Quelle ProcedureInterface.thy Sprache: Isabelle

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

section \<open>Procedure interface for RPC-Memory components\<close>

theory ProcedureInterface
imports "HOL-TLA.TLA" RPCMemoryParams
begin

typedecl ('a,'r) chan
  (* type of channels with argument type 'a and return type 'r.
     we model a channel as an array of variables (of type chan)
     rather than a single array-valued variable because the
     notation gets a little simpler.
  *)
type_synonym ('a,'r) channel =" (PrIds \ ('a,'r) chan) stfun"

(* data-level functions *)

consts
  cbit          :: "('a,'r) chan \ bit"
  rbit          :: "('a,'r) chan \ bit"
  arg           :: "('a,'r) chan \ 'a"
  res           :: "('a,'r) chan \ 'r"

(* state functions *)

definition caller :: "('a,'r) channel \ (PrIds \ (bit * 'a)) stfun"
  where "caller ch == \s p. (cbit (ch s p), arg (ch s p))"

definition rtrner :: "('a,'r) channel \ (PrIds \ (bit * 'r)) stfun"
  where "rtrner ch == \s p. (rbit (ch s p), res (ch s p))"

(* slice through array-valued state function *)

definition slice :: "('a \ 'b) stfun \ 'a \ 'b stfun"
  where "slice x i s \ x s i"

syntax
  "_slice" :: "[lift, 'a] \ lift" (\(_!_)\ [70,70] 70)
translations
  "_slice" \<rightleftharpoons> "CONST slice"

(* state predicates *)

definition Calling :: "('a,'r) channel \ PrIds \ stpred"
  where "Calling ch p == PRED cbit< ch!p > \ rbit< ch!p >"

(* actions *)

definition ACall :: "('a,'r) channel \ PrIds \ 'a stfun \ action"
  where "ACall ch p v \ ACT
      \<not> $Calling ch p
    \<and> (cbit<ch!p>$ \<noteq> $rbit<ch!p>)
    \<and> (arg<ch!p>$ = $v)"

definition AReturn :: "('a,'r) channel \ PrIds \ 'r stfun \ action"
  where "AReturn ch p v == ACT
      $Calling ch p
    \<and> (rbit<ch!p>$ = $cbit<ch!p>)
    \<and> (res<ch!p>$ = $v)"

syntax
  "_Call" :: "['a, 'b, lift] \ lift" (\(Call _ _ _)\ [90,90,90] 90)
  "_Return" :: "['a, 'b, lift] \ lift" (\(Return _ _ _)\ [90,90,90] 90)
translations
  "_Call" \<rightleftharpoons> "CONST ACall"
  "_Return" \<rightleftharpoons> "CONST AReturn"

(* temporal formulas *)

definition PLegalCaller :: "('a,'r) channel \ PrIds \ temporal"
  where "PLegalCaller ch p == TEMP
     Init(\<not> Calling ch p)
     \<and> \<box>[\<exists>a. Call ch p a ]_((caller ch)!p)"

definition LegalCaller :: "('a,'r) channel \ temporal"
  where "LegalCaller ch == TEMP (\p. PLegalCaller ch p)"

definition PLegalReturner :: "('a,'r) channel \ PrIds \ temporal"
  where "PLegalReturner ch p == TEMP \[\v. Return ch p v ]_((rtrner ch)!p)"

definition LegalReturner :: "('a,'r) channel \ temporal"
  where "LegalReturner ch == TEMP (\p. PLegalReturner ch p)"

declare slice_def [simp]

lemmas Procedure_defs = caller_def rtrner_def Calling_def ACall_def AReturn_def
  PLegalCaller_def LegalCaller_def PLegalReturner_def LegalReturner_def

(* Calls and returns change their subchannel *)
lemma Call_changed: "\ Call ch p v \ _((caller ch)!p)"
  by (auto simp: angle_def ACall_def caller_def Calling_def)

lemma Return_changed: "\ Return ch p v \ _((rtrner ch)!p)"
  by (auto simp: angle_def AReturn_def rtrner_def Calling_def)

end

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