(* Title: HOL/UNITY/Network
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
The Communication Network
From Misra, "A Logic for Concurrent Programming" (1994), section 5.7
*)
open Network;
val [rsA, rsB, sent_nondec, rcvd_nondec, rcvd_idle, sent_idle] =
goalw thy [stable_def]
"[| !! m. stable Acts {s. s(Bproc,Rcvd) <= s(Aproc,Sent)}; \
\ !! m. stable Acts {s. s(Aproc,Rcvd) <= s(Bproc,Sent)}; \
\ !! m proc. stable Acts {s. m <= s(proc,Sent)}; \
\ !! n proc. stable Acts {s. n <= s(proc,Rcvd)}; \
\ !! m proc. constrains Acts {s. s(proc,Idle) = 1 & s(proc,Rcvd) = m} \
\ {s. s(proc,Rcvd) = m --> s(proc,Idle) = 1}; \
\ !! n proc. constrains Acts {s. s(proc,Idle) = 1 & s(proc,Sent) = n} \
\ {s. s(proc,Sent) = n} \
\ |] ==> stable Acts {s. s(Aproc,Idle) = 1 & s(Bproc,Idle) = 1 & \
\ s(Aproc,Sent) = s(Bproc,Rcvd) & \
\ s(Bproc,Sent) = s(Aproc,Rcvd) & \
\ s(Aproc,Rcvd) = m & s(Bproc,Rcvd) = n}";
val sent_nondec_A = read_instantiate [("proc","Aproc")] sent_nondec;
val sent_nondec_B = read_instantiate [("proc","Bproc")] sent_nondec;
val rcvd_nondec_A = read_instantiate [("proc","Aproc")] rcvd_nondec;
val rcvd_nondec_B = read_instantiate [("proc","Bproc")] rcvd_nondec;
val rcvd_idle_A = read_instantiate [("proc","Aproc")] rcvd_idle;
val rcvd_idle_B = read_instantiate [("proc","Bproc")] rcvd_idle;
val sent_idle_A = read_instantiate [("proc","Aproc")] sent_idle;
val sent_idle_B = read_instantiate [("proc","Bproc")] sent_idle;
val rs_AB = [rsA, rsB] MRS constrains_Int;
val sent_nondec_AB = [sent_nondec_A, sent_nondec_B] MRS constrains_Int;
val rcvd_nondec_AB = [rcvd_nondec_A, rcvd_nondec_B] MRS constrains_Int;
val rcvd_idle_AB = [rcvd_idle_A, rcvd_idle_B] MRS constrains_Int;
val sent_idle_AB = [sent_idle_A, sent_idle_B] MRS constrains_Int;
val nondec_AB = [sent_nondec_AB, rcvd_nondec_AB] MRS constrains_Int;
val idle_AB = [rcvd_idle_AB, sent_idle_AB] MRS constrains_Int;
val nondec_idle = [nondec_AB, idle_AB] MRS constrains_Int;
by (rtac constrainsI 1);
by (dtac ([rs_AB, nondec_idle] MRS constrains_Int RS constrainsD) 1);
by (assume_tac 1);
by (ALLGOALS Asm_full_simp_tac);
by (Blast_tac 1);
by (Clarify_tac 1);
by (subgoals_tac ["s' (Aproc, Rcvd) = s (Aproc, Rcvd)",
"s' (Bproc, Rcvd) = s (Bproc, Rcvd)"] 1);
by (REPEAT (blast_tac (claset() addIs [le_anti_sym, le_trans, eq_imp_le]) 2));
by (Asm_simp_tac 1);
result();