src/HOL/TLA/Memory/RPC.thy

more symbols;
eliminated alternative syntax;

(*  Title:      HOL/TLA/Memory/RPC.thy
    Author:     Stephan Merz, University of Munich
*)

section {* RPC-Memory example: RPC specification *}

theory RPC
imports RPCParameters ProcedureInterface Memory
begin

type_synonym rpcSndChType = "(rpcOp,Vals) channel"
type_synonym rpcRcvChType = "memChType"
type_synonym rpcStType = "(PrIds \<Rightarrow> rpcState) stfun"

consts
  (* state predicates *)
  RPCInit      :: "rpcRcvChType \<Rightarrow> rpcStType \<Rightarrow> PrIds \<Rightarrow> stpred"

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

  (* temporal *)
  RPCIPSpec   :: "rpcSndChType \<Rightarrow> rpcRcvChType \<Rightarrow> rpcStType \<Rightarrow> PrIds \<Rightarrow> temporal"
  RPCISpec   :: "rpcSndChType \<Rightarrow> rpcRcvChType \<Rightarrow> rpcStType \<Rightarrow> temporal"

defs
  RPCInit_def:       "RPCInit rcv rst p == PRED ((rst!p = #rpcA) \<and> \<not>Calling rcv p)"

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

  RPCReject_def:     "RPCReject send rcv rst p == ACT
                           $(rst!p) = # rpcA
                         \<and> \<not>IsLegalRcvArg<arg<$(send!p)>>
                         \<and> Return send p #BadCall
                         \<and> unchanged ((rst!p), (caller rcv!p))"

  RPCFail_def:       "RPCFail send rcv rst p == ACT
                           \<not>$(Calling rcv p)
                         \<and> Return send p #RPCFailure
                         \<and> (rst!p)$ = #rpcA
                         \<and> unchanged (caller rcv!p)"

  RPCReply_def:      "RPCReply send rcv rst p == ACT
                           \<not>$(Calling rcv p)
                         \<and> $(rst!p) = #rpcB
                         \<and> Return send p res<rcv!p>
                         \<and> (rst!p)$ = #rpcA
                         \<and> unchanged (caller rcv!p)"

  RPCNext_def:       "RPCNext send rcv rst p == ACT
                        (  RPCFwd send rcv rst p
                         \<or> RPCReject send rcv rst p
                         \<or> RPCFail send rcv rst p
                         \<or> RPCReply send rcv rst p)"

  RPCIPSpec_def:     "RPCIPSpec send rcv rst p == TEMP
                           Init RPCInit rcv rst p
                         \<and> \<box>[ RPCNext send rcv rst p ]_(rst!p, rtrner send!p, caller rcv!p)
                         \<and> WF(RPCNext send rcv rst p)_(rst!p, rtrner send!p, caller rcv!p)"

  RPCISpec_def:      "RPCISpec send rcv rst == TEMP (\<forall>p. RPCIPSpec send rcv rst p)"


lemmas RPC_action_defs =
  RPCInit_def RPCFwd_def RPCReject_def RPCFail_def RPCReply_def RPCNext_def

lemmas RPC_temp_defs = RPCIPSpec_def RPCISpec_def


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

lemma RPCidle: "\<turnstile> \<not>$(Calling send p) \<longrightarrow> \<not>RPCNext send rcv rst p"
  by (auto simp: Return_def RPC_action_defs)

lemma RPCbusy: "\<turnstile> $(Calling rcv p) \<and> $(rst!p) = #rpcB \<longrightarrow> \<not>RPCNext send rcv rst p"
  by (auto simp: RPC_action_defs)

(* RPC failure actions are visible. *)
lemma RPCFail_vis: "\<turnstile> RPCFail send rcv rst p \<longrightarrow>  
    <RPCNext send rcv rst p>_(rst!p, rtrner send!p, caller rcv!p)"
  by (auto dest!: Return_changed [temp_use] simp: angle_def RPCNext_def RPCFail_def)

lemma RPCFail_Next_enabled: "\<turnstile> Enabled (RPCFail send rcv rst p) \<longrightarrow>  
    Enabled (<RPCNext send rcv rst p>_(rst!p, rtrner send!p, caller rcv!p))"
  by (force elim!: enabled_mono [temp_use] RPCFail_vis [temp_use])

(* Enabledness of some actions *)
lemma RPCFail_enabled: "\<And>p. basevars (rtrner send!p, caller rcv!p, rst!p) \<Longrightarrow>  
    \<turnstile> \<not>Calling rcv p \<and> Calling send p \<longrightarrow> Enabled (RPCFail send rcv rst p)"
  by (tactic {* action_simp_tac (@{context} addsimps [@{thm RPCFail_def},
    @{thm Return_def}, @{thm caller_def}, @{thm rtrner_def}]) [exI]
    [@{thm base_enabled}, @{thm Pair_inject}] 1 *})

lemma RPCReply_enabled: "\<And>p. basevars (rtrner send!p, caller rcv!p, rst!p) \<Longrightarrow>  
      \<turnstile> \<not>Calling rcv p \<and> Calling send p \<and> rst!p = #rpcB  
         \<longrightarrow> Enabled (RPCReply send rcv rst p)"
  by (tactic {* action_simp_tac (@{context} addsimps [@{thm RPCReply_def},
    @{thm Return_def}, @{thm caller_def}, @{thm rtrner_def}]) [exI]
    [@{thm base_enabled}, @{thm Pair_inject}] 1 *})

end