Import of Featherweight OCL release afp-Featherweight_OCL-2015-05-27 (Isabelle 2015).
This commit is contained in:
parent
8449924cbd
commit
ed232e8aa3
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@ -40,7 +40,7 @@
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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header{* Formalization I: Core Definitions *}
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chapter{* Formalization I: Core Definitions *}
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theory
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OCL_core
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17
OCL_lib.thy
17
OCL_lib.thy
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@ -40,7 +40,7 @@
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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header{* Formalization II: Library Definitions *}
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chapter{* Formalization II: Library Definitions *}
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theory OCL_lib
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imports OCL_core
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@ -1783,7 +1783,6 @@ proof -
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done
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qed
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(*declare [[names_long,show_types,show_sorts]]*)
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lemma OclIncludes_charn1:
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assumes def_X:"\<tau> \<Turnstile> (\<delta> X)"
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assumes val_x:"\<tau> \<Turnstile> (\<upsilon> x)"
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@ -2185,7 +2184,7 @@ proof -
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(* false *)
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(* false YES *)
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apply(case_tac "\<exists>x\<in>\<lceil>\<lceil>Rep_Set_0 (S->including(x) \<tau>)\<rceil>\<rceil>. P (\<lambda>_. x) \<tau> = false \<tau>", simp_all)
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apply(subst contradict_Rep_Set_0[where f = "\<lambda> x \<tau>. P x \<tau> = false \<tau>"], simp)+
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apply(subst contradict_Rep_Set_0[where f1 = "\<lambda> x \<tau>. P x \<tau> = false \<tau>"], simp)+
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apply(simp add: exists_including_invert[where f = "\<lambda> x \<tau>. P x \<tau> = false \<tau>", OF cp_eq])
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apply(simp add: cp_OclAnd[of "P x"])
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@ -2203,7 +2202,7 @@ proof -
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(* bot *)
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(* bot YES *)
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apply(case_tac "\<exists>x\<in>\<lceil>\<lceil>Rep_Set_0 (S->including(x) \<tau>)\<rceil>\<rceil>. P (\<lambda>_. x) \<tau> = bot \<tau>", simp_all)
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apply(subst contradict_Rep_Set_0[where f = "\<lambda> x \<tau>. P x \<tau> = bot \<tau>"], simp)+
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apply(subst contradict_Rep_Set_0[where f1 = "\<lambda> x \<tau>. P x \<tau> = bot \<tau>"], simp)+
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apply(simp add: exists_including_invert[where f = "\<lambda> x \<tau>. P x \<tau> = bot \<tau>", OF cp_eq])
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apply(simp add: cp_OclAnd[of "P x"])
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@ -2226,7 +2225,7 @@ proof -
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(* null *)
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(* null YES *)
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apply(case_tac "\<exists>x\<in>\<lceil>\<lceil>Rep_Set_0 (S->including(x) \<tau>)\<rceil>\<rceil>. P (\<lambda>_. x) \<tau> = null \<tau>", simp_all)
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apply(subst contradict_Rep_Set_0[where f = "\<lambda> x \<tau>. P x \<tau> = null \<tau>"], simp)+
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apply(subst contradict_Rep_Set_0[where f1 = "\<lambda> x \<tau>. P x \<tau> = null \<tau>"], simp)+
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apply(simp add: exists_including_invert[where f = "\<lambda> x \<tau>. P x \<tau> = null \<tau>", OF cp_eq])
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apply(simp add: cp_OclAnd[of "P x"])
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@ -2455,7 +2454,7 @@ proof -
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have OclSelect_body_bot: "\<And>\<tau>. \<tau> \<Turnstile> \<delta> X \<Longrightarrow> \<tau> \<Turnstile> \<upsilon> y \<Longrightarrow> P y \<tau> \<noteq> \<bottom> \<Longrightarrow>
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(\<exists>x\<in>\<lceil>\<lceil>Rep_Set_0 (X \<tau>)\<rceil>\<rceil>. P (\<lambda>_. x) \<tau> = \<bottom>) \<Longrightarrow> \<bottom> = ?select \<tau>"
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apply(drule ex_excluding1[where X = X and y = y and f = "\<lambda>x \<tau>. x \<tau> = \<bottom>"],
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apply(drule ex_excluding1[where X2 = X and y2 = y and f2 = "\<lambda>x \<tau>. x \<tau> = \<bottom>"],
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(simp add: P_cp[symmetric])+)
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apply(subgoal_tac "\<tau> \<Turnstile> (\<bottom> \<triangleq> ?select)", simp add: OclValid_def StrongEq_def true_def bot_fun_def)
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apply(simp add: OclSelect_body_def)
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@ -2464,7 +2463,7 @@ proof -
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apply(subgoal_tac "\<exists>x\<in>\<lceil>\<lceil>Rep_Set_0 (X->excluding(y) \<tau>)\<rceil>\<rceil>. P (\<lambda>_. x) \<tau> = \<bottom> \<tau>")
