# HG changeset patch
# User Christian Urban <urbanc@in.tum.de>
# Date 1283060163 -28800
# Node ID 9ffee4eb1ae10aa4b7c2d8c42b993a77e7274dde
# Parent  2f47291b6ff91a246cfeb7eab3607b8fc58fda3e
renamed NewParser to Nominal2

diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 IsaMakefile
--- a/IsaMakefile	Sun Aug 29 12:17:25 2010 +0800
+++ b/IsaMakefile	Sun Aug 29 13:36:03 2010 +0800
@@ -4,7 +4,7 @@
 default: test
 images: 
 
-all: test paper pearl pearl-jv qpaper
+all: tests paper pearl pearl-jv qpaper
 
 
 ## global settings
@@ -18,7 +18,7 @@
 
 ## Nominal2
 
-test: $(LOG)/HOL-Nominal2.gz
+tests: $(LOG)/HOL-Nominal2.gz
 
 $(LOG)/HOL-Nominal2.gz: Nominal/ROOT.ML Nominal/*.thy
 	@cd Nominal; $(USEDIR) -b -d "" HOL Nominal
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/Classical.thy
--- a/Nominal/Ex/Classical.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/Classical.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory Classical
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 (* example from my Urban's PhD *)
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/CoreHaskell.thy
--- a/Nominal/Ex/CoreHaskell.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/CoreHaskell.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory CoreHaskell
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 (* Core Haskell *)
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/Ex1.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/Ex1.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -0,0 +1,34 @@
+theory Ex1
+imports "../Nominal2"
+begin
+
+(* free names in bar are bound in foo *)
+
+atom_decl name
+
+nominal_datatype foo =
+  Foo0 "name"
+| 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
+binder
+  bv
+where
+  "bv (Bar0 x) = {}"
+| "bv (Bar1 v x b) = {atom v}"
+
+
+thm foo_bar.fv_defs[no_vars] foo_bar.bn_defs[no_vars]
+
+lemma
+  "fv_foo (Foo1 (Bar1 v x (Bar0 x)) (Foo0 v)) = {}"
+apply(simp only: foo_bar.fv_defs)
+apply(simp only: foo_bar.bn_defs)
+apply(simp only: supp_at_base)
+apply(simp)
+done
+
+end
+
+
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/ExPS3.thy
--- a/Nominal/Ex/ExPS3.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/ExPS3.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory ExPS3
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 (* example 3 from Peter Sewell's bestiary *)
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/ExPS7.thy
--- a/Nominal/Ex/ExPS7.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/ExPS7.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,6 +1,5 @@
-
 theory ExPS7
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 (* example 7 from Peter Sewell's bestiary *)
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/ExPS8.thy
--- a/Nominal/Ex/ExPS8.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/ExPS8.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory ExPS8
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 (* example 8 from Peter Sewell's bestiary *)
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/LF.thy
--- a/Nominal/Ex/LF.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/LF.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory LF
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 declare [[STEPS = 100]]
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/Lambda.thy
--- a/Nominal/Ex/Lambda.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/Lambda.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory Lambda
-imports "../NewParser" 
+imports "../Nominal2" 
 begin
 
 atom_decl name
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/Let.thy
--- a/Nominal/Ex/Let.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/Let.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory Let
-imports "../NewParser" 
+imports "../Nominal2" 
 begin
 
 text {* example 3 or example 5 from Terms.thy *}
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/LetFun.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Ex/LetFun.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -0,0 +1,25 @@
+theory LetFun
+imports "../Nominal2"
+begin
+
+atom_decl name
+
+(* x is bound in both e1 and e2
+   names in p are bound only in e1 *)
+
+nominal_datatype exp =
+  Var name
+| Pair exp exp
+| LetRec x::name p::pat e1::exp e2::exp  bind x in e2, bind x "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"
+
+end
\ No newline at end of file
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/LetPat.thy
--- a/Nominal/Ex/LetPat.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/LetPat.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory LetPat
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 declare [[STEPS = 100]]
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/LetRec.thy
--- a/Nominal/Ex/LetRec.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/LetRec.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory LetRec
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 atom_decl name
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/LetRec2.thy
--- a/Nominal/Ex/LetRec2.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/LetRec2.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory LetRec2
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 atom_decl name
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/Modules.thy
--- a/Nominal/Ex/Modules.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/Modules.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory Modules
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 (* example from Leroy'96 about modules; 
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/NoneExamples.thy
--- a/Nominal/Ex/NoneExamples.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/NoneExamples.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,85 +1,80 @@
 theory NoneExamples
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
+text {*
+  This example is not covered by our binding 
+  specification.
+*}
+
 atom_decl name
 
-
 text {* 
   "Weirdo" example from Peter Sewell's bestiary. 
 
