cleaned up (almost completely) the examples
authorChristian Urban <urbanc@in.tum.de>
Thu, 26 Aug 2010 02:08:00 +0800
changeset 2436 3885dc2669f9
parent 2435 3772bb3bd7ce
child 2437 319f469b8b67
child 2438 abafea9b39bb
cleaned up (almost completely) the examples
Nominal/Ex/Classical.thy
Nominal/Ex/CoreHaskell.thy
Nominal/Ex/Ex1rec.thy
Nominal/Ex/Ex2.thy
Nominal/Ex/Ex3.thy
Nominal/Ex/Ex4.thy
Nominal/Ex/ExLet.thy
Nominal/Ex/ExLetMult.thy
Nominal/Ex/ExLetRec.thy
Nominal/Ex/ExPS3.thy
Nominal/Ex/ExPS6.thy
Nominal/Ex/ExPS7.thy
Nominal/Ex/ExPS8.thy
Nominal/Ex/LF.thy
Nominal/Ex/Lambda.thy
Nominal/Ex/Let.thy
Nominal/Ex/LetPat.thy
Nominal/Ex/LetRec.thy
Nominal/Ex/LetRec2.thy
Nominal/Ex/Modules.thy
Nominal/Ex/NoneExamples.thy
Nominal/Ex/SingleLet.thy
Nominal/Ex/Term8.thy
Nominal/Ex/Test.thy
Nominal/Ex/TestMorePerm.thy
Nominal/Ex/TypeSchemes.thy
Nominal/Ex/TypeVarsTest.thy
Nominal/NewParser.thy
--- a/Nominal/Ex/Classical.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/Classical.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -7,8 +7,6 @@
 atom_decl name
 atom_decl coname
 
-declare [[STEPS = 21]]
-
 nominal_datatype trm =
    Ax "name" "coname"
 |  Cut n::"coname" t1::"trm" c::"coname" t2::"trm"             bind n in t1, bind c in t2
@@ -18,15 +16,15 @@
 |  ImpL c::"coname" t1::"trm" n::"name" t2::"trm" "name"       bind c in t1, bind n in t2
 |  ImpR c::"coname" n::"name" t::"trm" "coname"                bind n c in t
 
-thm distinct
-thm induct
-thm exhaust
-thm fv_defs
-thm bn_defs
-thm perm_simps
-thm eq_iff
-thm fv_bn_eqvt
-thm size_eqvt
+thm trm.distinct
+thm trm.induct
+thm trm.exhaust
+thm trm.fv_defs
+thm trm.bn_defs
+thm trm.perm_simps
+thm trm.eq_iff
+thm trm.fv_bn_eqvt
+thm trm.size_eqvt
 
 
 
--- a/Nominal/Ex/CoreHaskell.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/CoreHaskell.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -8,9 +8,10 @@
 atom_decl cvar
 atom_decl tvar
 
-declare [[STEPS = 21]]
+declare [[STEPS = 100]]
 
-nominal_datatype tkind =
+nominal_datatype core_haskell: 
+ tkind =
   KStar
 | KFun "tkind" "tkind"
 and ckind =
@@ -85,31 +86,19 @@
 | "bv_cvs CvsNil = []"
 | "bv_cvs (CvsCons v k t) = (atom v) # bv_cvs t"
 
-(* can lift *)
-
-thm distinct
-thm induct
-thm exhaust
-thm fv_defs
-thm bn_defs
-thm perm_simps
-thm eq_iff
-thm fv_bn_eqvt
-thm size_eqvt
-
+(* generated theorems *)
 
-
-
+thm core_haskell.distinct
+thm core_haskell.induct
+thm core_haskell.exhaust
+thm core_haskell.fv_defs
+thm core_haskell.bn_defs
+thm core_haskell.perm_simps
+thm core_haskell.eq_iff
+thm core_haskell.fv_bn_eqvt
+thm core_haskell.size_eqvt
 
-lemmas fv_supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.supp(1-9,11,13,15)
-lemmas supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.fv[simplified fv_supp]
-lemmas perm=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.perm
-lemmas eq_iff=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.eq_iff
-lemmas inducts=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.inducts
-
-lemmas alpha_inducts=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vars_raw_alpha_tvars_raw_alpha_cvars_raw_alpha_bv_raw_alpha_bv_vs_raw_alpha_bv_tvs_raw_alpha_bv_cvs_raw.inducts
-lemmas alpha_intros=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vars_raw_alpha_tvars_raw_alpha_cvars_raw_alpha_bv_raw_alpha_bv_vs_raw_alpha_bv_tvs_raw_alpha_bv_cvs_raw.intros
-
+(*
 lemma fresh_star_minus_perm: "as \<sharp>* - p = as \<sharp>* (p :: perm)"
   unfolding fresh_star_def Ball_def
   by auto (simp_all add: fresh_minus_perm)
@@ -397,7 +386,7 @@
     apply (tactic {* ALLGOALS (REPEAT o rtac allI) *})
     apply (tactic {* ALLGOALS (TRY o SOLVED' (simp_tac @{simpset} THEN_ALL_NEW resolve_tac @{thms assms} THEN_ALL_NEW asm_full_simp_tac @{simpset})) *})
 
-(* GOAL1 *)
+--"GOAL1"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> tvar))) \<sharp> c \<and>
                        supp (Abs (p \<bullet> {atom tvar}) (p \<bullet> ty)) \<sharp>* pa)")
     apply clarify
@@ -435,7 +424,7 @@
     apply (simp only: supp_abs eqvts)
     apply blast
 
-(* GOAL2 *)
+--"GOAL2"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> cvar))) \<sharp> e \<and>
                        supp (Abs (p \<bullet> {atom cvar}) (p \<bullet> co)) \<sharp>* pa)")
     apply clarify
@@ -474,7 +463,7 @@
     apply blast
 
 
-(* GOAL3 a copy-and-paste of Goal2 with consts and variable names changed *)
+--"GOAL3 a copy-and-paste of Goal2 with consts and variable names changed"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> tvar))) \<sharp> g \<and>
                        supp (Abs (p \<bullet> {atom tvar}) (p \<bullet> trm)) \<sharp>* pa)")
     apply clarify
@@ -512,7 +501,7 @@
     apply (simp only: supp_abs eqvts)
     apply blast
 
-(* GOAL4 a copy-and-paste *)
+--"GOAL4 a copy-and-paste"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> cvar))) \<sharp> g \<and>
                        supp (Abs (p \<bullet> {atom cvar}) (p \<bullet> trm)) \<sharp>* pa)")
     apply clarify
@@ -551,7 +540,7 @@
     apply blast
 
 
-(* GOAL5 a copy-and-paste *)
+--"GOAL5 a copy-and-paste"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> var))) \<sharp> g \<and>
                        supp (Abs (p \<bullet> {atom var}) (p \<bullet> trm)) \<sharp>* pa)")
     apply clarify
@@ -590,7 +579,7 @@
     apply blast
 
 
-(* GOAL6 a copy-and-paste *)
+--"GOAL6 a copy-and-paste"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> var))) \<sharp> g \<and>
                        supp (Abs (p \<bullet> {atom var}) (p \<bullet> trm2)) \<sharp>* pa)")
     apply clarify
@@ -629,7 +618,7 @@
     apply (simp only: supp_abs eqvts)
     apply blast
 
-(* MAIN ACons Goal *)
+--"MAIN ACons Goal"
     apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (set (bv (p \<bullet> pat)))) \<sharp>* h \<and>
                        supp (Abs_lst (p \<bullet> (bv pat)) (p \<bullet> trm)) \<sharp>* pa)")
     apply clarify
@@ -655,6 +644,7 @@
   moreover have "P9  i (permute_bv 0 (0 \<bullet> pt))" and "P10 j (permute_bv_vs 0 (0 \<bullet> vars))" and "P11 k (permute_bv_tvs 0 (0 \<bullet> tvars))" and "P12 l (permute_bv_cvs 0 (0 \<bullet> cvars))" using a1 a2 a3 a4 by (blast+)
   ultimately show ?thesis by (simp_all add: permute_bv_zero1 permute_bv_zero2)
 qed
+*)
 