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prefer 2
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apply (metis OCL_core.bot_fun_def foundation18')
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apply(subst if_same[where d = "\<bottom>"])
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apply(subst if_same[where d5 = "\<bottom>"])
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apply (metis defined7 transform1)
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apply(simp add: OclSelect_def bot_option_def bot_fun_def)
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apply(subst invert_including)
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@ -2522,7 +2521,7 @@ proof -
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apply(simp)
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(* *)
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apply(subst conj_comm, rule conjI)
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apply(drule_tac y = false in bool_invalid)
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apply(drule_tac y11 = false in bool_invalid)
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apply(simp only: OclSelect_body_def,
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metis OclIf_def OclValid_def defined_def foundation2 foundation22
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bot_fun_def invalid_def)
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@ -2917,7 +2916,7 @@ proof -
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proof - fix x F show "(\<delta> S) \<tau> = true \<tau> \<Longrightarrow> \<exists>x. x \<in> F \<Longrightarrow>
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?forall (\<lambda>b \<tau>. ?P_eq x b \<tau> \<or> ?P F b \<tau>) =
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((\<lambda>_. ?forall (?P F)) and (\<lambda>_. P (\<lambda>\<tau>. x) \<tau>)) \<tau>"
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apply(rule disjE4[OF destruct_ocl[where x = "P (\<lambda>\<tau>. x) \<tau>"]])
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apply(rule disjE4[OF destruct_ocl[where x1 = "P (\<lambda>\<tau>. x) \<tau>"]])
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apply(simp_all add: true_def false_def OclAnd_def
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null_fun_def null_option_def bot_fun_def bot_option_def)
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by (metis (lifting) option.distinct(1))+
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@ -40,7 +40,7 @@
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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header{* Formalization III: State Operations and Objects *}
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chapter{* Formalization III: State Operations and Objects *}
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theory OCL_state
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imports OCL_lib
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@ -1,8 +1,6 @@
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\part{A Proposal for Formal Semantics of OCL 2.5}
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% \input{session}
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\input{OCL_core.tex}
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\input{OCL_lib.tex}
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\input{OCL_state.tex}
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@ -10,13 +8,6 @@
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\input{OCL_main.tex}
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\renewcommand{\isamarkupheader}[1]{\section{#1}}
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\renewcommand{\isamarkupsection}[1]{\subsection{#1}}
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\renewcommand{\isamarkupsubsection}[1]{\subsubsection{#1}}
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\renewcommand{\isamarkupsubsubsection}[1]{\paragraph{#1}}
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\renewcommand{\isamarkupsect}[1]{\subsection{#1}}
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\renewcommand{\isamarkupsubsect}[1]{\paragraph{#1}}
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\renewcommand{\isamarkupsubsubsect}[1]{\paragraph{#1}}
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\part{Examples}
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\chapter{The Employee Analysis Model}
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\label{ex:employee-analysis}
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@ -66,13 +66,6 @@
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\isabellestyle{it}
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\newcommand{\ie}{i.\,e.\xspace}
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\newcommand{\eg}{e.\,g.\xspace}
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\renewcommand{\isamarkupheader}[1]{\chapter{#1}}
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\renewcommand{\isamarkupsection}[1]{\section{#1}}
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\renewcommand{\isamarkupsubsection}[1]{\subsection{#1}}
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\renewcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}}
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\renewcommand{\isamarkupsect}[1]{\section{#1}}
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\renewcommand{\isamarkupsubsect}[1]{\susubsection{#1}}
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\renewcommand{\isamarkupsubsubsect}[1]{\subsubsection{#1}}
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\begin{document}
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\renewcommand{\subsubsectionautorefname}{Section}
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@ -40,7 +40,7 @@
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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header{* The Employee Analysis Model (OCL) *}
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section{* The Employee Analysis Model (OCL) *}
