--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Basic_BNF_LFPs.thy Mon Dec 15 07:20:48 2014 +0100
@@ -0,0 +1,111 @@
+(* Title: HOL/Basic_BNF_LFPs.thy
+ Author: Jasmin Blanchette, TU Muenchen
+ Copyright 2014
+
+Registration of basic types as BNF least fixpoints (datatypes).
+*)
+
+theory Basic_BNF_LFPs
+imports BNF_Least_Fixpoint
+begin
+
+definition xtor :: "'a \<Rightarrow> 'a" where
+ "xtor x = x"
+
+lemma xtor_map: "f (xtor x) = xtor (f x)"
+ unfolding xtor_def by (rule refl)
+
+lemma xtor_set: "f (xtor x) = f x"
+ unfolding xtor_def by (rule refl)
+
+lemma xtor_rel: "R (xtor x) (xtor y) = R x y"
+ unfolding xtor_def by (rule refl)
+
+lemma xtor_induct: "(\<And>x. P (xtor x)) \<Longrightarrow> P z"
+ unfolding xtor_def by assumption
+
+lemma xtor_xtor: "xtor (xtor x) = x"
+ unfolding xtor_def by (rule refl)
+
+lemmas xtor_inject = xtor_rel[of "op ="]
+
+lemma xtor_rel_induct: "(\<And>x y. vimage2p id_bnf id_bnf R x y \<Longrightarrow> IR (xtor x) (xtor y)) \<Longrightarrow> R \<le> IR"
+ unfolding xtor_def vimage2p_def id_bnf_def by default
+
+lemma Inl_def_alt: "Inl \<equiv> (\<lambda>a. xtor (id_bnf (Inl a)))"
+ unfolding xtor_def id_bnf_def by (rule reflexive)
+
+lemma Inr_def_alt: "Inr \<equiv> (\<lambda>a. xtor (id_bnf (Inr a)))"
+ unfolding xtor_def id_bnf_def by (rule reflexive)
+
+lemma Pair_def_alt: "Pair \<equiv> (\<lambda>a b. xtor (id_bnf (a, b)))"
+ unfolding xtor_def id_bnf_def by (rule reflexive)
+
+definition ctor_rec :: "'a \<Rightarrow> 'a" where
+ "ctor_rec x = x"
+
+lemma ctor_rec: "g = id \<Longrightarrow> ctor_rec f (xtor x) = f ((id_bnf \<circ> g \<circ> id_bnf) x)"
+ unfolding ctor_rec_def id_bnf_def xtor_def comp_def id_def by hypsubst (rule refl)
+
+lemma ctor_rec_def_alt: "f = ctor_rec (f \<circ> id_bnf)"
+ unfolding ctor_rec_def id_bnf_def comp_def by (rule refl)
+
+lemma ctor_rec_o_map: "ctor_rec f \<circ> g = ctor_rec (f \<circ> (id_bnf \<circ> g \<circ> id_bnf))"
+ unfolding ctor_rec_def id_bnf_def comp_def by (rule refl)
+
+lemma eq_fst_iff: "a = fst p \<longleftrightarrow> (\<exists>b. p = (a, b))"
+ by (cases p) auto
+
+lemma eq_snd_iff: "b = snd p \<longleftrightarrow> (\<exists>a. p = (a, b))"
+ by (cases p) auto
+
+lemma ex_neg_all_pos: "((\<exists>x. P x) \<Longrightarrow> Q) \<equiv> (\<And>x. P x \<Longrightarrow> Q)"
+ by default blast+
+
+lemma hypsubst_in_prems: "(\<And>x. y = x \<Longrightarrow> z = f x \<Longrightarrow> P) \<equiv> (z = f y \<Longrightarrow> P)"
+ by default blast+
+
+lemma isl_map_sum:
+ "isl (map_sum f g s) = isl s"
+ by (cases s) simp_all
+
+lemma map_sum_sel:
+ "isl s \<Longrightarrow> projl (map_sum f g s) = f (projl s)"
+ "\<not> isl s \<Longrightarrow> projr (map_sum f g s) = g (projr s)"
+ by (case_tac [!] s) simp_all
+
+lemma set_sum_sel:
+ "isl s \<Longrightarrow> projl s \<in> setl s"
+ "\<not> isl s \<Longrightarrow> projr s \<in> setr s"
+ by (case_tac [!] s) (auto intro: setl.intros setr.intros)
+
