src/HOL/Bali/State.thy
author wenzelm
Wed Feb 10 00:45:16 2010 +0100 (2010-02-10)
changeset 35067 af4c18c30593
parent 33965 f57c11db4ad4
child 35416 d8d7d1b785af
permissions -rw-r--r--
modernized syntax translations, using mostly abbreviation/notation;
minor tuning;
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(*  Title:      HOL/Bali/State.thy
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    Author:     David von Oheimb
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*)
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header {* State for evaluation of Java expressions and statements *}
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theory State
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imports DeclConcepts
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begin
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text {*
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design issues:
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\begin{itemize}
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\item all kinds of objects (class instances, arrays, and class objects)
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  are handeled via a general object abstraction
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\item the heap and the map for class objects are combined into a single table
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  @{text "(recall (loc, obj) table \<times> (qtname, obj) table  ~=  (loc + qtname, obj) table)"}
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\end{itemize}
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*}
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section "objects"
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datatype  obj_tag =     --{* tag for generic object   *}
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          CInst qtname  --{* class instance           *}
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        | Arr  ty int   --{* array with component type and length *}
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    --{* | CStat qtname   the tag is irrelevant for a class object,
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                           i.e. the static fields of a class,
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                           since its type is given already by the reference to 
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                           it (see below) *}
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types   vn   = "fspec + int"                    --{* variable name      *}
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record  obj  = 
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          tag :: "obj_tag"                      --{* generalized object *}
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          "values" :: "(vn, val) table"      
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translations 
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  "fspec" <= (type) "vname \<times> qtname" 
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  "vn"    <= (type) "fspec + int"
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  "obj"   <= (type) "\<lparr>tag::obj_tag, values::vn \<Rightarrow> val option\<rparr>"
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  "obj"   <= (type) "\<lparr>tag::obj_tag, values::vn \<Rightarrow> val option,\<dots>::'a\<rparr>"
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constdefs
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  the_Arr :: "obj option \<Rightarrow> ty \<times> int \<times> (vn, val) table"
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 "the_Arr obj \<equiv> SOME (T,k,t). obj = Some \<lparr>tag=Arr T k,values=t\<rparr>"
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lemma the_Arr_Arr [simp]: "the_Arr (Some \<lparr>tag=Arr T k,values=cs\<rparr>) = (T,k,cs)"
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apply (auto simp: the_Arr_def)
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done
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lemma the_Arr_Arr1 [simp,intro,dest]:
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 "\<lbrakk>tag obj = Arr T k\<rbrakk> \<Longrightarrow> the_Arr (Some obj) = (T,k,values obj)"
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apply (auto simp add: the_Arr_def)
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done
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constdefs
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  upd_obj       :: "vn \<Rightarrow> val \<Rightarrow> obj \<Rightarrow> obj" 
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 "upd_obj n v \<equiv> \<lambda> obj . obj \<lparr>values:=(values obj)(n\<mapsto>v)\<rparr>"
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lemma upd_obj_def2 [simp]: 
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  "upd_obj n v obj = obj \<lparr>values:=(values obj)(n\<mapsto>v)\<rparr>" 
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apply (auto simp: upd_obj_def)
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done
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constdefs
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  obj_ty        :: "obj \<Rightarrow> ty"
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 "obj_ty obj    \<equiv> case tag obj of 
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                    CInst C \<Rightarrow> Class C 
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                  | Arr T k \<Rightarrow> T.[]"
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lemma obj_ty_eq [intro!]: "obj_ty \<lparr>tag=oi,values=x\<rparr> = obj_ty \<lparr>tag=oi,values=y\<rparr>" 
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by (simp add: obj_ty_def)
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lemma obj_ty_eq1 [intro!,dest]: 
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  "tag obj = tag obj' \<Longrightarrow> obj_ty obj = obj_ty obj'" 
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by (simp add: obj_ty_def)
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lemma obj_ty_cong [simp]: 
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  "obj_ty (obj \<lparr>values:=vs\<rparr>) = obj_ty obj" 
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by auto
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lemma obj_ty_CInst [simp]: 
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 "obj_ty \<lparr>tag=CInst C,values=vs\<rparr> = Class C" 
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by (simp add: obj_ty_def)
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lemma obj_ty_CInst1 [simp,intro!,dest]: 
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 "\<lbrakk>tag obj = CInst C\<rbrakk> \<Longrightarrow> obj_ty obj = Class C" 
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by (simp add: obj_ty_def)
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lemma obj_ty_Arr [simp]: 