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theory
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Employee_AnalysisModel_OCLPart
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@ -48,10 +48,10 @@ imports
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Employee_AnalysisModel_UMLPart
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begin
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text {* \label{ex:employee-analysis:ocl} *}
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section{* Standard State Infrastructure *}
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subsection{* Standard State Infrastructure *}
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text{* Ideally, these definitions are automatically generated from the class model. *}
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section{* Invariant *}
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subsection{* Invariant *}
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text{* These recursive predicates can be defined conservatively
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by greatest fix-point
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constructions---automatically. See~\cite{brucker.ea:hol-ocl-book:2006,brucker:interactive:2007}
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@ -81,7 +81,7 @@ coinductive inv :: "Person \<Rightarrow> (\<AA>)st \<Rightarrow> bool" where
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( (inv(self .boss))\<tau> )))
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\<Longrightarrow> ( inv self \<tau>)"
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section{* The Contract of a Recursive Query *}
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subsection{* The Contract of a Recursive Query *}
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text{* The original specification of a recursive query :
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\begin{ocl}
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context Person::contents():Set(Integer)
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@ -121,7 +121,7 @@ text{* These \inlineocl{@pre} variants on methods are only available on queries,
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operations without side-effect. *}
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section{* The Contract of a Method *}
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subsection{* The Contract of a Method *}
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text{*
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The specification in high-level OCL input syntax reads as follows:
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\begin{ocl}
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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header{* The Employee Analysis Model (UML) *}
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section{* The Employee Analysis Model (UML) *}
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theory
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Employee_AnalysisModel_UMLPart
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@ -50,7 +50,7 @@ begin
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text {* \label{ex:employee-analysis:uml} *}
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section{* Introduction *}
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subsection{* Introduction *}
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text{*
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For certain concepts like classes and class-types, only a generic
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definition for its resulting semantics can be given. Generic means,
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@ -69,7 +69,7 @@ text{* Such generic function or ``compiler'' can be implemented in
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concepts of the compilation informally, and present a concrete
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example which is verified in Isabelle/HOL. *}
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subsection{* Outlining the Example *}
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subsubsection{* Outlining the Example *}
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text{* We are presenting here an ``analysis-model'' of the (slightly
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modified) example Figure 7.3, page 20 of
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@ -95,7 +95,7 @@ by the attribute \inlineocl+boss+ and the operation \inlineocl+employees+ (to b
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captured by the subsequent theory).
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*}
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section{* Example Data-Universe and its Infrastructure *}
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subsection{* Example Data-Universe and its Infrastructure *}
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text{* Ideally, the following is generated automatically from a UML class model. *}
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(* @{text "'\<AA>"} -- \mathfrak{A} *)
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@ -160,7 +160,7 @@ end
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section{* Instantiation of the Generic Strict Equality *}
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subsection{* Instantiation of the Generic Strict Equality *}
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text{* We instantiate the referential equality
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on @{text "Person"} and @{text "OclAny"} *}
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@ -194,8 +194,8 @@ two operations to declare and to provide two overloading definitions for the two
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*}
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section{* OclAsType *}
