src/HOL/MicroJava/J/WellType.thy
author oheimb
Mon, 05 Feb 2001 20:14:15 +0100
changeset 11070 cc421547e744
parent 11026 a50365d21144
child 11372 648795477bb5
permissions -rw-r--r--
improved document (added headers etc)
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
     1
(*  Title:      HOL/MicroJava/J/WellType.thy
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
     2
    ID:         $Id$
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
     3
    Author:     David von Oheimb
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
     4
    Copyright   1999 Technische Universitaet Muenchen
11070
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
     5
*)
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
     6
11070
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
     7
header "Well-typedness Constraints"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
     8
11070
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
     9
theory WellType = Term + WellForm:
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    10
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    11
text {*
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    12
the formulation of well-typedness of method calls given below (as well as
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    13
the Java Specification 1.0) is a little too restrictive: Is does not allow
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    14
methods of class Object to be called upon references of interface type.
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    15
11070
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    16
\begin{description}
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    17
\item[simplifications:]\ \\
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    18
\begin{itemize}
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    19
\item the type rules include all static checks on expressions and statements, 
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    20
  e.g.\ definedness of names (of parameters, locals, fields, methods)
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    21
\end{itemize}
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    22
\end{description}
cc421547e744 improved document (added headers etc)
oheimb
parents: 11026
diff changeset
    23
*}
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    24
types	lenv (* local variables, including method parameters and This *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    25
	= "vname \<leadsto> ty"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    26
        'c env
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    27
	= "'c prog \<times> lenv"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    28
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    29
syntax
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
    30
  prg    :: "'c env => 'c prog"
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    31
  localT :: "'c env => (vname \<leadsto> ty)"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    32
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    33
translations	
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
    34
  "prg"    => "fst"
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
    35
  "localT" => "snd"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    36
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    37
consts
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    38
  more_spec :: "'c prog => (ty \<times> 'x) \<times> ty list =>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    39
                (ty \<times> 'x) \<times> ty list => bool"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    40
  appl_methds :: "'c prog =>  cname => sig => ((ty \<times> ty) \<times> ty list) set"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    41
  max_spec :: "'c prog =>  cname => sig => ((ty \<times> ty) \<times> ty list) set"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    42
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    43
defs
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    44
  more_spec_def: "more_spec G == \<lambda>((d,h),pTs). \<lambda>((d',h'),pTs'). G\<turnstile>d\<preceq>d' \<and>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    45
		                            list_all2 (\<lambda>T T'. G\<turnstile>T\<preceq>T') pTs pTs'"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    46
  
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    47
  (* applicable methods, cf. 15.11.2.1 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    48
  appl_methds_def: "appl_methds G C == \<lambda>(mn, pTs).
8105
2dda3e88d23f simplified definition of appl_methds, removing m_head
oheimb
parents: 8085
diff changeset
    49
		                 {((Class md,rT),pTs') |md rT mb pTs'.
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    50
		                  method (G,C)  (mn, pTs') = Some (md,rT,mb) \<and>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    51
		                  list_all2 (\<lambda>T T'. G\<turnstile>T\<preceq>T') pTs pTs'}"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    52
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    53
  (* maximally specific methods, cf. 15.11.2.2 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    54
  max_spec_def: "max_spec G C sig == {m. m \<in>appl_methds G C sig \<and> 
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    55
                                       (\<forall>m'\<in>appl_methds G C sig.
