src/HOL/NanoJava/TypeRel.thy
author wenzelm
Sun, 11 Feb 2018 12:51:23 +0100
changeset 67593 5efb88c90051
parent 67443 3abf6a722518
child 67613 ce654b0e6d69
permissions -rw-r--r--
clarified command-line defaults;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
     1
(*  Title:      HOL/NanoJava/TypeRel.thy
41589
bbd861837ebc tuned headers;
wenzelm
parents: 35416
diff changeset
     2
    Author:     David von Oheimb, Technische Universitaet Muenchen
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
     3
*)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
     4
58889
5b7a9633cfa8 modernized header uniformly as section;
wenzelm
parents: 58860
diff changeset
     5
section "Type relations"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
     6
55017
2df6ad1dbd66 adapted to move of Wfrec
blanchet
parents: 45605
diff changeset
     7
theory TypeRel
2df6ad1dbd66 adapted to move of Wfrec
blanchet
parents: 45605
diff changeset
     8
imports Decl
2df6ad1dbd66 adapted to move of Wfrec
blanchet
parents: 45605
diff changeset
     9
begin
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    10
63167
0909deb8059b isabelle update_cartouches -c -t;
wenzelm
parents: 62390
diff changeset
    11
text\<open>Direct subclass relation\<close>
44375
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
    12
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
    13
definition subcls1 :: "(cname \<times> cname) set"
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
    14
where
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
    15
  "subcls1 \<equiv> {(C,D). C\<noteq>Object \<and> (\<exists>c. class C = Some c \<and> super c=D)}"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    16
35102
cc7a0b9f938c modernized translations;
wenzelm
parents: 31166
diff changeset
    17
abbreviation
61990
39e4a93ad36e more symbols;
wenzelm
parents: 59682
diff changeset
    18
  subcls1_syntax :: "[cname, cname] => bool"  ("_ \<prec>C1 _" [71,71] 70)
39e4a93ad36e more symbols;
wenzelm
parents: 59682
diff changeset
    19
  where "C \<prec>C1 D == (C,D) \<in> subcls1"
35102
cc7a0b9f938c modernized translations;
wenzelm
parents: 31166
diff changeset
    20
abbreviation
61990
39e4a93ad36e more symbols;
wenzelm
parents: 59682
diff changeset
    21
  subcls_syntax  :: "[cname, cname] => bool" ("_ \<preceq>C _"  [71,71] 70)
39e4a93ad36e more symbols;
wenzelm
parents: 59682
diff changeset
    22
  where "C \<preceq>C D == (C,D) \<in> subcls1^*"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    23
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    24
11565
ab004c0ecc63 Minor improvements, added Example
oheimb
parents: 11558
diff changeset
    25
subsection "Declarations and properties not used in the meta theory"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    26
63167
0909deb8059b isabelle update_cartouches -c -t;
wenzelm
parents: 62390
diff changeset
    27
text\<open>Widening, viz. method invocation conversion\<close>
23755
1c4672d130b1 Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    28
inductive
1c4672d130b1 Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    29
  widen :: "ty => ty => bool"  ("_ \<preceq> _" [71,71] 70)
1c4672d130b1 Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    30
where
1c4672d130b1 Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    31
  refl [intro!, simp]: "T \<preceq> T"
1c4672d130b1 Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    32
| subcls: "C\<preceq>C D \<Longrightarrow> Class C \<preceq> Class D"
1c4672d130b1 Adapted to new inductive definition package.
berghofe
parents: 16417
diff changeset
    33
| null [intro!]: "NT \<preceq> R"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    34
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    35
lemma subcls1D: 
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    36
  "C\<prec>C1D \<Longrightarrow> C \<noteq> Object \<and> (\<exists>c. class C = Some c \<and> super c=D)"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    37
apply (unfold subcls1_def)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    38
apply auto
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    39
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    40
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    41
lemma subcls1I: "\<lbrakk>class C = Some m; super m = D; C \<noteq> Object\<rbrakk> \<Longrightarrow> C\<prec>C1D"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    42
apply (unfold subcls1_def)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    43
apply auto
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    44
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    45
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    46
lemma subcls1_def2: 
14952
47455995693d removal of x-symbol syntax <Sigma> for dependent products
paulson
parents: 14171
diff changeset
    47
  "subcls1 = 
47455995693d removal of x-symbol syntax <Sigma> for dependent products
paulson
parents: 14171
diff changeset
    48
    (SIGMA C: {C. is_class C} . {D. C\<noteq>Object \<and> super (the (class C)) = D})"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    49
apply (unfold subcls1_def is_class_def)
62390
842917225d56 more canonical names
nipkow
parents: 61990
diff changeset
    50
apply (auto split:if_split_asm)
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    51
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    52
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    53
lemma finite_subcls1: "finite subcls1"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    54
apply(subst subcls1_def2)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    55
apply(rule finite_SigmaI [OF finite_is_class])
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    56
apply(rule_tac B = "{super (the (class C))}" in finite_subset)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    57
apply  auto
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    58
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    59
35416
d8d7d1b785af replaced a couple of constsdefs by definitions (also some old primrecs by modern ones)
haftmann
parents: 35102
diff changeset
    60
definition ws_prog :: "bool" where
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    61
 "ws_prog \<equiv> \<forall>(C,c)\<in>set Prog. C\<noteq>Object \<longrightarrow> 
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    62
                              is_class (super c) \<and> (super c,C)\<notin>subcls1^+"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    63
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    64
lemma ws_progD: "\<lbrakk>class C = Some c; C\<noteq>Object; ws_prog\<rbrakk> \<Longrightarrow>  
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    65