 section {* test about equivariance for alpha *}
 
--- a/Nominal/Ex/Ex1rec.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,40 +0,0 @@
-theory Ex1rec
-imports "../NewParser"
-begin
-
-declare [[STEPS = 9]]
-
-atom_decl name
-
-nominal_datatype lam =
-  Var "name"
-| App "lam" "lam"
-| Lam x::"name" t::"lam"  bind_set x in t
-| Let bp::"bp" t::"lam"   bind_set "bi bp" in bp t
-and bp =
-  Bp "name" "lam"
-binder
-  bi::"bp \<Rightarrow> atom set"
-where
-  "bi (Bp x t) = {atom x}"
-
-
-thm alpha_lam_raw_alpha_bp_raw_alpha_bi_raw.intros
-
-thm lam_bp.fv
-thm lam_bp.eq_iff[no_vars]
-thm lam_bp.bn
-thm lam_bp.perm
-thm lam_bp.induct
-thm lam_bp.inducts
-thm lam_bp.distinct
-thm lam_bp.supp
-ML {* Sign.of_sort @{theory} (@{typ lam}, @{sort fs}) *}
-thm lam_bp.fv[simplified lam_bp.supp(1-2)]
-
-
-
-end
-
-
-
--- a/Nominal/Ex/Ex2.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,42 +0,0 @@
-theory Ex2
-imports "../NewParser"
-begin
-
-text {* example 2 *}
-declare [[STEPS = 9]]
-
-atom_decl name
-
-nominal_datatype trm =
-  Var "name"
-| App "trm" "trm"
-| Lam x::"name" t::"trm"          bind_set x in t
-| Let p::"pat" "trm" t::"trm"   bind_set "f p" in t
-and pat =
-  PN
-| PS "name"
-| PD "name" "name"
-binder
-  f::"pat \<Rightarrow> atom set"
-where
-  "f PN = {}"
-| "f (PD x y) = {atom x, atom y}"
-| "f (PS x) = {atom x}"
-
-thm fv_trm_raw.simps[no_vars] fv_pat_raw.simps[no_vars] fv_f_raw.simps[no_vars] f_raw.simps[no_vars]
-thm alpha_trm_raw_alpha_pat_raw_alpha_f_raw.intros[no_vars]
-
-
-
-
-thm trm_pat.bn
-thm trm_pat.perm
-thm trm_pat.induct
-thm trm_pat.distinct
-thm trm_pat.fv[simplified trm_pat.supp(1-2)]
-
-
-end
-
-
-
--- a/Nominal/Ex/Ex3.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,38 +0,0 @@
-theory Ex3
-imports "../NewParser"
-begin
-
-(* Example 3, identical to example 1 from Terms.thy *)
-
-atom_decl name
-
-nominal_datatype trm =
-  Var "name"
-| App "trm" "trm"
-| Lam x::"name" t::"trm"        bind_set x in t
-| Let p::"pat" "trm" t::"trm"   bind_set "f p" in t
-and pat =
-  PN
-| PS "name"
-| PD "pat" "pat"
-binder
-  f::"pat \<Rightarrow> atom set"
-where
-  "f PN = {}"
-| "f (PS x) = {atom x}"
-| "f (PD p1 p2) = (f p1) \<union> (f p2)"
-
-thm trm_pat.fv
-thm trm_pat.eq_iff
-thm trm_pat.bn
-thm trm_pat.perm
-thm trm_pat.induct
-thm trm_pat.distinct
-thm trm_pat.fv[simplified trm_pat.supp(1-2)]
-
-
-
-end
-
-
-
--- a/Nominal/Ex/Ex4.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,87 +0,0 @@
-theory Ex4
-imports "../NewParser"
-begin
-
-declare [[STEPS = 5]]
-
-atom_decl name
-
-nominal_datatype trm =
-  Var "name"
-| App "trm" "trm"
-| Lam x::"name" t::"trm"        bind_set x in t
-| Let p::"pat" "trm" t::"trm"   bind_set "f p" in t
-| Foo1 p::"pat" q::"pat" t::"trm" bind_set "f p" "f q" in t
-| Foo2 x::"name" p::"pat" t::"trm" bind_set x "f p" in t
-and pat =
-  PN
-| PS "name"
-| PD "pat" "pat"
-binder
-  f::"pat \<Rightarrow> atom set"
-where
-  "f PN = {}"
-| "f (PS x) = {atom x}"
-| "f (PD p1 p2) = (f p1) \<union> (f p2)"
-
-thm permute_trm_raw_permute_pat_raw.simps
-thm fv_trm_raw.simps fv_pat_raw.simps fv_f_raw.simps
-
-thm alpha_trm_raw_alpha_pat_raw_alpha_f_raw.intros[no_vars]
-
-(*
-inductive 
- alpha_trm_raw and alpha_pat_raw and alpha_f_raw
-where
-(* alpha_trm_raw *)
-  "name = namea \<Longrightarrow> alpha_trm_raw (Var_raw name) (Var_raw namea)"
-| "\<lbrakk>alpha_trm_raw trm_raw1 trm_raw1a; alpha_trm_raw trm_raw2 trm_raw2a\<rbrakk>
-   \<Longrightarrow> alpha_trm_raw (App_raw trm_raw1 trm_raw2) (App_raw trm_raw1a trm_raw2a)"
-| "\<exists>p. ({atom name}, trm_raw) \<approx>gen alpha_trm_raw fv_trm_raw p ({atom namea}, trm_rawa) \<Longrightarrow>
-   alpha_trm_raw (Lam_raw name trm_raw) (Lam_raw namea trm_rawa)"
-| "\<lbrakk>\<exists>p. (f_raw pat_raw, trm_raw2) \<approx>gen alpha_trm_raw fv_trm_raw p (f_raw pat_rawa, trm_raw2a);
-   alpha_f_raw pat_raw pat_rawa; alpha_trm_raw trm_raw1 trm_raw1a\<rbrakk>
-  \<Longrightarrow> alpha_trm_raw (Let_raw pat_raw trm_raw1 trm_raw2) (Let_raw pat_rawa trm_raw1a trm_raw2a)"
-| "\<lbrakk>\<exists>p. (f_raw pat_raw1 \<union> f_raw pat_raw2, trm_raw) \<approx>gen alpha_trm_raw fv_trm_raw p (f_raw pat_raw1a \<union> f_raw pat_raw2a, trm_rawa);
-   alpha_f_raw pat_raw1 pat_raw1a; alpha_f_raw pat_raw2 pat_raw2a\<rbrakk>
-   \<Longrightarrow> alpha_trm_raw (Foo1_raw pat_raw1 pat_raw2 trm_raw) (Foo1_raw pat_raw1a pat_raw2a trm_rawa)"
-| "\<lbrakk>\<exists>p. ({atom name} \<union> f_raw pat_raw, trm_raw) \<approx>gen alpha_trm_raw fv_trm_raw p ({atom namea} \<union> f_raw pat_rawa, trm_rawa);
-   alpha_f_raw pat_raw pat_rawa\<rbrakk>
-   \<Longrightarrow> alpha_trm_raw (Foo2_raw name pat_raw trm_raw) (Foo2_raw namea pat_rawa trm_rawa)"
-
-(* alpha_pat_raw *)
-| "alpha_pat_raw PN_raw PN_raw"
-| "name = namea \<Longrightarrow> alpha_pat_raw (PS_raw name) (PS_raw namea)"
-| "\<lbrakk>alpha_pat_raw pat_raw1 pat_raw1a; alpha_pat_raw pat_raw2 pat_raw2a\<rbrakk>
-   \<Longrightarrow> alpha_pat_raw (PD_raw pat_raw1 pat_raw2) (PD_raw pat_raw1a pat_raw2a)"
-
-(* alpha_f_raw *)
-| "alpha_f_raw PN_raw PN_raw"
-| "alpha_f_raw (PS_raw name) (PS_raw namea)"
-| "\<lbrakk>alpha_f_raw pat_raw1 pat_raw1a; alpha_f_raw pat_raw2 pat_raw2a\<rbrakk>
-  \<Longrightarrow> alpha_f_raw (PD_raw pat_raw1 pat_raw2) (PD_raw pat_raw1a pat_raw2a)"
-*)
-
-lemmas all = alpha_trm_raw_alpha_pat_raw_alpha_f_raw.intros
-
-lemma
-  shows "alpha_trm_raw (Foo2_raw x (PS_raw x) (Var_raw x))
-                       (Foo2_raw y (PS_raw y) (Var_raw y))"
-apply(rule all)
-apply(rule_tac x="(atom x \<rightleftharpoons> atom y)" in exI)
-apply(simp add: alphas)
-apply(simp add: supp_at_base fresh_star_def)
-apply(rule conjI)
-apply(rule all)
-apply(simp)
-apply(perm_simp)
-apply(simp)
-apply(rule all)
-done
-
-
-
-end
-
-
-
--- a/Nominal/Ex/ExLet.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,225 +0,0 @@
-theory ExLet
-imports "../NewParser" "../../Attic/Prove"
-begin
-
-text {* example 3 or example 5 from Terms.thy *}
-
-atom_decl name
-
-nominal_datatype trm =
-  Vr "name"
-| Ap "trm" "trm"
-| Lm x::"name" t::"trm"  bind_set x in t
-| Lt a::"lts" t::"trm"   bind "bn a" in t
-(*| L a::"lts" t1::"trm" t2::"trm"  bind "bn a" in t1, bind "bn a" in t2*)
-and lts =
-  Lnil
-| Lcons "name" "trm" "lts"
-binder
-  bn
-where
-  "bn Lnil = []"
-| "bn (Lcons x t l) = (atom x) # (bn l)"
-
-
-thm alpha_trm_raw_alpha_lts_raw_alpha_bn_raw.intros
-
-thm trm_lts.fv
-thm trm_lts.eq_iff
-thm trm_lts.bn
-thm trm_lts.perm
-thm trm_lts.induct[no_vars]
-thm trm_lts.inducts[no_vars]
-thm trm_lts.distinct
-(*thm trm_lts.supp*)
-thm trm_lts.fv[simplified trm_lts.supp(1-2)]
-
-
-primrec
-  permute_bn_raw
-where
-  "permute_bn_raw pi (Lnil_raw) = Lnil_raw"
-| "permute_bn_raw pi (Lcons_raw a t l) = Lcons_raw (pi \<bullet> a) t (permute_bn_raw pi l)"
-
-quotient_definition
-  "permute_bn :: perm \<Rightarrow> lts \<Rightarrow> lts"
-is
-  "permute_bn_raw"
-
-lemma [quot_respect]: "((op =) ===> alpha_lts_raw ===> alpha_lts_raw) permute_bn_raw permute_bn_raw"
-  apply simp
-  apply clarify
-  apply (erule alpha_trm_raw_alpha_lts_raw_alpha_bn_raw.inducts)
-  apply (rule TrueI)+
-  apply simp_all
-  apply (rule_tac [!] alpha_trm_raw_alpha_lts_raw_alpha_bn_raw.intros)
-  apply simp_all
-  done
-
-lemmas permute_bn = permute_bn_raw.simps[quot_lifted]
-
-lemma permute_bn_zero:
-  "permute_bn 0 a = a"
-  apply(induct a rule: trm_lts.inducts(2))
-  apply(rule TrueI)+
-  apply(simp_all add:permute_bn)
-  done
-
-lemma permute_bn_add:
-  "permute_bn (p + q) a = permute_bn p (permute_bn q a)"
-  oops
-
-lemma permute_bn_alpha_bn: "alpha_bn lts (permute_bn q lts)"
-  apply(induct lts rule: trm_lts.inducts(2))
-  apply(rule TrueI)+
