(* Title: HOL/TLA/Memory/MemClerk.thy
Author: Stephan Merz, University of Munich
*)
section {* RPC-Memory example: specification of the memory clerk *}
theory MemClerk
imports Memory RPC MemClerkParameters
begin
(* The clerk takes the same arguments as the memory and sends requests to the RPC *)
type_synonym mClkSndChType = "memChType"
type_synonym mClkRcvChType = "rpcSndChType"
type_synonym mClkStType = "(PrIds => mClkState) stfun"
definition
(* state predicates *)
MClkInit :: "mClkRcvChType => mClkStType => PrIds => stpred"
where "MClkInit rcv cst p = PRED (cst!p = #clkA & ~Calling rcv p)"
definition
(* actions *)
MClkFwd :: "mClkSndChType => mClkRcvChType => mClkStType => PrIds => action"
where "MClkFwd send rcv cst p = ACT
$Calling send p
& $(cst!p) = #clkA
& Call rcv p MClkRelayArg<arg<send!p>>
& (cst!p)$ = #clkB
& unchanged (rtrner send!p)"
definition
MClkRetry :: "mClkSndChType => mClkRcvChType => mClkStType => PrIds => action"
where "MClkRetry send rcv cst p = ACT
$(cst!p) = #clkB
& res<$(rcv!p)> = #RPCFailure
& Call rcv p MClkRelayArg<arg<send!p>>
& unchanged (cst!p, rtrner send!p)"
definition
MClkReply :: "mClkSndChType => mClkRcvChType => mClkStType => PrIds => action"
where "MClkReply send rcv cst p = ACT
~$Calling rcv p
& $(cst!p) = #clkB
& Return send p MClkReplyVal<res<rcv!p>>
& (cst!p)$ = #clkA
& unchanged (caller rcv!p)"
definition
MClkNext :: "mClkSndChType => mClkRcvChType => mClkStType => PrIds => action"
where "MClkNext send rcv cst p = ACT
( MClkFwd send rcv cst p
| MClkRetry send rcv cst p
| MClkReply send rcv cst p)"
definition
(* temporal *)
MClkIPSpec :: "mClkSndChType => mClkRcvChType => mClkStType => PrIds => temporal"
where "MClkIPSpec send rcv cst p = TEMP
Init MClkInit rcv cst p
& [][ MClkNext send rcv cst p ]_(cst!p, rtrner send!p, caller rcv!p)
& WF(MClkFwd send rcv cst p)_(cst!p, rtrner send!p, caller rcv!p)
& SF(MClkReply send rcv cst p)_(cst!p, rtrner send!p, caller rcv!p)"
definition
MClkISpec :: "mClkSndChType => mClkRcvChType => mClkStType => temporal"
where "MClkISpec send rcv cst = TEMP (ALL p. MClkIPSpec send rcv cst p)"
lemmas MC_action_defs =
MClkInit_def MClkFwd_def MClkRetry_def MClkReply_def MClkNext_def
lemmas MC_temp_defs = MClkIPSpec_def MClkISpec_def
(* The Clerk engages in an action for process p only if there is an outstanding,
unanswered call for that process.
*)
lemma MClkidle: "|- ~$Calling send p & $(cst!p) = #clkA --> ~MClkNext send rcv cst p"
by (auto simp: Return_def MC_action_defs)
lemma MClkbusy: "|- $Calling rcv p --> ~MClkNext send rcv cst p"
by (auto simp: Call_def MC_action_defs)
(* Enabledness of actions *)
lemma MClkFwd_enabled: "!!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 (tactic {* action_simp_tac (@{context} addsimps [@{thm MClkFwd_def},
@{thm Call_def}, @{thm caller_def}, @{thm rtrner_def}]) [exI]
[@{thm base_enabled}, @{thm Pair_inject}] 1 *})
lemma MClkFwd_ch_enabled: "|- Enabled (MClkFwd send rcv cst p) -->
Enabled (<MClkFwd send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p))"
by (auto elim!: enabled_mono simp: angle_def MClkFwd_def)
lemma MClkReply_change: "|- MClkReply send rcv cst p -->
<MClkReply send rcv cst p>_(cst!p, rtrner send!p, caller rcv!p)"
by (auto simp: angle_def MClkReply_def elim: Return_changed [temp_use])
lemma MClkReply_enabled: "!!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))"
apply (tactic {* action_simp_tac @{context}
[@{thm MClkReply_change} RSN (2, @{thm enabled_mono})] [] 1 *})
apply (tactic {* action_simp_tac (@{context} addsimps
[@{thm MClkReply_def}, @{thm Return_def}, @{thm caller_def}, @{thm rtrner_def}])
[exI] [@{thm base_enabled}, @{thm Pair_inject}] 1 *})
done
lemma MClkReplyNotRetry: "|- MClkReply send rcv cst p --> ~MClkRetry send rcv cst p"
by (auto simp: MClkReply_def MClkRetry_def)
end