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 "obj_ty \<lparr>tag=Arr T i,values=vs\<rparr> = T.[]"
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by (simp add: obj_ty_def)
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lemma obj_ty_Arr1 [simp,intro!,dest]: 
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 "\<lbrakk>tag obj = Arr T i\<rbrakk> \<Longrightarrow> obj_ty obj = T.[]"
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by (simp add: obj_ty_def)
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lemma obj_ty_widenD: 
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 "G\<turnstile>obj_ty obj\<preceq>RefT t \<Longrightarrow> (\<exists>C. tag obj = CInst C) \<or> (\<exists>T k. tag obj = Arr T k)"
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apply (unfold obj_ty_def)
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apply (auto split add: obj_tag.split_asm)
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done
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constdefs
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  obj_class :: "obj \<Rightarrow> qtname"
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 "obj_class obj \<equiv> case tag obj of 
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                    CInst C \<Rightarrow> C 
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                  | Arr T k \<Rightarrow> Object"
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lemma obj_class_CInst [simp]: "obj_class \<lparr>tag=CInst C,values=vs\<rparr> = C" 
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by (auto simp: obj_class_def)
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lemma obj_class_CInst1 [simp,intro!,dest]: 
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  "tag obj = CInst C \<Longrightarrow> obj_class obj = C" 
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by (auto simp: obj_class_def)
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lemma obj_class_Arr [simp]: "obj_class \<lparr>tag=Arr T k,values=vs\<rparr> = Object" 
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by (auto simp: obj_class_def)
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lemma obj_class_Arr1 [simp,intro!,dest]: 
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 "tag obj = Arr T k \<Longrightarrow> obj_class obj = Object" 
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by (auto simp: obj_class_def)
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lemma obj_ty_obj_class: "G\<turnstile>obj_ty obj\<preceq> Class statC = G\<turnstile>obj_class obj \<preceq>\<^sub>C statC"
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apply (case_tac "tag obj")
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apply (auto simp add: obj_ty_def obj_class_def)
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apply (case_tac "statC = Object")
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apply (auto dest: widen_Array_Class)
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done
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section "object references"
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types oref = "loc + qtname"         --{* generalized object reference *}
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syntax
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  Heap  :: "loc   \<Rightarrow> oref"
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  Stat  :: "qtname \<Rightarrow> oref"
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translations
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  "Heap" => "CONST Inl"
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  "Stat" => "CONST Inr"
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  "oref" <= (type) "loc + qtname"
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constdefs
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  fields_table::
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    "prog \<Rightarrow> qtname \<Rightarrow> (fspec \<Rightarrow> field \<Rightarrow> bool)  \<Rightarrow> (fspec, ty) table"
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 "fields_table G C P 
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    \<equiv> Option.map type \<circ> table_of (filter (split P) (DeclConcepts.fields G C))"
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lemma fields_table_SomeI: 
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"\<lbrakk>table_of (DeclConcepts.fields G C) n = Some f; P n f\<rbrakk> 
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 \<Longrightarrow> fields_table G C P n = Some (type f)"
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apply (unfold fields_table_def)
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apply clarsimp
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apply (rule exI)
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apply (rule conjI)
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apply (erule map_of_filter_in)
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apply assumption
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apply simp
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done
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(* unused *)
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lemma fields_table_SomeD': "fields_table G C P fn = Some T \<Longrightarrow>  
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  \<exists>f. (fn,f)\<in>set(DeclConcepts.fields G C) \<and> type f = T"
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apply (unfold fields_table_def)
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apply clarsimp
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apply (drule map_of_SomeD)
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apply auto
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done
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lemma fields_table_SomeD: 
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"\<lbrakk>fields_table G C P fn = Some T; unique (DeclConcepts.fields G C)\<rbrakk> \<Longrightarrow>  
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  \<exists>f. table_of (DeclConcepts.fields G C) fn = Some f \<and> type f = T"
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apply (unfold fields_table_def)
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apply clarsimp
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apply (rule exI)
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apply (rule conjI)
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apply (erule table_of_filter_unique_SomeD)
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apply assumption
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apply simp
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done
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constdefs
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  in_bounds :: "int \<Rightarrow> int \<Rightarrow> bool"            ("(_/ in'_bounds _)" [50, 51] 50)