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    56
                                         more_spec G m' m --> m' = m)}"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    57
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    58
lemma max_spec2appl_meths: 
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    59
  "x \<in> max_spec G C sig ==> x \<in> appl_methds G C sig"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    60
apply (unfold max_spec_def)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    61
apply (fast)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    62
done
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    63
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    64
lemma appl_methsD: 
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    65
"((md,rT),pTs')\<in>appl_methds G C (mn, pTs) ==>  
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    66
  \<exists>D b. md = Class D \<and> method (G,C) (mn, pTs') = Some (D,rT,b)  
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    67
  \<and> list_all2 (\<lambda>T T'. G\<turnstile>T\<preceq>T') pTs pTs'"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    68
apply (unfold appl_methds_def)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    69
apply (fast)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    70
done
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    71
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    72
lemmas max_spec2mheads = insertI1 [THEN [2] equalityD2 [THEN subsetD], 
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    73
                         THEN max_spec2appl_meths, THEN appl_methsD]
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    74
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
    75
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    76
consts
10042
7164dc0d24d8 unsymbolized
kleing
parents: 9348
diff changeset
    77
  typeof :: "(loc => ty option) => val => ty option"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    78
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    79
primrec
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    80
	"typeof dt  Unit    = Some (PrimT Void)"
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    81
	"typeof dt  Null    = Some NT"
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    82
	"typeof dt (Bool b) = Some (PrimT Boolean)"
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    83
	"typeof dt (Intg i) = Some (PrimT Integer)"
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    84
	"typeof dt (Addr a) = dt a"
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    85
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    86
lemma is_type_typeof [rule_format (no_asm), simp]: "(\<forall>a. v \<noteq> Addr a) --> (\<exists>T. typeof t v = Some T \<and> is_type G T)"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    87
apply (rule val.induct)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    88
apply     auto
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    89
done
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    90
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    91
lemma typeof_empty_is_type [rule_format (no_asm)]: 
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    92
  "typeof (\<lambda>a. None) v = Some T \<longrightarrow> is_type G T"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    93
apply (rule val.induct)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    94
apply     auto
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    95
done
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    96
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    97
types
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
    98
	java_mb = "vname list \<times> (vname \<times> ty) list \<times> stmt \<times> expr"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
    99
	(* method body with parameter names, local variables, block, result expression *)
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   100
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   101
consts
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   102
  ty_expr :: "java_mb env => (expr      \<times> ty     ) set"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   103
  ty_exprs:: "java_mb env => (expr list \<times> ty list) set"
10042
7164dc0d24d8 unsymbolized
kleing
parents: 9348
diff changeset
   104
  wt_stmt :: "java_mb env =>  stmt                 set"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   105
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   106
syntax
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   107
  ty_expr :: "java_mb env => [expr     , ty     ] => bool" ("_ \<turnstile> _ :: _"   [51,51,51]50)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   108
  ty_exprs:: "java_mb env => [expr list, ty list] => bool" ("_ \<turnstile> _ [::] _" [51,51,51]50)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   109
  wt_stmt :: "java_mb env =>  stmt                => bool" ("_ \<turnstile> _ \<surd>"      [51,51   ]50)
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   110
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   111
syntax (HTML)
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   112
  ty_expr :: "java_mb env => [expr     , ty     ] => bool" ("_ |- _ :: _"   [51,51,51]50)
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   113
  ty_exprs:: "java_mb env => [expr list, ty list] => bool" ("_ |- _ [::] _" [51,51,51]50)
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   114
  wt_stmt :: "java_mb env =>  stmt                => bool" ("_ |- _ [ok]"   [51,51   ]50)
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   115
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   116
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   117
translations
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   118
	"E\<turnstile>e :: T" == "(e,T) \<in> ty_expr  E"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   119
	"E\<turnstile>e[::]T" == "(e,T) \<in> ty_exprs E"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   120
	"E\<turnstile>c \<surd>"    == "c     \<in> wt_stmt  E"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   121
  
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   122
inductive "ty_expr E" "ty_exprs E" "wt_stmt E" intros
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   123
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   124
(* well-typed expressions *)
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   125
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   126
  (* cf. 15.8 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   127
  NewC:	"[| is_class (prg E) C |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   128
         E\<turnstile>NewC C::Class C"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   129
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   130
  (* cf. 15.15 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   131
  Cast:	"[| E\<turnstile>e::Class C; is_class (prg E) D;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   132
            prg E\<turnstile>C\<preceq>? D |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   133
         E\<turnstile>Cast D e::Class D"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   134
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   135
  (* cf. 15.7.1 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   136
  Lit:	  "[| typeof (\<lambda>v. None) x = Some T |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   137
         E\<turnstile>Lit x::T"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   138
9240
f4d76cb26433 added BinOp
oheimb
parents: 8178
diff changeset
   139
  
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   140
  (* cf. 15.13.1 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   141
  LAcc:	"[| localT E v = Some T; is_type (prg E) T |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   142
         E\<turnstile>LAcc v::T"
9240
f4d76cb26433 added BinOp
oheimb
parents: 8178
diff changeset
   143
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   144
  BinOp:"[| E\<turnstile>e1::T;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   145
            E\<turnstile>e2::T;
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   146
