--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/HOLCF/IOA/NTP/Abschannel.thy Sat Nov 27 16:08:10 2010 -0800
@@ -0,0 +1,141 @@
+(* Title: HOL/IOA/NTP/Abschannel.thy
+ Author: Olaf Müller
+*)
+
+header {* The (faulty) transmission channel (both directions) *}
+
+theory Abschannel
+imports IOA Action
+begin
+
+datatype 'a abs_action = S 'a | R 'a
+
+definition
+ ch_asig :: "'a abs_action signature" where
+ "ch_asig = (UN b. {S(b)}, UN b. {R(b)}, {})"
+
+definition
+ ch_trans :: "('a abs_action, 'a multiset)transition set" where
+ "ch_trans =
+ {tr. let s = fst(tr);
+ t = snd(snd(tr))
+ in
+ case fst(snd(tr))
+ of S(b) => t = addm s b |
+ R(b) => count s b ~= 0 & t = delm s b}"
+
+definition
+ ch_ioa :: "('a abs_action, 'a multiset)ioa" where
+ "ch_ioa = (ch_asig, {{|}}, ch_trans,{},{})"
+
+definition
+ rsch_actions :: "'m action => bool abs_action option" where
+ "rsch_actions (akt) =
+ (case akt of
+ S_msg(m) => None |
+ R_msg(m) => None |
+ S_pkt(packet) => None |
+ R_pkt(packet) => None |
+ S_ack(b) => Some(S(b)) |
+ R_ack(b) => Some(R(b)) |
+ C_m_s => None |
+ C_m_r => None |
+ C_r_s => None |
+ C_r_r(m) => None)"
+
+definition
+ srch_actions :: "'m action =>(bool * 'm) abs_action option" where
+ "srch_actions (akt) =
+ (case akt of
+ S_msg(m) => None |
+ R_msg(m) => None |
+ S_pkt(p) => Some(S(p)) |
+ R_pkt(p) => Some(R(p)) |
+ S_ack(b) => None |
+ R_ack(b) => None |
+ C_m_s => None |
+ C_m_r => None |
+ C_r_s => None |
+ C_r_r(m) => None)"
+
+definition
+ srch_ioa :: "('m action, 'm packet multiset)ioa" where
+ "srch_ioa = rename ch_ioa srch_actions"
+
+definition
+ rsch_ioa :: "('m action, bool multiset)ioa" where
+ "rsch_ioa = rename ch_ioa rsch_actions"
+
+definition
+ srch_asig :: "'m action signature" where
+ "srch_asig = asig_of(srch_ioa)"
+
+definition
+ rsch_asig :: "'m action signature" where
+ "rsch_asig = asig_of(rsch_ioa)"
+
+definition
+ srch_wfair :: "('m action)set set" where
+ "srch_wfair = wfair_of(srch_ioa)"
+definition
+ srch_sfair :: "('m action)set set" where
+ "srch_sfair = sfair_of(srch_ioa)"
+definition
+ rsch_sfair :: "('m action)set set" where
+ "rsch_sfair = sfair_of(rsch_ioa)"
+definition
+ rsch_wfair :: "('m action)set set" where
+ "rsch_wfair = wfair_of(rsch_ioa)"
+
+definition
+ srch_trans :: "('m action, 'm packet multiset)transition set" where
+ "srch_trans = trans_of(srch_ioa)"
+definition
+ rsch_trans :: "('m action, bool multiset)transition set" where
+ "rsch_trans = trans_of(rsch_ioa)"
+
+
+lemmas unfold_renaming =
+ srch_asig_def rsch_asig_def rsch_ioa_def srch_ioa_def ch_ioa_def
+ ch_asig_def srch_actions_def rsch_actions_def rename_def rename_set_def asig_of_def
+ actions_def srch_trans_def rsch_trans_def ch_trans_def starts_of_def
+ trans_of_def asig_projections
+
+lemma in_srch_asig:
+ "S_msg(m) ~: actions(srch_asig) &
+ R_msg(m) ~: actions(srch_asig) &
+ S_pkt(pkt) : actions(srch_asig) &
+ R_pkt(pkt) : actions(srch_asig) &
+ S_ack(b) ~: actions(srch_asig) &
+ R_ack(b) ~: actions(srch_asig) &
+ C_m_s ~: actions(srch_asig) &
+ C_m_r ~: actions(srch_asig) &
+ C_r_s ~: actions(srch_asig) & C_r_r(m) ~: actions(srch_asig)"
+ by (simp add: unfold_renaming)
+
+lemma in_rsch_asig:
+ "S_msg(m) ~: actions(rsch_asig) &
+ R_msg(m) ~: actions(rsch_asig) &
+ S_pkt(pkt) ~: actions(rsch_asig) &
+ R_pkt(pkt) ~: actions(rsch_asig) &
+ S_ack(b) : actions(rsch_asig) &
+ R_ack(b) : actions(rsch_asig) &
+ C_m_s ~: actions(rsch_asig) &
+ C_m_r ~: actions(rsch_asig) &
+ C_r_s ~: actions(rsch_asig) &
+ C_r_r(m) ~: actions(rsch_asig)"
+ by (simp add: unfold_renaming)
+
+lemma srch_ioa_thm: "srch_ioa =
+ (srch_asig, {{|}}, srch_trans,srch_wfair,srch_sfair)"
+apply (simp (no_asm) add: srch_asig_def srch_trans_def asig_of_def trans_of_def wfair_of_def sfair_of_def srch_wfair_def srch_sfair_def)
+apply (simp (no_asm) add: unfold_renaming)
+done
+
+lemma rsch_ioa_thm: "rsch_ioa =
+ (rsch_asig, {{|}}, rsch_trans,rsch_wfair,rsch_sfair)"
+apply (simp (no_asm) add: rsch_asig_def rsch_trans_def asig_of_def trans_of_def wfair_of_def sfair_of_def rsch_wfair_def rsch_sfair_def)
+apply (simp (no_asm) add: unfold_renaming)
+done
+
+end