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 "i in_bounds k \<equiv> 0 \<le> i \<and> i < k"
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  arr_comps :: "'a \<Rightarrow> int \<Rightarrow> int \<Rightarrow> 'a option"
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 "arr_comps T k \<equiv> \<lambda>i. if i in_bounds k then Some T else None"
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  var_tys       :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> (vn, ty) table"
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"var_tys G oi r 
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  \<equiv> case r of 
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      Heap a \<Rightarrow> (case oi of 
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                   CInst C \<Rightarrow> fields_table G C (\<lambda>n f. \<not>static f) (+) empty
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                 | Arr T k \<Rightarrow> empty (+) arr_comps T k)
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    | Stat C \<Rightarrow> fields_table G C (\<lambda>fn f. declclassf fn = C \<and> static f) 
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                (+) empty"
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lemma var_tys_Some_eq: 
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 "var_tys G oi r n = Some T 
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  = (case r of 
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       Inl a \<Rightarrow> (case oi of  
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                   CInst C \<Rightarrow> (\<exists>nt. n = Inl nt \<and> fields_table G C (\<lambda>n f. 
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                               \<not>static f) nt = Some T)  
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                 | Arr t k \<Rightarrow> (\<exists> i. n = Inr i  \<and> i in_bounds k \<and> t = T))  
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     | Inr C \<Rightarrow> (\<exists>nt. n = Inl nt \<and> 
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                 fields_table G C (\<lambda>fn f. declclassf fn = C \<and> static f) nt 
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                  = Some T))"
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apply (unfold var_tys_def arr_comps_def)
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apply (force split add: sum.split_asm sum.split obj_tag.split)
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done
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section "stores"
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types   globs               --{* global variables: heap and static variables *}
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        = "(oref , obj) table"
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        heap
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        = "(loc  , obj) table"
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(*      locals                   
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        = "(lname, val) table" *) (* defined in Value.thy local variables *)
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translations
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 "globs"  <= (type) "(oref , obj) table"
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 "heap"   <= (type) "(loc  , obj) table"
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(*  "locals" <= (type) "(lname, val) table" *)
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datatype st = (* pure state, i.e. contents of all variables *)
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         st globs locals
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subsection "access"
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constdefs
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  globs  :: "st \<Rightarrow> globs"
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 "globs  \<equiv> st_case (\<lambda>g l. g)"
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  locals :: "st \<Rightarrow> locals"
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 "locals \<equiv> st_case (\<lambda>g l. l)"
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  heap   :: "st \<Rightarrow> heap"
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 "heap s \<equiv> globs s \<circ> Heap"
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lemma globs_def2 [simp]: " globs (st g l) = g"
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by (simp add: globs_def)
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lemma locals_def2 [simp]: "locals (st g l) = l"
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by (simp add: locals_def)
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lemma heap_def2 [simp]:  "heap s a=globs s (Heap a)"
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by (simp add: heap_def)
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abbreviation val_this :: "st \<Rightarrow> val"
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  where "val_this s == the (locals s This)"
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abbreviation lookup_obj :: "st \<Rightarrow> val \<Rightarrow> obj"
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  where "lookup_obj s a' == the (heap s (the_Addr a'))"
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subsection "memory allocation"
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constdefs
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  new_Addr     :: "heap \<Rightarrow> loc option"
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 "new_Addr h   \<equiv> if (\<forall>a. h a \<noteq> None) then None else Some (SOME a. h a = None)"
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lemma new_AddrD: "new_Addr h = Some a \<Longrightarrow> h a = None"
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apply (auto simp add: new_Addr_def)
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apply (erule someI) 
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done
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lemma new_AddrD2: "new_Addr h = Some a \<Longrightarrow> \<forall>b. h b \<noteq> None \<longrightarrow> b \<noteq> a"
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apply (drule new_AddrD)
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apply auto
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done
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lemma new_Addr_SomeI: "h a = None \<Longrightarrow> \<exists>b. new_Addr h = Some b \<and> h b = None"
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apply (simp add: new_Addr_def)
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apply (fast intro: someI2)
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done