+lemma rel_sum_sel: "rel_sum R1 R2 a b = (isl a = isl b \<and>
+ (isl a \<longrightarrow> isl b \<longrightarrow> R1 (projl a) (projl b)) \<and>
+ (\<not> isl a \<longrightarrow> \<not> isl b \<longrightarrow> R2 (projr a) (projr b)))"
+ by (cases a b rule: sum.exhaust[case_product sum.exhaust]) simp_all
+
+lemma isl_transfer: "rel_fun (rel_sum A B) (op =) isl isl"
+ unfolding rel_fun_def rel_sum_sel by simp
+
+lemma rel_prod_sel: "rel_prod R1 R2 p q = (R1 (fst p) (fst q) \<and> R2 (snd p) (snd q))"
+ by (force simp: rel_prod.simps elim: rel_prod.cases)
+
+ML_file "Tools/BNF/bnf_lfp_basic_sugar.ML"
+
+ML_file "~~/src/HOL/Tools/Old_Datatype/old_size.ML"
+
+lemma size_bool[code]: "size (b\<Colon>bool) = 0"
+ by (cases b) auto
+
+declare prod.size[no_atp]
+
+lemma size_nat[simp, code]: "size (n\<Colon>nat) = n"
+ by (induct n) simp_all
+
+hide_const (open) xtor ctor_rec
+
+hide_fact (open)
+ xtor_def xtor_map xtor_set xtor_rel xtor_induct xtor_xtor xtor_inject ctor_rec_def ctor_rec
+ ctor_rec_def_alt ctor_rec_o_map xtor_rel_induct Inl_def_alt Inr_def_alt Pair_def_alt
+
+end
--- a/src/HOL/Basic_BNF_Least_Fixpoints.thy Fri Dec 12 14:42:37 2014 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,111 +0,0 @@
-(* Title: HOL/Basic_BNF_Least_Fixpoints.thy
- Author: Jasmin Blanchette, TU Muenchen
- Copyright 2014
-
-Registration of basic types as BNF least fixpoints (datatypes).
-*)
-
-theory Basic_BNF_Least_Fixpoints
-imports BNF_Least_Fixpoint
-begin
-
-definition xtor :: "'a \<Rightarrow> 'a" where
- "xtor x = x"
-
-lemma xtor_map: "f (xtor x) = xtor (f x)"
- unfolding xtor_def by (rule refl)
-
-lemma xtor_set: "f (xtor x) = f x"
- unfolding xtor_def by (rule refl)
-
-lemma xtor_rel: "R (xtor x) (xtor y) = R x y"
- unfolding xtor_def by (rule refl)
-
-lemma xtor_induct: "(\<And>x. P (xtor x)) \<Longrightarrow> P z"
- unfolding xtor_def by assumption
-
-lemma xtor_xtor: "xtor (xtor x) = x"
- unfolding xtor_def by (rule refl)
-
-lemmas xtor_inject = xtor_rel[of "op ="]
-
-lemma xtor_rel_induct: "(\<And>x y. vimage2p id_bnf id_bnf R x y \<Longrightarrow> IR (xtor x) (xtor y)) \<Longrightarrow> R \<le> IR"
- unfolding xtor_def vimage2p_def id_bnf_def by default
-
-lemma Inl_def_alt: "Inl \<equiv> (\<lambda>a. xtor (id_bnf (Inl a)))"
- unfolding xtor_def id_bnf_def by (rule reflexive)
-
-lemma Inr_def_alt: "Inr \<equiv> (\<lambda>a. xtor (id_bnf (Inr a)))"
- unfolding xtor_def id_bnf_def by (rule reflexive)
-
-lemma Pair_def_alt: "Pair \<equiv> (\<lambda>a b. xtor (id_bnf (a, b)))"
- unfolding xtor_def id_bnf_def by (rule reflexive)
-
-definition ctor_rec :: "'a \<Rightarrow> 'a" where
- "ctor_rec x = x"
-
-lemma ctor_rec: "g = id \<Longrightarrow> ctor_rec f (xtor x) = f ((id_bnf \<circ> g \<circ> id_bnf) x)"
- unfolding ctor_rec_def id_bnf_def xtor_def comp_def id_def by hypsubst (rule refl)
-
-lemma ctor_rec_def_alt: "f = ctor_rec (f \<circ> id_bnf)"
- unfolding ctor_rec_def id_bnf_def comp_def by (rule refl)
