Up to index of Isabelle/HOL/TLA/Memory
theory ProcedureInterface(* File: ProcedureInterface.thy ID: $Id: ProcedureInterface.thy,v 1.8 2008/03/20 11:01:13 haftmann Exp $ Author: Stephan Merz Copyright: 1997 University of Munich *) header {* Procedure interface for RPC-Memory components *} theory ProcedureInterface imports "../TLA" RPCMemoryParams begin typedecl (* 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. *) ('a,'r) chan types ('a,'r) channel =" (PrIds => ('a,'r) chan) stfun" consts (* data-level functions *) cbit :: "('a,'r) chan => bit" rbit :: "('a,'r) chan => bit" arg :: "('a,'r) chan => 'a" res :: "('a,'r) chan => 'r" (* state functions *) caller :: "('a,'r) channel => (PrIds => (bit * 'a)) stfun" rtrner :: "('a,'r) channel => (PrIds => (bit * 'r)) stfun" (* state predicates *) Calling :: "('a,'r) channel => PrIds => stpred" (* actions *) ACall :: "('a,'r) channel => PrIds => 'a stfun => action" AReturn :: "('a,'r) channel => PrIds => 'r stfun => action" (* temporal formulas *) PLegalCaller :: "('a,'r) channel => PrIds => temporal" LegalCaller :: "('a,'r) channel => temporal" PLegalReturner :: "('a,'r) channel => PrIds => temporal" LegalReturner :: "('a,'r) channel => temporal" (* slice through array-valued state function *) slice :: "('a => 'b) stfun => 'a => 'b stfun" syntax "_slice" :: "[lift, 'a] => lift" ("(_!_)" [70,70] 70) "_Call" :: "['a, 'b, lift] => lift" ("(Call _ _ _)" [90,90,90] 90) "_Return" :: "['a, 'b, lift] => lift" ("(Return _ _ _)" [90,90,90] 90) translations "_slice" == "slice" "_Call" == "ACall" "_Return" == "AReturn" defs slice_def: "(PRED (x!i)) s == x s i" caller_def: "caller ch == %s p. (cbit (ch s p), arg (ch s p))" rtrner_def: "rtrner ch == %s p. (rbit (ch s p), res (ch s p))" Calling_def: "Calling ch p == PRED cbit< ch!p > ~= rbit< ch!p >" Call_def: "(ACT Call ch p v) == ACT ~ $Calling ch p & (cbit<ch!p>$ ~= $rbit<ch!p>) & (arg<ch!p>$ = $v)" Return_def: "(ACT Return ch p v) == ACT $Calling ch p & (rbit<ch!p>$ = $cbit<ch!p>) & (res<ch!p>$ = $v)" PLegalCaller_def: "PLegalCaller ch p == TEMP Init(~ Calling ch p) & [][ ? a. Call ch p a ]_((caller ch)!p)" LegalCaller_def: "LegalCaller ch == TEMP (! p. PLegalCaller ch p)" PLegalReturner_def: "PLegalReturner ch p == TEMP [][ ? v. Return ch p v ]_((rtrner ch)!p)" LegalReturner_def: "LegalReturner ch == TEMP (! p. PLegalReturner ch p)" declare slice_def [simp] lemmas Procedure_defs = caller_def rtrner_def Calling_def Call_def Return_def PLegalCaller_def LegalCaller_def PLegalReturner_def LegalReturner_def (* Calls and returns change their subchannel *) lemma Call_changed: "|- Call ch p v --> <Call ch p v>_((caller ch)!p)" by (auto simp: angle_def Call_def caller_def Calling_def) lemma Return_changed: "|- Return ch p v --> <Return ch p v>_((rtrner ch)!p)" by (auto simp: angle_def Return_def rtrner_def Calling_def) end
lemma Procedure_defs:
caller ch == λs p. (cbit (ch s p), arg (ch s p))
rtrner ch == λs p. (rbit (ch s p), res (ch s p))
Calling ch p == cbit<ch!p> ≠ rbit<ch!p>
Call ch p v == ¬ $Calling ch p ∧ cbit<ch!p>$ ≠ $rbit<ch!p> ∧ arg<ch!p>$ = $v
Return ch p v == $Calling ch p ∧ rbit<ch!p>$ = $cbit<ch!p> ∧ res<ch!p>$ = $v
PLegalCaller ch p == Init ¬ Calling ch p ∧ [][∃a. Call ch p a]_(caller ch!p)
LegalCaller ch == ∀p. PLegalCaller ch p
PLegalReturner ch p == [][∃v. Return ch p v]_(rtrner ch!p)
LegalReturner ch == ∀p. PLegalReturner ch p
lemma Call_changed:
|- Call ch p v --> <Call ch p v>_(caller ch!p)
lemma Return_changed:
|- Return ch p v --> <Return ch p v>_(rtrner ch!p)