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subsection "initialization"
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abbreviation init_vals :: "('a, ty) table \<Rightarrow> ('a, val) table"
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  where "init_vals vs == Option.map default_val \<circ> vs"
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lemma init_arr_comps_base [simp]: "init_vals (arr_comps T 0) = empty"
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apply (unfold arr_comps_def in_bounds_def)
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apply (rule ext)
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apply auto
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done
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lemma init_arr_comps_step [simp]: 
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"0 < j \<Longrightarrow> init_vals (arr_comps T  j    ) =  
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           init_vals (arr_comps T (j - 1))(j - 1\<mapsto>default_val T)"
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apply (unfold arr_comps_def in_bounds_def)
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apply (rule ext)
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apply auto
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done
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subsection "update"
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constdefs
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  gupd       :: "oref  \<Rightarrow> obj \<Rightarrow> st \<Rightarrow> st"        ("gupd'(_\<mapsto>_')"[10,10]1000)
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 "gupd r obj  \<equiv> st_case (\<lambda>g l. st (g(r\<mapsto>obj)) l)"
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  lupd       :: "lname \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st"        ("lupd'(_\<mapsto>_')"[10,10]1000)
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 "lupd vn v   \<equiv> st_case (\<lambda>g l. st g (l(vn\<mapsto>v)))"
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  upd_gobj   :: "oref \<Rightarrow> vn \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st"
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 "upd_gobj r n v \<equiv> st_case (\<lambda>g l. st (chg_map (upd_obj n v) r g) l)"
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  set_locals  :: "locals \<Rightarrow> st \<Rightarrow> st"
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 "set_locals l \<equiv> st_case (\<lambda>g l'. st g l)"
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  init_obj    :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> st \<Rightarrow> st"
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 "init_obj G oi r \<equiv> gupd(r\<mapsto>\<lparr>tag=oi, values=init_vals (var_tys G oi r)\<rparr>)"
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abbreviation
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  init_class_obj :: "prog \<Rightarrow> qtname \<Rightarrow> st \<Rightarrow> st"
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  where "init_class_obj G C == init_obj G undefined (Inr C)"
schirmer@12854
   325
schirmer@12854
   326
lemma gupd_def2 [simp]: "gupd(r\<mapsto>obj) (st g l) = st (g(r\<mapsto>obj)) l"
schirmer@12854
   327
apply (unfold gupd_def)
schirmer@12854
   328
apply (simp (no_asm))
schirmer@12854
   329
done
schirmer@12854
   330
schirmer@12854
   331
lemma lupd_def2 [simp]: "lupd(vn\<mapsto>v) (st g l) = st g (l(vn\<mapsto>v))"
schirmer@12854
   332
apply (unfold lupd_def)
schirmer@12854
   333
apply (simp (no_asm))
schirmer@12854
   334
done
schirmer@12854
   335
schirmer@12854
   336
lemma globs_gupd [simp]: "globs  (gupd(r\<mapsto>obj) s) = globs s(r\<mapsto>obj)"
schirmer@12854
   337
apply (induct "s")
schirmer@12854
   338
by (simp add: gupd_def)
schirmer@12854
   339
schirmer@12854
   340
lemma globs_lupd [simp]: "globs  (lupd(vn\<mapsto>v ) s) = globs  s"
schirmer@12854
   341
apply (induct "s")
schirmer@12854
   342
by (simp add: lupd_def)
schirmer@12854
   343
schirmer@12854
   344
lemma locals_gupd [simp]: "locals (gupd(r\<mapsto>obj) s) = locals s"
schirmer@12854
   345
apply (induct "s")
schirmer@12854
   346
by (simp add: gupd_def)
schirmer@12854
   347
schirmer@12854
   348
lemma locals_lupd [simp]: "locals (lupd(vn\<mapsto>v ) s) = locals s(vn\<mapsto>v )"
schirmer@12854
   349
apply (induct "s")
schirmer@12854
   350
by (simp add: lupd_def)
schirmer@12854
   351
schirmer@12854
   352
lemma globs_upd_gobj_new [rule_format (no_asm), simp]: 
schirmer@12854
   353
  "globs s r = None \<longrightarrow> globs (upd_gobj r n v s) = globs s"
schirmer@12854
   354
apply (unfold upd_gobj_def)
schirmer@12854
   355
apply (induct "s")
schirmer@12854
   356
apply auto
schirmer@12854
   357
done
schirmer@12854
   358
schirmer@12854
   359
lemma globs_upd_gobj_upd [rule_format (no_asm), simp]: 
schirmer@12854
   360
"globs s r=Some obj\<longrightarrow> globs (upd_gobj r n v s) = globs s(r\<mapsto>upd_obj n v obj)"
schirmer@12854
   361
apply (unfold upd_gobj_def)
schirmer@12854
   362
apply (induct "s")
schirmer@12854
   363
apply auto
schirmer@12854
   364
done
schirmer@12854
   365
schirmer@12854
   366
lemma locals_upd_gobj [simp]: "locals (upd_gobj r n v s) = locals s"
schirmer@12854
   367
apply (induct "s")
schirmer@12854
   368
by (simp add: upd_gobj_def) 
schirmer@12854
   369
schirmer@12854
   370
schirmer@12854
   371
lemma globs_init_obj [simp]: "globs (init_obj G oi r s) t =  
schirmer@12854
   372
  (if t=r then Some \<lparr>tag=oi,values=init_vals (var_tys G oi r)\<rparr> else globs s t)"
schirmer@12854
   373
apply (unfold init_obj_def)
schirmer@12854
   374
apply (simp (no_asm))
schirmer@12854
   375
done
schirmer@12854
   376
schirmer@12854
   377
lemma locals_init_obj [simp]: "locals (init_obj G oi r s) = locals s"
schirmer@12854
   378
by (simp add: init_obj_def)
schirmer@12854
   379
  
schirmer@12854
   380
lemma surjective_st [simp]: "st (globs s) (locals s) = s"
schirmer@12854
   381
apply (induct "s")
schirmer@12854
   382
by auto
schirmer@12854
   383
schirmer@12854
   384
lemma surjective_st_init_obj: 
schirmer@12854
   385
 "st (globs (init_obj G oi r s)) (locals s) = init_obj G oi r s"
schirmer@12854
   386
apply (subst locals_init_obj [THEN sym])
schirmer@12854
   387
apply (rule surjective_st)
schirmer@12854
   388
done
schirmer@12854
   389
schirmer@12854
   390
lemma heap_heap_upd [simp]: 
schirmer@12854
   391
  "heap (st (g(Inl a\<mapsto>obj)) l) = heap (st g l)(a\<mapsto>obj)"
schirmer@12854
   392
apply (rule ext)
schirmer@12854
   393
apply (simp (no_asm))
schirmer@12854
   394
done
schirmer@12854
   395
lemma heap_stat_upd [simp]: "heap (st (g(Inr C\<mapsto>obj)) l) = heap (st g l)"
schirmer@12854
   396
apply (rule ext)
schirmer@12854
   397
apply (simp (no_asm))
schirmer@12854
   398
done
schirmer@12854
   399
lemma heap_local_upd [simp]: "heap (st g (l(vn\<mapsto>v))) = heap (st g l)"
schirmer@12854
   400
apply (rule ext)
schirmer@12854
