author | Cezary Kaliszyk <kaliszyk@in.tum.de> |
Wed, 20 Jul 2011 10:11:08 +0200 | |
changeset 43918 | 6ca79a354c51 |
parent 41550 | efa734d9b221 |
child 46783 | 3e89a5cab8d7 |
permissions | -rw-r--r-- |
14620
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
1 |
(* Title: HOL/Import/HOL4Setup.thy |
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
2 |
Author: Sebastian Skalberg (TU Muenchen) |
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
3 |
*) |
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
4 |
|
43918
6ca79a354c51
HOL/Import reorganization/cleaning. Factor 9 speedup. Remove Import XML parser in favor of much faster of Isabelle's XML parser. Remove ImportRecording since we can use Isabelle images.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
41550
diff
changeset
|
5 |
theory HOL4Setup imports MakeEqual |
31723
f5cafe803b55
discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents:
20326
diff
changeset
|
6 |
uses ("proof_kernel.ML") ("replay.ML") ("hol4rews.ML") ("import.ML") begin |
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section {* General Setup *} |
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lemma eq_imp: "P = Q \<Longrightarrow> P \<longrightarrow> Q" |
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by auto |
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lemma HOLallI: "(!! bogus. P bogus) \<Longrightarrow> (ALL bogus. P bogus)" |
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proof - |
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assume "!! bogus. P bogus" |
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thus "ALL x. P x" |
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.. |
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qed |
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consts |
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ONE_ONE :: "('a => 'b) => bool" |
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defs |
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ONE_ONE_DEF: "ONE_ONE f == ALL x y. f x = f y --> x = y" |
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lemma ONE_ONE_rew: "ONE_ONE f = inj_on f UNIV" |
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by (simp add: ONE_ONE_DEF inj_on_def) |
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lemma INFINITY_AX: "EX (f::ind \<Rightarrow> ind). (inj f & ~(surj f))" |
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proof (rule exI,safe) |
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show "inj Suc_Rep" |
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34208
a7acd6c68d9b
more regular axiom of infinity, with no (indirect) reference to overloaded constants
krauss
parents:
31723
diff
changeset
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by (rule injI) (rule Suc_Rep_inject) |
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next |
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assume "surj Suc_Rep" |
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hence "ALL y. EX x. y = Suc_Rep x" |
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by (simp add: surj_def) |
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hence "EX x. Zero_Rep = Suc_Rep x" |
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by (rule spec) |
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thus False |
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proof (rule exE) |
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fix x |
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assume "Zero_Rep = Suc_Rep x" |
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hence "Suc_Rep x = Zero_Rep" |
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.. |
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with Suc_Rep_not_Zero_Rep |
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show False |
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.. |
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qed |
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qed |
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lemma EXISTS_DEF: "Ex P = P (Eps P)" |
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proof (rule iffI) |
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assume "Ex P" |
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thus "P (Eps P)" |
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.. |
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next |
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assume "P (Eps P)" |
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thus "Ex P" |
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.. |
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qed |
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consts |
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TYPE_DEFINITION :: "('a => bool) => ('b => 'a) => bool" |
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defs |
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TYPE_DEFINITION: "TYPE_DEFINITION p rep == ((ALL x y. (rep x = rep y) --> (x = y)) & (ALL x. (p x = (EX y. x = rep y))))" |
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lemma ex_imp_nonempty: "Ex P ==> EX x. x : (Collect P)" |
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by simp |
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lemma light_ex_imp_nonempty: "P t ==> EX x. x : (Collect P)" |
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proof - |
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assume "P t" |
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hence "EX x. P x" |
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.. |
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thus ?thesis |
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by (rule ex_imp_nonempty) |
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qed |
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lemma light_imp_as: "[| Q --> P; P --> Q |] ==> P = Q" |
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by blast |
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lemma typedef_hol2hol4: |
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assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)" |
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shows "EX rep. TYPE_DEFINITION P (rep::'a=>'b)" |
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proof - |
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from a |
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have td: "(ALL x. P (Rep x)) & (ALL x. Abs (Rep x) = x) & (ALL y. P y \<longrightarrow> Rep (Abs y) = y)" |
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by (simp add: type_definition_def) |
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have ed: "TYPE_DEFINITION P Rep" |
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proof (auto simp add: TYPE_DEFINITION) |
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fix x y |
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assume b: "Rep x = Rep y" |
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from td have "x = Abs (Rep x)" |
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by auto |
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also have "Abs (Rep x) = Abs (Rep y)" |
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by (simp add: b) |
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also from td have "Abs (Rep y) = y" |
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by auto |
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finally show "x = y" . |
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next |
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fix x |
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assume "P x" |
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with td |
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have "Rep (Abs x) = x" |
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by auto |
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hence "x = Rep (Abs x)" |
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.. |
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thus "EX y. x = Rep y" |
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.. |
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next |
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fix y |
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from td |
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show "P (Rep y)" |
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by auto |
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qed |
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show ?thesis |
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apply (rule exI [of _ Rep]) |
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apply (rule ed) |
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. |
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qed |
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lemma typedef_hol2hollight: |
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assumes a: "type_definition (Rep::'a=>'b) Abs (Collect P)" |
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shows "(Abs (Rep a) = a) & (P r = (Rep (Abs r) = r))" |
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proof |
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from a |
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show "Abs (Rep a) = a" |
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by (rule type_definition.Rep_inverse) |
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next |
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show "P r = (Rep (Abs r) = r)" |
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proof |
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assume "P r" |
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hence "r \<in> (Collect P)" |
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by simp |
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with a |
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show "Rep (Abs r) = r" |
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by (rule type_definition.Abs_inverse) |
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next |
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assume ra: "Rep (Abs r) = r" |
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from a |
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have "Rep (Abs r) \<in> (Collect P)" |
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by (rule type_definition.Rep) |
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thus "P r" |
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by (simp add: ra) |
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qed |
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qed |
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lemma termspec_help: "[| Ex P ; c == Eps P |] ==> P c" |
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apply simp |
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apply (rule someI_ex) |
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. |
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lemma typedef_helper: "EX x. P x \<Longrightarrow> EX x. x \<in> (Collect P)" |
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by simp |
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use "hol4rews.ML" |
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setup hol4_setup |
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parse_ast_translation smarter_trueprop_parsing |
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use "proof_kernel.ML" |
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use "replay.ML" |
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31723
f5cafe803b55
discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents:
20326
diff
changeset
|
164 |
use "import.ML" |
14516 | 165 |
|
31723
f5cafe803b55
discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents:
20326
diff
changeset
|
166 |
setup Import.setup |
14516 | 167 |
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end |