
diff -r 2406350c358f -r 8b5a1ad60487 Nominal/TySch.thy
--- a/Nominal/TySch.thy	Tue Mar 23 08:46:44 2010 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,165 +0,0 @@
-theory TySch
-imports "Parser" "../Attic/Prove" "FSet"
-begin
-
-atom_decl name
-
-nominal_datatype t =
-  Var "name"
-| Fun "t" "t"
-and tyS =
-  All xs::"name fset" ty::"t" bind xs in ty
-
-lemma size_eqvt_raw:
-  "size (pi \<bullet> t :: t_raw) = size t"
-  "size (pi \<bullet> ts :: tyS_raw) = size ts"
-  apply (induct rule: t_raw_tyS_raw.inducts)
-  apply simp_all
-  done
-
-instantiation t and tyS :: size begin
-
-quotient_definition
-  "size_t :: t \<Rightarrow> nat"
-is
-  "size :: t_raw \<Rightarrow> nat"
-
-quotient_definition
-  "size_tyS :: tyS \<Rightarrow> nat"
-is
-  "size :: tyS_raw \<Rightarrow> nat"
-
-lemma size_rsp:
-  "alpha_t_raw x y \<Longrightarrow> size x = size y"
-  "alpha_tyS_raw a b \<Longrightarrow> size a = size b"
-  apply (induct rule: alpha_t_raw_alpha_tyS_raw.inducts)
-  apply (simp_all only: t_raw_tyS_raw.size)
-  apply (simp_all only: alpha_gen)
-  apply clarify
-  apply (simp_all only: size_eqvt_raw)
-  done
-
-lemma [quot_respect]:
-  "(alpha_t_raw ===> op =) size size"
-  "(alpha_tyS_raw ===> op =) size size"
-  by (simp_all add: size_rsp)
-
-lemma [quot_preserve]:
-  "(rep_t ---> id) size = size"
-  "(rep_tyS ---> id) size = size"
-  by (simp_all add: size_t_def size_tyS_def)
-
-instance
-  by default
-
-end
-
-thm t_raw_tyS_raw.size(4)[quot_lifted]
-thm t_raw_tyS_raw.size(5)[quot_lifted]
-thm t_raw_tyS_raw.size(6)[quot_lifted]
-
-
-thm t_tyS.fv
-thm t_tyS.eq_iff
-thm t_tyS.bn
-thm t_tyS.perm
-thm t_tyS.inducts
-thm t_tyS.distinct
-ML {* Sign.of_sort @{theory} (@{typ t}, @{sort fs}) *}
-
-lemmas t_tyS_supp = t_tyS.fv[simplified t_tyS.supp]
-
-lemma induct:
-  assumes a1: "\<And>name b. P b (Var name)"
-  and     a2: "\<And>t1 t2 b. \<lbrakk>\<And>c. P c t1; \<And>c. P c t2\<rbrakk> \<Longrightarrow> P b (Fun t1 t2)"
-  and     a3: "\<And>fset t b. \<lbrakk>\<And>c. P c t; fset_to_set (fmap atom fset) \<sharp>* b\<rbrakk> \<Longrightarrow> P' b (All fset t)"
-  shows "P (a :: 'a :: pt) t \<and> P' (d :: 'b :: {fs}) ts "
-proof -
-  have " (\<forall>p a. P a (p \<bullet> t)) \<and> (\<forall>p d. P' d (p \<bullet> ts))"
-    apply (rule t_tyS.induct)
-    apply (simp add: a1)
-    apply (simp)
-    apply (rule allI)+
-    apply (rule a2)
-    apply simp
-    apply simp
-    apply (rule allI)
-    apply (rule allI)
-    apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (fset_to_set (fmap atom (p \<bullet> fset)))) \<sharp>* d \<and> supp (p \<bullet> TySch.All fset t) \<sharp>* pa)")
-    apply clarify
-    apply(rule_tac t="p \<bullet> TySch.All fset t" and 
-                   s="pa \<bullet> (p \<bullet> TySch.All fset t)" in subst)
-    apply (rule supp_perm_eq)
-    apply assumption
-    apply (simp only: t_tyS.perm)
-    apply (rule a3)
-    apply(erule_tac x="(pa + p)" in allE)
-    apply simp
-    apply (simp add: eqvts eqvts_raw)
-    apply (rule at_set_avoiding2)
-    apply (simp add: fin_fset_to_set)
-    apply (simp add: finite_supp)
-    apply (simp add: eqvts finite_supp)
-    apply (subst atom_eqvt_raw[symmetric])
-    apply (subst fmap_eqvt[symmetric])
-    apply (subst fset_to_set_eqvt[symmetric])
-    apply (simp only: fresh_star_permute_iff)
-    apply (simp add: fresh_star_def)
-    apply clarify
-    apply (simp add: fresh_def)
-    apply (simp add: t_tyS_supp)
-    done
-  then have "P a (0 \<bullet> t) \<and> P' d (0 \<bullet> ts)" by blast
-  then show ?thesis by simp
-qed
-
-lemma
-  shows "All {|a, b|} (Fun (Var a) (Var b)) = All {|b, a|} (Fun (Var a) (Var b))"
-  apply(simp add: t_tyS.eq_iff)
-  apply(rule_tac x="0::perm" in exI)
-  apply(simp add: alpha_gen)
-  apply(auto)
-  apply(simp add: fresh_star_def fresh_zero_perm)
-  done
-
-lemma
-  shows "All {|a, b|} (Fun (Var a) (Var b)) = All {|a, b|} (Fun (Var b) (Var a))"
-  apply(simp add: t_tyS.eq_iff)
-  apply(rule_tac x="(atom a \<rightleftharpoons> atom b)" in exI)
-  apply(simp add: alpha_gen fresh_star_def eqvts)
-  apply auto
-  done
-
-lemma
-  shows "All {|a, b, c|} (Fun (Var a) (Var b)) = All {|a, b|} (Fun (Var a) (Var b))"
-  apply(simp add: t_tyS.eq_iff)
-  apply(rule_tac x="0::perm" in exI)
-  apply(simp add: alpha_gen fresh_star_def eqvts t_tyS.eq_iff)
-oops
-
-lemma
-  assumes a: "a \<noteq> b"
-  shows "\<not>(All {|a, b|} (Fun (Var a) (Var b)) = All {|c|} (Fun (Var c) (Var c)))"
-  using a
-  apply(simp add: t_tyS.eq_iff)
-  apply(clarify)
-  apply(simp add: alpha_gen fresh_star_def eqvts t_tyS.eq_iff)
-  apply auto
-  done
-
-(* PROBLEM:
-Type schemes with separate datatypes
-
-nominal_datatype T =
-  TVar "name"
-| TFun "T" "T"
-nominal_datatype TyS =
-  TAll xs::"name list" ty::"T" bind xs in ty
-
-*** exception Datatype raised
-*** (line 218 of "/usr/local/src/Isabelle_16-Mar-2010/src/HOL/Tools/Datatype/datatype_aux.ML")
-*** At command "nominal_datatype".
-*)
-
-
-end




