--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/programs/prove2.scala	Tue Nov 12 09:57:22 2013 +0000
@@ -0,0 +1,130 @@
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+
+abstract class Term 
+case class Var(s: String) extends Term 
+case class Const(s: String) extends Term 
+case class Fun(s: String, ts: List[Term]) extends Term
+
+abstract class Form
+case object True extends Form
+case object False extends Form
+case class Pred(s: String, ts: List[Term]) extends Form
+case class Imp(f1: Form, f2: Form) extends Form
+case class Says(p: String, f: Form) extends Form 
+case class And(f1: Form, f2: Form) extends Form 
+case class Or(f1: Form, f2: Form) extends Form 
+
+case class Judgement(gamma: Set[Form], f: Form) {
+  def lhs = gamma
+  def rhs = f
+}
+
+// some syntactic sugar
+implicit def FormOps(f1: Form) = new {
+  def -> (f2: Form) = Imp(f1, f2)
+}
+implicit def StringOps(p: String) = new {
+  def says (f: Form) = Says(p, f)
+}
+implicit def SetFormOps(gamma: Set[Form]) = new {
+  def |- (f: Form) : Judgement = Judgement(gamma, f)
+}
+
+val Admin = "Admin"
+val Bob = "Bob"
+val Del = Pred("del_file", Nil)
+
+val Gamma: Set[Form] = 
+  Set( (Admin says Del) -> Del,
+       (Admin says ((Bob says Del) -> Del)),
+       (Bob says Del) )
+
+val goal = Gamma |- Del // request: provable or not?
+
+def partitions[A](s: Set[A]): Set[(A, Set[A])]  = 
+  s.map (e => (e, s - e))
+
+
+def prove(j: Judgement, sc: () => Unit) : Unit = {
+  if (j.lhs.contains(j.rhs))  sc ()   // Axiom rule 
+  else prove1(j.lhs, j.rhs, sc) 
+}
+
+def prove1(lhs: Set[Form], rhs: Form, sc: () => Unit) : Unit = 
+  rhs match {
+    case True => sc ()
+    case False => ()
+    case Imp(f1, f2) => prove(lhs + f1 |- f2, sc) 
+    case Says(p, f1) => prove(lhs |- f1, sc) 
+    case Or(f1, f2) => 
+      { prove(lhs |- f1, sc);
+        prove(lhs |- f2, sc) }
+    case And(f1, f2) => 
+      prove(lhs |- f1, 
+            () => prove(lhs |- f2, sc))
+    case _ => { for ((f, lhs_rest) <- partitions(lhs))
+                  prove2(f, lhs_rest, rhs, sc) }
+  }
+
+def prove2(f: Form, lhs_rest: Set[Form], rhs: Form, sc: () => Unit) : Unit = 
+  f match {
+    case True => prove(lhs_rest |- rhs, sc)
+    case False => sc ()
+    case And(f1, f2) =>
+      prove(lhs_rest + f1 + f2 |- rhs, sc)
+    case Imp(f1, f2) => 
+      prove(lhs_rest |- f1, 
+            () => prove(lhs_rest + f2 |- rhs, sc))
+    case Or(f1, f2) => 
+      prove(lhs_rest + f1 |- rhs, 
+            () => prove(lhs_rest + f2 |- rhs, sc))
+    case Says(p, Imp(f1, f2)) => 
+      prove(lhs_rest |- Says(p, f1), 
+            () => prove(lhs_rest + Says(p, f2) |- rhs, sc)) 
+    case _ => ()
+  }
+
+  
+
+// function that calls prove and returns immediately once a proof is found
+def run (j : Judgement) : Unit = {
+  try { 
+    def sc () = { println ("Yes!"); throw new Exception }
+    prove(j, sc) 
+  }
+  catch { case e: Exception => () }
+} 
+
+run (Set[Form]() |- False -> Del)
+run (Set[Form]() |- True -> Del)
+run (Set[Form]() |- Del -> True)
+
+run (goal)
+
+val Gamma1 : Set[Form] = 
+  Set( Admin says ((Bob says Del) -> Del),
+       Bob says Del )
+
+val goal1 = Gamma1 |- Del // not provable
+
+run (goal1)
+
+run (Set[Form]() |- (Del -> Del))
+
+run (Set[Form]() |- (Del -> Or(False, Del)))
+
+
+val Chr = "Christian"
+val HoD = "Peter"
+val Email = Pred("may_btain_email", List(Const(Chr)))
+val AtLib = Pred("is_at_library", List(Const(Chr)))
+val Chr_Staff = Pred("is_staff", List(Const(Chr)))
+
+val Policy_HoD = (HoD says Chr_Staff) -> Chr_Staff
+val Policy_Lib = And(Chr_Staff, AtLib) -> Email
+val HoD_says = HoD says Chr_Staff
+
+run (Set[Form](AtLib, Policy_HoD, Policy_Lib, HoD_says) |- Email)
+
+