src/HOL/Bali/State.thy
author wenzelm
Wed Mar 03 00:33:02 2010 +0100 (2010-03-03)
changeset 35431 8758fe1fc9f8
parent 35416 d8d7d1b785af
child 37956 ee939247b2fb
permissions -rw-r--r--
cleanup type translations;
wenzelm@12857
     1
(*  Title:      HOL/Bali/State.thy
schirmer@12854
     2
    Author:     David von Oheimb
schirmer@12854
     3
*)
schirmer@12854
     4
header {* State for evaluation of Java expressions and statements *}
schirmer@12854
     5
haftmann@33965
     6
theory State
haftmann@33965
     7
imports DeclConcepts
haftmann@33965
     8
begin
schirmer@12854
     9
schirmer@12854
    10
text {*
schirmer@12854
    11
design issues:
schirmer@12854
    12
\begin{itemize}
schirmer@12854
    13
\item all kinds of objects (class instances, arrays, and class objects)
schirmer@12854
    14
  are handeled via a general object abstraction
schirmer@12854
    15
\item the heap and the map for class objects are combined into a single table
schirmer@12854
    16
  @{text "(recall (loc, obj) table \<times> (qtname, obj) table  ~=  (loc + qtname, obj) table)"}
schirmer@12854
    17
\end{itemize}
schirmer@12854
    18
*}
schirmer@12854
    19
schirmer@12854
    20
section "objects"
schirmer@12854
    21
schirmer@13688
    22
datatype  obj_tag =     --{* tag for generic object   *}
wenzelm@32960
    23
          CInst qtname  --{* class instance           *}
wenzelm@32960
    24
        | Arr  ty int   --{* array with component type and length *}
schirmer@13688
    25
    --{* | CStat qtname   the tag is irrelevant for a class object,
wenzelm@32960
    26
                           i.e. the static fields of a class,
schirmer@12925
    27
                           since its type is given already by the reference to 
schirmer@13688
    28
                           it (see below) *}
schirmer@12854
    29
wenzelm@32960
    30
types   vn   = "fspec + int"                    --{* variable name      *}
wenzelm@32960
    31
record  obj  = 
schirmer@13688
    32
          tag :: "obj_tag"                      --{* generalized object *}
haftmann@31127
    33
          "values" :: "(vn, val) table"      
schirmer@12854
    34
schirmer@12854
    35
translations 
wenzelm@35431
    36
  (type) "fspec" <= (type) "vname \<times> qtname" 
wenzelm@35431
    37
  (type) "vn"    <= (type) "fspec + int"
wenzelm@35431
    38
  (type) "obj"   <= (type) "\<lparr>tag::obj_tag, values::vn \<Rightarrow> val option\<rparr>"
wenzelm@35431
    39
  (type) "obj"   <= (type) "\<lparr>tag::obj_tag, values::vn \<Rightarrow> val option,\<dots>::'a\<rparr>"
schirmer@12854
    40
haftmann@35416
    41
definition the_Arr :: "obj option \<Rightarrow> ty \<times> int \<times> (vn, val) table" where
wenzelm@14766
    42
 "the_Arr obj \<equiv> SOME (T,k,t). obj = Some \<lparr>tag=Arr T k,values=t\<rparr>"
schirmer@12854
    43
schirmer@12854
    44
lemma the_Arr_Arr [simp]: "the_Arr (Some \<lparr>tag=Arr T k,values=cs\<rparr>) = (T,k,cs)"
schirmer@12854
    45
apply (auto simp: the_Arr_def)
schirmer@12854
    46
done
schirmer@12854
    47
schirmer@12854
    48
lemma the_Arr_Arr1 [simp,intro,dest]:
schirmer@12854
    49
 "\<lbrakk>tag obj = Arr T k\<rbrakk> \<Longrightarrow> the_Arr (Some obj) = (T,k,values obj)"
schirmer@12854
    50
apply (auto simp add: the_Arr_def)
schirmer@12854
    51
done
schirmer@12854
    52
haftmann@35416
    53
definition upd_obj :: "vn \<Rightarrow> val \<Rightarrow> obj \<Rightarrow> obj" where 
schirmer@12854
    54
 "upd_obj n v \<equiv> \<lambda> obj . obj \<lparr>values:=(values obj)(n\<mapsto>v)\<rparr>"
schirmer@12854
    55
schirmer@12854
    56
lemma upd_obj_def2 [simp]: 
schirmer@12854
    57
  "upd_obj n v obj = obj \<lparr>values:=(values obj)(n\<mapsto>v)\<rparr>" 
schirmer@12854
    58
apply (auto simp: upd_obj_def)
schirmer@12854
    59
done
schirmer@12854
    60
haftmann@35416
    61
definition obj_ty :: "obj \<Rightarrow> ty" where
schirmer@12854
    62
 "obj_ty obj    \<equiv> case tag obj of 
schirmer@12854
    63
                    CInst C \<Rightarrow> Class C 
schirmer@12854
    64
                  | Arr T k \<Rightarrow> T.[]"
schirmer@12854
    65
schirmer@12854
    66
lemma obj_ty_eq [intro!]: "obj_ty \<lparr>tag=oi,values=x\<rparr> = obj_ty \<lparr>tag=oi,values=y\<rparr>" 
schirmer@12854
    67
by (simp add: obj_ty_def)
schirmer@12854
    68
schirmer@12854
    69
schirmer@12854
    70
lemma obj_ty_eq1 [intro!,dest]: 
schirmer@12854
    71
  "tag obj = tag obj' \<Longrightarrow> obj_ty obj = obj_ty obj'" 
schirmer@12854
    72
by (simp add: obj_ty_def)
schirmer@12854
    73
schirmer@12854
    74
lemma obj_ty_cong [simp]: 
schirmer@12854
    75
  "obj_ty (obj \<lparr>values:=vs\<rparr>) = obj_ty obj" 
schirmer@12854
    76
by auto
schirmer@13688
    77
schirmer@12854
    78
lemma obj_ty_CInst [simp]: 
schirmer@12854
    79
 "obj_ty \<lparr>tag=CInst C,values=vs\<rparr> = Class C" 
schirmer@12854
    80
by (simp add: obj_ty_def)
schirmer@12854
    81
schirmer@12854
    82
lemma obj_ty_CInst1 [simp,intro!,dest]: 
schirmer@12854
    83
 "\<lbrakk>tag obj = CInst C\<rbrakk> \<Longrightarrow> obj_ty obj = Class C" 
schirmer@12854
    84
by (simp add: obj_ty_def)
schirmer@12854
    85
schirmer@12854
    86
lemma obj_ty_Arr [simp]: 
schirmer@12854
    87
 "obj_ty \<lparr>tag=Arr T i,values=vs\<rparr> = T.[]"
schirmer@12854
    88
by (simp add: obj_ty_def)
schirmer@12854
    89
schirmer@12854
    90
lemma obj_ty_Arr1 [simp,intro!,dest]: 
schirmer@12854
    91
 "\<lbrakk>tag obj = Arr T i\<rbrakk> \<Longrightarrow> obj_ty obj = T.[]"
schirmer@12854
    92
by (simp add: obj_ty_def)
schirmer@12854
    93
schirmer@12854
    94
lemma obj_ty_widenD: 
schirmer@12854
    95
 "G\<turnstile>obj_ty obj\<preceq>RefT t \<Longrightarrow> (\<exists>C. tag obj = CInst C) \<or> (\<exists>T k. tag obj = Arr T k)"
