Import of AFP entry for Isabelle 2018.

Featherweight_OCL/UML_Library.thy

@@ -153,7 +153,7 @@ where     "OclAsSeq\<^sub>P\<^sub>a\<^sub>i\<^sub>r S = Sequence{S .First(), S .
 subsection{* Definition: asBag *}
 
 definition OclAsBag\<^sub>S\<^sub>e\<^sub>q   :: "[('\<AA>,'\<alpha>::null)Sequence]\<Rightarrow>('\<AA>,'\<alpha>)Bag" ("(_)->asBag\<^sub>S\<^sub>e\<^sub>q'(')")
-where     "OclAsBag\<^sub>S\<^sub>e\<^sub>q S = (\<lambda>\<tau>. Abs_Bag\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor>\<lfloor>\<lambda>s. if list_ex (op = s) \<lceil>\<lceil>Rep_Sequence\<^sub>b\<^sub>a\<^sub>s\<^sub>e (S \<tau>)\<rceil>\<rceil> then 1 else 0\<rfloor>\<rfloor>)"
+where     "OclAsBag\<^sub>S\<^sub>e\<^sub>q S = (\<lambda>\<tau>. Abs_Bag\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor>\<lfloor>\<lambda>s. if list_ex ((=) s) \<lceil>\<lceil>Rep_Sequence\<^sub>b\<^sub>a\<^sub>s\<^sub>e (S \<tau>)\<rceil>\<rceil> then 1 else 0\<rfloor>\<rfloor>)"
 
 definition OclAsBag\<^sub>S\<^sub>e\<^sub>t   :: "[('\<AA>,'\<alpha>::null)Set]\<Rightarrow>('\<AA>,'\<alpha>)Bag" ("(_)->asBag\<^sub>S\<^sub>e\<^sub>t'(')")
 where     "OclAsBag\<^sub>S\<^sub>e\<^sub>t S = (\<lambda>\<tau>. Abs_Bag\<^sub>b\<^sub>a\<^sub>s\<^sub>e \<lfloor>\<lfloor>\<lambda>s. if s \<in> \<lceil>\<lceil>Rep_Set\<^sub>b\<^sub>a\<^sub>s\<^sub>e (S \<tau>)\<rceil>\<rceil> then 1 else 0\<rfloor>\<rfloor>)"

Featherweight_OCL/UML_Logic.thy

@@ -1063,9 +1063,9 @@ lemmas cp_intro[intro!,simp,code_unfold] =
        cp_defined[THEN allI[THEN allI[THEN cpI1], of defined]]
        cp_valid[THEN allI[THEN allI[THEN cpI1], of valid]]
        cp_OclNot[THEN allI[THEN allI[THEN cpI1], of not]]
-       cp_OclAnd[THEN allI[THEN allI[THEN allI[THEN cpI2]], of "op and"]]
+       cp_OclAnd[THEN allI[THEN allI[THEN allI[THEN cpI2]], of "(and)"]]
-       cp_OclOr[THEN allI[THEN allI[THEN allI[THEN cpI2]], of "op or"]]
+       cp_OclOr[THEN allI[THEN allI[THEN allI[THEN cpI2]], of "(or)"]]
-       cp_OclImplies[THEN allI[THEN allI[THEN allI[THEN cpI2]], of "op implies"]]
+       cp_OclImplies[THEN allI[THEN allI[THEN allI[THEN cpI2]], of "(implies)"]]
        cp_StrongEq[THEN allI[THEN allI[THEN allI[THEN cpI2]],
                    of "StrongEq"]]
 

Featherweight_OCL/UML_State.thy

@@ -291,11 +291,11 @@ qed
 
 lemma state_update_vs_allInstances_generic_empty:
 assumes [simp]: "\<And>a. pre_post (mk a) = a"
-shows   "(mk \<lparr>heap=empty, assocs=A\<rparr>) \<Turnstile> OclAllInstances_generic pre_post Type \<doteq> Set{}"
+shows   "(mk \<lparr>heap=Map.empty, assocs=A\<rparr>) \<Turnstile> OclAllInstances_generic pre_post Type \<doteq> Set{}"
 proof -
  have state_update_vs_allInstances_empty:
-  "(OclAllInstances_generic pre_post Type) (mk \<lparr>heap=empty, assocs=A\<rparr>) =
+  "(OclAllInstances_generic pre_post Type) (mk \<lparr>heap=Map.empty, assocs=A\<rparr>) =
-   Set{} (mk \<lparr>heap=empty, assocs=A\<rparr>)"
+   Set{} (mk \<lparr>heap=Map.empty, assocs=A\<rparr>)"
  by(simp add: OclAllInstances_generic_def mtSet_def)
  show ?thesis
   apply(simp only: OclValid_def, subst StrictRefEq\<^sub>S\<^sub>e\<^sub>t.cp0,
@@ -511,7 +511,7 @@ shows      "is_represented_in_state snd x H \<tau>"
 by(rule represented_generic_objects_in_state[OF A[simplified OclAllInstances_at_post_def]])
 
 lemma state_update_vs_allInstances_at_post_empty:
-shows   "(\<sigma>, \<lparr>heap=empty, assocs=A\<rparr>) \<Turnstile> Type .allInstances() \<doteq> Set{}"
+shows   "(\<sigma>, \<lparr>heap=Map.empty, assocs=A\<rparr>) \<Turnstile> Type .allInstances() \<doteq> Set{}"
 unfolding OclAllInstances_at_post_def
 by(rule state_update_vs_allInstances_generic_empty[OF snd_conv])
 