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subsection{* Definition *}
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subsection{* OclAsType *}
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subsubsection{* Definition *}
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consts OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> OclAny" ("(_) .oclAsType'(OclAny')")
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consts OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Person" ("(_) .oclAsType'(Person')")
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@ -236,7 +236,7 @@ lemmas [simp] =
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OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny
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OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person
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subsection{* Context Passing *}
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subsubsection{* Context Passing *}
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lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person: "cp P \<Longrightarrow> cp(\<lambda>X. (P (X::Person)::Person) .oclAsType(OclAny))"
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by(rule cpI1, simp_all add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
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@ -267,7 +267,7 @@ lemmas [simp] =
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cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
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cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
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subsection{* Execution with Invalid or Null as Argument *}
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subsubsection{* Execution with Invalid or Null as Argument *}
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lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_strict : "(invalid::OclAny) .oclAsType(OclAny) = invalid"
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by(simp)
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@ -296,8 +296,8 @@ by(simp)
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lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_nullstrict : "(null::Person) .oclAsType(Person) = null"
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by(simp)
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section{* OclIsTypeOf *}
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subsection{* Definition *}
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subsection{* OclIsTypeOf *}
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subsubsection{* Definition *}
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consts OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsTypeOf'(OclAny')")
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consts OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsTypeOf'(Person')")
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@ -332,7 +332,7 @@ defs (overloaded) OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Pe
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\<bottom> \<Rightarrow> invalid \<tau>
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| _ \<Rightarrow> true \<tau>)"
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subsection{* Context Passing *}
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subsubsection{* Context Passing *}
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lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person: "cp P \<Longrightarrow> cp(\<lambda>X.(P(X::Person)::Person).oclIsTypeOf(OclAny))"
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by(rule cpI1, simp_all add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
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@ -364,7 +364,7 @@ lemmas [simp] =
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cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
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cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
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subsection{* Execution with Invalid or Null as Argument *}
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subsubsection{* Execution with Invalid or Null as Argument *}
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lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_strict1[simp]:
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"(invalid::OclAny) .oclIsTypeOf(OclAny) = invalid"
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@ -399,7 +399,7 @@ lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_strict2
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by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def
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OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person)
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subsection{* Up Down Casting *}
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subsubsection{* Up Down Casting *}
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lemma actualType_larger_staticType:
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assumes isdef: "\<tau> \<Turnstile> (\<delta> X)"
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@ -456,8 +456,8 @@ shows "\<tau> \<Turnstile> (X .oclIsTypeOf(Person) implies (X .oclAsType(OclAny)
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by (simp add: OclImplies_true)
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section{* OclIsKindOf *}
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subsection{* Definition *}
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subsection{* OclIsKindOf *}
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subsubsection{* Definition *}
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consts OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsKindOf'(OclAny')")
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consts OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsKindOf'(Person')")