schirmer@12854
    96
apply (unfold obj_ty_def)
schirmer@12854
    97
apply (auto split add: obj_tag.split_asm)
schirmer@12854
    98
done
schirmer@12854
    99
haftmann@35416
   100
definition obj_class :: "obj \<Rightarrow> qtname" where
schirmer@12854
   101
 "obj_class obj \<equiv> case tag obj of 
schirmer@12854
   102
                    CInst C \<Rightarrow> C 
schirmer@12854
   103
                  | Arr T k \<Rightarrow> Object"
schirmer@12854
   104
schirmer@12854
   105
schirmer@12854
   106
lemma obj_class_CInst [simp]: "obj_class \<lparr>tag=CInst C,values=vs\<rparr> = C" 
schirmer@12854
   107
by (auto simp: obj_class_def)
schirmer@12854
   108
schirmer@12854
   109
lemma obj_class_CInst1 [simp,intro!,dest]: 
schirmer@12854
   110
  "tag obj = CInst C \<Longrightarrow> obj_class obj = C" 
schirmer@12854
   111
by (auto simp: obj_class_def)
schirmer@12854
   112
schirmer@12854
   113
lemma obj_class_Arr [simp]: "obj_class \<lparr>tag=Arr T k,values=vs\<rparr> = Object" 
schirmer@12854
   114
by (auto simp: obj_class_def)
schirmer@12854
   115
schirmer@12854
   116
lemma obj_class_Arr1 [simp,intro!,dest]: 
schirmer@12854
   117
 "tag obj = Arr T k \<Longrightarrow> obj_class obj = Object" 
schirmer@12854
   118
by (auto simp: obj_class_def)
schirmer@12854
   119
schirmer@12854
   120
lemma obj_ty_obj_class: "G\<turnstile>obj_ty obj\<preceq> Class statC = G\<turnstile>obj_class obj \<preceq>\<^sub>C statC"
schirmer@12854
   121
apply (case_tac "tag obj")
schirmer@12854
   122
apply (auto simp add: obj_ty_def obj_class_def)
schirmer@12854
   123
apply (case_tac "statC = Object")
schirmer@12854
   124
apply (auto dest: widen_Array_Class)
schirmer@12854
   125
done
schirmer@12854
   126
schirmer@12854
   127
section "object references"
schirmer@12854
   128
schirmer@13688
   129
types oref = "loc + qtname"         --{* generalized object reference *}
schirmer@12854
   130
syntax
schirmer@12854
   131
  Heap  :: "loc   \<Rightarrow> oref"
schirmer@12854
   132
  Stat  :: "qtname \<Rightarrow> oref"
schirmer@12854
   133
schirmer@12854
   134
translations
haftmann@33965
   135
  "Heap" => "CONST Inl"
haftmann@33965
   136
  "Stat" => "CONST Inr"
wenzelm@35431
   137
  (type) "oref" <= (type) "loc + qtname"
schirmer@12854
   138
haftmann@35416
   139
definition fields_table :: "prog \<Rightarrow> qtname \<Rightarrow> (fspec \<Rightarrow> field \<Rightarrow> bool)  \<Rightarrow> (fspec, ty) table" where
schirmer@12854
   140
 "fields_table G C P 
nipkow@30235
   141
    \<equiv> Option.map type \<circ> table_of (filter (split P) (DeclConcepts.fields G C))"
schirmer@12854
   142
schirmer@12854
   143
lemma fields_table_SomeI: 
schirmer@12854
   144
"\<lbrakk>table_of (DeclConcepts.fields G C) n = Some f; P n f\<rbrakk> 
schirmer@12854
   145
 \<Longrightarrow> fields_table G C P n = Some (type f)"
schirmer@12854
   146
apply (unfold fields_table_def)
schirmer@12854
   147
apply clarsimp
schirmer@12854
   148
apply (rule exI)
schirmer@12854
   149
apply (rule conjI)
schirmer@12854
   150
apply (erule map_of_filter_in)
schirmer@12854
   151
apply assumption
schirmer@12854
   152
apply simp
schirmer@12854
   153
done
schirmer@12854
   154
schirmer@12854
   155
(* unused *)
schirmer@12854
   156
lemma fields_table_SomeD': "fields_table G C P fn = Some T \<Longrightarrow>  
schirmer@12854
   157
  \<exists>f. (fn,f)\<in>set(DeclConcepts.fields G C) \<and> type f = T"
schirmer@12854
   158
apply (unfold fields_table_def)
schirmer@12854
   159
apply clarsimp
schirmer@12854
   160
apply (drule map_of_SomeD)
schirmer@12854
   161
apply auto
schirmer@12854
   162
done
schirmer@12854
   163
schirmer@12854
   164
lemma fields_table_SomeD: 
schirmer@12854
   165
"\<lbrakk>fields_table G C P fn = Some T; unique (DeclConcepts.fields G C)\<rbrakk> \<Longrightarrow>  
schirmer@12854
   166
  \<exists>f. table_of (DeclConcepts.fields G C) fn = Some f \<and> type f = T"
schirmer@12854
   167
apply (unfold fields_table_def)
schirmer@12854
   168
apply clarsimp
schirmer@12854
   169
apply (rule exI)
schirmer@12854
   170
apply (rule conjI)
schirmer@12854
   171
apply (erule table_of_filter_unique_SomeD)
schirmer@12854
   172
apply assumption
schirmer@12854
   173
apply simp
schirmer@12854
   174
done
schirmer@12854
   175
haftmann@35416
   176
definition in_bounds :: "int \<Rightarrow> int \<Rightarrow> bool" ("(_/ in'_bounds _)" [50, 51] 50) where
schirmer@12854
   177
 "i in_bounds k \<equiv> 0 \<le> i \<and> i < k"
schirmer@12854
   178
haftmann@35416
   179
definition arr_comps :: "'a \<Rightarrow> int \<Rightarrow> int \<Rightarrow> 'a option" where
schirmer@12854
   180
 "arr_comps T k \<equiv> \<lambda>i. if i in_bounds k then Some T else None"
schirmer@12854
   181
  
haftmann@35416
   182
definition var_tys       :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> (vn, ty) table" where
schirmer@12854
   183
"var_tys G oi r 
schirmer@12854
   184
  \<equiv> case r of 
schirmer@12854
   185
      Heap a \<Rightarrow> (case oi of 
schirmer@12854
   186
                   CInst C \<Rightarrow> fields_table G C (\<lambda>n f. \<not>static f) (+) empty
schirmer@12854
   187
                 | Arr T k \<Rightarrow> empty (+) arr_comps T k)
schirmer@12854
   188
    | Stat C \<Rightarrow> fields_table G C (\<lambda>fn f. declclassf fn = C \<and> static f) 
schirmer@12854
   189
                (+) empty"
schirmer@12854
   190
schirmer@12854
   191
lemma var_tys_Some_eq: 
schirmer@12854
   192
 "var_tys G oi r n = Some T 
schirmer@12854
   193
  = (case r of 
schirmer@12854
   194
       Inl a \<Rightarrow> (case oi of  
schirmer@12854
   195
                   CInst C \<Rightarrow> (\<exists>nt. n = Inl nt \<and> fields_table G C (\<lambda>n f. 