@@ -617,7 +617,7 @@ by(rule represented_generic_objects_in_state[OF A[simplified OclAllInstances_at_
 
 
 lemma state_update_vs_allInstances_at_pre_empty:
-shows   "(\<lparr>heap=empty, assocs=A\<rparr>, \<sigma>) \<Turnstile> Type .allInstances@pre() \<doteq> Set{}"
+shows   "(\<lparr>heap=Map.empty, assocs=A\<rparr>, \<sigma>) \<Turnstile> Type .allInstances@pre() \<doteq> Set{}"
 unfolding OclAllInstances_at_pre_def
 by(rule state_update_vs_allInstances_generic_empty[OF fst_conv])
 
@@ -1025,7 +1025,7 @@ section{* Accessors on Object *}
 subsection{* Definition *}
 
 definition "select_object mt incl smash deref l = smash (foldl incl mt (map deref l))
- (* smash returns null with mt in input (in this case, object contains null pointer) *)"
+ \<comment> \<open>smash returns null with \<open>mt\<close> in input (in this case, object contains null pointer)\<close>"
 
 text{* The continuation @{text f} is usually instantiated with a smashing
 function which is either the identity @{term id} or, for \inlineocl{0..1} cardinalities

Featherweight_OCL/basic_types/UML_Integer.thy

@@ -125,7 +125,7 @@ definition OclAdd\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r ::"('\
 where "x +\<^sub>i\<^sub>n\<^sub>t y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> + \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclAdd\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "op +\<^sub>i\<^sub>n\<^sub>t" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> + \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclAdd\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "(+\<^sub>i\<^sub>n\<^sub>t)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> + \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by unfold_locales (auto simp:OclAdd\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r_def bot_option_def null_option_def)
 
   
@@ -133,7 +133,7 @@ definition OclMinus\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r ::"(
 where "x -\<^sub>i\<^sub>n\<^sub>t y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> - \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclMinus\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "op -\<^sub>i\<^sub>n\<^sub>t" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> - \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclMinus\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "(-\<^sub>i\<^sub>n\<^sub>t)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> - \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclMinus\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r_def bot_option_def null_option_def)
 
                        
@@ -141,7 +141,7 @@ definition OclMult\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r ::"('
 where "x *\<^sub>i\<^sub>n\<^sub>t y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> * \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau>"
-interpretation OclMult\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "op *\<^sub>i\<^sub>n\<^sub>t" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> * \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclMult\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "OclMult\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> * \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclMult\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r_def bot_option_def null_option_def)
           
 text{* Here is the special case of division, which is defined as invalid for division
@@ -163,14 +163,14 @@ definition OclLess\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r ::"('
 where "x <\<^sub>i\<^sub>n\<^sub>t y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> < \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclLess\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "op <\<^sub>i\<^sub>n\<^sub>t" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> < \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclLess\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "(<\<^sub>i\<^sub>n\<^sub>t)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> < \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclLess\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r_def bot_option_def null_option_def)
 
 definition OclLe\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r ::"('\<AA>)Integer \<Rightarrow> ('\<AA>)Integer \<Rightarrow> ('\<AA>)Boolean" (infix "\<le>\<^sub>i\<^sub>n\<^sub>t" 35)
 where "x \<le>\<^sub>i\<^sub>n\<^sub>t y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> \<le> \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclLe\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "op \<le>\<^sub>i\<^sub>n\<^sub>t" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> \<le> \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclLe\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r : profile_bin\<^sub>d_\<^sub>d "(\<le>\<^sub>i\<^sub>n\<^sub>t)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> \<le> \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclLe\<^sub>I\<^sub>n\<^sub>t\<^sub>e\<^sub>g\<^sub>e\<^sub>r_def bot_option_def null_option_def)
 
 subsubsection{* Basic Properties *}

Featherweight_OCL/basic_types/UML_Real.thy

@@ -125,7 +125,7 @@ definition OclAdd\<^sub>R\<^sub>e\<^sub>a\<^sub>l ::"('\<AA>)Real \<Rightarrow>
 where "x +\<^sub>r\<^sub>e\<^sub>a\<^sub>l y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> + \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclAdd\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "op +\<^sub>r\<^sub>e\<^sub>a\<^sub>l" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> + \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclAdd\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "(+\<^sub>r\<^sub>e\<^sub>a\<^sub>l)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> + \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by unfold_locales (auto simp:OclAdd\<^sub>R\<^sub>e\<^sub>a\<^sub>l_def bot_option_def null_option_def)
 
 
@@ -133,7 +133,7 @@ definition OclMinus\<^sub>R\<^sub>e\<^sub>a\<^sub>l ::"('\<AA>)Real \<Rightarrow
 where "x -\<^sub>r\<^sub>e\<^sub>a\<^sub>l y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> - \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclMinus\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "op -\<^sub>r\<^sub>e\<^sub>a\<^sub>l" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> - \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclMinus\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "(-\<^sub>r\<^sub>e\<^sub>a\<^sub>l)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> - \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclMinus\<^sub>R\<^sub>e\<^sub>a\<^sub>l_def bot_option_def null_option_def)
 