   401
apply (simp (no_asm))
schirmer@12854
   402
done
schirmer@12854
   403
schirmer@12854
   404
lemma heap_gupd_Heap [simp]: "heap (gupd(Heap a\<mapsto>obj) s) = heap s(a\<mapsto>obj)"
schirmer@12854
   405
apply (rule ext)
schirmer@12854
   406
apply (simp (no_asm))
schirmer@12854
   407
done
schirmer@12854
   408
lemma heap_gupd_Stat [simp]: "heap (gupd(Stat C\<mapsto>obj) s) = heap s"
schirmer@12854
   409
apply (rule ext)
schirmer@12854
   410
apply (simp (no_asm))
schirmer@12854
   411
done
schirmer@12854
   412
lemma heap_lupd [simp]: "heap (lupd(vn\<mapsto>v) s) = heap s"
schirmer@12854
   413
apply (rule ext)
schirmer@12854
   414
apply (simp (no_asm))
schirmer@12854
   415
done
schirmer@12854
   416
schirmer@12854
   417
lemma heap_upd_gobj_Stat [simp]: "heap (upd_gobj (Stat C) n v s) = heap s"
schirmer@12854
   418
apply (rule ext)
schirmer@12854
   419
apply (simp (no_asm))
schirmer@12854
   420
apply (case_tac "globs s (Stat C)")
schirmer@12854
   421
apply  auto
schirmer@12854
   422
done
schirmer@12854
   423
schirmer@12854
   424
lemma set_locals_def2 [simp]: "set_locals l (st g l') = st g l"
schirmer@12854
   425
apply (unfold set_locals_def)
schirmer@12854
   426
apply (simp (no_asm))
schirmer@12854
   427
done
schirmer@12854
   428
schirmer@12854
   429
lemma set_locals_id [simp]: "set_locals (locals s) s = s"
schirmer@12854
   430
apply (unfold set_locals_def)
schirmer@12854
   431
apply (induct_tac "s")
schirmer@12854
   432
apply (simp (no_asm))
schirmer@12854
   433
done
schirmer@12854
   434
schirmer@12854
   435
lemma set_set_locals [simp]: "set_locals l (set_locals l' s) = set_locals l s"
schirmer@12854
   436
apply (unfold set_locals_def)
schirmer@12854
   437
apply (induct_tac "s")
schirmer@12854
   438
apply (simp (no_asm))
schirmer@12854
   439
done
schirmer@12854
   440
schirmer@12854
   441
lemma locals_set_locals [simp]: "locals (set_locals l s) = l"
schirmer@12854
   442
apply (unfold set_locals_def)
schirmer@12854
   443
apply (induct_tac "s")
schirmer@12854
   444
apply (simp (no_asm))
schirmer@12854
   445
done
schirmer@12854
   446
schirmer@12854
   447
lemma globs_set_locals [simp]: "globs (set_locals l s) = globs s"
schirmer@12854
   448
apply (unfold set_locals_def)
schirmer@12854
   449
apply (induct_tac "s")
schirmer@12854
   450
apply (simp (no_asm))
schirmer@12854
   451
done
schirmer@12854
   452
schirmer@12854
   453
lemma heap_set_locals [simp]: "heap (set_locals l s) = heap s"
schirmer@12854
   454
apply (unfold heap_def)
schirmer@12854
   455
apply (induct_tac "s")
schirmer@12854
   456
apply (simp (no_asm))
schirmer@12854
   457
done
schirmer@12854
   458
schirmer@12854
   459
schirmer@12854
   460
section "abrupt completion"
schirmer@12854
   461
schirmer@12854
   462
schirmer@12854
   463
schirmer@12854
   464
consts
schirmer@12854
   465
schirmer@12854
   466
  the_Xcpt :: "abrupt \<Rightarrow> xcpt"
schirmer@12854
   467
  the_Jump :: "abrupt => jump"
schirmer@12854
   468
  the_Loc  :: "xcpt \<Rightarrow> loc"
schirmer@12854
   469
  the_Std  :: "xcpt \<Rightarrow> xname"
schirmer@12854
   470
schirmer@12854
   471
primrec "the_Xcpt (Xcpt x) = x"
schirmer@12854
   472
primrec "the_Jump (Jump j) = j"
schirmer@12854
   473
primrec "the_Loc (Loc a) = a"
schirmer@12854
   474
primrec "the_Std (Std x) = x"
schirmer@12854
   475
schirmer@13337
   476
wenzelm@32960
   477
        
schirmer@12854
   478
schirmer@12854
   479
constdefs
schirmer@12854
   480
  abrupt_if    :: "bool \<Rightarrow> abopt \<Rightarrow> abopt \<Rightarrow> abopt"
schirmer@12854
   481
 "abrupt_if c x' x \<equiv> if c \<and> (x = None) then x' else x"
schirmer@12854
   482
schirmer@12854
   483
lemma abrupt_if_True_None [simp]: "abrupt_if True x None = x"
schirmer@12854
   484
by (simp add: abrupt_if_def)
schirmer@12854
   485
schirmer@12854
   486
lemma abrupt_if_True_not_None [simp]: "x \<noteq> None \<Longrightarrow> abrupt_if True x y \<noteq> None"
schirmer@12854
   487
by (simp add: abrupt_if_def)
schirmer@12854
   488
schirmer@12854
   489
lemma abrupt_if_False [simp]: "abrupt_if False x y = y"
schirmer@12854
   490
by (simp add: abrupt_if_def)
schirmer@12854
   491
schirmer@12854
   492
lemma abrupt_if_Some [simp]: "abrupt_if c x (Some y) = Some y"
schirmer@12854
   493
by (simp add: abrupt_if_def)
schirmer@12854
   494
schirmer@12854
   495
lemma abrupt_if_not_None [simp]: "y \<noteq> None \<Longrightarrow> abrupt_if c x y = y"
schirmer@12854
   496
apply (simp add: abrupt_if_def)
schirmer@12854
   497
by auto
schirmer@12854
   498
schirmer@12854
   499
schirmer@12854
   500
lemma split_abrupt_if: 
schirmer@12854
   501
"P (abrupt_if c x' x) = 
schirmer@12854
   502
      ((c \<and> x = None \<longrightarrow> P x') \<and> (\<not> (c \<and> x = None) \<longrightarrow> P x))"
schirmer@12854
   503
apply (unfold abrupt_if_def)
schirmer@12854
   504
apply (split split_if)
schirmer@12854
   505
apply auto
schirmer@12854
   506
done
schirmer@12854
   507
wenzelm@35067
   508
abbreviation raise_if :: "bool \<Rightarrow> xname \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   509
  where "raise_if c xn == abrupt_if c (Some (Xcpt (Std xn)))"
wenzelm@35067
   510
wenzelm@35067
   511
abbreviation np :: "val \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   512
  where "np v == raise_if (v = Null) NullPointer"
schirmer@12854
   513
wenzelm@35067
   514
abbreviation check_neg :: "val \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   515
  where "check_neg i' == raise_if (the_Intg i'<0) NegArrSize"
schirmer@12854
   516
wenzelm@35067
   517
abbreviation error_if :: "bool \<Rightarrow> error \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   518
  where "error_if c e == abrupt_if c (Some (Error e))"
schirmer@12854
   519
schirmer@12854
   520
lemma raise_if_None [simp]: "(raise_if c x y = None) = (\<not>c \<and> y = None)"
schirmer@12854
   521
apply (simp add: abrupt_if_def)
schirmer@12854
   522
by auto
schirmer@12854
   523
declare raise_if_None [THEN iffD1, dest!]
schirmer@12854
   524
schirmer@12854
   525
lemma if_raise_if_None [simp]: 
schirmer@12854
   526
  "((if b then y else raise_if c x y) = None) = ((c \<longrightarrow> b) \<and> y = None)"
schirmer@12854
   527
apply (simp add: abrupt_if_def)
schirmer@12854
   528
apply auto
schirmer@12854
   529
done
schirmer@12854
   530
schirmer@12854
   531
lemma raise_if_SomeD [dest!]:
schirmer@12854
   532
  "raise_if c x y = Some z \<Longrightarrow> c \<and> z=(Xcpt (Std x)) \<and> y=None \<or> (y=Some z)"
schirmer@12854
   533
apply (case_tac y)
schirmer@12854
   534
apply (case_tac c)
schirmer@12854
   535
apply (simp add: abrupt_if_def)
schirmer@12854
   536
apply (simp add: abrupt_if_def)
schirmer@12854
   537
apply auto
schirmer@12854
   538
done
schirmer@12854
   539
schirmer@12925
   540
lemma error_if_None [simp]: "(error_if c e y = None) = (\<not>c \<and> y = None)"
schirmer@12925
   541
apply (simp add: abrupt_if_def)
schirmer@12925
   542
by auto
schirmer@12925
   543
declare error_if_None [THEN iffD1, dest!]
