src/HOL/UNITY/Comp/TimerArray.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/UNITY/Comp/TimerArray.ML	Mon Mar 05 15:32:54 2001 +0100
@@ -0,0 +1,53 @@
+(*  Title:      HOL/UNITY/TimerArray.thy
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1998  University of Cambridge
+
+A trivial example of reasoning about an array of processes
+*)
+
+Addsimps [Timer_def RS def_prg_Init];
+program_defs_ref := [Timer_def];
+
+Addsimps [count_def, decr_def];
+
+(*Demonstrates induction, but not used in the following proof*)
+Goal "Timer : UNIV leadsTo {s. count s = 0}";
+by (res_inst_tac [("f", "count")] lessThan_induct 1);
+by (Simp_tac 1);
+by (case_tac "m" 1);
+by (force_tac (claset() addSIs [subset_imp_leadsTo], simpset()) 1);
+by (ensures_tac "decr" 1);
+qed "Timer_leadsTo_zero";
+
+Goal "Timer : preserves snd";
+by (rtac preservesI 1);
+by (constrains_tac 1);
+qed "Timer_preserves_snd";
+AddIffs [Timer_preserves_snd];
+
+Addsimps [PLam_stable];
+
+Goal "finite I \
+\     ==> (plam i: I. Timer) : UNIV leadsTo {(s,uu). ALL i:I. s i = 0}";
+by (eres_inst_tac [("A'1", "%i. lift_set i ({0} <*> UNIV)")]
+    (finite_stable_completion RS leadsTo_weaken) 1);
+by Auto_tac;
+(*Safety property, already reduced to the single Timer case*)
+by (constrains_tac 2);
+(*Progress property for the array of Timers*)
+by (res_inst_tac [("f", "sub i o fst")] lessThan_induct 1);
+by (case_tac "m" 1);
+(*Annoying need to massage the conditions to have the form (... <*> UNIV)*)
+by (auto_tac (claset() addIs [subset_imp_leadsTo], 
+	      simpset() addsimps [insert_absorb, lessThan_Suc RS sym,
+				  lift_set_Un_distrib RS sym,
+				  Times_Un_distrib1 RS sym,
+				  Times_Diff_distrib1 RS sym]));
+by (rename_tac "n" 1);
+by (rtac PLam_leadsTo_Basis 1);
+by (auto_tac (claset(), simpset() addsimps [lessThan_Suc RS sym]));
+by (constrains_tac 1);
+by (res_inst_tac [("act", "decr")] transientI 1);
+by (auto_tac (claset(), simpset() addsimps [Timer_def]));
+qed "TimerArray_leadsTo_zero";