-  apply(simp_all add:permute_bn eqvts trm_lts.eq_iff)
-  done
-
-lemma perm_bn:
-  "p \<bullet> bn l = bn(permute_bn p l)"
-  apply(induct l rule: trm_lts.inducts(2))
-  apply(rule TrueI)+
-  apply(simp_all add:permute_bn eqvts)
-  done
-
-lemma fv_perm_bn:
-  "fv_bn l = fv_bn (permute_bn p l)"
-  apply(induct l rule: trm_lts.inducts(2))
-  apply(rule TrueI)+
-  apply(simp_all add:permute_bn eqvts)
-  done
-
-lemma Lt_subst:
-  "supp (Abs_lst (bn lts) trm) \<sharp>* q \<Longrightarrow> (Lt lts trm) = Lt (permute_bn q lts) (q \<bullet> trm)"
-  apply (simp add: trm_lts.eq_iff permute_bn_alpha_bn)
-  apply (rule_tac x="q" in exI)
-  apply (simp add: alphas)
-  apply (simp add: perm_bn[symmetric])
-  apply(rule conjI)
-  apply(drule supp_perm_eq)
-  apply(simp add: abs_eq_iff)
-  apply(simp add: alphas_abs alphas)
-  apply(drule conjunct1)
-  apply (simp add: trm_lts.supp)
-  apply(simp add: supp_abs)
-  apply (simp add: trm_lts.supp)
-  done
-
-
-lemma fin_bn:
-  "finite (set (bn l))"
-  apply(induct l rule: trm_lts.inducts(2))
-  apply(simp_all add:permute_bn eqvts)
-  done
-
-thm trm_lts.inducts[no_vars]
-
-lemma 
-  fixes t::trm
-  and   l::lts
-  and   c::"'a::fs"
-  assumes a1: "\<And>name c. P1 c (Vr name)"
-  and     a2: "\<And>trm1 trm2 c. \<lbrakk>\<And>d. P1 d trm1; \<And>d. P1 d trm2\<rbrakk> \<Longrightarrow> P1 c (Ap trm1 trm2)"
-  and     a3: "\<And>name trm c. \<lbrakk>atom name \<sharp> c; \<And>d. P1 d trm\<rbrakk> \<Longrightarrow> P1 c (Lm name trm)"
-  and     a4: "\<And>lts trm c. \<lbrakk>set (bn lts) \<sharp>* c; \<And>d. P2 d lts; \<And>d. P1 d trm\<rbrakk> \<Longrightarrow> P1 c (Lt lts trm)"
-  and     a5: "\<And>c. P2 c Lnil"
-  and     a6: "\<And>name trm lts c. \<lbrakk>\<And>d. P1 d trm; \<And>d. P2 d lts\<rbrakk> \<Longrightarrow> P2 c (Lcons name trm lts)"
-  shows "P1 c t" and "P2 c l"
-proof -
-  have "(\<And>(p::perm) (c::'a::fs). P1 c (p \<bullet> t))" and
-       b': "(\<And>(p::perm) (q::perm) (c::'a::fs). P2 c (permute_bn p (q \<bullet> l)))"
-    apply(induct rule: trm_lts.inducts)
-    apply(simp)
-    apply(rule a1)
-    apply(simp)
-    apply(rule a2)
-    apply(simp)
-    apply(simp)
-    apply(simp)
-    apply(subgoal_tac "\<exists>q. (q \<bullet> (atom (p \<bullet> name))) \<sharp> c \<and> supp (Lm (p \<bullet> name) (p \<bullet> trm)) \<sharp>* q")
-    apply(erule exE)
-    apply(rule_tac t="Lm (p \<bullet> name) (p \<bullet> trm)" 
-               and s="q\<bullet> Lm (p \<bullet> name) (p \<bullet> trm)" in subst)
-    apply(rule supp_perm_eq)
-    apply(simp)
-    apply(simp)
-    apply(rule a3)
-    apply(simp add: atom_eqvt)
-    apply(subst permute_plus[symmetric])
-    apply(blast)
-    apply(rule at_set_avoiding2_atom)
-    apply(simp add: finite_supp)
-    apply(simp add: finite_supp)
-    apply(simp add: fresh_def)
-    apply(simp add: trm_lts.fv[simplified trm_lts.supp])
-    apply(simp)
-    apply(subgoal_tac "\<exists>q. (q \<bullet> set (bn (p \<bullet> lts))) \<sharp>* c \<and> supp (Abs_lst (bn (p \<bullet> lts)) (p \<bullet> trm)) \<sharp>* q")
-    apply(erule exE)
-    apply(erule conjE)
-    thm Lt_subst
-    apply(subst Lt_subst)
-    apply assumption
-    apply(rule a4)
-    apply(simp add:perm_bn[symmetric])
-    apply(simp add: eqvts)
-    apply (simp add: fresh_star_def fresh_def)
-    apply(rotate_tac 1)
-    apply(drule_tac x="q + p" in meta_spec)
-    apply(simp)
-    apply(rule at_set_avoiding2)
-    apply(rule fin_bn)
-    apply(simp add: finite_supp)
-    apply(simp add: finite_supp)
-    apply(simp add: fresh_star_def fresh_def supp_abs)
-    apply(simp add: eqvts permute_bn)
-    apply(rule a5)
-    apply(simp add: permute_bn)
-    apply(rule a6)
-    apply simp
-    apply simp
-    done
-  then have a: "P1 c (0 \<bullet> t)" by blast
-  have "P2 c (permute_bn 0 (0 \<bullet> l))" using b' by blast
-  then show "P1 c t" and "P2 c l" using a permute_bn_zero by simp_all
-qed
-
-
-
-lemma lets_bla:
-  "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt (Lcons x (Vr y) Lnil) (Vr x)) \<noteq> (Lt (Lcons x (Vr z) Lnil) (Vr x))"
-  by (simp add: trm_lts.eq_iff)
-
-lemma lets_ok:
-  "(Lt (Lcons x (Vr y) Lnil) (Vr x)) = (Lt (Lcons y (Vr y) Lnil) (Vr y))"
-  apply (simp add: trm_lts.eq_iff)
-  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
-  apply (simp_all add: alphas eqvts supp_at_base fresh_star_def)
-  done
-
-lemma lets_ok3:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff)
-  done
-
-
-lemma lets_not_ok1:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff fresh_star_def eqvts)
-  done
-
-lemma lets_nok:
-  "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Ap (Vr z) (Vr z)) (Lcons y (Vr z) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Vr z) (Lcons x (Ap (Vr z) (Vr z)) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff fresh_star_def)
-  done
-
-
-end
-
-
-
--- a/Nominal/Ex/ExLetMult.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,30 +0,0 @@
-theory ExLetMult
-imports "../NewParser"
-begin
-
-atom_decl name
-
-nominal_datatype trm =
-  Vr "name"
-| Ap "trm" "trm"
-| Lm x::"name" t::"trm" bind_set x in t
-| Lt l::"lts" t::"trm" s::"trm" bind "bn l" in t s
-and lts =
-  Lnil
-| Lcons "name" "trm" "lts"
-binder
-  bn
-where
-  "bn Lnil = []"
-| "bn (Lcons x t l) = (atom x) # (bn l)"
-
-thm trm_lts.eq_iff
-thm trm_lts.induct
-thm trm_lts.fv[simplified trm_lts.supp]
-
-
-
-end
-
-
-
--- a/Nominal/Ex/ExLetRec.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,85 +0,0 @@
-theory ExLetRec
-imports "../NewParser"
-begin
-
-
-text {* example 3 or example 5 from Terms.thy *}
-
-atom_decl name
-
-ML {* val _ = cheat_equivp := true *}
-
-nominal_datatype trm =
-  Vr "name"
-| Ap "trm" "trm"
-| Lm x::"name" t::"trm"  bind_set x in t
-| Lt a::"lts" t::"trm"   bind "bn a" in a t
-and lts =
-  Lnil
-| Lcons "name" "trm" "lts"
-binder
-  bn
-where
-  "bn Lnil = []"
-| "bn (Lcons x t l) = (atom x) # (bn l)"
-
-thm trm_lts.fv
-thm trm_lts.eq_iff
-thm trm_lts.bn
-thm trm_lts.perm
-thm trm_lts.induct
-thm trm_lts.distinct
-thm trm_lts.supp
-thm trm_lts.fv[simplified trm_lts.supp]
-
-
-(* why is this not in HOL simpset? *)
-lemma set_sub: "{a, b} - {b} = {a} - {b}"
-by auto
-
-lemma lets_bla:
-  "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt (Lcons x (Vr y) Lnil) (Vr x)) \<noteq> (Lt (Lcons x (Vr z) Lnil) (Vr x))"
-  apply (auto simp add: trm_lts.eq_iff alphas set_sub supp_at_base)
-  done
-
-lemma lets_ok:
-  "(Lt (Lcons x (Vr x) Lnil) (Vr x)) = (Lt (Lcons y (Vr y) Lnil) (Vr y))"
-  apply (simp add: trm_lts.eq_iff)
-  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
-  apply (simp_all add: alphas fresh_star_def eqvts supp_at_base)
-  done
-
-lemma lets_ok3:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff)
-  done
-
-
-lemma lets_not_ok1:
-  "x \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff)
-  done
-
-lemma lets_nok:
-  "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
-   (Lt (Lcons x (Ap (Vr z) (Vr z)) (Lcons y (Vr z) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
-   (Lt (Lcons y (Vr z) (Lcons x (Ap (Vr z) (Vr z)) Lnil)) (Ap (Vr x) (Vr y)))"
-  apply (simp add: alphas trm_lts.eq_iff fresh_star_def)
-  done
-
-lemma lets_ok4:
-  "(Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) =
-   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr y) (Vr x)))"
-  apply (simp add: alphas trm_lts.eq_iff supp_at_base)
-  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
-  apply (simp add: atom_eqvt fresh_star_def)
-  done
-
-end
-
-
-
--- a/Nominal/Ex/ExPS3.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/ExPS3.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -6,14 +6,11 @@
 
