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(* Title: HOL/HOLCF/IOA/ABP/Abschannel_finite.thy
Author: Olaf Müller
*)
section \<open>The transmission channel -- finite version\<close>
theory Abschannel_finite
imports Abschannel IOA.IOA Action Lemmas
begin
primrec reverse :: "'a list => 'a list"
where
reverse_Nil: "reverse([]) = []"
| reverse_Cons: "reverse(x#xs) = reverse(xs)@[x]"
definition
ch_fin_asig :: "'a abs_action signature" where
"ch_fin_asig = ch_asig"
definition
ch_fin_trans :: "('a abs_action, 'a list)transition set" where
"ch_fin_trans =
{tr. let s = fst(tr);
t = snd(snd(tr))
in
case fst(snd(tr))
of S(b) => ((t = s) |
(if (b=hd(reverse(s)) & s~=[]) then t=s else t=s@[b])) |
R(b) => s ~= [] &
b = hd(s) &
((t = s) | (t = tl(s)))}"
definition
ch_fin_ioa :: "('a abs_action, 'a list)ioa" where
"ch_fin_ioa = (ch_fin_asig, {[]}, ch_fin_trans,{},{})"
definition
srch_fin_ioa :: "('m action, 'm packet list)ioa" where
"srch_fin_ioa = rename ch_fin_ioa srch_actions"
definition
rsch_fin_ioa :: "('m action, bool list)ioa" where
"rsch_fin_ioa = rename ch_fin_ioa rsch_actions"
definition
srch_fin_asig :: "'m action signature" where
"srch_fin_asig = asig_of(srch_fin_ioa)"
definition
rsch_fin_asig :: "'m action signature" where
"rsch_fin_asig = asig_of(rsch_fin_ioa)"
definition
srch_fin_trans :: "('m action, 'm packet list)transition set" where
"srch_fin_trans = trans_of(srch_fin_ioa)"
definition
rsch_fin_trans :: "('m action, bool list)transition set" where
"rsch_fin_trans = trans_of(rsch_fin_ioa)"
end
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