schirmer@12925
   544
schirmer@12925
   545
lemma if_error_if_None [simp]: 
schirmer@12925
   546
  "((if b then y else error_if c e y) = None) = ((c \<longrightarrow> b) \<and> y = None)"
schirmer@12925
   547
apply (simp add: abrupt_if_def)
schirmer@12925
   548
apply auto
schirmer@12925
   549
done
schirmer@12925
   550
wenzelm@13524
   551
lemma error_if_SomeD [dest!]:
schirmer@12925
   552
  "error_if c e y = Some z \<Longrightarrow> c \<and> z=(Error e) \<and> y=None \<or> (y=Some z)"
schirmer@12925
   553
apply (case_tac y)
schirmer@12925
   554
apply (case_tac c)
schirmer@12925
   555
apply (simp add: abrupt_if_def)
schirmer@12925
   556
apply (simp add: abrupt_if_def)
schirmer@12925
   557
apply auto
schirmer@12925
   558
done
schirmer@12925
   559
schirmer@12854
   560
constdefs
schirmer@12854
   561
   absorb :: "jump \<Rightarrow> abopt \<Rightarrow> abopt"
schirmer@12854
   562
  "absorb j a \<equiv> if a=Some (Jump j) then None else a"
schirmer@12854
   563
schirmer@12854
   564
lemma absorb_SomeD [dest!]: "absorb j a = Some x \<Longrightarrow> a = Some x"
schirmer@12854
   565
by (auto simp add: absorb_def)
schirmer@12854
   566
schirmer@12854
   567
lemma absorb_same [simp]: "absorb j (Some (Jump j)) = None"
schirmer@12854
   568
by (auto simp add: absorb_def)
schirmer@12854
   569
schirmer@12854
   570
lemma absorb_other [simp]: "a \<noteq> Some (Jump j) \<Longrightarrow> absorb j a = a"
schirmer@12854
   571
by (auto simp add: absorb_def)
schirmer@12854
   572
schirmer@13688
   573
lemma absorb_Some_NoneD: "absorb j (Some abr) = None \<Longrightarrow> abr = Jump j"
schirmer@13688
   574
  by (simp add: absorb_def)
schirmer@13688
   575
schirmer@13688
   576
lemma absorb_Some_JumpD: "absorb j s = Some (Jump j') \<Longrightarrow> j'\<noteq>j"
schirmer@13688
   577
  by (simp add: absorb_def)
schirmer@13688
   578
schirmer@12854
   579
schirmer@12854
   580
section "full program state"
schirmer@12854
   581
schirmer@12854
   582
types
schirmer@13688
   583
  state = "abopt \<times> st"          --{* state including abruption information *}
schirmer@12854
   584
schirmer@12854
   585
translations
schirmer@12854
   586
  "abopt"       <= (type) "State.abrupt option"
schirmer@12854
   587
  "abopt"       <= (type) "abrupt option"
schirmer@12854
   588
  "state"      <= (type) "abopt \<times> State.st"
schirmer@12854
   589
  "state"      <= (type) "abopt \<times> st"
schirmer@12854
   590
wenzelm@35067
   591
abbreviation
wenzelm@35067
   592
  Norm :: "st \<Rightarrow> state"
wenzelm@35067
   593
  where "Norm s == (None, s)"
schirmer@12854
   594
wenzelm@35067
   595
abbreviation (input)
wenzelm@35067
   596
  abrupt :: "state \<Rightarrow> abopt"
wenzelm@35067
   597
  where "abrupt == fst"
wenzelm@35067
   598
wenzelm@35067
   599
abbreviation (input)
wenzelm@35067
   600
  store :: "state \<Rightarrow> st"
wenzelm@35067
   601
  where "store == snd"
schirmer@12854
   602
schirmer@12854
   603
lemma single_stateE: "\<forall>Z. Z = (s::state) \<Longrightarrow> False"
schirmer@12854
   604
apply (erule_tac x = "(Some k,y)" in all_dupE)
schirmer@12854
   605
apply (erule_tac x = "(None,y)" in allE)
schirmer@12854
   606
apply clarify
schirmer@12854
   607
done
schirmer@12854
   608
schirmer@12854
   609
lemma state_not_single: "All (op = (x::state)) \<Longrightarrow> R"
schirmer@12854
   610
apply (drule_tac x = "(if abrupt x = None then Some ?x else None,?y)" in spec)
schirmer@12854
   611
apply clarsimp
schirmer@12854
   612
done
schirmer@12854
   613
schirmer@12854
   614
constdefs
schirmer@12854
   615
schirmer@12854
   616
  normal     :: "state \<Rightarrow> bool"
schirmer@12854
   617
 "normal \<equiv> \<lambda>s. abrupt s = None"
schirmer@12854
   618
schirmer@12854
   619
lemma normal_def2 [simp]: "normal s = (abrupt s = None)"
schirmer@12854
   620
apply (unfold normal_def)
schirmer@12854
   621
apply (simp (no_asm))
schirmer@12854
   622
done
schirmer@12854
   623
schirmer@12854
   624
constdefs
schirmer@12854
   625
  heap_free :: "nat \<Rightarrow> state \<Rightarrow> bool"
schirmer@12854
   626
 "heap_free n \<equiv> \<lambda>s. atleast_free (heap (store s)) n"
schirmer@12854
   627
schirmer@12854
   628
lemma heap_free_def2 [simp]: "heap_free n s = atleast_free (heap (store s)) n"
schirmer@12854
   629
apply (unfold heap_free_def)
schirmer@12854
   630
apply simp
schirmer@12854
   631
done
schirmer@12854
   632
schirmer@12854
   633
subsection "update"
schirmer@12854
   634
schirmer@12854
   635
constdefs
schirmer@12854
   636
 
schirmer@12854
   637
  abupd     :: "(abopt \<Rightarrow> abopt) \<Rightarrow> state \<Rightarrow> state"
schirmer@12854
   638
 "abupd f \<equiv> prod_fun f id"
schirmer@12854
   639
schirmer@12854
   640
  supd     :: "(st \<Rightarrow> st) \<Rightarrow> state \<Rightarrow> state" 
