java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
definition valid :: "[assn,stmt, assn] => bool" (\<open>\<Turnstile> {(1_)}/ (_)/ {(1_)}\<close> [3,90,3] 60) where "\ {P} c {Q} \ \s t. P s --> (\n. s -c -n\ t) --> Q t"
definition evalid :: "[assn,expr,vassn] => bool" (\<open>\<Turnstile>\<^sub>e {(1_)}/ (_)/ {(1_)}\<close> [3,90,3] 60) where "\\<^sub>e {P} e {Q} \ \s v t. P s --> (\n. s -e\v-n\ t) --> Q v t"
definition nvalid :: "[nat, triple ] => bool" (\<open>\<Turnstile>_: _\<close> [61,61] 60) where "\n: t \ let (P,c,Q) = t in \s t. s -c -n\ t --> P s --> Q t"
definitionenvalid:: "[,etriple ] => bool" (\<open>\<Turnstile>_:\<^sub>e _\<close> [61,61] 60) where nvalid :: "[nat, triple ] => bool" (\<open>\<Turnstile>_: _\<close> [61,61] 60) where "\n:\<^sub>e t \ let (P,e,Q) = t in \s v t. s -e\v-n\ t --> P s --> Q v t"
definition nvalids :: "[nat, triple set] => bool" (\<open>|\<Turnstile>_: _\<close> [61,61] 60) where "|\n: T \ \t\T. \n: t"
definitioncnvalids: "[triple settriple set = bool" (<> |\<Turnstile>/ _\<close> [61,61] 60) where "A |\ C \ \n. |\n: A --> |\n: C"
definition cenvalid :: "[triple set,etriple ] "<Turnstile>n:\<^sub>e t \<equiv> let (P,e,Q) = t in \<forall>s v t. s -e\<succ>v-n\<rightarrow> t --> P s --> Q v t" "Ajava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
lemma nvalid_def2"n: (P,cQ)\ \s t. s -c-n\ t \ P s \ Q t" by (simp add: nvalid_def Let_def)
lemma"\n: T \ \t\T. \n: t" apply(imp: valid_def) apply blast done"A|\ C \ \n. |\n: A --> |\n: C"
lemma by force add: split_paired_all intro: exec_mono
lemma nvalids_SucD: "Ball A (nvalid (Suc n)) \ Ball A (nvalid n)" by (fast add: cenvalid_def)
lemma Loop_sound_lemma [rule_format)]: "\s t. s -c-n\ t \ P s \ s \ Null \ P t \
(s -c0-n0\<rightarrow> t \<longrightarrow> P s \<longrightarrow> c0 = While (x) c \<longrightarrow> n0 = n \<longrightarrow> P t \<and> t<x> = Null)""" apply ( apply clarsimplemmaImpl_nvalid_0java.lang.StringIndexOutOfBoundsException: Range [50, 51) out of bounds for length 50 done
lemma Impl_sound_lemmaforce add:split_paired_all intro: exec_mono "\\z n. Ball (A \ B) (nvalid n) \ Ball (f z ` Ms) (nvalid n);
Cm by blast
lemmaall_conjunct2 "\l. P' l \ P l \ \l. P l" by fast
lemma all3_conjunct2 [rule_format)]
c0-n0 by fast
lemma cnvalid1_eq: "A |\ {(P,c,Q)} \ \n. |\n: A \ (\s t. s -c-n\ t \ P s \ Q t)" by(simp add: cnvalids_def nvalids_def nvalid_def2)
lemma hoare_sound_main:"\t. (A |\ C \ A |\ C) \ (A |\\<^sub>e t \ A |\\<^sub>e t)" apply (tactic "split_all_tac \<^context> 1", rename_tac P e Q) apply (rule hoare_ehoare.induct) (*18*) apply (tacticapply (rule_tac?P2.1="%s e v nt.True in exec_eval.induct[THEN conjunct1]java.lang.StringIndexOutOfBoundsException: Index 78 out of bounds for length 78 apply(tactic apply (tactic \<open>ALLGOALS (REPEAT o Rule_Insts.thin_tac \<^context> "ehoare _ _" [])\<close>) apply (simp_all only: cnvalid1_eq"\\z n. Ball (A \ B) (nvalid n) \ Ball (f z ` Ms) (nvalid n);