-  This example is not covered by our binding 
-  specification.
-
+  p2 occurs in two bodies
 *}
 
+(*
 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"
+text {* 
+  this example binds bound names and therefore the 
+  fv-function is not respectful - the proof just fails.
+*}
 
-
-(* this example binds bound names and
-   so is not respectful *)
 (*
 nominal_datatype trm =
-  Vr "name"
-| Lm x::"name" t::"trm"         bind x in t
-| Lt left::"trm" right::"trm"   bind "bv left" in right
+  Var "name"
+| Lam x::"name" t::"trm"         bind x in t
+| Let left::"trm" right::"trm"   bind (set) "bv left" in right
 binder
   bv
 where
-  "bv (Vr n) = {}"
-| "bv (Lm n t) = {atom n} \<union> bv t"
-| "bv (Lt l r) = bv l \<union> bv r"
+  "bv (Var n) = {}"
+| "bv (Lam n t) = {atom n} \<union> bv t"
+| "bv (Let l r) = bv l \<union> bv r"
 *)
 
-(* this example uses "-" in the binding function; 
-   at the moment this is unsupported *)
+text {* 
+  this example uses "-" in the binding function; 
+  at the moment this is unsupported 
+*}
+
 (*
 nominal_datatype trm' =
-  Vr' "name"
-| Lm' l::"name" r::"trm'"   bind l in r
-| Lt' l::"trm'" r::"trm'"   bind "bv' l" in r
+  Var "name"
+| Lam l::"name" r::"trm'"   bind l in r
+| Let l::"trm'" r::"trm'"   bind (set) "bv' l" in r
 binder
   bv'
 where
-  "bv' (Vr' n) = {atom n}"
-| "bv' (Lm' n t) = bv' t - {atom n}"
-| "bv' (Lt' l r) = bv' l \<union> bv' r"
+  "bv' (Var n) = {atom n}"
+| "bv' (Lam n t) = bv' t - {atom n}"
+| "bv' (Let l r) = bv' l \<union> bv' r"
 *)
 
-(* this example again binds bound names  *)
+text {* 
+  again this example binds bound names - so not respectful
+*}
+
 (*
-nominal_datatype trm'' =
-  Va'' "name"
-| Lm'' n::"name" l::"trm''" bind n in l
-and bla'' =
-  Bla'' f::"trm''" s::"trm''" bind "bv'' f" in s
+nominal_datatype trm =
+  Var "name"
+| Lam n::"name" l::"trm" bind n in l
+and bla =
+  Bla f::"trm" s::"trm" bind (set) "bv f" in s
 binder
-  bv''
+  bv :: "trm \<Rightarrow> atom set"
 where
-  "bv'' (Vm'' x) = {}"
-| "bv'' (Lm'' x b) = {atom x}"
+  "bv (Vam x) = {}"
+| "bv (Lam x b) = {atom x}"
 *)
 
 end
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/SingleLet.thy
--- a/Nominal/Ex/SingleLet.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/SingleLet.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory SingleLet
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 atom_decl name
@@ -38,17 +38,19 @@
 
 
 
-
+(*
 lemma test: 
   "(\<exists>p. (bs, x) \<approx>lst (op=) f p (cs, y)) \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>lst (op=) supp p (cs, y))"
-sorry
+oops
 
 lemma Abs_eq_iff:
   shows "Abs bs x = Abs cs y \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>gen (op =) supp p (cs, y))"
   and   "Abs_res bs x = Abs_res cs y \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>res (op =) supp p (cs, y))"
   and   "Abs_lst bsl x = Abs_lst csl y \<longleftrightarrow> (\<exists>p. (bsl, x) \<approx>lst (op =) supp p (csl, y))"
   by (lifting alphas_abs)
+*)
 
