(*
File: ProcedureInterface.thy
Author: Stephan Merz
Copyright: 1997 University of Munich
Theory Name: ProcedureInterface
Logic Image: TLA
Procedure interface for RPC-Memory components.
*)
ProcedureInterface = TLA + RPCMemoryParams +
types
(* 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
('a,'r) channel = (PrIds => ('a,'r) chan) stfun
arities
chan :: (term,term) term
consts
(* data-level functions *)
cbit,rbit :: "('a,'r) chan => bit"
arg :: "('a,'r) chan => 'a"
res :: "('a,'r) chan => 'r"
(* slice through array-valued state function *)
"@" :: "('a => 'b) stfun => 'a => 'b stfun" (infixl 20)
(* 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 *)
Call :: "('a,'r) channel => PrIds => 'a trfct => action"
Return :: "('a,'r) channel => PrIds => 'r trfct => 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"
rules
slice_def "(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 "$(Calling ch p) .= (cbit[$(ch@p)] .~= rbit[$(ch@p)])"
Call_def "Call ch p v == .~ $(Calling ch p)
.& (cbit[$(ch@p)])` .~= rbit[$(ch@p)]
.& (arg[$(ch@p)])` .= v"
Return_def "Return ch p v == $(Calling ch p)
.& (rbit[$(ch@p)])` .= cbit[$(ch@p)]
.& (res[$(ch@p)])` .= v"
PLegalCaller_def "PLegalCaller ch p ==
Init(.~ $(Calling ch p))
.& [][ REX a. Call ch p (#a) ]_((caller ch)@p)"
LegalCaller_def "LegalCaller ch == RALL p. PLegalCaller ch p"
PLegalReturner_def "PLegalReturner ch p ==
[][ REX v. Return ch p (#v) ]_((rtrner ch)@p)"
LegalReturner_def "LegalReturner ch == RALL p. PLegalReturner ch p"
end