 
@@ -141,7 +141,7 @@ definition OclMult\<^sub>R\<^sub>e\<^sub>a\<^sub>l ::"('\<AA>)Real \<Rightarrow>
 where "x *\<^sub>r\<^sub>e\<^sub>a\<^sub>l y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> * \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau>"
-interpretation OclMult\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "op *\<^sub>r\<^sub>e\<^sub>a\<^sub>l" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> * \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclMult\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "OclMult\<^sub>R\<^sub>e\<^sub>a\<^sub>l" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> * \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclMult\<^sub>R\<^sub>e\<^sub>a\<^sub>l_def bot_option_def null_option_def)
           
 text{* Here is the special case of division, which is defined as invalid for division
@@ -164,14 +164,14 @@ definition OclLess\<^sub>R\<^sub>e\<^sub>a\<^sub>l ::"('\<AA>)Real \<Rightarrow>
 where "x <\<^sub>r\<^sub>e\<^sub>a\<^sub>l y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> < \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclLess\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "op <\<^sub>r\<^sub>e\<^sub>a\<^sub>l" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> < \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclLess\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "(<\<^sub>r\<^sub>e\<^sub>a\<^sub>l)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> < \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclLess\<^sub>R\<^sub>e\<^sub>a\<^sub>l_def bot_option_def null_option_def)
 
 definition OclLe\<^sub>R\<^sub>e\<^sub>a\<^sub>l ::"('\<AA>)Real \<Rightarrow> ('\<AA>)Real \<Rightarrow> ('\<AA>)Boolean" (infix "\<le>\<^sub>r\<^sub>e\<^sub>a\<^sub>l" 35)
 where "x \<le>\<^sub>r\<^sub>e\<^sub>a\<^sub>l y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>\<lceil>\<lceil>x \<tau>\<rceil>\<rceil> \<le> \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclLe\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "op \<le>\<^sub>r\<^sub>e\<^sub>a\<^sub>l" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> \<le> \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
+interpretation OclLe\<^sub>R\<^sub>e\<^sub>a\<^sub>l : profile_bin\<^sub>d_\<^sub>d "(\<le>\<^sub>r\<^sub>e\<^sub>a\<^sub>l)" "\<lambda> x y. \<lfloor>\<lfloor>\<lceil>\<lceil>x\<rceil>\<rceil> \<le> \<lceil>\<lceil>y\<rceil>\<rceil>\<rfloor>\<rfloor>"
          by   unfold_locales  (auto simp:OclLe\<^sub>R\<^sub>e\<^sub>a\<^sub>l_def bot_option_def null_option_def)
 
 subsubsection{* Basic Properties *}

Featherweight_OCL/basic_types/UML_String.thy

@@ -106,7 +106,7 @@ definition OclAdd\<^sub>S\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g ::"('\<AA>)Str
 where "x +\<^sub>s\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g y \<equiv> \<lambda> \<tau>. if (\<delta> x) \<tau> = true \<tau> \<and> (\<delta> y) \<tau> = true \<tau>
                        then \<lfloor>\<lfloor>concat [\<lceil>\<lceil>x \<tau>\<rceil>\<rceil>, \<lceil>\<lceil>y \<tau>\<rceil>\<rceil>]\<rfloor>\<rfloor>
                        else invalid \<tau> "
-interpretation OclAdd\<^sub>S\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g : profile_bin\<^sub>d_\<^sub>d "op +\<^sub>s\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g" "\<lambda> x y. \<lfloor>\<lfloor>concat [\<lceil>\<lceil>x\<rceil>\<rceil>, \<lceil>\<lceil>y\<rceil>\<rceil>]\<rfloor>\<rfloor>"
+interpretation OclAdd\<^sub>S\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g : profile_bin\<^sub>d_\<^sub>d "(+\<^sub>s\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g)" "\<lambda> x y. \<lfloor>\<lfloor>concat [\<lceil>\<lceil>x\<rceil>\<rceil>, \<lceil>\<lceil>y\<rceil>\<rceil>]\<rfloor>\<rfloor>"
          by unfold_locales (auto simp:OclAdd\<^sub>S\<^sub>t\<^sub>r\<^sub>i\<^sub>n\<^sub>g_def bot_option_def null_option_def)
          
 (* TODO : size(), concat, substring(s:string) toInteger, toReal, at(i:Integer), characters() etc. *)

Featherweight_OCL/collection_types/UML_Set.thy

@@ -3072,11 +3072,11 @@ lemma StrictRefEq\<^sub>S\<^sub>e\<^sub>t_exec[simp,code_unfold] :
   (if \<delta> x then (if \<delta> y
                 then ((x->forAll\<^sub>S\<^sub>e\<^sub>t(z| y->includes\<^sub>S\<^sub>e\<^sub>t(z)) and (y->forAll\<^sub>S\<^sub>e\<^sub>t(z| x->includes\<^sub>S\<^sub>e\<^sub>t(z)))))
                 else if \<upsilon> y
-                      then false (* x'->includes = null *)
+                      then false \<comment> \<open>\<open>x'->includes = null\<close>\<close>
                       else invalid
                       endif
                 endif)
-         else if \<upsilon> x (* null = ??? *)
+         else if \<upsilon> x \<comment> \<open>\<open>null = ???\<close>\<close>
               then if \<upsilon> y then not(\<delta> y) else invalid endif
               else invalid
               endif