+(*
 lemma supp_fv:
   "supp t = fv_trm t \<and> supp b = fv_bn b"
 apply(rule single_let.induct)
@@ -73,7 +75,7 @@
 apply(subst test)
 apply(rule refl)
 sorry
-
+*)
 (*
 consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm"
 consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg"
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/SingleLetFoo.thy
--- a/Nominal/Ex/SingleLetFoo.thy	Sun Aug 29 12:17:25 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,81 +0,0 @@
-theory SingleLetFoo
-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 a::"assg" t::"trm"  bind_set "bn a" in t
-| Foo1 a1::"assg" a2::"assg" t::"trm" bind_set "bn a1" "bn a2" in t
-| Foo2 x::name a::"assg" t::"trm" bind_set x "bn a" in t
-
-and assg =
-  As "name" "trm"
-binder
-  bn::"assg \<Rightarrow> atom set"
-where
-  "bn (As x t) = {atom x}"
-
-thm trm_assg.distinct
-thm trm_assg.eq_iff
-thm trm_assg.supp
-thm trm_assg.perm
-thm trm_assg.fv[simplified trm_assg.supp(1-2),no_vars]
-
-thm permute_trm_raw_permute_assg_raw.simps
-thm fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps[no_vars]
-
-thm alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros[no_vars]
-
-
-lemmas all = alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros
-
-lemma test: "p \<bullet> bn_raw \<equiv> bn_raw" sorry
-
-lemma
-  assumes "distinct [x,y, z, u]"
-  shows "alpha_trm_raw (Foo2_raw z (As_raw x (Var_raw z)) (Var_raw z))
-                       (Foo2_raw u (As_raw y (Var_raw z)) (Var_raw u))"
-using assms
-apply(rule_tac all)
-apply(rule_tac x="(z \<leftrightarrow> u) + (x \<leftrightarrow> y)" in exI)
-apply(simp only: alphas)
-apply(rule conjI)
-apply(simp)
-apply(simp add: supp_at_base fresh_star_def)
-apply(rule conjI)
-apply(simp add: supp_at_base fresh_star_def)
-apply(rule conjI)
-apply(simp)
-apply(rule all)
-apply(simp)
-unfolding flip_def
-apply(perm_simp add: test)
-unfolding flip_def[symmetric]
-apply(simp)
-apply(subst flip_at_base_simps(3))
-apply(auto)[2]
-apply(simp)
-apply(rule all)
-apply(rule all)
-apply(simp)
-done
-
-lemma
-  assumes "distinct [x,y,z,u]"
-  shows "fv_trm_raw (Foo2_raw z (As_raw x (Var_raw z)) (Var_raw z)) = {atom z}"
-using assms
-apply(simp add: supp_at_base)
-done
-
-
-end
-
-
-
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/Term8.thy
--- a/Nominal/Ex/Term8.thy	Sun Aug 29 12:17:25 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,27 +0,0 @@
-theory Term8
-imports "../NewParser"
-begin
-
-(* example 8 *)
-
-atom_decl name
-
-nominal_datatype foo =
-  Foo0 "name"
-| 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
-binder
-  bv
-where
-  "bv (Bar0 x) = {}"
-| "bv (Bar1 v x b) = {atom v}"
-
-(*
-thm foo_bar.supp
-*)
-
-end
-
-
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/TypeSchemes.thy
--- a/Nominal/Ex/TypeSchemes.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/TypeSchemes.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory TypeSchemes
-imports "../NewParser"
+imports "../Nominal2"
 begin
 
 section {*** Type Schemes ***}
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Ex/TypeVarsTest.thy
--- a/Nominal/Ex/TypeVarsTest.thy	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/Ex/TypeVarsTest.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -1,5 +1,5 @@
 theory TypeVarsTest
-imports "../NewParser" 
+imports "../Nominal2" 
 begin
 
