src/HOL/UNITY/Simple/Channel.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/UNITY/Simple/Channel.ML	Mon Mar 05 15:47:11 2001 +0100
@@ -0,0 +1,57 @@
+(*  Title:      HOL/UNITY/Channel
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1998  University of Cambridge
+
+Unordered Channel
+
+From Misra, "A Logic for Concurrent Programming" (1994), section 13.3
+*)
+
+(*None represents "infinity" while Some represents proper integers*)
+Goalw [minSet_def] "minSet A = Some x --> x : A";
+by (Simp_tac 1);
+by (fast_tac (claset() addIs [LeastI]) 1);
+qed_spec_mp "minSet_eq_SomeD";
+
+Goalw [minSet_def] " minSet{} = None";
+by (Asm_simp_tac 1);
+qed_spec_mp "minSet_empty";
+Addsimps [minSet_empty];
+
+Goalw [minSet_def] "x:A ==> minSet A = Some (LEAST x. x: A)";
+by Auto_tac;
+qed_spec_mp "minSet_nonempty";
+
+Goal "F : (minSet -` {Some x}) leadsTo (minSet -` (Some`greaterThan x))";
+by (rtac leadsTo_weaken 1);
+by (res_inst_tac [("x1","x")] ([UC2, UC1] MRS psp) 1);
+by Safe_tac;
+by (auto_tac (claset() addDs [minSet_eq_SomeD], 
+	      simpset() addsimps [linorder_neq_iff]));
+qed "minSet_greaterThan";
+
+(*The induction*)
+Goal "F : (UNIV-{{}}) leadsTo (minSet -` (Some`atLeast y))";
+by (rtac leadsTo_weaken_R 1);
+by (res_inst_tac  [("l", "y"), ("f", "the o minSet"), ("B", "{}")]
+     greaterThan_bounded_induct 1);
+by Safe_tac;
+by (ALLGOALS Asm_simp_tac);
+by (dtac minSet_nonempty 2);
+by (Asm_full_simp_tac 2);
+by (rtac (minSet_greaterThan RS leadsTo_weaken) 1);
+by Safe_tac;
+by (ALLGOALS Asm_full_simp_tac);
+by (dtac minSet_nonempty 1);
+by (Asm_full_simp_tac 1);
+val lemma = result();
+
+
+Goal "!!y::nat. F : (UNIV-{{}}) leadsTo {s. y ~: s}";
+by (rtac (lemma RS leadsTo_weaken_R) 1);
+by (Clarify_tac 1);
+by (ftac minSet_nonempty 1);
+by (auto_tac (claset() addDs [Suc_le_lessD, not_less_Least], 
+	      simpset()));
+qed "Channel_progress";