schirmer@12854
   196
                               \<not>static f) nt = Some T)  
schirmer@12854
   197
                 | Arr t k \<Rightarrow> (\<exists> i. n = Inr i  \<and> i in_bounds k \<and> t = T))  
schirmer@12854
   198
     | Inr C \<Rightarrow> (\<exists>nt. n = Inl nt \<and> 
schirmer@12854
   199
                 fields_table G C (\<lambda>fn f. declclassf fn = C \<and> static f) nt 
schirmer@12854
   200
                  = Some T))"
schirmer@12854
   201
apply (unfold var_tys_def arr_comps_def)
schirmer@12854
   202
apply (force split add: sum.split_asm sum.split obj_tag.split)
schirmer@12854
   203
done
schirmer@12854
   204
schirmer@12854
   205
schirmer@12854
   206
section "stores"
schirmer@12854
   207
wenzelm@32960
   208
types   globs               --{* global variables: heap and static variables *}
wenzelm@32960
   209
        = "(oref , obj) table"
wenzelm@32960
   210
        heap
wenzelm@32960
   211
        = "(loc  , obj) table"
wenzelm@32960
   212
(*      locals                   
wenzelm@32960
   213
        = "(lname, val) table" *) (* defined in Value.thy local variables *)
schirmer@12854
   214
schirmer@12854
   215
translations
wenzelm@35431
   216
 (type) "globs"  <= (type) "(oref , obj) table"
wenzelm@35431
   217
 (type) "heap"   <= (type) "(loc  , obj) table"
wenzelm@35431
   218
(*  (type) "locals" <= (type) "(lname, val) table" *)
schirmer@12854
   219
schirmer@12854
   220
datatype st = (* pure state, i.e. contents of all variables *)
wenzelm@32960
   221
         st globs locals
schirmer@12854
   222
schirmer@12854
   223
subsection "access"
schirmer@12854
   224
haftmann@35416
   225
definition globs :: "st \<Rightarrow> globs" where
schirmer@12854
   226
 "globs  \<equiv> st_case (\<lambda>g l. g)"
schirmer@12854
   227
  
haftmann@35416
   228
definition locals :: "st \<Rightarrow> locals" where
schirmer@12854
   229
 "locals \<equiv> st_case (\<lambda>g l. l)"
schirmer@12854
   230
haftmann@35416
   231
definition heap   :: "st \<Rightarrow> heap" where
schirmer@12854
   232
 "heap s \<equiv> globs s \<circ> Heap"
schirmer@12854
   233
schirmer@12854
   234
schirmer@12854
   235
lemma globs_def2 [simp]: " globs (st g l) = g"
schirmer@12854
   236
by (simp add: globs_def)
schirmer@12854
   237
schirmer@12854
   238
lemma locals_def2 [simp]: "locals (st g l) = l"
schirmer@12854
   239
by (simp add: locals_def)
schirmer@12854
   240
schirmer@12854
   241
lemma heap_def2 [simp]:  "heap s a=globs s (Heap a)"
schirmer@12854
   242
by (simp add: heap_def)
schirmer@12854
   243
schirmer@12854
   244
wenzelm@35067
   245
abbreviation val_this :: "st \<Rightarrow> val"
wenzelm@35067
   246
  where "val_this s == the (locals s This)"
schirmer@12854
   247
wenzelm@35067
   248
abbreviation lookup_obj :: "st \<Rightarrow> val \<Rightarrow> obj"
wenzelm@35067
   249
  where "lookup_obj s a' == the (heap s (the_Addr a'))"
schirmer@12854
   250
schirmer@12854
   251
subsection "memory allocation"
schirmer@12854
   252
haftmann@35416
   253
definition new_Addr :: "heap \<Rightarrow> loc option" where
wenzelm@14766
   254
 "new_Addr h   \<equiv> if (\<forall>a. h a \<noteq> None) then None else Some (SOME a. h a = None)"
schirmer@12854
   255
schirmer@12854
   256
lemma new_AddrD: "new_Addr h = Some a \<Longrightarrow> h a = None"
nipkow@18576
   257
apply (auto simp add: new_Addr_def)
paulson@18447
   258
apply (erule someI) 
schirmer@12854
   259
done
schirmer@12854
   260
schirmer@12854
   261
lemma new_AddrD2: "new_Addr h = Some a \<Longrightarrow> \<forall>b. h b \<noteq> None \<longrightarrow> b \<noteq> a"
schirmer@12854
   262
apply (drule new_AddrD)
schirmer@12854
   263
apply auto
schirmer@12854
   264
done
schirmer@12854
   265
schirmer@12854
   266
lemma new_Addr_SomeI: "h a = None \<Longrightarrow> \<exists>b. new_Addr h = Some b \<and> h b = None"
nipkow@18576
   267
apply (simp add: new_Addr_def)
paulson@18447
   268
apply (fast intro: someI2)
schirmer@12854
   269
done
schirmer@12854
   270
schirmer@12854
   271
schirmer@12854
   272
subsection "initialization"
schirmer@12854
   273
wenzelm@35067
   274
abbreviation init_vals :: "('a, ty) table \<Rightarrow> ('a, val) table"
wenzelm@35067
   275
  where "init_vals vs == Option.map default_val \<circ> vs"
schirmer@12854
   276
schirmer@12854
   277
lemma init_arr_comps_base [simp]: "init_vals (arr_comps T 0) = empty"
schirmer@12854
   278
apply (unfold arr_comps_def in_bounds_def)
schirmer@12854
   279
apply (rule ext)
schirmer@12854
   280
apply auto
schirmer@12854
   281
done
schirmer@12854
   282
schirmer@12854
   283
lemma init_arr_comps_step [simp]: 
schirmer@12854
   284
"0 < j \<Longrightarrow> init_vals (arr_comps T  j    ) =  
schirmer@12854
   285
           init_vals (arr_comps T (j - 1))(j - 1\<mapsto>default_val T)"
schirmer@12854
   286
apply (unfold arr_comps_def in_bounds_def)
schirmer@12854
   287
apply (rule ext)
schirmer@12854
   288
apply auto
schirmer@12854
   289
done
schirmer@12854
   290
schirmer@12854
   291
subsection "update"
schirmer@12854
   292
haftmann@35416
   293
definition gupd :: "oref  \<Rightarrow> obj \<Rightarrow> st \<Rightarrow> st" ("gupd'(_\<mapsto>_')"[10,10]1000) where
schirmer@12854
   294
 "gupd r obj  \<equiv> st_case (\<lambda>g l. st (g(r\<mapsto>obj)) l)"
schirmer@12854
   295
haftmann@35416
   296
definition lupd       :: "lname \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st" ("lupd'(_\<mapsto>_')"[10,10]1000) where