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@ -488,7 +488,7 @@ defs (overloaded) OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Pe
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\<bottom> \<Rightarrow> invalid \<tau>
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| _ \<Rightarrow> true \<tau>)"
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subsection{* Context Passing *}
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subsubsection{* Context Passing *}
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lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person: "cp P \<Longrightarrow> cp(\<lambda>X.(P(X::Person)::Person).oclIsKindOf(OclAny))"
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by(rule cpI1, simp_all add: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
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@ -519,7 +519,7 @@ lemmas [simp] =
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cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
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cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
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subsection{* Execution with Invalid or Null as Argument *}
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subsubsection{* Execution with Invalid or Null as Argument *}
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lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_strict1[simp] : "(invalid::OclAny) .oclIsKindOf(OclAny) = invalid"
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by(rule ext, simp add: invalid_def bot_option_def
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@ -553,7 +553,7 @@ lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_strict2
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by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def
|
||||
OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person)
|
||||
|
||||
subsection{* Up Down Casting *}
|
||||
subsubsection{* Up Down Casting *}
|
||||
|
||||
lemma actualKind_larger_staticKind:
|
||||
assumes isdef: "\<tau> \<Turnstile> (\<delta> X)"
|
||||
|
|
@ -572,7 +572,7 @@ apply(auto simp : bot_fun_def null_fun_def null_option_def bot_option_def null_d
|
|||
split: option.split type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split type\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
|
||||
by(simp add: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny OclValid_def false_def true_def)
|
||||
|
||||
section{* OclAllInstances *}
|
||||
subsection{* OclAllInstances *}
|
||||
|
||||
text{* To denote OCL-types occuring in OCL expressions syntactically---as, for example, as
|
||||
``argument'' of \inlineisar{oclAllInstances()}---we use the inverses of the injection
|
||||
|
|
@ -603,7 +603,7 @@ lemma OclAllInstances_at_pre\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exe
|
|||
unfolding OclAllInstances_at_pre_def
|
||||
by(rule OclAllInstances_generic\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec)
|
||||
|
||||
subsection{* OclIsTypeOf *}
|
||||
subsubsection{* OclIsTypeOf *}
|
||||
|
||||
lemma OclAny_allInstances_generic_oclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1:
|
||||
assumes [simp]: "\<And>x. pre_post (x, x) = x"
|
||||
|
|
@ -667,7 +667,7 @@ lemma Person_allInstances_at_pre_oclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^s
|
|||
unfolding OclAllInstances_at_pre_def
|
||||
by(rule Person_allInstances_generic_oclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
|
||||
|
||||
subsection{* OclIsKindOf *}
|
||||
subsubsection{* OclIsKindOf *}
|
||||
lemma OclAny_allInstances_generic_oclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y:
|
||||
"\<tau> \<Turnstile> ((OclAllInstances_generic pre_post OclAny)->forAll(X|X .oclIsKindOf(OclAny)))"
|
||||
apply(simp add: OclValid_def del: OclAllInstances_generic_def)
|
||||
|
|
@ -725,12 +725,12 @@ lemma Person_allInstances_at_pre_oclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^s
|
|||
unfolding OclAllInstances_at_pre_def
|
||||
by(rule Person_allInstances_generic_oclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
|
||||
|
||||
section{* The Accessors (any, boss, salary) *}
|
||||
subsection{* The Accessors (any, boss, salary) *}
|
||||
text{*\label{sec:eam-accessors}*}
|
||||
text{* Should be generated entirely from a class-diagram. *}
|
||||
|
||||
|
||||
subsection{* Definition (of the association Employee-Boss) *}
|
||||
subsubsection{* Definition (of the association Employee-Boss) *}
|
||||
|
||||
text{* We start with a oid for the association; this oid can be used
|
||||
in presence of association classes to represent the association inside an object,
|
||||
|
|
@ -891,7 +891,7 @@ lemmas [simp] =
|
|||
dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S>_at_pre_def
|
||||
dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R>\<Y>_at_pre_def
|
||||
|
||||
subsection{* Context Passing *}
|
||||
subsubsection{* Context Passing *}
|
||||
|
||||
lemmas [simp] = eval_extract_def
|
||||
|
||||
|
|
@ -924,7 +924,7 @@ lemmas cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R
|
|||
cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R>\<Y>_at_pre[THEN allI[THEN allI],
|
||||
of "\<lambda> X _. X" "\<lambda> _ \<tau>. \<tau>", THEN cpI1]
|
||||
|
||||
subsection{* Execution with Invalid or Null as Argument *}
|
||||
subsubsection{* Execution with Invalid or Null as Argument *}
|
||||
|
||||
lemma dot\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<A>\<N>\<Y>_nullstrict [simp]: "(null).any = invalid"
|
||||
by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def)
|
||||
|
|
@ -956,7 +956,7 @@ lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R>\<Y
|
|||
by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def)
|
||||
|
||||
|
||||
section{* A Little Infra-structure on Example States *}
|
||||
subsection{* A Little Infra-structure on Example States *}
|
||||
|
||||
text{*
|
||||
The example we are defining in this section comes from the figure~\ref{fig:eam1_system-states}.