schirmer@12854
   641
 "supd \<equiv> prod_fun id"
schirmer@12854
   642
  
schirmer@12854
   643
lemma abupd_def2 [simp]: "abupd f (x,s) = (f x,s)"
schirmer@12854
   644
by (simp add: abupd_def)
schirmer@12854
   645
schirmer@12854
   646
lemma abupd_abrupt_if_False [simp]: "\<And> s. abupd (abrupt_if False xo) s = s"
schirmer@12854
   647
by simp
schirmer@12854
   648
schirmer@12854
   649
lemma supd_def2 [simp]: "supd f (x,s) = (x,f s)"
schirmer@12854
   650
by (simp add: supd_def)
schirmer@12854
   651
schirmer@12854
   652
lemma supd_lupd [simp]: 
schirmer@12854
   653
 "\<And> s. supd (lupd vn v ) s = (abrupt s,lupd vn v (store s))"
schirmer@12854
   654
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   655
apply (simp (no_asm))
schirmer@12854
   656
done
schirmer@12854
   657
schirmer@12854
   658
schirmer@12854
   659
lemma supd_gupd [simp]: 
schirmer@12854
   660
 "\<And> s. supd (gupd r obj) s = (abrupt s,gupd r obj (store s))"
schirmer@12854
   661
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   662
apply (simp (no_asm))
schirmer@12854
   663
done
schirmer@12854
   664
schirmer@12854
   665
lemma supd_init_obj [simp]: 
schirmer@12854
   666
 "supd (init_obj G oi r) s = (abrupt s,init_obj G oi r (store s))"
schirmer@12854
   667
apply (unfold init_obj_def)
schirmer@12854
   668
apply (simp (no_asm))
schirmer@12854
   669
done
schirmer@12854
   670
schirmer@13688
   671
lemma abupd_store_invariant [simp]: "store (abupd f s) = store s"
schirmer@13688
   672
  by (cases s) simp
schirmer@13688
   673
schirmer@13688
   674
lemma supd_abrupt_invariant [simp]: "abrupt (supd f s) = abrupt s"
schirmer@13688
   675
  by (cases s) simp
schirmer@13688
   676
wenzelm@35067
   677
abbreviation set_lvars :: "locals \<Rightarrow> state \<Rightarrow> state"
wenzelm@35067
   678
  where "set_lvars l == supd (set_locals l)"
schirmer@12854
   679
wenzelm@35067
   680
abbreviation restore_lvars :: "state  \<Rightarrow> state \<Rightarrow> state"
wenzelm@35067
   681
  where "restore_lvars s' s == set_lvars (locals (store s')) s"
schirmer@12854
   682
schirmer@12854
   683
lemma set_set_lvars [simp]: "\<And> s. set_lvars l (set_lvars l' s) = set_lvars l s"
schirmer@12854
   684
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   685
apply (simp (no_asm))
schirmer@12854
   686
done
schirmer@12854
   687
schirmer@12854
   688
lemma set_lvars_id [simp]: "\<And> s. set_lvars (locals (store s)) s = s"
schirmer@12854
   689
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   690
apply (simp (no_asm))
schirmer@12854
   691
done
schirmer@12854
   692
schirmer@12854
   693
section "initialisation test"
schirmer@12854
   694
schirmer@12854
   695
constdefs
schirmer@12854
   696
schirmer@12854
   697
  inited   :: "qtname \<Rightarrow> globs \<Rightarrow> bool"
schirmer@12854
   698
 "inited C g \<equiv> g (Stat C) \<noteq> None"
schirmer@12854
   699
schirmer@12854
   700
  initd    :: "qtname \<Rightarrow> state \<Rightarrow> bool"
schirmer@12854
   701
 "initd C \<equiv> inited C \<circ> globs \<circ> store"
schirmer@12854
   702
schirmer@12854
   703
lemma not_inited_empty [simp]: "\<not>inited C empty"
schirmer@12854
   704
apply (unfold inited_def)
schirmer@12854
   705
apply (simp (no_asm))
schirmer@12854
   706
done
schirmer@12854
   707
schirmer@12854
   708
lemma inited_gupdate [simp]: "inited C (g(r\<mapsto>obj)) = (inited C g \<or> r = Stat C)"
schirmer@12854
   709
apply (unfold inited_def)
schirmer@12854
   710
apply (auto split add: st.split)
schirmer@12854
   711
done
schirmer@12854
   712
schirmer@12854
   713
lemma inited_init_class_obj [intro!]: "inited C (globs (init_class_obj G C s))"
schirmer@12854
   714
apply (unfold inited_def)
schirmer@12854
   715
apply (simp (no_asm))
schirmer@12854
   716
done
schirmer@12854
   717
schirmer@12854
   718
lemma not_initedD: "\<not> inited C g \<Longrightarrow> g (Stat C) = None"
schirmer@12854
   719
apply (unfold inited_def)
schirmer@12854
   720
apply (erule notnotD)
schirmer@12854
   721
done
schirmer@12854
   722
schirmer@12854
   723
lemma initedD: "inited C g \<Longrightarrow> \<exists> obj. g (Stat C) = Some obj"
schirmer@12854
   724
apply (unfold inited_def)
schirmer@12854
   725
apply auto
schirmer@12854
   726
done
schirmer@12854
   727
schirmer@12854
   728
lemma initd_def2 [simp]: "initd C s = inited C (globs (store s))"
schirmer@12854
   729
apply (unfold initd_def)
schirmer@12854
   730
apply (simp (no_asm))
schirmer@12854
   731
done
schirmer@12854
   732
schirmer@12925
   733
section {* @{text error_free} *}
schirmer@12925
   734
constdefs error_free:: "state \<Rightarrow> bool"
schirmer@12925
   735
"error_free s \<equiv> \<not> (\<exists> err. abrupt s = Some (Error err))"
schirmer@12854
   736
schirmer@12925
   737