schirmer@12854
   297
 "lupd vn v   \<equiv> st_case (\<lambda>g l. st g (l(vn\<mapsto>v)))"
schirmer@12854
   298
haftmann@35416
   299
definition upd_gobj   :: "oref \<Rightarrow> vn \<Rightarrow> val \<Rightarrow> st \<Rightarrow> st" where
schirmer@12854
   300
 "upd_gobj r n v \<equiv> st_case (\<lambda>g l. st (chg_map (upd_obj n v) r g) l)"
schirmer@12854
   301
haftmann@35416
   302
definition set_locals  :: "locals \<Rightarrow> st \<Rightarrow> st" where
schirmer@12854
   303
 "set_locals l \<equiv> st_case (\<lambda>g l'. st g l)"
nipkow@30235
   304
haftmann@35416
   305
definition init_obj    :: "prog \<Rightarrow> obj_tag \<Rightarrow> oref \<Rightarrow> st \<Rightarrow> st" where
schirmer@12854
   306
 "init_obj G oi r \<equiv> gupd(r\<mapsto>\<lparr>tag=oi, values=init_vals (var_tys G oi r)\<rparr>)"
schirmer@12854
   307
wenzelm@35067
   308
abbreviation
schirmer@12854
   309
  init_class_obj :: "prog \<Rightarrow> qtname \<Rightarrow> st \<Rightarrow> st"
wenzelm@35067
   310
  where "init_class_obj G C == init_obj G undefined (Inr C)"
schirmer@12854
   311
schirmer@12854
   312
lemma gupd_def2 [simp]: "gupd(r\<mapsto>obj) (st g l) = st (g(r\<mapsto>obj)) l"
schirmer@12854
   313
apply (unfold gupd_def)
schirmer@12854
   314
apply (simp (no_asm))
schirmer@12854
   315
done
schirmer@12854
   316
schirmer@12854
   317
lemma lupd_def2 [simp]: "lupd(vn\<mapsto>v) (st g l) = st g (l(vn\<mapsto>v))"
schirmer@12854
   318
apply (unfold lupd_def)
schirmer@12854
   319
apply (simp (no_asm))
schirmer@12854
   320
done
schirmer@12854
   321
schirmer@12854
   322
lemma globs_gupd [simp]: "globs  (gupd(r\<mapsto>obj) s) = globs s(r\<mapsto>obj)"
schirmer@12854
   323
apply (induct "s")
schirmer@12854
   324
by (simp add: gupd_def)
schirmer@12854
   325
schirmer@12854
   326
lemma globs_lupd [simp]: "globs  (lupd(vn\<mapsto>v ) s) = globs  s"
schirmer@12854
   327
apply (induct "s")
schirmer@12854
   328
by (simp add: lupd_def)
schirmer@12854
   329
schirmer@12854
   330
lemma locals_gupd [simp]: "locals (gupd(r\<mapsto>obj) s) = locals s"
schirmer@12854
   331
apply (induct "s")
schirmer@12854
   332
by (simp add: gupd_def)
schirmer@12854
   333
schirmer@12854
   334
lemma locals_lupd [simp]: "locals (lupd(vn\<mapsto>v ) s) = locals s(vn\<mapsto>v )"
schirmer@12854
   335
apply (induct "s")
schirmer@12854
   336
by (simp add: lupd_def)
schirmer@12854
   337
schirmer@12854
   338
lemma globs_upd_gobj_new [rule_format (no_asm), simp]: 
schirmer@12854
   339
  "globs s r = None \<longrightarrow> globs (upd_gobj r n v s) = globs s"
schirmer@12854
   340
apply (unfold upd_gobj_def)
schirmer@12854
   341
apply (induct "s")
schirmer@12854
   342
apply auto
schirmer@12854
   343
done
schirmer@12854
   344
schirmer@12854
   345
lemma globs_upd_gobj_upd [rule_format (no_asm), simp]: 
schirmer@12854
   346
"globs s r=Some obj\<longrightarrow> globs (upd_gobj r n v s) = globs s(r\<mapsto>upd_obj n v obj)"
schirmer@12854
   347
apply (unfold upd_gobj_def)
schirmer@12854
   348
apply (induct "s")
schirmer@12854
   349
apply auto
schirmer@12854
   350
done
schirmer@12854
   351
schirmer@12854
   352
lemma locals_upd_gobj [simp]: "locals (upd_gobj r n v s) = locals s"
schirmer@12854
   353
apply (induct "s")
schirmer@12854
   354
by (simp add: upd_gobj_def) 
schirmer@12854
   355
schirmer@12854
   356
schirmer@12854
   357
lemma globs_init_obj [simp]: "globs (init_obj G oi r s) t =  
schirmer@12854
   358
  (if t=r then Some \<lparr>tag=oi,values=init_vals (var_tys G oi r)\<rparr> else globs s t)"
schirmer@12854
   359
apply (unfold init_obj_def)
schirmer@12854
   360
apply (simp (no_asm))
schirmer@12854
   361
done
schirmer@12854
   362
schirmer@12854
   363
lemma locals_init_obj [simp]: "locals (init_obj G oi r s) = locals s"
schirmer@12854
   364
by (simp add: init_obj_def)
schirmer@12854
   365
  
schirmer@12854
   366
lemma surjective_st [simp]: "st (globs s) (locals s) = s"
schirmer@12854
   367
apply (induct "s")
schirmer@12854
   368
by auto
schirmer@12854
   369
schirmer@12854
   370
lemma surjective_st_init_obj: 
schirmer@12854
   371
 "st (globs (init_obj G oi r s)) (locals s) = init_obj G oi r s"
schirmer@12854
   372
apply (subst locals_init_obj [THEN sym])
schirmer@12854
   373
apply (rule surjective_st)
schirmer@12854
   374
done
schirmer@12854
   375
schirmer@12854
   376
lemma heap_heap_upd [simp]: 
schirmer@12854
   377
  "heap (st (g(Inl a\<mapsto>obj)) l) = heap (st g l)(a\<mapsto>obj)"
schirmer@12854
   378
apply (rule ext)
schirmer@12854
   379
apply (simp (no_asm))
schirmer@12854
   380
done
schirmer@12854
   381
lemma heap_stat_upd [simp]: "heap (st (g(Inr C\<mapsto>obj)) l) = heap (st g l)"
schirmer@12854
   382
apply (rule ext)
schirmer@12854
   383
apply (simp (no_asm))
schirmer@12854
   384
done
schirmer@12854
   385
lemma heap_local_upd [simp]: "heap (st g (l(vn\<mapsto>v))) = heap (st g l)"
schirmer@12854
   386
apply (rule ext)
schirmer@12854
   387
apply (simp (no_asm))
schirmer@12854
   388
done
schirmer@12854
   389
schirmer@12854
   390
lemma heap_gupd_Heap [simp]: "heap (gupd(Heap a\<mapsto>obj) s) = heap s(a\<mapsto>obj)"
schirmer@12854
   391
apply (rule ext)
schirmer@12854
   392
apply (simp (no_asm))
schirmer@12854
   393
done
schirmer@12854
   394
lemma heap_gupd_Stat [simp]: "heap (gupd(Stat C\<mapsto>obj) s) = heap s"
schirmer@12854
   395
apply (rule ext)
schirmer@12854
   396
apply (simp (no_asm))
schirmer@12854
   397
done
schirmer@12854
   398