|
||||
|
|
|
|||
|
|
@ -40,7 +40,7 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
header{* The Employee Design Model (OCL) *}
|
||||
section{* The Employee Design Model (OCL) *}
|
||||
|
||||
theory
|
||||
Employee_DesignModel_OCLPart
|
||||
|
|
@ -48,10 +48,10 @@ imports
|
|||
Employee_DesignModel_UMLPart
|
||||
begin
|
||||
text {* \label{ex:employee-design:ocl} *}
|
||||
section{* Standard State Infrastructure *}
|
||||
subsection{* Standard State Infrastructure *}
|
||||
text{* Ideally, these definitions are automatically generated from the class model. *}
|
||||
|
||||
section{* Invariant *}
|
||||
subsection{* Invariant *}
|
||||
text{* These recursive predicates can be defined conservatively
|
||||
by greatest fix-point
|
||||
constructions---automatically. See~\cite{brucker.ea:hol-ocl-book:2006,brucker:interactive:2007}
|
||||
|
|
@ -81,7 +81,7 @@ coinductive inv :: "Person \<Rightarrow> (\<AA>)st \<Rightarrow> bool" where
|
|||
( (inv(self .boss))\<tau> )))
|
||||
\<Longrightarrow> ( inv self \<tau>)"
|
||||
|
||||
section{* The Contract of a Recursive Query *}
|
||||
subsection{* The Contract of a Recursive Query *}
|
||||
text{* The original specification of a recursive query :
|
||||
\begin{ocl}
|
||||
context Person::contents():Set(Integer)
|
||||
|
|
@ -121,7 +121,7 @@ text{* These \inlineocl{@pre} variants on methods are only available on queries,
|
|||
operations without side-effect. *}
|
||||
|
||||
|
||||
section{* The Contract of a Method *}
|
||||
subsection{* The Contract of a Method *}
|
||||
text{*
|
||||
The specification in high-level OCL input syntax reads as follows:
|
||||
\begin{ocl}
|
||||
|
|
|
|||
|
|
@ -40,7 +40,7 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
header{* The Employee Design Model (UML) *}
|
||||
section{* The Employee Design Model (UML) *}
|
||||
|
||||
theory
|
||||
Employee_DesignModel_UMLPart
|
||||
|
|
@ -50,7 +50,7 @@ begin
|
|||
|
||||
text {* \label{ex:employee-design:uml} *}
|
||||
|
||||
section{* Introduction *}
|
||||
subsection{* Introduction *}
|
||||
text{*
|
||||
For certain concepts like classes and class-types, only a generic
|
||||
definition for its resulting semantics can be given. Generic means,
|
||||
|
|
@ -69,7 +69,7 @@ text{* Such generic function or ``compiler'' can be implemented in
|
|||
concepts of the compilation informally, and present a concrete
|
||||
example which is verified in Isabelle/HOL. *}
|
||||
|
||||
subsection{* Outlining the Example *}
|
||||
subsubsection{* Outlining the Example *}
|
||||
|
||||
text{* We are presenting here a ``design-model'' of the (slightly
|
||||
modified) example Figure 7.3, page 20 of
|
||||
|
|
@ -90,7 +90,7 @@ by the attribute \inlineocl+boss+ and the operation \inlineocl+employees+ (to b
|
|||
captured by the subsequent theory).
|
||||
*}
|
||||
|
||||
section{* Example Data-Universe and its Infrastructure *}
|
||||
subsection{* Example Data-Universe and its Infrastructure *}
|
||||
text{* Ideally, the following is generated automatically from a UML class model. *}
|
||||
|
||||
(* @{text "'\<AA>"} -- \mathfrak{A} *)
|
||||
|
|
@ -156,7 +156,7 @@ end
|
|||
|
||||
|
||||
|
||||
section{* Instantiation of the Generic Strict Equality *}
|
||||
subsection{* Instantiation of the Generic Strict Equality *}
|
||||
text{* We instantiate the referential equality
|
||||
on @{text "Person"} and @{text "OclAny"} *}
|
||||
|
||||
|
|
@ -190,8 +190,8 @@ two operations to declare and to provide two overloading definitions for the two
|
|||
*}
|
||||
|
||||
|
||||
section{* OclAsType *}
|
||||
subsection{* Definition *}
|
||||
subsection{* OclAsType *}
|
||||
subsubsection{* Definition *}
|
||||
|
||||
consts OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> OclAny" ("(_) .oclAsType'(OclAny')")
|
||||
consts OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Person" ("(_) .oclAsType'(Person')")
|
||||
|
|
@ -232,7 +232,7 @@ lemmas [simp] =
|
|||
OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny
|
||||
OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person
|
||||
|
||||
subsection{* Context Passing *}
|
||||
subsubsection{* Context Passing *}
|
||||
|
||||
lemma cp_OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person: "cp P \<Longrightarrow> cp(\<lambda>X. (P (X::Person)::Person) .oclAsType(OclAny))"