Featherweight_OCL/examples/Employee_Model/Analysis/Analysis_OCL.thy

@@ -82,7 +82,7 @@ oops
    occur in the state. *)
 
 lemma REC_pre : "\<tau> \<Turnstile> Person_label\<^sub>g\<^sub>l\<^sub>o\<^sub>b\<^sub>a\<^sub>l\<^sub>i\<^sub>n\<^sub>v 
-       \<Longrightarrow> \<tau> \<Turnstile> Person .allInstances()->includes\<^sub>S\<^sub>e\<^sub>t(X) (* X represented object in state *)
+       \<Longrightarrow> \<tau> \<Turnstile> Person .allInstances()->includes\<^sub>S\<^sub>e\<^sub>t(X) \<comment> \<open>\<open>X\<close> represented object in state\<close>
        \<Longrightarrow> \<exists> REC.  \<tau> \<Turnstile> REC(X)  \<triangleq> (Person_label\<^sub>i\<^sub>n\<^sub>v (X) and (X .boss <> null implies REC(X .boss)))"
 oops (* Attempt to allegiate the burden of he following axiomatizations: could be
         a witness for a constant specification ...*)       
@@ -227,8 +227,8 @@ axiomatization where contentsATpre_def:
 " (self).contents@pre() = (\<lambda> \<tau>.
       SOME res. let res = \<lambda> _. res in
       if \<tau> \<Turnstile> (\<delta> self)
-      then ((\<tau> \<Turnstile> true) \<and>                                  (* pre *)
+      then ((\<tau> \<Turnstile> true) \<and>                            \<comment> \<open>pre\<close>
-            (\<tau> \<Turnstile> (res \<triangleq> if (self).boss@pre \<doteq> null  (* post *)
+            (\<tau> \<Turnstile> (res \<triangleq> if (self).boss@pre \<doteq> null  \<comment> \<open>post\<close>
                          then Set{(self).salary@pre}
                          else (self).boss@pre .contents@pre()
                                     ->including\<^sub>S\<^sub>e\<^sub>t(self .salary@pre)

Featherweight_OCL/examples/Employee_Model/Analysis/Analysis_UML.thy

@@ -194,7 +194,7 @@ lemmas cps23 =
     StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_strict2
                         [of "x::Person",
                          simplified StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n[symmetric]]
-
+  for x y \<tau> P Q
 text{* For each Class \emph{C}, we will have a casting operation \inlineocl{.oclAsType($C$)},
    a test on the actual type \inlineocl{.oclIsTypeOf($C$)} as well as its relaxed form
    \inlineocl{.oclIsKindOf($C$)} (corresponding exactly to Java's \verb+instanceof+-operator.
@@ -244,7 +244,7 @@ begin
                    (\<lambda>\<tau>. case X \<tau> of
                               \<bottom>   \<Rightarrow> invalid \<tau>
                             | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> null \<tau>
-                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow>  invalid \<tau>   (* down-cast exception *)
+                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow>  invalid \<tau>   \<comment> \<open>down-cast exception\<close>
                             | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>a\<rfloor> \<rfloor>\<rfloor> \<Rightarrow>  \<lfloor>\<lfloor>mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid a\<rfloor>\<rfloor>)"
 end
 
@@ -320,7 +320,7 @@ begin
         "(X::OclAny) .oclIsTypeOf(OclAny) \<equiv>
                    (\<lambda>\<tau>. case X \<tau> of
                               \<bottom>   \<Rightarrow> invalid \<tau>
-                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  (* invalid ?? *)
+                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  \<comment> \<open>invalid ??\<close>
                             | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow> true \<tau>
                             | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>_\<rfloor> \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)"
 end
@@ -328,7 +328,7 @@ end
 lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny':
          "(X::OclAny) .oclIsTypeOf(OclAny) = 
                     (\<lambda> \<tau>. if \<tau> \<Turnstile> \<upsilon> X then (case X \<tau> of
-                                              \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  (* invalid ?? *)
+                                              \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  \<comment> \<open>invalid ??\<close>
                                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow> true \<tau>
                                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>_\<rfloor> \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)
                                            else invalid \<tau>)"
@@ -339,7 +339,7 @@ interpretation OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAn
        profile_mono_schemeV 
        "OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::OclAny \<Rightarrow> Boolean" 
        "\<lambda> X. (case X of
-                    \<lfloor>None\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>True\<rfloor>\<rfloor>  (* invalid ?? *)
+                    \<lfloor>None\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>True\<rfloor>\<rfloor>  \<comment> \<open>invalid ??\<close>
                   | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid None \<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>True\<rfloor>\<rfloor>
                   | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>_\<rfloor> \<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>False\<rfloor>\<rfloor>)"                     
       apply(unfold_locales, simp add: atomize_eq, rule ext)
@@ -352,8 +352,8 @@ begin
         "(X::Person) .oclIsTypeOf(OclAny) \<equiv>
                    (\<lambda>\<tau>. case X \<tau> of
                               \<bottom>   \<Rightarrow> invalid \<tau>
-                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>    (* invalid ?? *)
+                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>    \<comment> \<open>invalid ??\<close>
-                            | \<lfloor>\<lfloor> _ \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)"  (* must have actual type Person otherwise  *)
+                            | \<lfloor>\<lfloor> _ \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)  \<comment> \<open>must have actual type \<open>Person\<close> otherwise\<close>"
 end
 
