src/HOL/TLA/Memory/MemClerk.ML

adapted to new arithmetic simprocs;

(* 
    File:        MemClerk.ML
    Author:      Stephan Merz
    Copyright:   1997 University of Munich

    RPC-Memory example: Memory clerk specification (theorems and proofs)
*)

val MC_action_defs = 
   [MClkInit_def, MClkFwd_def, MClkRetry_def, MClkReply_def, MClkNext_def];

val MC_temp_defs = [MClkIPSpec_def, MClkISpec_def];

val mem_css = (claset(), simpset());

(* The Clerk engages in an action for process p only if there is an outstanding,
   unanswered call for that process.
*)

qed_goal "MClkidle" MemClerk.thy
   "|- ~$Calling send p & $(cst!p) = #clkA --> ~MClkNext send rcv cst p"
   (fn _ => [ auto_tac (mem_css addsimps2 (Return_def::MC_action_defs)) ]);

qed_goal "MClkbusy" MemClerk.thy
   "|- $Calling rcv p --> ~MClkNext send rcv cst p"
   (fn _ => [ auto_tac (mem_css addsimps2 (MC_action_defs @ [Call_def])) ]);

(* Enabledness of actions *)

qed_goal "MClkFwd_enabled" MemClerk.thy
   "!!p. basevars (rtrner send!p, caller rcv!p, cst!p) ==> \
\        |- Calling send p & ~Calling rcv p & cst!p = #clkA  \
\           --> Enabled (MClkFwd send rcv cst p)"
   (fn _ => [action_simp_tac (simpset() addsimps [MClkFwd_def,Call_def,caller_def,rtrner_def])
                             [exI] [base_enabled,Pair_inject] 1]);

qed_goal "MClkFwd_ch_enabled" MemClerk.thy
   "|- Enabled (MClkFwd send rcv cst p)  -->  \
\      Enabled (<MClkFwd send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p))"
   (fn _ => [auto_tac (mem_css addSEs2 [enabled_mono]
	                       addsimps2 [angle_def,MClkFwd_def])
  	    ]);

qed_goal "MClkReply_change" MemClerk.thy
   "|- MClkReply send rcv cst p --> <MClkReply send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p)"
   (fn _ => [auto_tac (mem_css addsimps2 [angle_def,MClkReply_def]
			       addEs2 [Return_changed])
            ]);

qed_goal "MClkReply_enabled" MemClerk.thy
   "!!p. basevars (rtrner send!p, caller rcv!p, cst!p) ==> \
\        |- Calling send p & ~Calling rcv p & cst!p = #clkB  \
\           --> Enabled (<MClkReply send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p))"
   (fn _ => [action_simp_tac (simpset()) [MClkReply_change RSN (2,enabled_mono)] [] 1,
	     action_simp_tac (simpset() addsimps [MClkReply_def,Return_def,caller_def,rtrner_def])
                             [exI] [base_enabled,Pair_inject] 1
	    ]);

qed_goal "MClkReplyNotRetry" MemClerk.thy
   "|- MClkReply send rcv cst p --> ~MClkRetry send rcv cst p"
   (fn _ => [ auto_tac (mem_css addsimps2 [MClkReply_def,MClkRetry_def]) ]);