lemma heap_lupd [simp]: "heap (lupd(vn\<mapsto>v) s) = heap s"
schirmer@12854
   399
apply (rule ext)
schirmer@12854
   400
apply (simp (no_asm))
schirmer@12854
   401
done
schirmer@12854
   402
schirmer@12854
   403
lemma heap_upd_gobj_Stat [simp]: "heap (upd_gobj (Stat C) n v s) = heap s"
schirmer@12854
   404
apply (rule ext)
schirmer@12854
   405
apply (simp (no_asm))
schirmer@12854
   406
apply (case_tac "globs s (Stat C)")
schirmer@12854
   407
apply  auto
schirmer@12854
   408
done
schirmer@12854
   409
schirmer@12854
   410
lemma set_locals_def2 [simp]: "set_locals l (st g l') = st g l"
schirmer@12854
   411
apply (unfold set_locals_def)
schirmer@12854
   412
apply (simp (no_asm))
schirmer@12854
   413
done
schirmer@12854
   414
schirmer@12854
   415
lemma set_locals_id [simp]: "set_locals (locals s) s = s"
schirmer@12854
   416
apply (unfold set_locals_def)
schirmer@12854
   417
apply (induct_tac "s")
schirmer@12854
   418
apply (simp (no_asm))
schirmer@12854
   419
done
schirmer@12854
   420
schirmer@12854
   421
lemma set_set_locals [simp]: "set_locals l (set_locals l' s) = set_locals l s"
schirmer@12854
   422
apply (unfold set_locals_def)
schirmer@12854
   423
apply (induct_tac "s")
schirmer@12854
   424
apply (simp (no_asm))
schirmer@12854
   425
done
schirmer@12854
   426
schirmer@12854
   427
lemma locals_set_locals [simp]: "locals (set_locals l s) = l"
schirmer@12854
   428
apply (unfold set_locals_def)
schirmer@12854
   429
apply (induct_tac "s")
schirmer@12854
   430
apply (simp (no_asm))
schirmer@12854
   431
done
schirmer@12854
   432
schirmer@12854
   433
lemma globs_set_locals [simp]: "globs (set_locals l s) = globs s"
schirmer@12854
   434
apply (unfold set_locals_def)
schirmer@12854
   435
apply (induct_tac "s")
schirmer@12854
   436
apply (simp (no_asm))
schirmer@12854
   437
done
schirmer@12854
   438
schirmer@12854
   439
lemma heap_set_locals [simp]: "heap (set_locals l s) = heap s"
schirmer@12854
   440
apply (unfold heap_def)
schirmer@12854
   441
apply (induct_tac "s")
schirmer@12854
   442
apply (simp (no_asm))
schirmer@12854
   443
done
schirmer@12854
   444
schirmer@12854
   445
schirmer@12854
   446
section "abrupt completion"
schirmer@12854
   447
schirmer@12854
   448
schirmer@12854
   449
schirmer@12854
   450
consts
schirmer@12854
   451
schirmer@12854
   452
  the_Xcpt :: "abrupt \<Rightarrow> xcpt"
schirmer@12854
   453
  the_Jump :: "abrupt => jump"
schirmer@12854
   454
  the_Loc  :: "xcpt \<Rightarrow> loc"
schirmer@12854
   455
  the_Std  :: "xcpt \<Rightarrow> xname"
schirmer@12854
   456
schirmer@12854
   457
primrec "the_Xcpt (Xcpt x) = x"
schirmer@12854
   458
primrec "the_Jump (Jump j) = j"
schirmer@12854
   459
primrec "the_Loc (Loc a) = a"
schirmer@12854
   460
primrec "the_Std (Std x) = x"
schirmer@12854
   461
schirmer@13337
   462
wenzelm@32960
   463
        
schirmer@12854
   464
haftmann@35416
   465
definition abrupt_if :: "bool \<Rightarrow> abopt \<Rightarrow> abopt \<Rightarrow> abopt" where
schirmer@12854
   466
 "abrupt_if c x' x \<equiv> if c \<and> (x = None) then x' else x"
schirmer@12854
   467
schirmer@12854
   468
lemma abrupt_if_True_None [simp]: "abrupt_if True x None = x"
schirmer@12854
   469
by (simp add: abrupt_if_def)
schirmer@12854
   470
schirmer@12854
   471
lemma abrupt_if_True_not_None [simp]: "x \<noteq> None \<Longrightarrow> abrupt_if True x y \<noteq> None"
schirmer@12854
   472
by (simp add: abrupt_if_def)
schirmer@12854
   473
schirmer@12854
   474
lemma abrupt_if_False [simp]: "abrupt_if False x y = y"
schirmer@12854
   475
by (simp add: abrupt_if_def)
schirmer@12854
   476
schirmer@12854
   477
lemma abrupt_if_Some [simp]: "abrupt_if c x (Some y) = Some y"
schirmer@12854
   478
by (simp add: abrupt_if_def)
schirmer@12854
   479
schirmer@12854
   480
lemma abrupt_if_not_None [simp]: "y \<noteq> None \<Longrightarrow> abrupt_if c x y = y"
schirmer@12854
   481
apply (simp add: abrupt_if_def)
schirmer@12854
   482
by auto
schirmer@12854
   483
schirmer@12854
   484
schirmer@12854
   485
lemma split_abrupt_if: 
schirmer@12854
   486
"P (abrupt_if c x' x) = 
schirmer@12854
   487
      ((c \<and> x = None \<longrightarrow> P x') \<and> (\<not> (c \<and> x = None) \<longrightarrow> P x))"
schirmer@12854
   488
apply (unfold abrupt_if_def)
schirmer@12854
   489
apply (split split_if)
schirmer@12854
   490
apply auto
schirmer@12854
   491
done
schirmer@12854
   492
wenzelm@35067
   493
abbreviation raise_if :: "bool \<Rightarrow> xname \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   494
  where "raise_if c xn == abrupt_if c (Some (Xcpt (Std xn)))"
wenzelm@35067
   495
wenzelm@35067
   496
abbreviation np :: "val \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   497
  where "np v == raise_if (v = Null) NullPointer"
schirmer@12854
   498
wenzelm@35067
   499
abbreviation check_neg :: "val \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   500
  where "check_neg i' == raise_if (the_Intg i'<0) NegArrSize"
schirmer@12854
   501
wenzelm@35067
   502
abbreviation error_if :: "bool \<Rightarrow> error \<Rightarrow> abopt \<Rightarrow> abopt"
wenzelm@35067
   503
  where "error_if c e == abrupt_if c (Some (Error e))"
schirmer@12854
   504
schirmer@12854
   505
lemma raise_if_None [simp]: "(raise_if c x y = None) = (\<not>c \<and> y = None)"
schirmer@12854
   506
apply (simp add: abrupt_if_def)
schirmer@12854
   507
by auto
schirmer@12854
   508
declare raise_if_None [THEN iffD1, dest!]
