functor T_fp (D : G4IP) :> TEST =
struct
  exception Error

  val ==> = P.Implies
  val & = P.And
  val v = P.Or
  val f = P.False
  val t = P.True
  val ~ = P.Not
  val <=> = fn (A,B) => P.And (P.Implies (A, B), P.Implies (B, A))
  val <== = fn (A,B) => P.Implies (B, A)

  infix 9 &
  infix 8 v
  infixr 7 ==> 
  infix 7 <==
  infix 6 <=>
  val A = P.Atom("A")
  val B = P.Atom("B")
  val C = P.Atom("C")
  val D = P.Atom("D")

  fun cfalse (A) = if D.decide A then raise Error else ()
  fun ctrue (A) = if D.decide A then () else raise Error

  val ex281 = (A ==> (B ==> C)) <=> ((A & B) ==> C);        val _ = ctrue ex281;
  val ex282 = (A ==> (B & C)) <=> ((A ==> B) & (A ==> C));  val _ = ctrue ex282;
  val ex283a = (A ==> (B v C)) ==> ((A ==> B) v (A ==> C)); val _ = cfalse ex283a;
  val ex283b = (A ==> (B v C)) <== ((A ==> B) v (A ==> C)); val _ = ctrue ex283b;
  val ex284a = ((A ==> B) ==> C) ==> ((A v B) & (B ==> C)); val _ = cfalse ex284a;
  val ex284b = ((A ==> B) ==> C) <== ((A v B) & (B ==> C)); val _ = ctrue ex284b;
  val ex285 = ((A v B) ==> C) <=> ((A ==> C) & (B ==> C));  val _ = ctrue ex285;
  val ex286 = (A & (B v C)) <=> ((A & B) v (A & C));        val _ = ctrue ex286;
  val ex287 = (A v (B & C)) <=> ((A v B) & (A v C));        val _ = ctrue ex287;

  val ex291a = ~ (A & B) ==> ~ A v ~ B; val _ = cfalse ex291a;
  val ex291b = ~ (A & B) <== ~ A v ~ B; val _ = ctrue ex291b;
  val ex292 = ~ (A v B) <=> ~ A & ~ B;  val _ = ctrue ex292;
  val ex293a = ~ (A ==> B) ==> A & ~ B; val _ = cfalse ex293a;
  val ex293b = ~ (A ==> B) <== A & ~ B; val _ = ctrue ex293b;
  val ex294a = ~ (~ A) ==> A;		val _ = cfalse ex294a;
  val ex294b = ~ (~ A) <== A;           val _ = ctrue ex294b;
  val ex295 = ~ t <=> f;		val _ = ctrue ex295;
  val ex296 = ~ f <=> t;		val _ = ctrue ex296;

  val t1 = ~ (~ (~ A)) <=> ~ A;         val _ = ctrue t1;
  val t2 = (A ==> B) ==> (B ==> C) ==> (C ==> D) ==> (A ==> D);
                                        val _ = ctrue t2;

  val k = (A ==> (B ==> A));		val _ = ctrue k;
  val s = (A ==> B) ==> (A ==> (B ==> C)) ==> (A ==> C);
                                        val _ = ctrue s;
  val p = ((A ==> B) ==> A) ==> A;      val _ = cfalse p;

  val _ = print "Tests passed\n"

end;

structure X = T_fp (G_fp);