--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/programs/prove1.scala	Sat Oct 04 13:17:18 2014 +0100
@@ -0,0 +1,119 @@
+
+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 {
+  def -> (that: Form) = Imp(this, that)
+}
+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: List[Form], F: Form) {
+  def lhs = Gamma
+  def rhs = F
+}
+
+val Admin = "Admin"
+val Bob = "Bob"
+val Del = Pred("del_file", Nil)
+
+val Gamma = 
+  List( Says(Admin, Del) -> Del,
+        Says(Admin, Says(Bob, Del) -> Del),
+        Says(Bob, Del) )
+
+val goal = Judgement(Gamma, Del) // request: provable or not?
+
+def partitions[A](ls: List[A]): List[(A, List[A])]  = 
+  ls.map (s => (s, ls diff List(s)))
+
+
+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: List[Form], rhs: Form, sc: () => Unit) : Unit = 
+  rhs match {
+    case True => sc ()
+    case False => ()
+    case Imp(f1, f2) => prove(Judgement(f1::lhs, f2), sc) 
+    case Says(p, f1) => prove(Judgement(lhs, f1), sc) 
+    case Or(f1, f2) => 
+      { prove(Judgement(lhs, f1), sc);
+        prove(Judgement(lhs, f2), sc) }
+    case And(f1, f2) => 
+      prove(Judgement(lhs, f1), 
+            () => prove(Judgement(lhs, f2), sc))
+    case _ => { for ((f, lhs_rest) <- partitions(lhs))
+                  prove2(f, lhs_rest, rhs, sc) }
+  }
+
+def prove2(f: Form, lhs_rest: List[Form], rhs: Form, sc: () => Unit) : Unit = 
+  f match {
+    case True => prove(Judgement(lhs_rest, rhs), sc)
+    case False => sc()
+    case And(f1, f2) =>
+      prove(Judgement(f1::f2::lhs_rest, rhs), sc)
+    case Imp(f1, f2) => 
+      prove(Judgement(lhs_rest, f1), 
+            () => prove(Judgement(f2::lhs_rest, rhs), sc))
+    case Or(f1, f2) => 
+      prove(Judgement(f1::lhs_rest, rhs), 
+            () => prove(Judgement(f2::lhs_rest, rhs), sc))
+    case Says(p, Imp(f1, f2)) => 
+      prove(Judgement(lhs_rest, Says(p, f1)), 
+            () => prove(Judgement(Says(p, f2)::lhs_rest, 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 (Judgement (Nil, False -> Del))
+run (Judgement (Nil, True -> Del))
+run (Judgement (Nil, Del -> True))
+
+run (goal)
+
+val Gamma1 = 
+  List( Says(Admin, Says(Bob, Del) -> Del),
+        Says(Bob, Del) )
+
+val goal1 = Judgement(Gamma1, Del) // not provable
+
+run (goal1)
+
+run (Judgement(Nil, Del -> Del))
+
+run (Judgement(Nil, 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 = Says(HoD, Chr_Staff) -> Chr_Staff
+val Policy_Lib = And(Chr_Staff, AtLib) -> Email
+val HoD_says = Says(HoD, Chr_Staff)
+
+run (Judgement (List(AtLib, Policy_HoD, Policy_Lib, HoD_says), Email))
+
+