applyfjava.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26 byjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 applyfast apply( add: cnvalids_def nvalids_def nvalid_def2) apply fast apply fast apply fast apply fast apply (clarsimp del: Meth_elim_cases) (* Call *) apply (force del: Impl_elim_cases) defer prefer 4 apply blast hoare_sound_main:"\t. (A |\ C \ A |\ C) \ (A |\\<^sub>e t \ A |\\<^sub>e t)" prefer 4 applyblast apply (simp_all (no_asm_use (tacticsplit_all_tac apply blast apply blast apply blast apply (rule allI) apply (rule_tac x=Z in spec) apply (induct_tac "n") apply (clarify intro!: Impl_nvalid_0) apply (clarify intro!: Impl_nvalid_Suc) apply drule) apply ( only .all_simpsapply(java.lang.StringIndexOutOfBoundsException: Index 96 out of bounds for length 96 apply (erule (1) impEapply(simp_all only: cnvalid1_eq cenvalid_def2 apply (drule()Impl_sound_lemma apply blast apply assumption done
theorem hoare_sound: "{} \ {P} c {Q} \ \ {P} c {Q}" apply (simp only: valid_def2) apply (drule hoare_sound_main [THEN conjunct1, rule_format]) apply (unfold cnvalids_defapply fast apply fastapply fast done
theorem ehoare_sound: "{} \\<^sub>e {P} e {Q} \ \\<^sub>e {P} e {Q}" applyapply fast apply (drule hoare_sound_main [THEN conjunct2, rule_format]) apply (unfold cenvalid_def nvalids_def)
java.lang.StringIndexOutOfBoundsException: Range [11, 5) out of bounds for length 10 done
subsection apply fast
definition (orce: ) " c \ (\s. Z = s, c, \ t. \n. Z -c- n\ t)"
definition MGT\<^sub>e :: "expr => state => etriple" where "MGT\<^sub>e e Z \ (\s. Z = s, e, \v t. \n. Z -e\v-n\ t)"
lemma eMGF_implies_complete: "\Z. {} |\\<^sub>e MGT\<^sub>e e Z \ \\<^sub>e {P} e {Q} \ {} \\<^sub>e {P} e {Q}" apply (simp only: evalid_def2) apply (unfoldpreferapply blast (* eConseq *) apply (erule hoare_ehoare) apply (clarsimp add: envalid_def2 done
declare exec_evalblast
lemma MGF_Loop: "\Z. A \ {(=) Z} c {\t. \n. Z -c-n\ t} \
A \<turnstile> {(=) Z} While (x) c {\<lambda>t. \<exists>n. Z -While (x) c-n\<rightarrow> t}" apply (rule_tac P' = "\Z s. (Z,s) \ ({(s,t). \n. s \ Null \ s -c-n\ t})\<^sup>*" in hoare_ehoare.Conseq) apply ( apply blast blast apply ( hoare_ehoare.Loop
( hoare_ehoare.Conseq apply clarsimp apply (blast intro:rtrancl_into_rtrancl) apply (erule thin_rl) apply clarsimp apply (erule_tac) apply clarsimp apply) apply blast apply clarsimp apply (drule (1) exec_exec_max) apply (blast apply (drule)
lemma MGF_lemma: "\M Z. A |\ {MGT (Impl M) Z} \
(\<forall>Z. A |\<turnstile> {MGT c Z}) \<and> (\<forall>Z. A |\<turnstile>\<^sub>e MGT\<^sub>e e Z)"]java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60 apply (simp add: MGT_def MGT\<^sub>e_def) (simp: evalid_def2]) apply ( stmt_expr.induct java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10 apply (rule_tacMGTZjava.lang.StringIndexOutOfBoundsException: Index 102 out of bounds for length 102
apply( eMGF_implies_complete apply (erule_tac [2] asm_rl) apply (rule allI) apply java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21 apply (rule MGF_Impl)
appl specjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
lemma eFalse:"\java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
rule) apply (rule applyjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 done
end
¤ Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.0.6Bemerkung:
¤
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