schirmer@12854
   509
schirmer@12854
   510
lemma if_raise_if_None [simp]: 
schirmer@12854
   511
  "((if b then y else raise_if c x y) = None) = ((c \<longrightarrow> b) \<and> y = None)"
schirmer@12854
   512
apply (simp add: abrupt_if_def)
schirmer@12854
   513
apply auto
schirmer@12854
   514
done
schirmer@12854
   515
schirmer@12854
   516
lemma raise_if_SomeD [dest!]:
schirmer@12854
   517
  "raise_if c x y = Some z \<Longrightarrow> c \<and> z=(Xcpt (Std x)) \<and> y=None \<or> (y=Some z)"
schirmer@12854
   518
apply (case_tac y)
schirmer@12854
   519
apply (case_tac c)
schirmer@12854
   520
apply (simp add: abrupt_if_def)
schirmer@12854
   521
apply (simp add: abrupt_if_def)
schirmer@12854
   522
apply auto
schirmer@12854
   523
done
schirmer@12854
   524
schirmer@12925
   525
lemma error_if_None [simp]: "(error_if c e y = None) = (\<not>c \<and> y = None)"
schirmer@12925
   526
apply (simp add: abrupt_if_def)
schirmer@12925
   527
by auto
schirmer@12925
   528
declare error_if_None [THEN iffD1, dest!]
schirmer@12925
   529
schirmer@12925
   530
lemma if_error_if_None [simp]: 
schirmer@12925
   531
  "((if b then y else error_if c e y) = None) = ((c \<longrightarrow> b) \<and> y = None)"
schirmer@12925
   532
apply (simp add: abrupt_if_def)
schirmer@12925
   533
apply auto
schirmer@12925
   534
done
schirmer@12925
   535
wenzelm@13524
   536
lemma error_if_SomeD [dest!]:
schirmer@12925
   537
  "error_if c e y = Some z \<Longrightarrow> c \<and> z=(Error e) \<and> y=None \<or> (y=Some z)"
schirmer@12925
   538
apply (case_tac y)
schirmer@12925
   539
apply (case_tac c)
schirmer@12925
   540
apply (simp add: abrupt_if_def)
schirmer@12925
   541
apply (simp add: abrupt_if_def)
schirmer@12925
   542
apply auto
schirmer@12925
   543
done
schirmer@12925
   544
haftmann@35416
   545
definition absorb :: "jump \<Rightarrow> abopt \<Rightarrow> abopt" where
schirmer@12854
   546
  "absorb j a \<equiv> if a=Some (Jump j) then None else a"
schirmer@12854
   547
schirmer@12854
   548
lemma absorb_SomeD [dest!]: "absorb j a = Some x \<Longrightarrow> a = Some x"
schirmer@12854
   549
by (auto simp add: absorb_def)
schirmer@12854
   550
schirmer@12854
   551
lemma absorb_same [simp]: "absorb j (Some (Jump j)) = None"
schirmer@12854
   552
by (auto simp add: absorb_def)
schirmer@12854
   553
schirmer@12854
   554
lemma absorb_other [simp]: "a \<noteq> Some (Jump j) \<Longrightarrow> absorb j a = a"
schirmer@12854
   555
by (auto simp add: absorb_def)
schirmer@12854
   556
schirmer@13688
   557
lemma absorb_Some_NoneD: "absorb j (Some abr) = None \<Longrightarrow> abr = Jump j"
schirmer@13688
   558
  by (simp add: absorb_def)
schirmer@13688
   559
schirmer@13688
   560
lemma absorb_Some_JumpD: "absorb j s = Some (Jump j') \<Longrightarrow> j'\<noteq>j"
schirmer@13688
   561
  by (simp add: absorb_def)
schirmer@13688
   562
schirmer@12854
   563
schirmer@12854
   564
section "full program state"
schirmer@12854
   565
schirmer@12854
   566
types
schirmer@13688
   567
  state = "abopt \<times> st"          --{* state including abruption information *}
schirmer@12854
   568
schirmer@12854
   569
translations
wenzelm@35431
   570
  (type) "abopt" <= (type) "abrupt option"
wenzelm@35431
   571
  (type) "state" <= (type) "abopt \<times> st"
schirmer@12854
   572
wenzelm@35067
   573
abbreviation
wenzelm@35067
   574
  Norm :: "st \<Rightarrow> state"
wenzelm@35067
   575
  where "Norm s == (None, s)"
schirmer@12854
   576
wenzelm@35067
   577
abbreviation (input)
wenzelm@35067
   578
  abrupt :: "state \<Rightarrow> abopt"
wenzelm@35067
   579
  where "abrupt == fst"
wenzelm@35067
   580
wenzelm@35067
   581
abbreviation (input)
wenzelm@35067
   582
  store :: "state \<Rightarrow> st"
wenzelm@35067
   583
  where "store == snd"
schirmer@12854
   584
schirmer@12854
   585
lemma single_stateE: "\<forall>Z. Z = (s::state) \<Longrightarrow> False"
schirmer@12854
   586
apply (erule_tac x = "(Some k,y)" in all_dupE)
schirmer@12854
   587
apply (erule_tac x = "(None,y)" in allE)
schirmer@12854
   588
apply clarify
schirmer@12854
   589
done
schirmer@12854
   590
schirmer@12854
   591
lemma state_not_single: "All (op = (x::state)) \<Longrightarrow> R"
schirmer@12854
   592
apply (drule_tac x = "(if abrupt x = None then Some ?x else None,?y)" in spec)
schirmer@12854
   593
apply clarsimp
schirmer@12854
   594
done
schirmer@12854
   595
haftmann@35416
   596
definition normal :: "state \<Rightarrow> bool" where
schirmer@12854
   597
 "normal \<equiv> \<lambda>s. abrupt s = None"
schirmer@12854
   598
schirmer@12854
   599
lemma normal_def2 [simp]: "normal s = (abrupt s = None)"
schirmer@12854
   600
apply (unfold normal_def)
schirmer@12854
   601
apply (simp (no_asm))
schirmer@12854
   602
done
schirmer@12854
   603
haftmann@35416
   604
definition heap_free :: "nat \<Rightarrow> state \<Rightarrow> bool" where
schirmer@12854
   605
 "heap_free n \<equiv> \<lambda>s. atleast_free (heap (store s)) n"
schirmer@12854
   606
schirmer@12854
   607