 atom_decl name
 
-ML {* val _ = cheat_equivp := true *}
-ML {* val _ = cheat_alpha_bn_rsp := true *}
-
 nominal_datatype exp =
   Var "name"
 | App "exp" "exp"
-| Lam x::"name" e::"exp" bind_set x in e
-| Let x::"name" p::"pat" e1::"exp" e2::"exp" bind_set x in e2, bind_set "bp p" in e1
+| Lam x::"name" e::"exp" bind x in e
+| Let x::"name" p::"pat" e1::"exp" e2::"exp" bind (set) x in e2, bind (set) "bp p" in e1
 and pat =
   PVar "name"
 | PUnit
@@ -25,16 +22,16 @@
 | "bp (PUnit) = {}"
 | "bp (PPair p1 p2) = bp p1 \<union> bp p2"
 
-thm exp_pat.fv
-thm exp_pat.eq_iff
-thm exp_pat.bn
-thm exp_pat.perm
+
+thm exp_pat.distinct
 thm exp_pat.induct
-thm exp_pat.distinct
-thm exp_pat.fv
-thm exp_pat.supp(1-2)
-
-
+thm exp_pat.exhaust
+thm exp_pat.fv_defs
+thm exp_pat.bn_defs
+thm exp_pat.perm_simps
+thm exp_pat.eq_iff
+thm exp_pat.fv_bn_eqvt
+thm exp_pat.size_eqvt
 
 
 end
--- a/Nominal/Ex/ExPS6.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,41 +0,0 @@
-theory ExPS6
-imports "../NewParser"
-begin
-
-(* example 6 from Peter Sewell's bestiary *)
-
-atom_decl name
-
-(* Is this binding structure supported - I think not 
-   because e1 occurs twice as body *)
-
-nominal_datatype exp =
-  Var name
-| Pair exp exp
-| LetRec x::name p::pat e1::exp e2::exp  bind x in e1 e2, bind "bp p" in e1
-and pat =
-  PVar name
-| PUnit
-| PPair pat pat
-binder
-  bp :: "pat \<Rightarrow> atom list"
-where
-  "bp (PVar x) = [atom x]"
-| "bp (PUnit) = []"
-| "bp (PPair p1 p2) = bp p1 @ bp p2"
-
-thm exp_pat.fv
-thm exp_pat.eq_iff
-thm exp_pat.bn
-thm exp_pat.perm
-thm exp_pat.induct
-thm exp_pat.distinct
-thm exp_pat.supp
-
-
-
-
-end
-
-
-
--- a/Nominal/Ex/ExPS7.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/ExPS7.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -11,7 +11,7 @@
   Var name
 | Unit
 | Pair exp exp
-| LetRec l::"lrbs" e::"exp"  bind_set "bs l" in l e
+| LetRec l::"lrbs" e::"exp"  bind (set) "bs l" in l e
 and lrb =
   Assign name exp
 and lrbs =
@@ -25,8 +25,6 @@
 | "bs (Single a) = b a"
 | "bs (More a as) = (b a) \<union> (bs as)"
 
-thm exp_lrb_lrbs.eq_iff
-thm exp_lrb_lrbs.supp
 
 
 end
--- a/Nominal/Ex/ExPS8.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/ExPS8.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -6,17 +6,13 @@
 
 atom_decl name
 
-ML {* val _ = cheat_fv_rsp := true *}
-ML {* val _ = cheat_equivp := true *}
-ML {* val _ = cheat_alpha_bn_rsp := true *}
-
 nominal_datatype exp =
   EVar name
 | EUnit
 | EPair exp exp
-| ELetRec l::lrbs e::exp bind_set "b_lrbs l" in l e
+| ELetRec l::lrbs e::exp bind (set) "b_lrbs l" in l e
 and fnclause =
-  K x::name p::pat f::exp bind_set "b_pat p" in f
+  K x::name p::pat f::exp bind (set) "b_pat p" in f
 and fnclauses =
   S fnclause
 | ORs fnclause fnclauses
@@ -46,8 +42,6 @@
 | "b_lrb (Clause fcs) = (b_fnclauses fcs)"
 | "b_fnclause (K x pat exp) = {atom x}"
 
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.fv
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.eq_iff
 
 end
 
--- a/Nominal/Ex/LF.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/LF.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -2,7 +2,7 @@
 imports "../NewParser"
 begin
 
-declare [[STEPS = 9]]
+declare [[STEPS = 20]]
 
 atom_decl name
 atom_decl ident
@@ -13,17 +13,14 @@
 and ty =
     TConst "ident"
   | TApp "ty" "trm"
-  | TPi "ty" n::"name" t::"ty"   bind n in t
+  | TPi "ty" n::"name" ty::"ty"   bind n in ty
 and trm =
     Const "ident"
   | Var "name"
   | App "trm" "trm"
   | Lam "ty" n::"name" t::"trm"  bind n in t
 
-thm kind_ty_trm.supp
-
-
-
+(*thm kind_ty_trm.supp*)
 
 
 end
--- a/Nominal/Ex/Lambda.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/Lambda.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -5,32 +5,22 @@
 atom_decl name
 declare [[STEPS = 21]]
 
-class s1
-class s2
-
-nominal_datatype lambda: 
- ('a, 'b) lam =
+nominal_datatype lam =
   Var "name"
-| App "('a::s1, 'b::s2) lam" "('a, 'b) lam"
-| Lam x::"name" l::"('a, 'b) lam"  bind x in l
+| App "lam" "lam"
+| Lam x::"name" l::"lam"  bind x in l
 
-thm distinct
-thm induct
-thm exhaust
-thm fv_defs
-thm bn_defs
-thm perm_simps
-thm eq_iff
-thm fv_bn_eqvt
-thm size_eqvt
+thm lam.distinct
+thm lam.induct
+thm lam.exhaust
+thm lam.fv_defs
+thm lam.bn_defs
+thm lam.perm_simps
+thm lam.eq_iff
+thm lam.fv_bn_eqvt
+thm lam.size_eqvt
 