 overloading OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: OclAny \<Rightarrow> Boolean"
@@ -681,8 +681,8 @@ by(rule OclAny_allInstances_generic_oclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\
 lemma OclAny_allInstances_generic_oclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2:
 assumes [simp]: "\<And>x. pre_post (x, x) = x"
 shows "\<exists>\<tau>. (\<tau> \<Turnstile> not ((OclAllInstances_generic pre_post OclAny)->forAll\<^sub>S\<^sub>e\<^sub>t(X|X .oclIsTypeOf(OclAny))))"
-proof - fix oid a let ?t0 = "\<lparr>heap = empty(oid \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>a\<rfloor>)),
+proof - fix oid a let ?t0 = "\<lparr>heap = Map.empty(oid \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>a\<rfloor>)),
-                              assocs = empty\<rparr>" show ?thesis
+                              assocs = Map.empty\<rparr>" show ?thesis
  apply(rule_tac x = "(?t0, ?t0)" in exI, simp add: OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True
                   OclAllInstances_generic_defined[simplified OclValid_def])
@@ -801,8 +801,8 @@ definition eval_extract :: "('\<AA>,('a::object) option option) val
                             \<Rightarrow> (oid \<Rightarrow> ('\<AA>,'c::null) val)
                             \<Rightarrow> ('\<AA>,'c::null) val"
 where "eval_extract X f = (\<lambda> \<tau>. case X \<tau> of
-                                    \<bottom> \<Rightarrow> invalid \<tau>   (* exception propagation *)
+                                    \<bottom> \<Rightarrow> invalid \<tau>   \<comment> \<open>exception propagation\<close>
-                               | \<lfloor>  \<bottom> \<rfloor> \<Rightarrow> invalid \<tau> (* dereferencing null pointer *)
+                               | \<lfloor>  \<bottom> \<rfloor> \<Rightarrow> invalid \<tau> \<comment> \<open>dereferencing null pointer\<close>
                                | \<lfloor>\<lfloor> obj \<rfloor>\<rfloor> \<Rightarrow> f (oid_of obj) \<tau>)"
 
 definition "choose\<^sub>2_1 = fst"
@@ -1054,30 +1054,30 @@ definition "person9 \<equiv> mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n
 text_raw{* \endisatagafp*}
 
 definition
-      "\<sigma>\<^sub>1  \<equiv> \<lparr> heap = empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid0 \<lfloor>1000\<rfloor>))
+      "\<sigma>\<^sub>1  \<equiv> \<lparr> heap = Map.empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid0 \<lfloor>1000\<rfloor>))
                            (oid1 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid1 \<lfloor>1200\<rfloor>))
-                          (*oid2*)
+                           \<^cancel>\<open>oid2\<close>
                            (oid3 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid3 \<lfloor>2600\<rfloor>))
                            (oid4 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person5)
                            (oid5 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid5 \<lfloor>2300\<rfloor>))
-                          (*oid6*)
+                           \<^cancel>\<open>oid6\<close>
-                          (*oid7*)
+                           \<^cancel>\<open>oid7\<close>
                            (oid8 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person9),
-               assocs = empty(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S> \<mapsto> [[[oid0],[oid1]],[[oid3],[oid4]],[[oid5],[oid3]]]) \<rparr>"
+               assocs = Map.empty(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S> \<mapsto> [[[oid0],[oid1]],[[oid3],[oid4]],[[oid5],[oid3]]]) \<rparr>"
 
 definition
-      "\<sigma>\<^sub>1' \<equiv> \<lparr> heap = empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person1)
+      "\<sigma>\<^sub>1' \<equiv> \<lparr> heap = Map.empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person1)
                            (oid1 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person2)
                            (oid2 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person3)
                            (oid3 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person4)
-                          (*oid4*)
+                           \<^cancel>\<open>oid4\<close>
                            (oid5 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person6)
                            (oid6 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person7)
                            (oid7 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person8)
                            (oid8 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person9),
-               assocs = empty(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S> \<mapsto> [[[oid0],[oid1]],[[oid1],[oid1]],[[oid5],[oid6]],[[oid6],[oid6]]]) \<rparr>"
+               assocs = Map.empty(oid\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S> \<mapsto> [[[oid0],[oid1]],[[oid1],[oid1]],[[oid5],[oid6]],[[oid6],[oid6]]]) \<rparr>"
 
-definition "\<sigma>\<^sub>0 \<equiv> \<lparr> heap = empty, assocs = empty \<rparr>"
+definition "\<sigma>\<^sub>0 \<equiv> \<lparr> heap = Map.empty, assocs = Map.empty \<rparr>"
 
 
 lemma basic_\<tau>_wff: "WFF(\<sigma>\<^sub>1,\<sigma>\<^sub>1')"
@@ -1087,10 +1087,10 @@ by(auto simp: WFF_def \<sigma>\<^sub>1_def \<sigma>\<^sub>1'_def
               person1_def person2_def person3_def person4_def
               person5_def person6_def person7_def person8_def person9_def)
 
-lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1) = {oid0,oid1,(*,oid2*)oid3,oid4,oid5(*,oid6,oid7*),oid8}"
+lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1) = {oid0,oid1\<^cancel>\<open>,oid2\<close>,oid3,oid4,oid5\<^cancel>\<open>,oid6,oid7\<close>,oid8}"
 by(auto simp: \<sigma>\<^sub>1_def)
 
-lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1') = {oid0,oid1,oid2,oid3,(*,oid4*)oid5,oid6,oid7,oid8}"
+lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1') = {oid0,oid1,oid2,oid3\<^cancel>\<open>,oid4\<close>,oid5,oid6,oid7,oid8}"
 by(auto simp: \<sigma>\<^sub>1'_def)
 
 text_raw{* \isatagafp *}
@@ -1238,13 +1238,13 @@ Assert "\<And>s\<^sub>p\<^sub>r\<^sub>e s\<^sub>p\<^sub>o\<^sub>s\<^sub>t.   (s\
 
 lemma \<sigma>_modifiedonly: "(\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny)
                       , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny)
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)\<close>
                       , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny)
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)\<close>
                       , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny)
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)\<close>
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)\<close>
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)*)}->oclIsModifiedOnly())"
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)\<close>}->oclIsModifiedOnly())"
  apply(simp add: OclIsModifiedOnly_def OclValid_def
                  oid0_def oid1_def oid2_def oid3_def oid4_def oid5_def oid6_def oid7_def oid8_def
                  X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
@@ -1292,13 +1292,13 @@ proof -
  show ?thesis
   apply(rule framing[where X = "Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny)
                        , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny)
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)\<close>
                        , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny)
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)\<close>
                        , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny)
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)\<close>
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)\<close>
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)*)}"])
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)\<close>}"])
    apply(cut_tac \<sigma>_modifiedonly)
    apply(simp only: OclValid_def
                     X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
@@ -1320,12 +1320,12 @@ proof -
  done
 qed
 
