Theory RPC

Up to index of Isabelle/HOL/TLA/Memory

theory RPC
imports RPCParameters ProcedureInterface Memory
uses [RPC.ML]
begin

(*
    File:        RPC.thy
    ID:          $Id: RPC.thy,v 1.5 2005/09/07 18:22:43 wenzelm Exp $
    Author:      Stephan Merz
    Copyright:   1997 University of Munich

    Theory Name: RPC
    Logic Image: TLA

    RPC-Memory example: RPC specification
*)

theory RPC
imports RPCParameters ProcedureInterface Memory
begin

types
  rpcSndChType  = "(rpcOp,Vals) channel"
  rpcRcvChType  = "memChType"
  rpcStType     = "(PrIds => rpcState) stfun"

consts
  (* state predicates *)
  RPCInit      :: "rpcRcvChType => rpcStType => PrIds => stpred"

  (* actions *)
  RPCFwd     :: "rpcSndChType => rpcRcvChType => rpcStType => PrIds => action"
  RPCReject  :: "rpcSndChType => rpcRcvChType => rpcStType => PrIds => action"
  RPCFail    :: "rpcSndChType => rpcRcvChType => rpcStType => PrIds => action"
  RPCReply   :: "rpcSndChType => rpcRcvChType => rpcStType => PrIds => action"
  RPCNext    :: "rpcSndChType => rpcRcvChType => rpcStType => PrIds => action"

  (* temporal *)
  RPCIPSpec   :: "rpcSndChType => rpcRcvChType => rpcStType => PrIds => temporal"
  RPCISpec   :: "rpcSndChType => rpcRcvChType => rpcStType => temporal"

defs
  RPCInit_def:       "RPCInit rcv rst p == PRED ((rst!p = #rpcA) & ~Calling rcv p)"

  RPCFwd_def:        "RPCFwd send rcv rst p == ACT
                         $(Calling send p)
                         & $(rst!p) = # rpcA
                         & IsLegalRcvArg<arg<$(send!p)>>
                         & Call rcv p RPCRelayArg<arg<send!p>>
                         & (rst!p)$ = # rpcB
                         & unchanged (rtrner send!p)"

  RPCReject_def:     "RPCReject send rcv rst p == ACT
                           $(rst!p) = # rpcA
                         & ~IsLegalRcvArg<arg<$(send!p)>>
                         & Return send p #BadCall
                         & unchanged ((rst!p), (caller rcv!p))"

  RPCFail_def:       "RPCFail send rcv rst p == ACT
                           ~$(Calling rcv p)
                         & Return send p #RPCFailure
                         & (rst!p)$ = #rpcA
                         & unchanged (caller rcv!p)"

  RPCReply_def:      "RPCReply send rcv rst p == ACT
                           ~$(Calling rcv p)
                         & $(rst!p) = #rpcB
                         & Return send p res<rcv!p>
                         & (rst!p)$ = #rpcA
                         & unchanged (caller rcv!p)"

  RPCNext_def:       "RPCNext send rcv rst p == ACT
                        (  RPCFwd send rcv rst p
                         | RPCReject send rcv rst p
                         | RPCFail send rcv rst p
                         | RPCReply send rcv rst p)"

  RPCIPSpec_def:     "RPCIPSpec send rcv rst p == TEMP
                           Init RPCInit rcv rst p
                         & [][ RPCNext send rcv rst p ]_(rst!p, rtrner send!p, caller rcv!p)
                         & WF(RPCNext send rcv rst p)_(rst!p, rtrner send!p, caller rcv!p)"

  RPCISpec_def:      "RPCISpec send rcv rst == TEMP (ALL p. RPCIPSpec send rcv rst p)"

ML {* use_legacy_bindings (the_context ()) *}

end

theorem RPCidle:

  |- ¬ $Calling send p --> ¬ RPCNext send rcv rst p

theorem RPCbusy:

  |- $Calling rcv p ∧ $(rst!p) = #rpcB --> ¬ RPCNext send rcv rst p

theorem RPCFail_vis:

  |- RPCFail send rcv rst p -->
     <RPCNext send rcv rst p>_(rst!p, rtrner send!p, caller rcv!p)

theorem RPCFail_Next_enabled:

  |- Enabled RPCFail send rcv rst p -->
     Enabled (<RPCNext send rcv rst p>_(rst!p, rtrner send!p, caller rcv!p))

theorem RPCFail_enabled:

  basevars (rtrner send!p, caller rcv!p, rst!p)
  ==> |- ¬ Calling rcv p ∧ Calling send p --> Enabled RPCFail send rcv rst p

theorem RPCReply_enabled:

  basevars (rtrner send!p, caller rcv!p, rst!p)
  ==> |- ¬ Calling rcv p ∧ Calling send prst!p = #rpcB -->
         Enabled RPCReply send rcv rst p