lemma error_free_Norm [simp,intro]: "error_free (Norm s)"
schirmer@12925
   738
by (simp add: error_free_def)
schirmer@12925
   739
schirmer@12925
   740
lemma error_free_normal [simp,intro]: "normal s \<Longrightarrow> error_free s"
schirmer@12925
   741
by (simp add: error_free_def)
schirmer@12925
   742
schirmer@12925
   743
lemma error_free_Xcpt [simp]: "error_free (Some (Xcpt x),s)"
schirmer@12925
   744
by (simp add: error_free_def)
schirmer@12925
   745
schirmer@12925
   746
lemma error_free_Jump [simp,intro]: "error_free (Some (Jump j),s)"
schirmer@12925
   747
by (simp add: error_free_def)
schirmer@12925
   748
schirmer@12925
   749
lemma error_free_Error [simp]: "error_free (Some (Error e),s) = False"
schirmer@12925
   750
by (simp add: error_free_def)  
schirmer@12925
   751
schirmer@12925
   752
lemma error_free_Some [simp,intro]: 
schirmer@12925
   753
 "\<not> (\<exists> err. x=Error err) \<Longrightarrow> error_free ((Some x),s)"
schirmer@12925
   754
by (auto simp add: error_free_def)
schirmer@12925
   755
wenzelm@13524
   756
lemma error_free_abupd_absorb [simp,intro]: 
schirmer@12925
   757
 "error_free s \<Longrightarrow> error_free (abupd (absorb j) s)"
schirmer@12925
   758
by (cases s) 
schirmer@12925
   759
   (auto simp add: error_free_def absorb_def
schirmer@12925
   760
         split: split_if_asm)
schirmer@12925
   761
schirmer@12925
   762
lemma error_free_absorb [simp,intro]: 
schirmer@12925
   763
 "error_free (a,s) \<Longrightarrow> error_free (absorb j a, s)"
schirmer@12925
   764
by (auto simp add: error_free_def absorb_def
schirmer@12925
   765
            split: split_if_asm)
schirmer@12925
   766
schirmer@12925
   767
lemma error_free_abrupt_if [simp,intro]:
schirmer@12925
   768
"\<lbrakk>error_free s; \<not> (\<exists> err. x=Error err)\<rbrakk>
schirmer@12925
   769
 \<Longrightarrow> error_free (abupd (abrupt_if p (Some x)) s)"
schirmer@12925
   770
by (cases s)
schirmer@12925
   771
   (auto simp add: abrupt_if_def
schirmer@12925
   772
            split: split_if)
schirmer@12925
   773
schirmer@12925
   774
lemma error_free_abrupt_if1 [simp,intro]:
schirmer@12925
   775
"\<lbrakk>error_free (a,s); \<not> (\<exists> err. x=Error err)\<rbrakk>
schirmer@12925
   776
 \<Longrightarrow> error_free (abrupt_if p (Some x) a, s)"
schirmer@12925
   777
by  (auto simp add: abrupt_if_def
schirmer@12925
   778
            split: split_if)
schirmer@12925
   779
schirmer@12925
   780
lemma error_free_abrupt_if_Xcpt [simp,intro]:
schirmer@12925
   781
 "error_free s 
schirmer@12925
   782
  \<Longrightarrow> error_free (abupd (abrupt_if p (Some (Xcpt x))) s)"
schirmer@12925
   783
by simp 
schirmer@12925
   784
schirmer@12925
   785
lemma error_free_abrupt_if_Xcpt1 [simp,intro]:
schirmer@12925
   786
 "error_free (a,s) 
schirmer@12925
   787
  \<Longrightarrow> error_free (abrupt_if p (Some (Xcpt x)) a, s)" 
schirmer@12925
   788
by simp 
schirmer@12925
   789
schirmer@12925
   790
lemma error_free_abrupt_if_Jump [simp,intro]:
schirmer@12925
   791
 "error_free s 
schirmer@12925
   792
  \<Longrightarrow> error_free (abupd (abrupt_if p (Some (Jump j))) s)" 
schirmer@12925
   793
by simp
schirmer@12925
   794
schirmer@12925
   795
lemma error_free_abrupt_if_Jump1 [simp,intro]:
schirmer@12925
   796
 "error_free (a,s) 
schirmer@12925
   797
  \<Longrightarrow> error_free (abrupt_if p (Some (Jump j)) a, s)" 
schirmer@12925
   798
by simp
schirmer@12925
   799
schirmer@12925
   800
lemma error_free_raise_if [simp,intro]:
schirmer@12925
   801
 "error_free s \<Longrightarrow> error_free (abupd (raise_if p x) s)"
schirmer@12925
   802
by simp 
schirmer@12925
   803
schirmer@12925
   804
lemma error_free_raise_if1 [simp,intro]:
schirmer@12925
   805
 "error_free (a,s) \<Longrightarrow> error_free ((raise_if p x a), s)"
schirmer@12925
   806
by simp 
schirmer@12925
   807
schirmer@12925
   808
lemma error_free_supd [simp,intro]:
schirmer@12925
   809
 "error_free s \<Longrightarrow> error_free (supd f s)"
schirmer@12925
   810
by (cases s) (simp add: error_free_def)
schirmer@12925
   811
schirmer@12925
   812
lemma error_free_supd1 [simp,intro]:
schirmer@12925
   813
 "error_free (a,s) \<Longrightarrow> error_free (a,f s)"
schirmer@12925
   814
by (simp add: error_free_def)
schirmer@12925
   815
schirmer@12925
   816
lemma error_free_set_lvars [simp,intro]:
schirmer@12925
   817
"error_free s \<Longrightarrow> error_free ((set_lvars l) s)"
schirmer@12925
   818
by (cases s) simp
schirmer@12925
   819
schirmer@12925
   820
lemma error_free_set_locals [simp,intro]: 
schirmer@12925
   821
"error_free (x, s)
schirmer@12925
   822
       \<Longrightarrow> error_free (x, set_locals l s')"
schirmer@12925
   823
by (simp add: error_free_def)
schirmer@12854
   824
schirmer@13688
   825
schirmer@12854
   826
end
schirmer@12854
   827