 
-thm lam.fv
-thm lam.supp
-lemmas supp_fn' = lam.fv[simplified lam.supp]
-
-declare lam.perm[eqvt]
-
 
 section {* Strong Induction Principles*}
 
@@ -38,6 +28,7 @@
   Old way of establishing strong induction
   principles by chosing a fresh name.
 *)
+(*
 lemma
   fixes c::"'a::fs"
   assumes a1: "\<And>name c. P c (Var name)"
@@ -79,11 +70,12 @@
   then have "P c (0 \<bullet> lam)" by blast
   then show "P c lam" by simp
 qed
-
+*)
 (* 
   New way of establishing strong induction
   principles by using a appropriate permutation.
 *)
+(*
 lemma
   fixes c::"'a::fs"
   assumes a1: "\<And>name c. P c (Var name)"
@@ -121,6 +113,7 @@
   then have "P c (0 \<bullet> lam)" by blast
   then show "P c lam" by simp
 qed
+*)
 
 section {* Typing *}
 
@@ -131,6 +124,7 @@
 notation
  TFun ("_ \<rightarrow> _") 
 
+(*
 declare ty.perm[eqvt]
 
 inductive
@@ -237,7 +231,7 @@
       apply(simp add: finite_supp)
       apply(rule_tac p="-p" in permute_boolE)
       apply(perm_strict_simp add: permute_minus_cancel)
-	(* supplied by the user *)
+	--"supplied by the user"
       apply(simp add: fresh_star_prod)
       apply(simp add: fresh_star_def)
       sorry
@@ -246,86 +240,9 @@
   then show "P c \<Gamma> t T" by simp
 qed
 
-
-
-
-
-
-
-inductive
-  tt :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool)"  
-  for r :: "('a \<Rightarrow> 'a \<Rightarrow> bool)"
-where
-    aa: "tt r a a"
-  | bb: "tt r a b ==> tt r a c"
-
-(* PROBLEM: derived eqvt-theorem does not conform with [eqvt]
-equivariance tt
 *)
 
 
-inductive
- alpha_lam_raw'
-where
-  a1: "name = namea \<Longrightarrow> alpha_lam_raw' (Var_raw name) (Var_raw namea)"
-| a2: "\<lbrakk>alpha_lam_raw' lam_raw1 lam_raw1a; alpha_lam_raw' lam_raw2 lam_raw2a\<rbrakk> \<Longrightarrow>
-   alpha_lam_raw' (App_raw lam_raw1 lam_raw2) (App_raw lam_raw1a lam_raw2a)"
-| a3: "\<exists>pi. ({atom name}, lam_raw) \<approx>gen alpha_lam_raw' fv_lam_raw pi ({atom namea}, lam_rawa) \<Longrightarrow>
-   alpha_lam_raw' (Lam_raw name lam_raw) (Lam_raw namea lam_rawa)"
-
-equivariance alpha_lam_raw'
-
-thm eqvts_raw
-
-section {* size function *}
-
-lemma size_eqvt_raw:
-  fixes t::"lam_raw"
-  shows "size (pi \<bullet> t)  = size t"
-  apply (induct rule: lam_raw.inducts)
-  apply simp_all
-  done
-
-instantiation lam :: size 
-begin
-
-quotient_definition
-  "size_lam :: lam \<Rightarrow> nat"
-is
-  "size :: lam_raw \<Rightarrow> nat"
-
-lemma size_rsp:
-  "alpha_lam_raw x y \<Longrightarrow> size x = size y"
-  apply (induct rule: alpha_lam_raw.inducts)
-  apply (simp_all only: lam_raw.size)
-  apply (simp_all only: alphas)
-  apply clarify
-  apply (simp_all only: size_eqvt_raw)
-  done
-
-lemma [quot_respect]:
-  "(alpha_lam_raw ===> op =) size size"
-  by (simp_all add: size_rsp)
-
-lemma [quot_preserve]:
-  "(rep_lam ---> id) size = size"
-  by (simp_all add: size_lam_def)
-
-instance
-  by default
-
-end
-
-lemmas size_lam[simp] = 
-  lam_raw.size(4)[quot_lifted]
-  lam_raw.size(5)[quot_lifted]
-  lam_raw.size(6)[quot_lifted]
-
-(* is this needed? *)
-lemma [measure_function]: 
-  "is_measure (size::lam\<Rightarrow>nat)" 
-  by (rule is_measure_trivial)
-
 section {* Matching *}
 
 definition
@@ -512,6 +429,7 @@
 | "match_App_raw (App_raw x y) = Some (x, y)"
 | "match_App_raw (Lam_raw n t) = None"
 
+(*
 quotient_definition
   "match_App :: lam \<Rightarrow> (lam \<times> lam) option"
 is match_App_raw
@@ -547,7 +465,7 @@
   apply (simp add: lam_half_inj)
   apply auto
   done
-
+*)
 (*
 lemma match_Lam_simps2:
   "atom n \<sharp> ((S :: 'a :: fs), Lam n s) \<Longrightarrow> match_Lam S (Lam n s) = Some (n, s)"
@@ -627,7 +545,7 @@
 
 lemmas match_Lam_simps = match_Lam_raw.simps[quot_lifted]
 *)
-
+(*
 lemma app_some: "match_App x = Some (a, b) \<Longrightarrow> x = App a b"
 by (induct x rule: lam.induct) (simp_all add: match_App_simps)
 
@@ -767,7 +685,7 @@
   apply (simp only: option.simps)
   apply (simp only: prod.simps)
   sorry
-
+*)
 end
 
