author | wenzelm |
Thu, 21 Feb 2002 20:09:48 +0100 | |
changeset 12920 | 32292d83367b |
parent 12437 | 6d4e02b6dd43 |
child 13469 | 70d8dfef587d |
permissions | -rw-r--r-- |
7700 | 1 |
(* Title: HOL/Inductive.thy |
2 |
ID: $Id$ |
|
10402 | 3 |
Author: Markus Wenzel, TU Muenchen |
10727 | 4 |
License: GPL (GNU GENERAL PUBLIC LICENSE) |
11688 | 5 |
*) |
10727 | 6 |
|
11688 | 7 |
header {* Support for inductive sets and types *} |
1187 | 8 |
|
12920 | 9 |
theory Inductive = Gfp + Sum_Type + Relation + Record |
7700 | 10 |
files |
10402 | 11 |
("Tools/inductive_package.ML") |
12437
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
12 |
("Tools/inductive_codegen.ML") |
10402 | 13 |
("Tools/datatype_aux.ML") |
14 |
("Tools/datatype_prop.ML") |
|
15 |
("Tools/datatype_rep_proofs.ML") |
|
16 |
("Tools/datatype_abs_proofs.ML") |
|
17 |
("Tools/datatype_package.ML") |
|
12437
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
18 |
("Tools/datatype_codegen.ML") |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
19 |
("Tools/recfun_codegen.ML") |
10402 | 20 |
("Tools/primrec_package.ML"): |
21 |
||
10727 | 22 |
|
11688 | 23 |
subsection {* Inductive sets *} |
24 |
||
25 |
text {* Inversion of injective functions. *} |
|
11436 | 26 |
|
27 |
constdefs |
|
28 |
myinv :: "('a => 'b) => ('b => 'a)" |
|
29 |
"myinv (f :: 'a => 'b) == \<lambda>y. THE x. f x = y" |
|
30 |
||
31 |
lemma myinv_f_f: "inj f ==> myinv f (f x) = x" |
|
32 |
proof - |
|
33 |
assume "inj f" |
|
34 |
hence "(THE x'. f x' = f x) = (THE x'. x' = x)" |
|
35 |
by (simp only: inj_eq) |
|
36 |
also have "... = x" by (rule the_eq_trivial) |
|
11439 | 37 |
finally show ?thesis by (unfold myinv_def) |
11436 | 38 |
qed |
39 |
||
40 |
lemma f_myinv_f: "inj f ==> y \<in> range f ==> f (myinv f y) = y" |
|
41 |
proof (unfold myinv_def) |
|
42 |
assume inj: "inj f" |
|
43 |
assume "y \<in> range f" |
|
44 |
then obtain x where "y = f x" .. |
|
45 |
hence x: "f x = y" .. |
|
46 |
thus "f (THE x. f x = y) = y" |
|
47 |
proof (rule theI) |
|
48 |
fix x' assume "f x' = y" |
|
49 |
with x have "f x' = f x" by simp |
|
50 |
with inj show "x' = x" by (rule injD) |
|
51 |
qed |
|
52 |
qed |
|
53 |
||
54 |
hide const myinv |
|
55 |
||
56 |
||
11688 | 57 |
text {* Package setup. *} |
10402 | 58 |
|
59 |
use "Tools/inductive_package.ML" |
|
6437 | 60 |
setup InductivePackage.setup |
10402 | 61 |
|
11688 | 62 |
theorems basic_monos [mono] = |
63 |
subset_refl imp_refl disj_mono conj_mono ex_mono all_mono if_def2 |
|
64 |
Collect_mono in_mono vimage_mono |
|
65 |
imp_conv_disj not_not de_Morgan_disj de_Morgan_conj |
|
66 |
not_all not_ex |
|
67 |
Ball_def Bex_def |
|
11990 | 68 |
induct_rulify2 |
11688 | 69 |
|
70 |
||
12023 | 71 |
subsection {* Inductive datatypes and primitive recursion *} |
11688 | 72 |
|
11825 | 73 |
text {* Package setup. *} |
74 |
||
12437
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
75 |
use "Tools/recfun_codegen.ML" |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
76 |
setup RecfunCodegen.setup |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
77 |
|
10402 | 78 |
use "Tools/datatype_aux.ML" |
79 |
use "Tools/datatype_prop.ML" |
|
80 |
use "Tools/datatype_rep_proofs.ML" |
|
81 |
use "Tools/datatype_abs_proofs.ML" |
|
82 |
use "Tools/datatype_package.ML" |
|
7700 | 83 |
setup DatatypePackage.setup |
10402 | 84 |
|
12437
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
85 |
use "Tools/datatype_codegen.ML" |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
86 |
setup DatatypeCodegen.setup |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
87 |
|
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
88 |
use "Tools/inductive_codegen.ML" |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
89 |
setup InductiveCodegen.setup |
6d4e02b6dd43
Moved code generator setup from Recdef to Inductive.
berghofe
parents:
12023
diff
changeset
|
90 |
|
10402 | 91 |
use "Tools/primrec_package.ML" |
7700 | 92 |
|
6437 | 93 |
end |