File MemClerk.ML (Isabelle2005: October 2005)

# File MemClerk.ML

    (*
        File:        MemClerk.ML
        ID:          $Id: MemClerk.ML,v 1.6 2005/09/07 18:22:41 wenzelm Exp $
        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.
    *)
    Goal "|- ~$Calling send p & $(cst!p) = #clkA --> ~MClkNext send rcv cst p";
    by (auto_tac (mem_css addsimps2 (Return_def::MC_action_defs)));
    qed "MClkidle";

    Goal "|- $Calling rcv p --> ~MClkNext send rcv cst p";
    by (auto_tac (mem_css addsimps2 (Call_def::MC_action_defs)));
    qed "MClkbusy";

    (* Enabledness of actions *)

    Goal "!!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)";
    by (action_simp_tac (simpset() addsimps [MClkFwd_def,Call_def,caller_def,rtrner_def])
                        [exI] [base_enabled,Pair_inject] 1);
    qed "MClkFwd_enabled";

    Goal "|- Enabled (MClkFwd send rcv cst p)  -->  \
    \        Enabled (<MClkFwd send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p))";
    by (auto_tac (mem_css addSEs2 [enabled_mono] addsimps2 [angle_def,MClkFwd_def]));
    qed "MClkFwd_ch_enabled";

    Goal "|- MClkReply send rcv cst p --> \
    \        <MClkReply send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p)";
    by (auto_tac (mem_css addsimps2 [angle_def,MClkReply_def]
                          addEs2 [Return_changed]));
    qed "MClkReply_change";

    Goal "!!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))";
    by (action_simp_tac (simpset()) [MClkReply_change RSN (2,enabled_mono)] [] 1);
    by (action_simp_tac (simpset() addsimps [MClkReply_def,Return_def,caller_def,rtrner_def])
                        [exI] [base_enabled,Pair_inject] 1);
    qed "MClkReply_enabled";

    Goal "|- MClkReply send rcv cst p --> ~MClkRetry send rcv cst p";
    by (auto_tac (mem_css addsimps2 [MClkReply_def,MClkRetry_def]));
    qed "MClkReplyNotRetry";