--- a/src/HOLCF/Domain.thy Wed Nov 10 17:56:08 2010 -0800
+++ b/src/HOLCF/Domain.thy Wed Nov 10 18:15:21 2010 -0800
@@ -5,115 +5,10 @@
header {* Domain package *}
theory Domain
-imports Ssum Sprod Up One Tr Fixrec Representable
+imports Representable
uses
- ("Tools/cont_consts.ML")
- ("Tools/cont_proc.ML")
- ("Tools/Domain/domain_constructors.ML")
- ("Tools/Domain/domain_axioms.ML")
- ("Tools/Domain/domain_induction.ML")
- ("Tools/Domain/domain.ML")
+ "Tools/Domain/domain_axioms.ML"
+ "Tools/Domain/domain.ML"
begin
-default_sort pcpo
-
-
-subsection {* Casedist *}
-
-text {* Lemmas for proving nchotomy rule: *}
-
-lemma ex_one_bottom_iff:
- "(\<exists>x. P x \<and> x \<noteq> \<bottom>) = P ONE"
-by simp
-
-lemma ex_up_bottom_iff:
- "(\<exists>x. P x \<and> x \<noteq> \<bottom>) = (\<exists>x. P (up\<cdot>x))"
-by (safe, case_tac x, auto)
-
-lemma ex_sprod_bottom_iff:
- "(\<exists>y. P y \<and> y \<noteq> \<bottom>) =
- (\<exists>x y. (P (:x, y:) \<and> x \<noteq> \<bottom>) \<and> y \<noteq> \<bottom>)"
-by (safe, case_tac y, auto)
-
-lemma ex_sprod_up_bottom_iff:
- "(\<exists>y. P y \<and> y \<noteq> \<bottom>) =
- (\<exists>x y. P (:up\<cdot>x, y:) \<and> y \<noteq> \<bottom>)"
-by (safe, case_tac y, simp, case_tac x, auto)
-
-lemma ex_ssum_bottom_iff:
- "(\<exists>x. P x \<and> x \<noteq> \<bottom>) =
- ((\<exists>x. P (sinl\<cdot>x) \<and> x \<noteq> \<bottom>) \<or>
- (\<exists>x. P (sinr\<cdot>x) \<and> x \<noteq> \<bottom>))"
-by (safe, case_tac x, auto)
-
-lemma exh_start: "p = \<bottom> \<or> (\<exists>x. p = x \<and> x \<noteq> \<bottom>)"
- by auto
-
-lemmas ex_bottom_iffs =
- ex_ssum_bottom_iff
- ex_sprod_up_bottom_iff
- ex_sprod_bottom_iff
- ex_up_bottom_iff
- ex_one_bottom_iff
-
-text {* Rules for turning nchotomy into exhaust: *}
-
-lemma exh_casedist0: "\<lbrakk>R; R \<Longrightarrow> P\<rbrakk> \<Longrightarrow> P" (* like make_elim *)
- by auto
-
-lemma exh_casedist1: "((P \<or> Q \<Longrightarrow> R) \<Longrightarrow> S) \<equiv> (\<lbrakk>P \<Longrightarrow> R; Q \<Longrightarrow> R\<rbrakk> \<Longrightarrow> S)"
- by rule auto
-
-lemma exh_casedist2: "(\<exists>x. P x \<Longrightarrow> Q) \<equiv> (\<And>x. P x \<Longrightarrow> Q)"
- by rule auto
-
-lemma exh_casedist3: "(P \<and> Q \<Longrightarrow> R) \<equiv> (P \<Longrightarrow> Q \<Longrightarrow> R)"
- by rule auto
-
-lemmas exh_casedists = exh_casedist1 exh_casedist2 exh_casedist3
-
-
-subsection {* Installing the domain package *}
-
-lemmas con_strict_rules =
- sinl_strict sinr_strict spair_strict1 spair_strict2
-
-lemmas con_bottom_iff_rules =
- sinl_bottom_iff sinr_bottom_iff spair_bottom_iff up_defined ONE_defined
-
-lemmas con_below_iff_rules =
- sinl_below sinr_below sinl_below_sinr sinr_below_sinl con_bottom_iff_rules
-
-lemmas con_eq_iff_rules =
- sinl_eq sinr_eq sinl_eq_sinr sinr_eq_sinl con_bottom_iff_rules
-
-lemmas sel_strict_rules =
- cfcomp2 sscase1 sfst_strict ssnd_strict fup1
-
-lemma sel_app_extra_rules:
- "sscase\<cdot>ID\<cdot>\<bottom>\<cdot>(sinr\<cdot>x) = \<bottom>"
- "sscase\<cdot>ID\<cdot>\<bottom>\<cdot>(sinl\<cdot>x) = x"
- "sscase\<cdot>\<bottom>\<cdot>ID\<cdot>(sinl\<cdot>x) = \<bottom>"
- "sscase\<cdot>\<bottom>\<cdot>ID\<cdot>(sinr\<cdot>x) = x"
- "fup\<cdot>ID\<cdot>(up\<cdot>x) = x"
-by (cases "x = \<bottom>", simp, simp)+
-
-lemmas sel_app_rules =
- sel_strict_rules sel_app_extra_rules
- ssnd_spair sfst_spair up_defined spair_defined
-
-lemmas sel_bottom_iff_rules =
- cfcomp2 sfst_bottom_iff ssnd_bottom_iff
-
-lemmas take_con_rules =
- ssum_map_sinl' ssum_map_sinr' sprod_map_spair' u_map_up
- deflation_strict deflation_ID ID1 cfcomp2
-
-use "Tools/cont_consts.ML"
-use "Tools/cont_proc.ML"
-use "Tools/Domain/domain_axioms.ML"
-use "Tools/Domain/domain_constructors.ML"
-use "Tools/Domain/domain_induction.ML"
-use "Tools/Domain/domain.ML"
-
end