|
||||
by(rule cpI1, simp_all add: OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
|
||||
|
|
@ -263,7 +263,7 @@ lemmas [simp] =
|
|||
cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
|
||||
cp_OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
|
||||
|
||||
subsection{* Execution with Invalid or Null as Argument *}
|
||||
subsubsection{* Execution with Invalid or Null as Argument *}
|
||||
|
||||
lemma OclAsType\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_strict : "(invalid::OclAny) .oclAsType(OclAny) = invalid"
|
||||
by(simp)
|
||||
|
|
@ -292,8 +292,8 @@ by(simp)
|
|||
lemma OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_nullstrict : "(null::Person) .oclAsType(Person) = null"
|
||||
by(simp)
|
||||
|
||||
section{* OclIsTypeOf *}
|
||||
subsection{* Definition *}
|
||||
subsection{* OclIsTypeOf *}
|
||||
subsubsection{* Definition *}
|
||||
|
||||
consts OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsTypeOf'(OclAny')")
|
||||
consts OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsTypeOf'(Person')")
|
||||
|
|
@ -328,7 +328,7 @@ defs (overloaded) OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Pe
|
|||
\<bottom> \<Rightarrow> invalid \<tau>
|
||||
| _ \<Rightarrow> true \<tau>)"
|
||||
|
||||
subsection{* Context Passing *}
|
||||
subsubsection{* Context Passing *}
|
||||
|
||||
lemma cp_OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person: "cp P \<Longrightarrow> cp(\<lambda>X.(P(X::Person)::Person).oclIsTypeOf(OclAny))"
|
||||
by(rule cpI1, simp_all add: OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
|
||||
|
|
@ -360,7 +360,7 @@ lemmas [simp] =
|
|||
cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
|
||||
cp_OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
|
||||
|
||||
subsection{* Execution with Invalid or Null as Argument *}
|
||||
subsubsection{* Execution with Invalid or Null as Argument *}
|
||||
|
||||
lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_strict1[simp]:
|
||||
"(invalid::OclAny) .oclIsTypeOf(OclAny) = invalid"
|
||||
|
|
@ -395,7 +395,7 @@ lemma OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_strict2
|
|||
by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def
|
||||
OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person)
|
||||
|
||||
subsection{* Up Down Casting *}
|
||||
subsubsection{* Up Down Casting *}
|
||||
|
||||
lemma actualType_larger_staticType:
|
||||
assumes isdef: "\<tau> \<Turnstile> (\<delta> X)"
|
||||
|
|
@ -452,8 +452,8 @@ shows "\<tau> \<Turnstile> (X .oclIsTypeOf(Person) implies (X .oclAsType(OclAny)
|
|||
by (simp add: OclImplies_true)
|
||||
|
||||
|
||||
section{* OclIsKindOf *}
|
||||
subsection{* Definition *}
|
||||
subsection{* OclIsKindOf *}
|
||||
subsubsection{* Definition *}
|
||||
|
||||
consts OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsKindOf'(OclAny')")
|
||||
consts OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: "'\<alpha> \<Rightarrow> Boolean" ("(_).oclIsKindOf'(Person')")
|
||||
|
|
@ -484,7 +484,7 @@ defs (overloaded) OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Pe
|
|||
\<bottom> \<Rightarrow> invalid \<tau>
|
||||
| _ \<Rightarrow> true \<tau>)"
|
||||
|
||||
subsection{* Context Passing *}
|
||||
subsubsection{* Context Passing *}
|
||||
|
||||
lemma cp_OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person_Person: "cp P \<Longrightarrow> cp(\<lambda>X.(P(X::Person)::Person).oclIsKindOf(OclAny))"
|
||||
by(rule cpI1, simp_all add: OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_Person)
|
||||
|
|
@ -515,7 +515,7 @@ lemmas [simp] =
|
|||
cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_OclAny
|
||||
cp_OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny_Person
|
||||
|
||||
subsection{* Execution with Invalid or Null as Argument *}
|
||||
subsubsection{* Execution with Invalid or Null as Argument *}
|
||||
|
||||
lemma OclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny_strict1[simp] : "(invalid::OclAny) .oclIsKindOf(OclAny) = invalid"
|
||||
by(rule ext, simp add: invalid_def bot_option_def
|
||||
|
|
@ -549,7 +549,7 @@ lemma OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person_strict2
|
|||
by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def
|
||||
OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_Person)