-lemma perm_\<sigma>\<^sub>1' : "\<sigma>\<^sub>1' = \<lparr> heap = empty
+lemma perm_\<sigma>\<^sub>1' : "\<sigma>\<^sub>1' = \<lparr> heap = Map.empty
                            (oid8 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person9)
                            (oid7 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person8)
                            (oid6 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person7)
                            (oid5 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person6)
-                          (*oid4*)
+                           \<^cancel>\<open>oid4\<close>
                            (oid3 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person4)
                            (oid2 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person3)
                            (oid1 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person2)
@@ -1349,8 +1349,8 @@ qed
 declare const_ss [simp]
 
 lemma "\<And>\<sigma>\<^sub>1.
- (\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (Person .allInstances() \<doteq> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4(*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5*), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6,
+ (\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (Person .allInstances() \<doteq> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<close>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6,
-                                           X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person)(*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8*), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 })"
+                                           X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person)\<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<close>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 })"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: oid0_def oid1_def oid2_def oid3_def oid4_def oid5_def oid6_def oid7_def oid8_def
                   X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
@@ -1371,7 +1371,7 @@ by(simp_all add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>
 lemma "\<And>\<sigma>\<^sub>1.
  (\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (OclAny .allInstances() \<doteq> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny),
                                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny)
-                                           (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5*), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny),
+                                           \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<close>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny),
                                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny) })"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: oid0_def oid1_def oid2_def oid3_def oid4_def oid5_def oid6_def oid7_def oid8_def

Featherweight_OCL/examples/Employee_Model/Design/Design_OCL.thy

@@ -82,7 +82,7 @@ oops
    occur in the state. *)
 
 lemma REC_pre : "\<tau> \<Turnstile> Person_label\<^sub>g\<^sub>l\<^sub>o\<^sub>b\<^sub>a\<^sub>l\<^sub>i\<^sub>n\<^sub>v 
-       \<Longrightarrow> \<tau> \<Turnstile> Person .allInstances()->includes\<^sub>S\<^sub>e\<^sub>t(X) (* X represented object in state *)
+       \<Longrightarrow> \<tau> \<Turnstile> Person .allInstances()->includes\<^sub>S\<^sub>e\<^sub>t(X) \<comment> \<open>\<open>X\<close> represented object in state\<close>
        \<Longrightarrow> \<exists> REC.  \<tau> \<Turnstile> REC(X)  \<triangleq> (Person_label\<^sub>i\<^sub>n\<^sub>v (X) and (X .boss <> null implies REC(X .boss)))"
 oops (* Attempt to allegiate the burden of he following axiomatizations: could be
         a witness for a constant specification ...*)       

Featherweight_OCL/examples/Employee_Model/Design/Design_UML.thy

@@ -184,7 +184,7 @@ lemmas cps23 =
     StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_strict2
                         [of "x::Person",
                          simplified StrictRefEq\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n[symmetric]]
-
+  for x y \<tau> P Q
 text{* For each Class \emph{C}, we will have a casting operation \inlineocl{.oclAsType($C$)},
    a test on the actual type \inlineocl{.oclIsTypeOf($C$)} as well as its relaxed form
    \inlineocl{.oclIsKindOf($C$)} (corresponding exactly to Java's \verb+instanceof+-operator.
@@ -234,7 +234,7 @@ begin
                    (\<lambda>\<tau>. case X \<tau> of
                               \<bottom>   \<Rightarrow> invalid \<tau>
                             | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> null \<tau>
-                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow>  invalid \<tau>   (* down-cast exception *)
+                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow>  invalid \<tau>   \<comment> \<open>down-cast exception\<close>
                             | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>(a,b)\<rfloor> \<rfloor>\<rfloor> \<Rightarrow>  \<lfloor>\<lfloor>mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid a b \<rfloor>\<rfloor>)"
 end
 
@@ -309,7 +309,7 @@ begin
         "(X::OclAny) .oclIsTypeOf(OclAny) \<equiv>
                    (\<lambda>\<tau>. case X \<tau> of
                               \<bottom>   \<Rightarrow> invalid \<tau>
-                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  (* invalid ?? *)
+                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  \<comment> \<open>invalid ??\<close>
                             | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow> true \<tau>
                             | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>_\<rfloor> \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)"
 end
@@ -317,7 +317,7 @@ end
 lemma OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAny':
          "(X::OclAny) .oclIsTypeOf(OclAny) = 
                     (\<lambda> \<tau>. if \<tau> \<Turnstile> \<upsilon> X then (case X \<tau> of
-                                              \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  (* invalid ?? *)
+                                              \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>  \<comment> \<open>invalid ??\<close>
                                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<bottom> \<rfloor>\<rfloor> \<Rightarrow> true \<tau>
                                            | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>_\<rfloor> \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)
                                            else invalid \<tau>)"
@@ -328,7 +328,7 @@ interpretation OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y_OclAn
        profile_mono_schemeV 
        "OclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y::OclAny \<Rightarrow> Boolean" 
        "\<lambda> X. (case X of
-                    \<lfloor>None\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>True\<rfloor>\<rfloor>  (* invalid ?? *)
+                    \<lfloor>None\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>True\<rfloor>\<rfloor>  \<comment> \<open>invalid ??\<close>
                   | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid None \<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>True\<rfloor>\<rfloor>
                   | \<lfloor>\<lfloor>mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>_\<rfloor> \<rfloor>\<rfloor> \<Rightarrow> \<lfloor>\<lfloor>False\<rfloor>\<rfloor>)"                     
       apply(unfold_locales, simp add: atomize_eq, rule ext)
@@ -341,8 +341,8 @@ begin
         "(X::Person) .oclIsTypeOf(OclAny) \<equiv>
                    (\<lambda>\<tau>. case X \<tau> of
                               \<bottom>   \<Rightarrow> invalid \<tau>
-                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>    (* invalid ?? *)
+                            | \<lfloor>\<bottom>\<rfloor> \<Rightarrow> true \<tau>    \<comment> \<open>invalid ??\<close>
-                            | \<lfloor>\<lfloor> _ \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)"  (* must have actual type Person otherwise  *)
+                            | \<lfloor>\<lfloor> _ \<rfloor>\<rfloor> \<Rightarrow> false \<tau>)  \<comment> \<open>must have actual type \<open>Person\<close> otherwise\<close>"
 end
 