lemma heap_free_def2 [simp]: "heap_free n s = atleast_free (heap (store s)) n"
schirmer@12854
   608
apply (unfold heap_free_def)
schirmer@12854
   609
apply simp
schirmer@12854
   610
done
schirmer@12854
   611
schirmer@12854
   612
subsection "update"
schirmer@12854
   613
haftmann@35416
   614
definition abupd :: "(abopt \<Rightarrow> abopt) \<Rightarrow> state \<Rightarrow> state" where
schirmer@12854
   615
 "abupd f \<equiv> prod_fun f id"
schirmer@12854
   616
haftmann@35416
   617
definition supd     :: "(st \<Rightarrow> st) \<Rightarrow> state \<Rightarrow> state" where
schirmer@12854
   618
 "supd \<equiv> prod_fun id"
schirmer@12854
   619
  
schirmer@12854
   620
lemma abupd_def2 [simp]: "abupd f (x,s) = (f x,s)"
schirmer@12854
   621
by (simp add: abupd_def)
schirmer@12854
   622
schirmer@12854
   623
lemma abupd_abrupt_if_False [simp]: "\<And> s. abupd (abrupt_if False xo) s = s"
schirmer@12854
   624
by simp
schirmer@12854
   625
schirmer@12854
   626
lemma supd_def2 [simp]: "supd f (x,s) = (x,f s)"
schirmer@12854
   627
by (simp add: supd_def)
schirmer@12854
   628
schirmer@12854
   629
lemma supd_lupd [simp]: 
schirmer@12854
   630
 "\<And> s. supd (lupd vn v ) s = (abrupt s,lupd vn v (store s))"
schirmer@12854
   631
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   632
apply (simp (no_asm))
schirmer@12854
   633
done
schirmer@12854
   634
schirmer@12854
   635
schirmer@12854
   636
lemma supd_gupd [simp]: 
schirmer@12854
   637
 "\<And> s. supd (gupd r obj) s = (abrupt s,gupd r obj (store s))"
schirmer@12854
   638
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   639
apply (simp (no_asm))
schirmer@12854
   640
done
schirmer@12854
   641
schirmer@12854
   642
lemma supd_init_obj [simp]: 
schirmer@12854
   643
 "supd (init_obj G oi r) s = (abrupt s,init_obj G oi r (store s))"
schirmer@12854
   644
apply (unfold init_obj_def)
schirmer@12854
   645
apply (simp (no_asm))
schirmer@12854
   646
done
schirmer@12854
   647
schirmer@13688
   648
lemma abupd_store_invariant [simp]: "store (abupd f s) = store s"
schirmer@13688
   649
  by (cases s) simp
schirmer@13688
   650
schirmer@13688
   651
lemma supd_abrupt_invariant [simp]: "abrupt (supd f s) = abrupt s"
schirmer@13688
   652
  by (cases s) simp
schirmer@13688
   653
wenzelm@35067
   654
abbreviation set_lvars :: "locals \<Rightarrow> state \<Rightarrow> state"
wenzelm@35067
   655
  where "set_lvars l == supd (set_locals l)"
schirmer@12854
   656
wenzelm@35067
   657
abbreviation restore_lvars :: "state  \<Rightarrow> state \<Rightarrow> state"
wenzelm@35067
   658
  where "restore_lvars s' s == set_lvars (locals (store s')) s"
schirmer@12854
   659
schirmer@12854
   660
lemma set_set_lvars [simp]: "\<And> s. set_lvars l (set_lvars l' s) = set_lvars l 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 set_lvars_id [simp]: "\<And> s. set_lvars (locals (store s)) s = s"
schirmer@12854
   666
apply (simp (no_asm_simp) only: split_tupled_all)
schirmer@12854
   667
apply (simp (no_asm))
schirmer@12854
   668
done
schirmer@12854
   669
schirmer@12854
   670
section "initialisation test"
schirmer@12854
   671
haftmann@35416
   672
definition inited :: "qtname \<Rightarrow> globs \<Rightarrow> bool" where
schirmer@12854
   673
 "inited C g \<equiv> g (Stat C) \<noteq> None"
schirmer@12854
   674
haftmann@35416
   675
definition initd    :: "qtname \<Rightarrow> state \<Rightarrow> bool" where
schirmer@12854
   676
 "initd C \<equiv> inited C \<circ> globs \<circ> store"
schirmer@12854
   677
schirmer@12854
   678
lemma not_inited_empty [simp]: "\<not>inited C empty"
schirmer@12854
   679
apply (unfold inited_def)
schirmer@12854
   680
apply (simp (no_asm))
schirmer@12854
   681
done
schirmer@12854
   682
schirmer@12854
   683
lemma inited_gupdate [simp]: "inited C (g(r\<mapsto>obj)) = (inited C g \<or> r = Stat C)"
schirmer@12854
   684
apply (unfold inited_def)
schirmer@12854
   685
apply (auto split add: st.split)
schirmer@12854
   686
done
schirmer@12854
   687
schirmer@12854
   688
lemma inited_init_class_obj [intro!]: "inited C (globs (init_class_obj G C s))"
schirmer@12854
   689
apply (unfold inited_def)
schirmer@12854
   690
apply (simp (no_asm))
schirmer@12854
   691
done
schirmer@12854
   692
schirmer@12854
   693
lemma not_initedD: "\<not> inited C g \<Longrightarrow> g (Stat C) = None"
schirmer@12854
   694
apply (unfold inited_def)
schirmer@12854
   695
apply (erule notnotD)
schirmer@12854
   696
done
schirmer@12854
   697
schirmer@12854
   698
lemma initedD: "inited C g \<Longrightarrow> \<exists> obj. g (Stat C) = Some obj"
schirmer@12854
   699
apply (unfold inited_def)
schirmer@12854
   700
apply auto
schirmer@12854
   701
done
schirmer@12854
   702
schirmer@12854
   703
lemma initd_def2 [simp]: "initd C s = inited C (globs (store s))"
schirmer@12854
   704
apply (unfold initd_def)
schirmer@12854
   705
apply (simp (no_asm))
schirmer@12854
   706
done
schirmer@12854
   707
schirmer@12925
   708
section {* @{text error_free} *}
haftmann@35416
   709
