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(* 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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