            if bop = Eq then T' = PrimT Boolean
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   147
                        else T' = T \<and> T = PrimT Integer|] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   148
         E\<turnstile>BinOp bop e1 e2::T'"
9240
f4d76cb26433 added BinOp
oheimb
parents: 8178
diff changeset
   149
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   150
  (* cf. 15.25, 15.25.1 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   151
  LAss: "[| E\<turnstile>LAcc v::T;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   152
	          E\<turnstile>e::T';
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   153
            prg E\<turnstile>T'\<preceq>T |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   154
         E\<turnstile>v::=e::T'"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   155
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   156
  (* cf. 15.10.1 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   157
  FAcc: "[| E\<turnstile>a::Class C; 
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   158
            field (prg E,C) fn = Some (fd,fT) |] ==>
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   159
         E\<turnstile>{fd}a..fn::fT"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   160
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   161
  (* cf. 15.25, 15.25.1 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   162
  FAss: "[| E\<turnstile>{fd}a..fn::T;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   163
            E\<turnstile>v        ::T';
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   164
            prg E\<turnstile>T'\<preceq>T |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   165
         E\<turnstile>{fd}a..fn:=v::T'"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   166
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   167
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   168
  (* cf. 15.11.1, 15.11.2, 15.11.3 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   169
  Call: "[| E\<turnstile>a::Class C;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   170
            E\<turnstile>ps[::]pTs;
10061
fe82134773dc added HTML syntax; added spaces in normal syntax for better documents
kleing
parents: 10042
diff changeset
   171
            max_spec (prg E) C (mn, pTs) = {((md,rT),pTs')} |] ==>
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   172
         E\<turnstile>{C}a..mn({pTs'}ps)::rT"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   173
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   174
(* well-typed expression lists *)
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   175
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   176
  (* cf. 15.11.??? *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   177
  Nil: "E\<turnstile>[][::][]"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   178
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   179
  (* cf. 15.11.??? *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   180
  Cons:"[| E\<turnstile>e::T;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   181
           E\<turnstile>es[::]Ts |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   182
        E\<turnstile>e#es[::]T#Ts"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   183
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   184
(* well-typed statements *)
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   185
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   186
  Skip:"E\<turnstile>Skip\<surd>"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   187
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   188
  Expr:"[| E\<turnstile>e::T |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   189
        E\<turnstile>Expr e\<surd>"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   190
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   191
  Comp:"[| E\<turnstile>s1\<surd>; 
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   192
           E\<turnstile>s2\<surd> |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   193
        E\<turnstile>s1;; s2\<surd>"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   194
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   195
  (* cf. 14.8 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   196
  Cond:"[| E\<turnstile>e::PrimT Boolean;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   197
           E\<turnstile>s1\<surd>;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   198
           E\<turnstile>s2\<surd> |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   199
         E\<turnstile>If(e) s1 Else s2\<surd>"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   200
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   201
  (* cf. 14.10 *)
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   202
  Loop:"[| E\<turnstile>e::PrimT Boolean;
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   203
           E\<turnstile>s\<surd> |] ==>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   204
        E\<turnstile>While(e) s\<surd>"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   205
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   206
constdefs
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   207
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   208
 wf_java_mdecl :: "java_mb prog => cname => java_mb mdecl => bool"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   209
"wf_java_mdecl G C == \<lambda>((mn,pTs),rT,(pns,lvars,blk,res)).
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   210
	length pTs = length pns \<and>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   211
	nodups pns \<and>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   212
	unique lvars \<and>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   213
	(\<forall>pn\<in>set pns. map_of lvars pn = None) \<and>
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   214
	(\<forall>(vn,T)\<in>set lvars. is_type G T) &
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   215
	(let E = (G,map_of lvars(pns[\<mapsto>]pTs)(This\<mapsto>Class C)) in
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   216
	 E\<turnstile>blk\<surd> \<and> (\<exists>T. E\<turnstile>res::T \<and> G\<turnstile>T\<preceq>rT))"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   217
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   218
 wf_java_prog :: "java_mb prog => bool"
10042
7164dc0d24d8 unsymbolized
kleing
parents: 9348
diff changeset
   219
"wf_java_prog G == wf_prog wf_java_mdecl G"
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   220
11026
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   221
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   222
lemma wt_is_type: "wf_prog wf_mb G \<Longrightarrow> ((G,L)\<turnstile>e::T \<longrightarrow> is_type G T) \<and>  
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   223
       ((G,L)\<turnstile>es[::]Ts \<longrightarrow> Ball (set Ts) (is_type G)) \<and> ((G,L)\<turnstile>c \<surd> \<longrightarrow> True)"
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   224
apply (rule ty_expr_ty_exprs_wt_stmt.induct)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   225
apply auto
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   226
apply (   erule typeof_empty_is_type)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   227
apply (  simp split add: split_if_asm)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   228
apply ( drule field_fields)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   229
apply ( drule (1) fields_is_type)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   230
apply (  simp (no_asm_simp))
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   231
apply  (assumption)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   232
apply (auto dest!: max_spec2mheads method_wf_mdecl is_type_rTI simp add: wf_mdecl_def)
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   233
done
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   234
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   235
lemmas ty_expr_is_type = wt_is_type [THEN conjunct1,THEN mp, COMP swap_prems_rl]
a50365d21144 converted to Isar, simplifying recursion on class hierarchy
oheimb
parents: 10763
diff changeset
   236
8011
d14c4e9e9c8e *** empty log message ***
nipkow
parents:
diff changeset
   237
end