--- a/src/HOL/Basic_BNF_Least_Fixpoints.thy Thu Sep 18 16:47:40 2014 +0200
+++ b/src/HOL/Basic_BNF_Least_Fixpoints.thy Thu Sep 18 16:47:40 2014 +0200
@@ -9,32 +9,6 @@
imports BNF_Least_Fixpoint
begin
-subsection {* Size setup (TODO: Merge with rest of file) *}
-
-lemma size_bool[code]: "size (b\<Colon>bool) = 0"
- by (cases b) auto
-
-lemma size_nat[simp, code]: "size (n\<Colon>nat) = n"
- by (induct n) simp_all
-
-declare prod.size[no_atp]
-
-lemma size_sum_o_map: "size_sum g1 g2 \<circ> map_sum f1 f2 = size_sum (g1 \<circ> f1) (g2 \<circ> f2)"
- by (rule ext) (case_tac x, auto)
-
-lemma size_prod_o_map: "size_prod g1 g2 \<circ> map_prod f1 f2 = size_prod (g1 \<circ> f1) (g2 \<circ> f2)"
- by (rule ext) auto
-
-setup {*
-BNF_LFP_Size.register_size_global @{type_name sum} @{const_name size_sum} @{thms sum.size}
- @{thms size_sum_o_map}
-#> BNF_LFP_Size.register_size_global @{type_name prod} @{const_name size_prod} @{thms prod.size}
- @{thms size_prod_o_map}
-*}
-
-
-subsection {* FP sugar setup *}
-
definition xtor :: "'a \<Rightarrow> 'a" where
"xtor x = x"
@@ -55,15 +29,6 @@
lemmas xtor_inject = xtor_rel[of "op ="]
-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_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 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
@@ -76,12 +41,30 @@
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)
+
ML_file "Tools/BNF/bnf_lfp_basic_sugar.ML"
+thm sum.rec_o_map
+thm sum.size_o_map
+
+thm prod.rec_o_map
+thm prod.size_o_map
+
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_o_map xtor_rel_induct Inl_def_alt Inr_def_alt Pair_def_alt
+ ctor_rec_def_alt ctor_rec_o_map xtor_rel_induct Inl_def_alt Inr_def_alt Pair_def_alt
end