-
-lemma ctor_rec_o_map: "ctor_rec f \<circ> g = ctor_rec (f \<circ> (id_bnf \<circ> g \<circ> id_bnf))"
- unfolding ctor_rec_def id_bnf_def comp_def by (rule refl)
-
-lemma eq_fst_iff: "a = fst p \<longleftrightarrow> (\<exists>b. p = (a, b))"
- by (cases p) auto
-
-lemma eq_snd_iff: "b = snd p \<longleftrightarrow> (\<exists>a. p = (a, b))"
- by (cases p) auto
-
-lemma ex_neg_all_pos: "((\<exists>x. P x) \<Longrightarrow> Q) \<equiv> (\<And>x. P x \<Longrightarrow> Q)"
- by default blast+
-
-lemma hypsubst_in_prems: "(\<And>x. y = x \<Longrightarrow> z = f x \<Longrightarrow> P) \<equiv> (z = f y \<Longrightarrow> P)"
- by default blast+
-
-lemma isl_map_sum:
- "isl (map_sum f g s) = isl s"
- by (cases s) simp_all
-
-lemma map_sum_sel:
- "isl s \<Longrightarrow> projl (map_sum f g s) = f (projl s)"
- "\<not> isl s \<Longrightarrow> projr (map_sum f g s) = g (projr s)"
- by (case_tac [!] s) simp_all
-
-lemma set_sum_sel:
- "isl s \<Longrightarrow> projl s \<in> setl s"
- "\<not> isl s \<Longrightarrow> projr s \<in> setr s"
- by (case_tac [!] s) (auto intro: setl.intros setr.intros)
-
-lemma rel_sum_sel: "rel_sum R1 R2 a b = (isl a = isl b \<and>
- (isl a \<longrightarrow> isl b \<longrightarrow> R1 (projl a) (projl b)) \<and>
- (\<not> isl a \<longrightarrow> \<not> isl b \<longrightarrow> R2 (projr a) (projr b)))"
- by (cases a b rule: sum.exhaust[case_product sum.exhaust]) simp_all
-
-lemma isl_transfer: "rel_fun (rel_sum A B) (op =) isl isl"
- unfolding rel_fun_def rel_sum_sel by simp
-
-lemma rel_prod_sel: "rel_prod R1 R2 p q = (R1 (fst p) (fst q) \<and> R2 (snd p) (snd q))"
- by (force simp: rel_prod.simps elim: rel_prod.cases)
-
-ML_file "Tools/BNF/bnf_lfp_basic_sugar.ML"
-
-ML_file "~~/src/HOL/Tools/Old_Datatype/old_size.ML"
-
-lemma size_bool[code]: "size (b\<Colon>bool) = 0"
- by (cases b) auto
-
-declare prod.size[no_atp]
-
-lemma size_nat[simp, code]: "size (n\<Colon>nat) = n"
- by (induct n) simp_all
-
-hide_const (open) xtor ctor_rec
-
-hide_fact (open)
- xtor_def xtor_map xtor_set xtor_rel xtor_induct xtor_xtor xtor_inject ctor_rec_def ctor_rec
- ctor_rec_def_alt ctor_rec_o_map xtor_rel_induct Inl_def_alt Inr_def_alt Pair_def_alt
-
-end
--- a/src/HOL/Fun_Def.thy Fri Dec 12 14:42:37 2014 +0100
+++ b/src/HOL/Fun_Def.thy Mon Dec 15 07:20:48 2014 +0100
@@ -5,7 +5,7 @@
section {* Function Definitions and Termination Proofs *}
theory Fun_Def
-imports Basic_BNF_Least_Fixpoints Partial_Function SAT
+imports Basic_BNF_LFPs Partial_Function SAT
keywords "function" "termination" :: thy_goal and "fun" "fun_cases" :: thy_decl
begin
--- a/src/HOL/Transfer.thy Fri Dec 12 14:42:37 2014 +0100
+++ b/src/HOL/Transfer.thy Mon Dec 15 07:20:48 2014 +0100
@@ -6,7 +6,7 @@
section {* Generic theorem transfer using relations *}
theory Transfer
-imports Hilbert_Choice Metis Basic_BNF_Least_Fixpoints
+imports Hilbert_Choice Metis Basic_BNF_LFPs
begin
subsection {* Relator for function space *}