes".

*)

fun yesno(true) = "Yes" |
    yesno(false) = "No";

fun transitive(p, q, r) =
 let val first  = not p orelse q;
     val second = not q orelse r;
     val third  = not p orelse r
 in
     map yesno
         [first,second,third,
          (not (first andalso second)) orelse third]
 end

(*
Sample call:
transitive(true, true, true);
  *)