(*
   CSCI 3155: Project 1: Boolean Formulae: Tests
   PRACTICE
*)

val test_to_nnf1 =
    Or (True, Not (Var "x")) = to_nnf (Not (And (False, Var "x")))

fun test_sat (f: formula) (expected: bool) : bool =
    case sat f of
      NONE => expected = false
    | SOME _ => expected = true

val f1 =
    And (Not (Var "a"),
	 Or (Var "a",
	     Forall ("x", Or (Var "b", Var "x"))))
val test_sat1 =
    test_sat f1 true

(* pad : int -> vec -> vec
   Pads v to length n with Falses. *)
fun pad (n: int) (v: vec) : vec =
    let
	fun pad' (n, nil, acc) =
	    if n <= 0 then acc else pad' (n - 1, nil, False :: acc)
	  | pad' (n, h :: t, acc) = pad' (n - 1, t, h :: acc)
    in
	List.rev (pad' (n, v, []))
    end

(* vecvar : string -> int -> vec
   Create a vector consisting of Vars. *)
fun vecvar (prefix: string) (n: int) : vec =
    List.tabulate (n, fn i => Var (prefix ^ (Int.toString i)))

val test_is_magic1 =
    let
	val $ = (pad 4) o vec_of_int
	val var = vecvar "b" 4
    in
	case sat (is_magic [$8, $1, $6,
			    $3, var, $7,
			    $4, $9, $2]) of
	    NONE => false
	  | SOME a => (int_of_vec (subst a var)) = 5
    end