 overloading OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n \<equiv> "OclIsTypeOf\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n :: OclAny \<Rightarrow> Boolean"
@@ -670,8 +670,8 @@ by(rule OclAny_allInstances_generic_oclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\
 lemma OclAny_allInstances_generic_oclIsTypeOf\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y2:
 assumes [simp]: "\<And>x. pre_post (x, x) = x"
 shows "\<exists>\<tau>. (\<tau> \<Turnstile> not ((OclAllInstances_generic pre_post OclAny)->forAll\<^sub>S\<^sub>e\<^sub>t(X|X .oclIsTypeOf(OclAny))))"
-proof - fix oid a let ?t0 = "\<lparr>heap = empty(oid \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>a\<rfloor>)),
+proof - fix oid a let ?t0 = "\<lparr>heap = Map.empty(oid \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y (mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y oid \<lfloor>a\<rfloor>)),
-                              assocs = empty\<rparr>" show ?thesis
+                              assocs = Map.empty\<rparr>" show ?thesis
  apply(rule_tac x = "(?t0, ?t0)" in exI, simp add: OclValid_def del: OclAllInstances_generic_def)
  apply(simp only: UML_Set.OclForall_def refl if_True
                   OclAllInstances_generic_defined[simplified OclValid_def])
@@ -778,8 +778,8 @@ definition eval_extract :: "('\<AA>,('a::object) option option) val
                             \<Rightarrow> (oid \<Rightarrow> ('\<AA>,'c::null) val)
                             \<Rightarrow> ('\<AA>,'c::null) val"
 where "eval_extract X f = (\<lambda> \<tau>. case X \<tau> of
-                                    \<bottom> \<Rightarrow> invalid \<tau>   (* exception propagation *)
+                                    \<bottom> \<Rightarrow> invalid \<tau>   \<comment> \<open>exception propagation\<close>
-                               | \<lfloor>  \<bottom> \<rfloor> \<Rightarrow> invalid \<tau> (* dereferencing null pointer *)
+                               | \<lfloor>  \<bottom> \<rfloor> \<Rightarrow> invalid \<tau> \<comment> \<open>dereferencing null pointer\<close>
                                | \<lfloor>\<lfloor> obj \<rfloor>\<rfloor> \<Rightarrow> f (oid_of obj) \<tau>)"
 
 
@@ -810,7 +810,7 @@ definition "select\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y\<A>\<N>\<Y> f
 
 
 definition "select\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n\<B>\<O>\<S>\<S> f = (\<lambda> X. case X of
-                     (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n _ _ \<bottom>) \<Rightarrow> null  (* object contains null pointer *)
+                     (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n _ _ \<bottom>) \<Rightarrow> null  \<comment> \<open>object contains null pointer\<close>
                    | (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n _ _ \<lfloor>boss\<rfloor>) \<Rightarrow> f (\<lambda>x _. \<lfloor>\<lfloor>x\<rfloor>\<rfloor>) boss)"
 
 
@@ -1012,30 +1012,30 @@ definition "person8 \<equiv> mk\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y
 definition "person9 \<equiv> mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid8 \<lfloor>0\<rfloor> None"
 
 definition
-      "\<sigma>\<^sub>1  \<equiv> \<lparr> heap = empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid0 \<lfloor>1000\<rfloor> \<lfloor>oid1\<rfloor>))
+      "\<sigma>\<^sub>1  \<equiv> \<lparr> heap = Map.empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid0 \<lfloor>1000\<rfloor> \<lfloor>oid1\<rfloor>))
                            (oid1 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid1 \<lfloor>1200\<rfloor>  None))
-                          (*oid2*)
+                           \<^cancel>\<open>oid2\<close>
                            (oid3 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid3 \<lfloor>2600\<rfloor> \<lfloor>oid4\<rfloor>))
                            (oid4 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person5)
                            (oid5 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n (mk\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n oid5 \<lfloor>2300\<rfloor> \<lfloor>oid3\<rfloor>))
-                          (*oid6*)
+                           \<^cancel>\<open>oid6\<close>
-                          (*oid7*)
+                           \<^cancel>\<open>oid7\<close>
                            (oid8 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person9),
-               assocs = empty \<rparr>"
+               assocs = Map.empty \<rparr>"
 
 definition
-      "\<sigma>\<^sub>1' \<equiv> \<lparr> heap = empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person1)
+      "\<sigma>\<^sub>1' \<equiv> \<lparr> heap = Map.empty(oid0 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person1)
                            (oid1 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person2)
                            (oid2 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person3)
                            (oid3 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person4)
-                          (*oid4*)
+                           \<^cancel>\<open>oid4\<close>
                            (oid5 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person6)
                            (oid6 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person7)
                            (oid7 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person8)
                            (oid8 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person9),
-               assocs = empty \<rparr>"
+               assocs = Map.empty \<rparr>"
 
