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(* Title: HOL/IOA/example/Sender.thy
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ID: $Id$
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Author: Tobias Nipkow & Konrad Slind
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Copyright 1994 TU Muenchen
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The implementation: sender
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*)
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Sender = IOA + Action + List + Lemmas +
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types
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'm sender_state = "'m list * bool"
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(* messages Alternating Bit *)
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consts
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sender_asig :: "'m action signature"
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sender_trans :: "('m action, 'm sender_state)transition set"
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sender_ioa :: "('m action, 'm sender_state)ioa"
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sq :: "'m sender_state => 'm list"
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sbit :: "'m sender_state => bool"
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defs
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sq_def "sq == fst"
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sbit_def "sbit == snd"
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sender_asig_def
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"sender_asig == ((UN m. {S_msg(m)}) Un (UN b. {R_ack(b)}),
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UN pkt. {S_pkt(pkt)},
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{})"
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sender_trans_def "sender_trans ==
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{tr. let s = fst(tr);
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t = snd(snd(tr))
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in case fst(snd(tr))
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of
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Next => if sq(s)=[] then t=s else False |
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S_msg(m) => sq(t)=sq(s)@[m] &
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sbit(t)=sbit(s) |
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R_msg(m) => False |
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S_pkt(pkt) => sq(s) ~= [] &
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hdr(pkt) = sbit(s) &
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msg(pkt) = hd(sq(s)) &
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sq(t) = sq(s) &
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sbit(t) = sbit(s) |
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R_pkt(pkt) => False |
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S_ack(b) => False |
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R_ack(b) => if b = sbit(s) then
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sq(t)=tl(sq(s)) & sbit(t)=(~sbit(s)) else
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sq(t)=sq(s) & sbit(t)=sbit(s)}"
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sender_ioa_def "sender_ioa ==
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(sender_asig, {([],True)}, sender_trans)"
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end
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