  is_class (super c) \<and> (super c,C)\<notin>subcls1^+"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    66
apply (unfold ws_prog_def class_def)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    67
apply (drule_tac map_of_SomeD)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    68
apply auto
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    69
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    70
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    71
lemma subcls1_irrefl_lemma1: "ws_prog \<Longrightarrow> subcls1^-1 \<inter> subcls1^+ = {}"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    72
by (fast dest: subcls1D ws_progD)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    73
13867
1fdecd15437f just a few mods to a few thms
nipkow
parents: 12264
diff changeset
    74
(* irrefl_tranclI in Transitive_Closure.thy is more general *)
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    75
lemma irrefl_tranclI': "r^-1 Int r^+ = {} ==> !x. (x, x) ~: r^+"
13867
1fdecd15437f just a few mods to a few thms
nipkow
parents: 12264
diff changeset
    76
by(blast elim: tranclE dest: trancl_into_rtrancl)
1fdecd15437f just a few mods to a few thms
nipkow
parents: 12264
diff changeset
    77
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    78
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    79
lemmas subcls1_irrefl_lemma2 = subcls1_irrefl_lemma1 [THEN irrefl_tranclI']
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    80
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    81
lemma subcls1_irrefl: "\<lbrakk>(x, y) \<in> subcls1; ws_prog\<rbrakk> \<Longrightarrow> x \<noteq> y"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    82
apply (rule irrefl_trancl_rD)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    83
apply (rule subcls1_irrefl_lemma2)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    84
apply auto
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    85
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    86
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44375
diff changeset
    87
lemmas subcls1_acyclic = subcls1_irrefl_lemma2 [THEN acyclicI]
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    88
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    89
lemma wf_subcls1: "ws_prog \<Longrightarrow> wf (subcls1\<inverse>)"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    90
by (auto intro: finite_acyclic_wf_converse finite_subcls1 subcls1_acyclic)
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    91
44146
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
    92
definition class_rec ::"cname \<Rightarrow> (class \<Rightarrow> ('a \<times> 'b) list) \<Rightarrow> ('a \<rightharpoonup> 'b)"
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
    93
where
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
    94
  "class_rec \<equiv> wfrec (subcls1\<inverse>) (\<lambda>rec C f.
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
    95
     case class C of None \<Rightarrow> undefined
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
    96
      | Some m \<Rightarrow> (if C = Object then empty else rec (super m) f) ++ map_of (f m))"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    97
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    98
lemma class_rec: "\<lbrakk>class C = Some m;  ws_prog\<rbrakk> \<Longrightarrow>
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
    99
 class_rec C f = (if C = Object then empty else class_rec (super m) f) ++ 
44146
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
   100
                 map_of (f m)"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   101
apply (drule wf_subcls1)
44146
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
   102
apply (subst def_wfrec[OF class_rec_def], auto)
8bc84fa57a13 eliminated use of recdef
krauss
parents: 44013
diff changeset
   103
apply (subst cut_apply, auto intro: subcls1I)
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   104
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   105
67443
3abf6a722518 standardized towards new-style formal comments: isabelle update_comments;
wenzelm
parents: 63167
diff changeset
   106
\<comment> \<open>Methods of a class, with inheritance and hiding\<close>
59682
d662d096f72b quote "method" to allow Eisbach using this keyword;
wenzelm
parents: 58889
diff changeset
   107
definition "method" :: "cname => (mname \<rightharpoonup> methd)" where
44375
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
   108
  "method C \<equiv> class_rec C methods"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   109
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   110
lemma method_rec: "\<lbrakk>class C = Some m; ws_prog\<rbrakk> \<Longrightarrow>
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   111
method C = (if C=Object then empty else method (super m)) ++ map_of (methods m)"
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   112
apply (unfold method_def)
58860
fee7cfa69c50 eliminated spurious semicolons;
wenzelm
parents: 55017
diff changeset
   113
apply (erule (1) class_rec [THEN trans])
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   114
apply simp
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   115
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   116
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   117
67443
3abf6a722518 standardized towards new-style formal comments: isabelle update_comments;
wenzelm
parents: 63167
diff changeset
   118
\<comment> \<open>Fields of a class, with inheritance and hiding\<close>
44375
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
   119
definition field  :: "cname => (fname \<rightharpoonup> ty)" where
dfc2e722fe47 modernized specifications
krauss
parents: 44146
diff changeset
   120
  "field C \<equiv> class_rec C flds"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   121
12264
9c356e2da72f renamed "fields" to "flds" (avoid clash with new "fields" operation);
wenzelm
parents: 11626
diff changeset
   122
lemma flds_rec: "\<lbrakk>class C = Some m; ws_prog\<rbrakk> \<Longrightarrow>
9c356e2da72f renamed "fields" to "flds" (avoid clash with new "fields" operation);
wenzelm
parents: 11626
diff changeset
   123
field C = (if C=Object then empty else field (super m)) ++ map_of (flds m)"
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   124
apply (unfold field_def)
58860
fee7cfa69c50 eliminated spurious semicolons;
wenzelm
parents: 55017
diff changeset
   125
apply (erule (1) class_rec [THEN trans])
11376
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   126
apply simp
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   127
done
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   128
bf98ad1c22c6 added NanoJava
oheimb
parents:
diff changeset
   129
end