 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/Let.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -0,0 +1,224 @@
+theory Let
+imports "../NewParser" 
+begin
+
+text {* example 3 or example 5 from Terms.thy *}
+
+atom_decl name
+
+nominal_datatype trm =
+  Var "name"
+| App "trm" "trm"
+| Lam x::"name" t::"trm"  bind  x in t
+| Let a::"lts" t::"trm"   bind "bn a" in t
+and lts =
+  Lnil
+| Lcons "name" "trm" "lts"
+binder
+  bn
+where
+  "bn Lnil = []"
+| "bn (Lcons x t l) = (atom x) # (bn l)"
+
+
+(*
+
+thm trm_lts.fv
+thm trm_lts.eq_iff
+thm trm_lts.bn
+thm trm_lts.perm
+thm trm_lts.induct[no_vars]
+thm trm_lts.inducts[no_vars]
+thm trm_lts.distinct
+thm trm_lts.supp
+thm trm_lts.fv[simplified trm_lts.supp(1-2)]
+
+
+primrec
+  permute_bn_raw
+where
+  "permute_bn_raw pi (Lnil_raw) = Lnil_raw"
+| "permute_bn_raw pi (Lcons_raw a t l) = Lcons_raw (pi \<bullet> a) t (permute_bn_raw pi l)"
+
+quotient_definition
+  "permute_bn :: perm \<Rightarrow> lts \<Rightarrow> lts"
+is
+  "permute_bn_raw"
+
+lemma [quot_respect]: "((op =) ===> alpha_lts_raw ===> alpha_lts_raw) permute_bn_raw permute_bn_raw"
+  apply simp
+  apply clarify
+  apply (erule alpha_trm_raw_alpha_lts_raw_alpha_bn_raw.inducts)
+  apply (rule TrueI)+
+  apply simp_all
+  apply (rule_tac [!] alpha_trm_raw_alpha_lts_raw_alpha_bn_raw.intros)
+  apply simp_all
+  done
+
+lemmas permute_bn = permute_bn_raw.simps[quot_lifted]
+
+lemma permute_bn_zero:
+  "permute_bn 0 a = a"
+  apply(induct a rule: trm_lts.inducts(2))
+  apply(rule TrueI)+
+  apply(simp_all add:permute_bn)
+  done
+
+lemma permute_bn_add:
+  "permute_bn (p + q) a = permute_bn p (permute_bn q a)"
+  oops
+
+lemma permute_bn_alpha_bn: "alpha_bn lts (permute_bn q lts)"
+  apply(induct lts rule: trm_lts.inducts(2))
+  apply(rule TrueI)+
+  apply(simp_all add:permute_bn eqvts trm_lts.eq_iff)
+  done
+
+lemma perm_bn:
+  "p \<bullet> bn l = bn(permute_bn p l)"
+  apply(induct l rule: trm_lts.inducts(2))
+  apply(rule TrueI)+
+  apply(simp_all add:permute_bn eqvts)
+  done
+
+lemma fv_perm_bn:
+  "fv_bn l = fv_bn (permute_bn p l)"
+  apply(induct l rule: trm_lts.inducts(2))
+  apply(rule TrueI)+
+  apply(simp_all add:permute_bn eqvts)
+  done
+
+lemma Lt_subst:
+  "supp (Abs_lst (bn lts) trm) \<sharp>* q \<Longrightarrow> (Lt lts trm) = Lt (permute_bn q lts) (q \<bullet> trm)"
+  apply (simp add: trm_lts.eq_iff permute_bn_alpha_bn)
+  apply (rule_tac x="q" in exI)
+  apply (simp add: alphas)
+  apply (simp add: perm_bn[symmetric])
+  apply(rule conjI)
+  apply(drule supp_perm_eq)
+  apply(simp add: abs_eq_iff)
+  apply(simp add: alphas_abs alphas)
+  apply(drule conjunct1)
+  apply (simp add: trm_lts.supp)
+  apply(simp add: supp_abs)
+  apply (simp add: trm_lts.supp)
+  done
+
+
+lemma fin_bn:
+  "finite (set (bn l))"
+  apply(induct l rule: trm_lts.inducts(2))
+  apply(simp_all add:permute_bn eqvts)
+  done
+
+thm trm_lts.inducts[no_vars]
+
+lemma 
+  fixes t::trm
+  and   l::lts
+  and   c::"'a::fs"
+  assumes a1: "\<And>name c. P1 c (Vr name)"
+  and     a2: "\<And>trm1 trm2 c. \<lbrakk>\<And>d. P1 d trm1; \<And>d. P1 d trm2\<rbrakk> \<Longrightarrow> P1 c (Ap trm1 trm2)"
+  and     a3: "\<And>name trm c. \<lbrakk>atom name \<sharp> c; \<And>d. P1 d trm\<rbrakk> \<Longrightarrow> P1 c (Lm name trm)"
+  and     a4: "\<And>lts trm c. \<lbrakk>set (bn lts) \<sharp>* c; \<And>d. P2 d lts; \<And>d. P1 d trm\<rbrakk> \<Longrightarrow> P1 c (Lt lts trm)"
+  and     a5: "\<And>c. P2 c Lnil"
+  and     a6: "\<And>name trm lts c. \<lbrakk>\<And>d. P1 d trm; \<And>d. P2 d lts\<rbrakk> \<Longrightarrow> P2 c (Lcons name trm lts)"
+  shows "P1 c t" and "P2 c l"
+proof -
+  have "(\<And>(p::perm) (c::'a::fs). P1 c (p \<bullet> t))" and
+       b': "(\<And>(p::perm) (q::perm) (c::'a::fs). P2 c (permute_bn p (q \<bullet> l)))"
+    apply(induct rule: trm_lts.inducts)
+    apply(simp)
+    apply(rule a1)
+    apply(simp)
+    apply(rule a2)
+    apply(simp)
+    apply(simp)
+    apply(simp)
+    apply(subgoal_tac "\<exists>q. (q \<bullet> (atom (p \<bullet> name))) \<sharp> c \<and> supp (Lm (p \<bullet> name) (p \<bullet> trm)) \<sharp>* q")
+    apply(erule exE)
+    apply(rule_tac t="Lm (p \<bullet> name) (p \<bullet> trm)" 
+               and s="q\<bullet> Lm (p \<bullet> name) (p \<bullet> trm)" in subst)
+    apply(rule supp_perm_eq)
+    apply(simp)
+    apply(simp)
+    apply(rule a3)
+    apply(simp add: atom_eqvt)
+    apply(subst permute_plus[symmetric])
+    apply(blast)
+    apply(rule at_set_avoiding2_atom)
+    apply(simp add: finite_supp)
+    apply(simp add: finite_supp)
+    apply(simp add: fresh_def)
+    apply(simp add: trm_lts.fv[simplified trm_lts.supp])
+    apply(simp)
+    apply(subgoal_tac "\<exists>q. (q \<bullet> set (bn (p \<bullet> lts))) \<sharp>* c \<and> supp (Abs_lst (bn (p \<bullet> lts)) (p \<bullet> trm)) \<sharp>* q")
+    apply(erule exE)
+    apply(erule conjE)
+    thm Lt_subst
+    apply(subst Lt_subst)
+    apply assumption
+    apply(rule a4)
+    apply(simp add:perm_bn[symmetric])
+    apply(simp add: eqvts)
+    apply (simp add: fresh_star_def fresh_def)
+    apply(rotate_tac 1)
+    apply(drule_tac x="q + p" in meta_spec)
+    apply(simp)
+    apply(rule at_set_avoiding2)
+    apply(rule fin_bn)
+    apply(simp add: finite_supp)
+    apply(simp add: finite_supp)
+    apply(simp add: fresh_star_def fresh_def supp_abs)
+    apply(simp add: eqvts permute_bn)
+    apply(rule a5)
+    apply(simp add: permute_bn)
+    apply(rule a6)
+    apply simp
+    apply simp
+    done
+  then have a: "P1 c (0 \<bullet> t)" by blast
+  have "P2 c (permute_bn 0 (0 \<bullet> l))" using b' by blast
+  then show "P1 c t" and "P2 c l" using a permute_bn_zero by simp_all
+qed
+
+
+
+lemma lets_bla:
+  "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt (Lcons x (Vr y) Lnil) (Vr x)) \<noteq> (Lt (Lcons x (Vr z) Lnil) (Vr x))"
+  by (simp add: trm_lts.eq_iff)
+
+lemma lets_ok:
+  "(Lt (Lcons x (Vr y) Lnil) (Vr x)) = (Lt (Lcons y (Vr y) Lnil) (Vr y))"
+  apply (simp add: trm_lts.eq_iff)
+  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
+  apply (simp_all add: alphas eqvts supp_at_base fresh_star_def)
+  done
+
+lemma lets_ok3:
+  "x \<noteq> y \<Longrightarrow>
+   (Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
+   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff)
+  done
+
+
+lemma lets_not_ok1:
+  "x \<noteq> y \<Longrightarrow>
+   (Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
+   (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff fresh_star_def eqvts)
+  done
+
+lemma lets_nok:
+  "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
+   (Lt (Lcons x (Ap (Vr z) (Vr z)) (Lcons y (Vr z) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
+   (Lt (Lcons y (Vr z) (Lcons x (Ap (Vr z) (Vr z)) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff fresh_star_def)
+  done
+*)
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/LetPat.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -0,0 +1,39 @@
+theory LetPat
+imports "../NewParser"
+begin
+
+declare [[STEPS = 100]]
+
+atom_decl name
+
+nominal_datatype trm =
+  Var "name"
+| App "trm" "trm"
+| Lam x::"name" t::"trm"       bind (set) x in t
+| Let p::"pat" "trm" t::"trm"  bind (set) "f p" in t
+and pat =
+  PN
+| PS "name"
+| PD "name" "name"
+binder
+  f::"pat \<Rightarrow> atom set"
+where
+  "f PN = {}"
+| "f (PD x y) = {atom x, atom y}"
+| "f (PS x) = {atom x}"
+
+thm trm_pat.distinct
+thm trm_pat.induct
+thm trm_pat.exhaust
+thm trm_pat.fv_defs
+thm trm_pat.bn_defs
+thm trm_pat.perm_simps
+thm trm_pat.eq_iff
+thm trm_pat.fv_bn_eqvt
+thm trm_pat.size_eqvt
+
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/LetRec.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -0,0 +1,36 @@
+theory LetRec
+imports "../NewParser"
+begin
+
+declare [[STEPS = 14]]
+
+atom_decl name
+
+nominal_datatype let_rec:
+ lam =
+  Var "name"
+| App "lam" "lam"
+| Lam x::"name" t::"lam"     bind (set) x in t
+| Let_Rec bp::"bp" t::"lam"  bind (set) "bi bp" in bp t
+and bp =
+  Bp "name" "lam"
+binder
+  bi::"bp \<Rightarrow> atom set"
+where
+  "bi (Bp x t) = {atom x}"
+
+thm let_rec.distinct
+thm let_rec.induct
+thm let_rec.exhaust
+thm let_rec.fv_defs
+thm let_rec.bn_defs
+thm let_rec.perm_simps
+thm let_rec.eq_iff
+thm let_rec.fv_bn_eqvt
+thm let_rec.size_eqvt
+
+
+end
+
+
+
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/LetRec2.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -0,0 +1,82 @@
+theory LetRec2
+imports "../NewParser"
+begin
+
+atom_decl name
+
+nominal_datatype trm =
+  Vr "name"
+| Ap "trm" "trm"
+| Lm x::"name" t::"trm"  bind (set) x in t
+| Lt a::"lts" t::"trm"   bind "bn a" in a t
+and lts =
+  Lnil
+| Lcons "name" "trm" "lts"
+binder
+  bn
+where
+  "bn Lnil = []"
+| "bn (Lcons x t l) = (atom x) # (bn l)"
+
+
+thm trm_lts.fv
+thm trm_lts.eq_iff
+thm trm_lts.bn
+thm trm_lts.perm
+thm trm_lts.induct
+thm trm_lts.distinct
+thm trm_lts.supp
+thm trm_lts.fv[simplified trm_lts.supp]
+
+
+(* why is this not in HOL simpset? *)
+(*
+lemma set_sub: "{a, b} - {b} = {a} - {b}"
+by auto
+
+lemma lets_bla:
+  "x \<noteq> z \<Longrightarrow> y \<noteq> z \<Longrightarrow> x \<noteq> y \<Longrightarrow>(Lt (Lcons x (Vr y) Lnil) (Vr x)) \<noteq> (Lt (Lcons x (Vr z) Lnil) (Vr x))"
+  apply (auto simp add: trm_lts.eq_iff alphas set_sub supp_at_base)
+  done
+
+lemma lets_ok:
+  "(Lt (Lcons x (Vr x) Lnil) (Vr x)) = (Lt (Lcons y (Vr y) Lnil) (Vr y))"
+  apply (simp add: trm_lts.eq_iff)
+  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
+  apply (simp_all add: alphas fresh_star_def eqvts supp_at_base)
+  done
+
+lemma lets_ok3:
+  "x \<noteq> y \<Longrightarrow>
+   (Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
+   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff)
+  done
+
+
+lemma lets_not_ok1:
+  "x \<noteq> y \<Longrightarrow>
+   (Lt (Lcons x (Vr x) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
+   (Lt (Lcons y (Vr x) (Lcons x (Vr y) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff)
+  done
+
+lemma lets_nok:
+  "x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
+   (Lt (Lcons x (Ap (Vr z) (Vr z)) (Lcons y (Vr z) Lnil)) (Ap (Vr x) (Vr y))) \<noteq>
+   (Lt (Lcons y (Vr z) (Lcons x (Ap (Vr z) (Vr z)) Lnil)) (Ap (Vr x) (Vr y)))"
+  apply (simp add: alphas trm_lts.eq_iff fresh_star_def)
+  done
+
+lemma lets_ok4:
+  "(Lt (Lcons x (Ap (Vr y) (Vr x)) (Lcons y (Vr y) Lnil)) (Ap (Vr x) (Vr y))) =
+   (Lt (Lcons y (Ap (Vr x) (Vr y)) (Lcons x (Vr x) Lnil)) (Ap (Vr y) (Vr x)))"
+  apply (simp add: alphas trm_lts.eq_iff supp_at_base)
+  apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
+  apply (simp add: atom_eqvt fresh_star_def)
+  done
+
+end
+
+
+
--- a/Nominal/Ex/Modules.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/Modules.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -7,15 +7,16 @@
 