|
||||
|
||||
subsection{* Up Down Casting *}
|
||||
subsubsection{* Up Down Casting *}
|
||||
|
||||
lemma actualKind_larger_staticKind:
|
||||
assumes isdef: "\<tau> \<Turnstile> (\<delta> X)"
|
||||
|
|
@ -568,7 +568,7 @@ apply(auto simp : bot_fun_def null_fun_def null_option_def bot_option_def null_d
|
|||
split: option.split type\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y.split type\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n.split)
|
||||
by(simp add: OclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_OclAny OclValid_def false_def true_def)
|
||||
|
||||
section{* OclAllInstances *}
|
||||
subsection{* OclAllInstances *}
|
||||
|
||||
text{* To denote OCL-types occuring in OCL expressions syntactically---as, for example, as
|
||||
``argument'' of \inlineisar{oclAllInstances()}---we use the inverses of the injection
|
||||
|
|
@ -599,7 +599,7 @@ lemma OclAllInstances_at_pre\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exe
|
|||
unfolding OclAllInstances_at_pre_def
|
||||
by(rule OclAllInstances_generic\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_exec)
|
||||
|
||||
subsection{* OclIsTypeOf *}
|
||||
subsubsection{* OclIsTypeOf *}
|
||||
|
||||
lemma OclAny_allInstances_generic_oclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y1:
|
||||
assumes [simp]: "\<And>x. pre_post (x, x) = x"
|
||||
|
|
@ -663,7 +663,7 @@ lemma Person_allInstances_at_pre_oclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^s
|
|||
unfolding OclAllInstances_at_pre_def
|
||||
by(rule Person_allInstances_generic_oclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
|
||||
|
||||
subsection{* OclIsKindOf *}
|
||||
subsubsection{* OclIsKindOf *}
|
||||
lemma OclAny_allInstances_generic_oclIsKindOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y:
|
||||
"\<tau> \<Turnstile> ((OclAllInstances_generic pre_post OclAny)->forAll(X|X .oclIsKindOf(OclAny)))"
|
||||
apply(simp add: OclValid_def del: OclAllInstances_generic_def)
|
||||
|
|
@ -721,12 +721,12 @@ lemma Person_allInstances_at_pre_oclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^s
|
|||
unfolding OclAllInstances_at_pre_def
|
||||
by(rule Person_allInstances_generic_oclIsKindOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n)
|
||||
|
||||
section{* The Accessors (any, boss, salary) *}
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subsection{* The Accessors (any, boss, salary) *}
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text{*\label{sec:edm-accessors}*}
|
||||
text{* Should be generated entirely from a class-diagram. *}
|
||||
|
||||
|
||||
subsection{* Definition *}
|
||||
subsubsection{* Definition *}
|
||||
|
||||
definition eval_extract :: "('\<AA>,('a::object) option option) val
|
||||
\<Rightarrow> (oid \<Rightarrow> ('\<AA>,'c::null) val)
|
||||
|
|
@ -823,7 +823,7 @@ lemmas [simp] =
|
|||
dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S>_at_pre_def
|
||||
dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R>\<Y>_at_pre_def
|
||||
|
||||
subsection{* Context Passing *}
|
||||
subsubsection{* Context Passing *}
|
||||
|
||||
lemmas [simp] = eval_extract_def
|
||||
|
||||
|
|
@ -856,7 +856,7 @@ lemmas cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R
|
|||
cp_dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R>\<Y>_at_pre[THEN allI[THEN allI],
|
||||
of "\<lambda> X _. X" "\<lambda> _ \<tau>. \<tau>", THEN cpI1]
|
||||
|
||||
subsection{* Execution with Invalid or Null as Argument *}
|
||||
subsubsection{* Execution with Invalid or Null as Argument *}
|
||||
|
||||
lemma dot\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<A>\<N>\<Y>_nullstrict [simp]: "(null).any = invalid"
|
||||
by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def)
|
||||
|
|
@ -888,7 +888,7 @@ lemma dot\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<S>\<A>\<L>\<A>\<R>\<Y
|
|||
by(rule ext, simp add: null_fun_def null_option_def bot_option_def null_def invalid_def)
|
||||
|
||||
|
||||
section{* A Little Infra-structure on Example States *}
|
||||
subsection{* A Little Infra-structure on Example States *}
|
||||
|
||||
text{*
|
||||
The example we are defining in this section comes from the figure~\ref{fig:edm1_system-states}.
|
||||
|
|
|
|||
Loading…
Reference in New Issue