-definition "\<sigma>\<^sub>0 \<equiv> \<lparr> heap = empty, assocs = empty \<rparr>"
+definition "\<sigma>\<^sub>0 \<equiv> \<lparr> heap = Map.empty, assocs = Map.empty \<rparr>"
 
 
 lemma basic_\<tau>_wff: "WFF(\<sigma>\<^sub>1,\<sigma>\<^sub>1')"
@@ -1045,10 +1045,10 @@ by(auto simp: WFF_def \<sigma>\<^sub>1_def \<sigma>\<^sub>1'_def
               person1_def person2_def person3_def person4_def
               person5_def person6_def person7_def person8_def person9_def)
 
-lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1) = {oid0,oid1,(*,oid2*)oid3,oid4,oid5(*,oid6,oid7*),oid8}"
+lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1) = {oid0,oid1\<^cancel>\<open>,oid2\<close>,oid3,oid4,oid5\<^cancel>\<open>,oid6,oid7\<close>,oid8}"
 by(auto simp: \<sigma>\<^sub>1_def)
 
-lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1') = {oid0,oid1,oid2,oid3,(*,oid4*)oid5,oid6,oid7,oid8}"
+lemma [simp,code_unfold]: "dom (heap \<sigma>\<^sub>1') = {oid0,oid1,oid2,oid3\<^cancel>\<open>,oid4\<close>,oid5,oid6,oid7,oid8}"
 by(auto simp: \<sigma>\<^sub>1'_def)
 
 text_raw{* \isatagafp *}
@@ -1191,13 +1191,13 @@ Assert "\<And>s\<^sub>p\<^sub>r\<^sub>e s\<^sub>p\<^sub>o\<^sub>s\<^sub>t.   (s\
 
 lemma \<sigma>_modifiedonly: "(\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny)
                       , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny)
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)\<close>
                       , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny)
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)\<close>
                       , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny)
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)\<close>
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)*)
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)\<close>
-                    (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)*)}->oclIsModifiedOnly())"
+                      \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)\<close>}->oclIsModifiedOnly())"
  apply(simp add: OclIsModifiedOnly_def OclValid_def
                  oid0_def oid1_def oid2_def oid3_def oid4_def oid5_def oid6_def oid7_def oid8_def
                  X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
@@ -1245,13 +1245,13 @@ proof -
  show ?thesis
   apply(rule framing[where X = "Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny)
                        , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny)
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny)\<close>
                        , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny)
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5 .oclAsType(OclAny)\<close>
                        , X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny)
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(OclAny)\<close>
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)*)
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8 .oclAsType(OclAny)\<close>
-                     (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)*)}"])
+                       \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny)\<close>}"])
    apply(cut_tac \<sigma>_modifiedonly)
    apply(simp only: OclValid_def
                     X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
@@ -1273,12 +1273,12 @@ proof -
  done
 qed
 
-lemma perm_\<sigma>\<^sub>1' : "\<sigma>\<^sub>1' = \<lparr> heap = empty
+lemma perm_\<sigma>\<^sub>1' : "\<sigma>\<^sub>1' = \<lparr> heap = Map.empty
                            (oid8 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person9)
                            (oid7 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person8)
                            (oid6 \<mapsto> in\<^sub>O\<^sub>c\<^sub>l\<^sub>A\<^sub>n\<^sub>y person7)
                            (oid5 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person6)
-                          (*oid4*)
+                           \<^cancel>\<open>oid4\<close>
                            (oid3 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person4)
                            (oid2 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person3)
                            (oid1 \<mapsto> in\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n person2)
@@ -1302,8 +1302,8 @@ qed
 declare const_ss [simp]
 
 lemma "\<And>\<sigma>\<^sub>1.
- (\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (Person .allInstances() \<doteq> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4(*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5*), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6,
+ (\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (Person .allInstances() \<doteq> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4\<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<close>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6,
-                                           X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person)(*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8*), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 })"
+                                           X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7 .oclAsType(Person)\<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8\<close>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 })"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: oid0_def oid1_def oid2_def oid3_def oid4_def oid5_def oid6_def oid7_def oid8_def
                   X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3_def X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4_def
@@ -1324,7 +1324,7 @@ by(simp_all add: OclAsType\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n_\<AA>
 lemma "\<And>\<sigma>\<^sub>1.
  (\<sigma>\<^sub>1,\<sigma>\<^sub>1') \<Turnstile> (OclAny .allInstances() \<doteq> Set{ X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n1 .oclAsType(OclAny), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n2 .oclAsType(OclAny),
                                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n3 .oclAsType(OclAny), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n4 .oclAsType(OclAny)
-                                           (*, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5*), X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny),
+                                           \<^cancel>\<open>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n5\<close>, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n6 .oclAsType(OclAny),
                                            X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n7, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n8, X\<^sub>P\<^sub>e\<^sub>r\<^sub>s\<^sub>o\<^sub>n9 .oclAsType(OclAny) })"
  apply(subst perm_\<sigma>\<^sub>1')
  apply(simp only: oid0_def oid1_def oid2_def oid3_def oid4_def oid5_def oid6_def oid7_def oid8_def