 atom_decl name
 
-nominal_datatype mexp =
+nominal_datatype modules: 
+ mexp =
   Acc "path"
 | Stru "body"
-| Funct x::"name" "sexp" m::"mexp"    bind_set x in m
+| Funct x::"name" "sexp" m::"mexp"    bind (set) x in m
 | FApp "mexp" "path"
 | Ascr "mexp" "sexp"
 and body =
   Empty
-| Seq c::defn d::"body"     bind_set "cbinders c" in d
+| Seq c::"defn" d::"body"     bind (set) "cbinders c" in d
 and defn =
   Type "name" "ty"
 | Dty "name"
@@ -26,7 +27,7 @@
 | SFunc "name" "sexp" "sexp"
 and sbody =
   SEmpty
-| SSeq C::spec D::sbody    bind_set "Cbinders C" in D
+| SSeq C::"spec" D::"sbody"    bind (set) "Cbinders C" in D
 and spec =
   Type1 "name"
 | Type2 "name" "ty"
@@ -42,7 +43,7 @@
 and trm =
   Tref1 "name"
 | Tref2 "path" "name"
-| Lam' v::"name" "ty" M::"trm"  bind_set v in M
+| Lam' v::"name" "ty" M::"trm"  bind (set) v in M
 | App' "trm" "trm"
 | Let' "body" "trm"
 binder
@@ -58,15 +59,16 @@
 | "Cbinders (SStru x S) = {atom x}"
 | "Cbinders (SVal v T) = {atom v}"
 
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.fv
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.eq_iff
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.bn
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.perm
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.induct
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.inducts
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.distinct
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.supp(1-3,5-7,9-10)
-thm mexp_body_defn_sexp_sbody_spec_ty_path_trm.fv[simplified mexp_body_defn_sexp_sbody_spec_ty_path_trm.supp(1-3,5-7,9-10)]
+
+thm modules.distinct
+thm modules.induct
+thm modules.exhaust
+thm modules.fv_defs
+thm modules.bn_defs
+thm modules.perm_simps
+thm modules.eq_iff
+thm modules.fv_bn_eqvt
+thm modules.size_eqvt
 
 
 
--- a/Nominal/Ex/NoneExamples.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/NoneExamples.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -4,6 +4,40 @@
 
 atom_decl name
 
+
+text {* 
+  "Weirdo" example from Peter Sewell's bestiary. 
+
+  This example is not covered by our binding 
+  specification.
+
+*}
+
+nominal_datatype weird =
+  Foo_var "name"
+| Foo_pair "weird" "weird" 
+| Foo x::"name" y::"name" p1::"weird" p2::"weird" p3::"weird"
+    bind x in p1 p2, 
+    bind y in p2 p3
+
+(* e1 occurs in two bodies *)
+
+nominal_datatype exp =
+  Var name
+| Pair exp exp
+| LetRec x::name p::pat e1::exp e2::exp  bind x in e1 e2, bind "bp p" in e1
+and pat =
+  PVar name
+| PUnit
+| PPair pat pat
+binder
+  bp :: "pat \<Rightarrow> atom list"
+where
+  "bp (PVar x) = [atom x]"
+| "bp (PUnit) = []"
+| "bp (PPair p1 p2) = bp p1 @ bp p2"
+
+
 (* this example binds bound names and
    so is not respectful *)
 (*
--- a/Nominal/Ex/SingleLet.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/SingleLet.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -4,9 +4,9 @@
 
 atom_decl name
 
-declare [[STEPS = 21]]
+declare [[STEPS = 100]]
 
-nominal_datatype singlelet: trm  =
+nominal_datatype single_let: trm  =
   Var "name"
 | App "trm" "trm"
 | Lam x::"name" t::"trm"  bind x in t
@@ -21,19 +21,18 @@
 where
   "bn (As x y t) = {atom x}"
 
-
-thm distinct
-thm induct
-thm exhaust
-thm fv_defs
-thm bn_defs
-thm perm_simps
-thm eq_iff
-thm fv_bn_eqvt
-thm size_eqvt
+thm single_let.distinct
+thm single_let.induct
+thm single_let.exhaust
+thm single_let.fv_defs
+thm single_let.bn_defs
+thm single_let.perm_simps
+thm single_let.eq_iff
+thm single_let.fv_bn_eqvt
+thm single_let.size_eqvt
 
 
-
+(*
 
 
 lemma supp_fv:
@@ -67,10 +66,9 @@
 thm trm_assg.inducts
 thm trm_assg.distinct
 ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
+*)
 
-(* TEMPORARY
-thm trm_assg.fv[simplified trm_assg.supp(1-2)]
-*)
+
 
 end
 
--- a/Nominal/Ex/Term8.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/Term8.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -6,21 +6,21 @@
 
 atom_decl name
 
-ML {* val _ = cheat_alpha_bn_rsp := true *}
-
 nominal_datatype foo =
   Foo0 "name"
-| Foo1 b::"bar" f::"foo" bind_set "bv b" in f
+| Foo1 b::"bar" f::"foo" bind (set) "bv b" in f
 and bar =
   Bar0 "name"
-| Bar1 "name" s::"name" b::"bar" bind_set s in b
+| Bar1 "name" s::"name" b::"bar" bind (set) s in b
 binder
   bv
 where
   "bv (Bar0 x) = {}"
 | "bv (Bar1 v x b) = {atom v}"
 
+(*
 thm foo_bar.supp
+*)
 
 end
 
--- a/Nominal/Ex/Test.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,40 +0,0 @@
-theory Test
-imports "../NewParser"
-begin
-
-declare [[STEPS = 4]]
-
-atom_decl name
-
-(*
-nominal_datatype trm =
-  Vr "name"
-| Ap "trm" "trm"
-
-thm fv_trm_raw.simps[no_vars]
-*)
-
-(* This file contains only the examples that are not supposed to work yet. *)
-
-
-declare [[STEPS = 2]]
-
-
-(* example 4 from Terms.thy *)
-(* fv_eqvt does not work, we need to repaire defined permute functions
-   defined fv and defined alpha... *)
-(* lists-datastructure does not work yet *)
-
-nominal_datatype trm =
-  Vr "name"
-| Ap "trm" "trm list"
-| Lm x::"name" t::"trm"  bind x in t
-
-(*
-thm alpha_trm4_raw_alpha_trm4_raw_list.intros[no_vars]
-thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]
-*)
-
-end
-
-
--- a/Nominal/Ex/TestMorePerm.thy	Wed Aug 25 23:16:42 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,35 +0,0 @@
-theory TestMorePerm
-imports "../NewParser"
-begin
-
-text {* 
-  "Weirdo" example from Peter Sewell's bestiary. 
-
-  This example is not covered by our binding 
-  specification.
-
-*}
-ML {* val _ = cheat_equivp := true *}
-
-atom_decl name
-
-nominal_datatype weird =
-  Foo_var "name"
-| Foo_pair "weird" "weird" 
-| Foo x::"name" y::"name" p1::"weird" p2::"weird" p3::"weird"
-    bind x in p1 p2, 
-    bind y in p2 p3
-
-thm alpha_weird_raw.intros[no_vars]
-
-thm permute_weird_raw.simps[no_vars]
-thm alpha_weird_raw.intros[no_vars]
-thm fv_weird_raw.simps[no_vars]
-
-equivariance alpha_weird_raw
-
-
-end
-
-
-
--- a/Nominal/Ex/TypeSchemes.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/Ex/TypeSchemes.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -6,7 +6,7 @@
 
 atom_decl name
 
-declare [[STEPS = 21]]
+declare [[STEPS = 100]]
 
 nominal_datatype ty =
   Var "name"
@@ -19,74 +19,11 @@
   Var2 "name"
 | Fun2 "ty2" "ty2"
 
