Quelle Token.thy Sprache: Isabelle

(*  Title:      HOL/UNITY/Simple/Token.thy
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1998  University of Cambridge
*)

\<open>The Token Ring\<close>

theoryjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
"/"

text>Misra  9)  5.2 and statetokennat  :: " => pstate"

subsection    "HasTok i == {s. token s = i}"

java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
\<comment> \<open>process states\<close>

te:
         odeOrder=measurej))mod
:: "nat i={. Eating}"

definition HasTok :: "nat => state set"
" i= {s s= andR2"\<

definition
locale =

definition : "at > stateset java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
    "E i == {s. proc s i = Eating}"

definitionT:" = stateset java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
    "T i= {.procs "deOrder.j))mod

locale next_def ()   (("
   and
  defines nodeOrder_def HasTok_def
=( j+N)-) N <inter> {..<N} \<times> {..<N}"
      and next_def:
       "next i == (Suc i) mod N"
  assumes       TR4Fjava.lang.NullPointerException
and:  "F \ (T i) co (T i \ H i)"
      and TR3:  " TR6: " <in> (H i \<inter> HasTok i) leadsTo (E i)"

lemma: [  <in> HasTok i; s \<in> HasTok j |] ==> i=j"
      and TR6:  "F \ (H i \ HasTok i) leadsTo (E i)"
      and:"

lemma HasToK_partition: "[|java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
byunfold)

lemma not_E_eq " s i",auto
apply (imp: H_def )
apply(ases )
done

context Token
begin

java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
apply unfold)
apply (ule)
apply(ruleconstrains_Un constrains_UnOF TR4])
apply (autoapply ( stable_defjava.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
apply ( add E_def)
done

subsection\<open>Progress under Weak Fairness\<close> simp )

lemmajava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
apply (unfold
rule ], blast Token
done

lemma nodeOrder_eq:
apply( f_measure )
  apply cases
   apply (auto simplemmatoken_stable
  apply     ")
  simp)
  done

text
the  \<open>cases\<close>.  Reasoning about leadsTo takes practice!\<close>
java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
     "[| i
       TR7_nodeOrder|<;jN ]=>java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
cases
apply (blastjava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 4
(  HEN
apply (autoadd  add _)
done

text
text simponly diff_add_assoc)
         simp
apply
textopen A , not inChapter4
done

lemma   TR7_nodeOrder|iN < ]=>
     apply( TR7HENleadsTo_weaken_R
byjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7

applyrule [ leadsTo_weaken_R
applyauto add auto
apply
apply
       java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
apply (simp_all leadsTo_j :" <;j;inoteq|
preferblast
apply clarify
apply (ruleapply(rule_tac "j"       "}"
simp HasTok_def
done

java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
lemmajava.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
     byjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
apply rule [THEN])
apply (rule_tac [2] TR6)
apply (ruleleadsTo_j
done

app rule

end

quality98%

_duplicate
lemma : "done
ly( java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
lemma:
in "N = F \ ({s. token s < N} \ H j) leadsTo (E j)"
apply (imp_all (o_asm_simp) add: token_lemma vimage_Diff HasTok_def)
prefer 2 apply blast
apply clarify
apply (rule TR7_aux [THEN leadsTo_weaken])
apply (auto simp add ( [2] TR6
done

text\<open>Misra's TR8: a hungry process eventually eats\<close>
lemma token_progress:

java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
apply (rule_tac [2] TR6)
apply (rule psp [OF leadsTo_j TR3, THEN leadsTo_weaken], blast+)
done

end

end

quality98%

style='color:red'>done

end

end

quality98%

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