definition error_free :: "state \<Rightarrow> bool" where
schirmer@12925
   710
"error_free s \<equiv> \<not> (\<exists> err. abrupt s = Some (Error err))"
schirmer@12854
   711
schirmer@12925
   712
lemma error_free_Norm [simp,intro]: "error_free (Norm s)"
schirmer@12925
   713
by (simp add: error_free_def)
schirmer@12925
   714
schirmer@12925
   715
lemma error_free_normal [simp,intro]: "normal s \<Longrightarrow> error_free s"
schirmer@12925
   716
by (simp add: error_free_def)
schirmer@12925
   717
schirmer@12925
   718
lemma error_free_Xcpt [simp]: "error_free (Some (Xcpt x),s)"
schirmer@12925
   719
by (simp add: error_free_def)
schirmer@12925
   720
schirmer@12925
   721
lemma error_free_Jump [simp,intro]: "error_free (Some (Jump j),s)"
schirmer@12925
   722
by (simp add: error_free_def)
schirmer@12925
   723
schirmer@12925
   724
lemma error_free_Error [simp]: "error_free (Some (Error e),s) = False"
schirmer@12925
   725
by (simp add: error_free_def)  
schirmer@12925
   726
schirmer@12925
   727
lemma error_free_Some [simp,intro]: 
schirmer@12925
   728
 "\<not> (\<exists> err. x=Error err) \<Longrightarrow> error_free ((Some x),s)"
schirmer@12925
   729
by (auto simp add: error_free_def)
schirmer@12925
   730
wenzelm@13524
   731
lemma error_free_abupd_absorb [simp,intro]: 
schirmer@12925
   732
 "error_free s \<Longrightarrow> error_free (abupd (absorb j) s)"
schirmer@12925
   733
by (cases s) 
schirmer@12925
   734
   (auto simp add: error_free_def absorb_def
schirmer@12925
   735
         split: split_if_asm)
schirmer@12925
   736
schirmer@12925
   737
lemma error_free_absorb [simp,intro]: 
schirmer@12925
   738
 "error_free (a,s) \<Longrightarrow> error_free (absorb j a, s)"
schirmer@12925
   739
by (auto simp add: error_free_def absorb_def
schirmer@12925
   740
            split: split_if_asm)
schirmer@12925
   741
schirmer@12925
   742
lemma error_free_abrupt_if [simp,intro]:
schirmer@12925
   743
"\<lbrakk>error_free s; \<not> (\<exists> err. x=Error err)\<rbrakk>
schirmer@12925
   744
 \<Longrightarrow> error_free (abupd (abrupt_if p (Some x)) s)"
schirmer@12925
   745
by (cases s)
schirmer@12925
   746
   (auto simp add: abrupt_if_def
schirmer@12925
   747
            split: split_if)
schirmer@12925
   748
schirmer@12925
   749
lemma error_free_abrupt_if1 [simp,intro]:
schirmer@12925
   750
"\<lbrakk>error_free (a,s); \<not> (\<exists> err. x=Error err)\<rbrakk>
schirmer@12925
   751
 \<Longrightarrow> error_free (abrupt_if p (Some x) a, s)"
schirmer@12925
   752
by  (auto simp add: abrupt_if_def
schirmer@12925
   753
            split: split_if)
schirmer@12925
   754
schirmer@12925
   755
lemma error_free_abrupt_if_Xcpt [simp,intro]:
schirmer@12925
   756
 "error_free s 
schirmer@12925
   757
  \<Longrightarrow> error_free (abupd (abrupt_if p (Some (Xcpt x))) s)"
schirmer@12925
   758
by simp 
schirmer@12925
   759
schirmer@12925
   760
lemma error_free_abrupt_if_Xcpt1 [simp,intro]:
schirmer@12925
   761
 "error_free (a,s) 
schirmer@12925
   762
  \<Longrightarrow> error_free (abrupt_if p (Some (Xcpt x)) a, s)" 
schirmer@12925
   763
by simp 
schirmer@12925
   764
schirmer@12925
   765
lemma error_free_abrupt_if_Jump [simp,intro]:
schirmer@12925
   766
 "error_free s 
schirmer@12925
   767
  \<Longrightarrow> error_free (abupd (abrupt_if p (Some (Jump j))) s)" 
schirmer@12925
   768
by simp
schirmer@12925
   769
schirmer@12925
   770
lemma error_free_abrupt_if_Jump1 [simp,intro]:
schirmer@12925
   771
 "error_free (a,s) 
schirmer@12925
   772
  \<Longrightarrow> error_free (abrupt_if p (Some (Jump j)) a, s)" 
schirmer@12925
   773
by simp
schirmer@12925
   774
schirmer@12925
   775
lemma error_free_raise_if [simp,intro]:
schirmer@12925
   776
 "error_free s \<Longrightarrow> error_free (abupd (raise_if p x) s)"
schirmer@12925
   777
by simp 
schirmer@12925
   778
schirmer@12925
   779
lemma error_free_raise_if1 [simp,intro]:
schirmer@12925
   780
 "error_free (a,s) \<Longrightarrow> error_free ((raise_if p x a), s)"
schirmer@12925
   781
by simp 
schirmer@12925
   782
schirmer@12925
   783
lemma error_free_supd [simp,intro]:
schirmer@12925
   784
 "error_free s \<Longrightarrow> error_free (supd f s)"
schirmer@12925
   785
by (cases s) (simp add: error_free_def)
schirmer@12925
   786
schirmer@12925
   787
lemma error_free_supd1 [simp,intro]:
schirmer@12925
   788
 "error_free (a,s) \<Longrightarrow> error_free (a,f s)"
schirmer@12925
   789
by (simp add: error_free_def)
schirmer@12925
   790
schirmer@12925
   791
lemma error_free_set_lvars [simp,intro]:
schirmer@12925
   792
"error_free s \<Longrightarrow> error_free ((set_lvars l) s)"
schirmer@12925
   793
by (cases s) simp
schirmer@12925
   794
schirmer@12925
   795
lemma error_free_set_locals [simp,intro]: 
schirmer@12925
   796
"error_free (x, s)
schirmer@12925
   797
       \<Longrightarrow> error_free (x, set_locals l s')"
schirmer@12925
   798
by (simp add: error_free_def)
schirmer@12854
   799
schirmer@13688
   800
schirmer@12854
   801
end
schirmer@12854
   802