-
 nominal_datatype tys2 =
   All2 xs::"name fset" ty::"ty2" bind (res) xs in ty
 
 
-lemmas ty_tys_supp = ty_tys.fv[simplified ty_tys.supp]
-
-
-
-(* below we define manually the function for size *)
-
-lemma size_eqvt_raw:
-  "size (pi \<bullet> t  :: ty_raw)  = size t"
-  "size (pi \<bullet> ts :: tys_raw) = size ts"
-  apply (induct rule: ty_raw_tys_raw.inducts)
-  apply simp_all
-  done
-
-instantiation ty and tys :: size 
-begin
-
-quotient_definition
-  "size_ty :: ty \<Rightarrow> nat"
-is
-  "size :: ty_raw \<Rightarrow> nat"
-
-quotient_definition
-  "size_tys :: tys \<Rightarrow> nat"
-is
-  "size :: tys_raw \<Rightarrow> nat"
-
-lemma size_rsp:
-  "alpha_ty_raw x y \<Longrightarrow> size x = size y"
-  "alpha_tys_raw a b \<Longrightarrow> size a = size b"
-  apply (induct rule: alpha_ty_raw_alpha_tys_raw.inducts)
-  apply (simp_all only: ty_raw_tys_raw.size)
-  apply (simp_all only: alphas)
-  apply clarify
-  apply (simp_all only: size_eqvt_raw)
-  done
-
-lemma [quot_respect]:
-  "(alpha_ty_raw ===> op =) size size"
-  "(alpha_tys_raw ===> op =) size size"
-  by (simp_all add: size_rsp)
-
-lemma [quot_preserve]:
-  "(rep_ty ---> id) size = size"
-  "(rep_tys ---> id) size = size"
-  by (simp_all add: size_ty_def size_tys_def)
-
-instance
-  by default
-
-end
-
-thm ty_raw_tys_raw.size(4)[quot_lifted]
-thm ty_raw_tys_raw.size(5)[quot_lifted]
-thm ty_raw_tys_raw.size(6)[quot_lifted]
-
-
-thm ty_tys.fv
-thm ty_tys.eq_iff
-thm ty_tys.bn
-thm ty_tys.perm
-thm ty_tys.inducts
-thm ty_tys.distinct
-
+(*
 ML {* Sign.of_sort @{theory} (@{typ ty}, @{sort fs}) *}
 
 lemma strong_induct:
@@ -278,19 +215,6 @@
   done
 
 end
-
-(* 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".
 *)
 
 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/TypeVarsTest.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -0,0 +1,30 @@
+theory TypeVarsTest
+imports "../NewParser" 
+begin
+
+atom_decl name
+declare [[STEPS = 21]]
+
+class s1
+class s2
+
+nominal_datatype ('a, 'b) lam =
+  Var "name"
+| App "('a::s1, 'b::s2) lam" "('a, 'b) lam"
+| Lam x::"name" l::"('a, 'b) lam"  bind x in l
+
+thm lam.distinct
+thm lam.induct
+thm lam.exhaust
+thm lam.fv_defs
+thm lam.bn_defs
+thm lam.perm_simps
+thm lam.eq_iff
+thm lam.fv_bn_eqvt
+thm lam.size_eqvt
+
+
+end
+
+
+
--- a/Nominal/NewParser.thy	Wed Aug 25 23:16:42 2010 +0800
+++ b/Nominal/NewParser.thy	Thu Aug 26 02:08:00 2010 +0800
@@ -251,7 +251,7 @@
 (* for testing porposes - to exit the procedure early *)
 exception TEST of Proof.context
 
-val (STEPS, STEPS_setup) = Attrib.config_int "STEPS" (K 0);
+val (STEPS, STEPS_setup) = Attrib.config_int "STEPS" (K 100);
 
 fun get_STEPS ctxt = Config.get ctxt STEPS
 *}
@@ -259,7 +259,7 @@
 setup STEPS_setup
 
 ML {*
-fun nominal_datatype2 thm_name dts bn_funs bn_eqs bclauses lthy =
+fun nominal_datatype2 opt_thms_name dts bn_funs bn_eqs bclauses lthy =
 let
   (* definition of the raw datatypes *)
   val _ = warning "Definition of raw datatypes";
@@ -437,7 +437,6 @@
   val qty_full_names = map (fst o dest_Type) qtys
   val qty_names = map Long_Name.base_name qty_full_names             
 
-
   (* defining of quotient term-constructors, binding functions, free vars functions *)
   val _ = warning "Defining the quotient constants"
   val qconstrs_descr = 
@@ -517,24 +516,24 @@
       ||>> lift_thms qtys [] raw_exhaust_thms
     else raise TEST lthyA
 
-  
-  (* temporary theorem bindings *)
+  (* noting the theorems *)  
+
+  (* generating the prefix for the theorem names *)
+  val thms_name = 
+    the_default (Binding.name (space_implode "_" qty_names)) opt_thms_name 
+  fun thms_suffix s = Binding.qualified true s thms_name 
+
   val (_, lthy9') = lthyB
-     |> Local_Theory.note ((@{binding "distinct"}, []), qdistincts) 
-     ||>> Local_Theory.note ((@{binding "eq_iff"}, []), qeq_iffs)
-     ||>> Local_Theory.note ((@{binding "fv_defs"}, []), qfv_defs) 
-     ||>> Local_Theory.note ((@{binding "bn_defs"}, []), qbn_defs) 
-     ||>> Local_Theory.note ((@{binding "perm_simps"}, []), qperm_simps) 
-     ||>> Local_Theory.note ((@{binding "fv_bn_eqvt"}, []), qfv_qbn_eqvts) 
-     ||>> Local_Theory.note ((@{binding "size_eqvt"}, []), qsize_eqvt)
-     ||>> Local_Theory.note ((@{binding "induct"}, []), [qinduct]) 
-     ||>> Local_Theory.note ((@{binding "exhaust"}, []), qexhausts)
+     |> Local_Theory.note ((thms_suffix "distinct", []), qdistincts) 
+     ||>> Local_Theory.note ((thms_suffix "eq_iff", []), qeq_iffs)
+     ||>> Local_Theory.note ((thms_suffix "fv_defs", []), qfv_defs) 
+     ||>> Local_Theory.note ((thms_suffix "bn_defs", []), qbn_defs) 
+     ||>> Local_Theory.note ((thms_suffix "perm_simps", []), qperm_simps) 
+     ||>> Local_Theory.note ((thms_suffix "fv_bn_eqvt", []), qfv_qbn_eqvts) 
+     ||>> Local_Theory.note ((thms_suffix "size_eqvt", []), qsize_eqvt)
+     ||>> Local_Theory.note ((thms_suffix "induct", []), [qinduct]) 
+     ||>> Local_Theory.note ((thms_suffix "exhaust", []), qexhausts)
      
-
-  val _ = 
-    if get_STEPS lthy > 21
-    then true else raise TEST lthy9'
-  
 in
   (0, lthy9')
 end handle TEST ctxt => (0, ctxt)
@@ -692,11 +691,10 @@
 *}
 
 ML {*
-fun nominal_datatype2_cmd (opt_thm_name, dt_strs, bn_fun_strs, bn_eq_strs) lthy = 
+fun nominal_datatype2_cmd (opt_thms_name, dt_strs, bn_fun_strs, bn_eq_strs) lthy = 
 let
-  val (pre_typ_names, pre_typs) = split_list
-    (map (fn (tvs, tname, mx, _) =>
-      (Binding.name_of tname, (tname, length tvs, mx))) dt_strs)
+  val pre_typs = 
+    map (fn (tvs, tname, mx, _) => (tname, length tvs, mx)) dt_strs
 
   (* this theory is used just for parsing *)
   val thy = ProofContext.theory_of lthy  
@@ -710,10 +708,8 @@
     ||>> prepare_bclauses dt_strs 
 
   val bclauses' = complete dt_strs bclauses
-  val thm_name = 
-    the_default (Binding.name (space_implode "_" pre_typ_names)) opt_thm_name 
 in
-  timeit (fn () => nominal_datatype2 thm_name dts bn_funs bn_eqs bclauses' lthy |> snd)
+  timeit (fn () => nominal_datatype2 opt_thms_name dts bn_funs bn_eqs bclauses' lthy |> snd)
 end
 *}