 atom_decl name
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/NewParser.thy
--- a/Nominal/NewParser.thy	Sun Aug 29 12:17:25 2010 +0800
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,811 +0,0 @@
-theory NewParser
-imports 
-  "../Nominal-General/Nominal2_Base" 
-  "../Nominal-General/Nominal2_Eqvt" 
-  "../Nominal-General/Nominal2_Supp" 
-  "Nominal2_FSet"
-  "Abs"
-uses ("nominal_dt_rawperm.ML")
-     ("nominal_dt_rawfuns.ML")
-     ("nominal_dt_alpha.ML")
-     ("nominal_dt_quot.ML")
-     ("nominal_dt_supp.ML")
-begin
-
-use "nominal_dt_rawperm.ML"
-ML {* open Nominal_Dt_RawPerm *}
-
-use "nominal_dt_rawfuns.ML"
-ML {* open Nominal_Dt_RawFuns *}
-
-use "nominal_dt_alpha.ML"
-ML {* open Nominal_Dt_Alpha *}
-
-use "nominal_dt_quot.ML"
-ML {* open Nominal_Dt_Quot *}
-
-use "nominal_dt_supp.ML"
-ML {* open Nominal_Dt_Supp *}
-
-section{* Interface for nominal_datatype *}
-
-ML {*
-(* attributes *)
-val eqvt_attr = Attrib.internal (K Nominal_ThmDecls.eqvt_add)
-val rsp_attr = Attrib.internal (K Quotient_Info.rsp_rules_add)
-val simp_attr = Attrib.internal (K Simplifier.simp_add)
-
-*}
-
-ML {* print_depth 50 *}
-
-ML {*
-fun get_cnstrs dts =
-  map (fn (_, _, _, constrs) => constrs) dts
-
-fun get_typed_cnstrs dts =
-  flat (map (fn (_, bn, _, constrs) => 
-   (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)
-
-fun get_cnstr_strs dts =
-  map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts))
-
-fun get_bn_fun_strs bn_funs =
-  map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs
-*}
-
-
-text {* Infrastructure for adding "_raw" to types and terms *}
-
-ML {*
-fun add_raw s = s ^ "_raw"
-fun add_raws ss = map add_raw ss
-fun raw_bind bn = Binding.suffix_name "_raw" bn
-
-fun replace_str ss s = 
-  case (AList.lookup (op=) ss s) of 
-     SOME s' => s'
-   | NONE => s
-
-fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)
-  | replace_typ ty_ss T = T  
-
-fun raw_dts ty_ss dts =
-let
-  fun raw_dts_aux1 (bind, tys, mx) =
-    (raw_bind bind, map (replace_typ ty_ss) tys, mx)
-
-  fun raw_dts_aux2 (ty_args, bind, mx, constrs) =
-    (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)
-in
-  map raw_dts_aux2 dts
-end
-
-fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)
-  | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)
-  | replace_aterm trm_ss trm = trm
-
-fun replace_term trm_ss ty_ss trm =
-  trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) 
-*}
-
-ML {*
-fun rawify_dts dt_names dts dts_env =
-let
-  val raw_dts = raw_dts dts_env dts
-  val raw_dt_names = add_raws dt_names
-in
-  (raw_dt_names, raw_dts)
-end 
-*}
-
-ML {*
-fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs =
-let
-  val bn_funs' = map (fn (bn, ty, mx) => 
-    (raw_bind bn, SOME (replace_typ dts_env ty), mx)) bn_funs
-  
-  val bn_eqs' = map (fn (attr, trm) => 
-    (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs
-in
-  (bn_funs', bn_eqs') 
-end 
-*}
-
-ML {* 
-fun rawify_bclauses dts_env cnstrs_env bn_fun_env bclauses =
-let
-  fun rawify_bnds bnds = 
-    map (apfst (Option.map (replace_term (cnstrs_env @ bn_fun_env) dts_env))) bnds
-
-  fun rawify_bclause (BC (mode, bnds, bdys)) = BC (mode, rawify_bnds bnds, bdys)
-in
-  map (map (map rawify_bclause)) bclauses
-end
-*}
-
-(* strip_bn_fun takes a rhs of a bn function: this can only contain unions or
-   appends of elements; in case of recursive calls it retruns also the applied
-   bn function *)
-ML {*
-fun strip_bn_fun lthy args t =
-let 
-  fun aux t =
-    case t of
-      Const (@{const_name sup}, _) $ l $ r => aux l @ aux r
-    | Const (@{const_name append}, _) $ l $ r => aux l @ aux r
-    | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ (x as Var _)) $ y =>
-        (find_index (equal x) args, NONE) :: aux y
-    | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ (x as Var _)) $ y =>
-        (find_index (equal x) args, NONE) :: aux y
-    | Const (@{const_name bot}, _) => []
-    | Const (@{const_name Nil}, _) => []
-    | (f as Const _) $ (x as Var _) => [(find_index (equal x) args, SOME f)]
-    | _ => error ("Unsupported binding function: " ^ (Syntax.string_of_term lthy t))
-in
-  aux t
-end  
-*}
-
-ML {*
-(** definition of the raw binding functions **)
-
-(* TODO: needs cleaning *)
-fun find [] _ = error ("cannot find element")
-  | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y
-
-fun prep_bn_info lthy dt_names dts eqs = 
-let
-  fun aux eq = 
-  let
-    val (lhs, rhs) = eq
-      |> HOLogic.dest_Trueprop
-      |> HOLogic.dest_eq
-    val (bn_fun, [cnstr]) = strip_comb lhs
-    val (_, ty) = dest_Const bn_fun
-    val (ty_name, _) = dest_Type (domain_type ty)
-    val dt_index = find_index (fn x => x = ty_name) dt_names
-    val (cnstr_head, cnstr_args) = strip_comb cnstr    
-    val rhs_elements = strip_bn_fun lthy cnstr_args rhs
-  in
-    (dt_index, (bn_fun, (cnstr_head, rhs_elements)))
-  end
-  fun order dts i ts = 
-  let
-    val dt = nth dts i
-    val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt)
-    val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts
-  in
-    map (find ts') cts
-  end
-
-  val unordered = AList.group (op=) (map aux eqs)
-  val unordered' = map (fn (x, y) =>  (x, AList.group (op=) y)) unordered
-  val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered' 
-  val ordered' = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) ordered)
-
-  (*val _ = tracing ("eqs\n" ^ cat_lines (map (Syntax.string_of_term lthy) eqs))*)
-  (*val _ = tracing ("map eqs\n" ^ @{make_string} (map aux2 eqs))*)
-  (*val _ = tracing ("ordered'\n" ^ @{make_string} ordered')*)
-in
-  ordered'
-end
-
-
-fun define_raw_bns dt_names dts raw_bn_funs raw_bn_eqs constr_thms size_thms lthy =
-  if null raw_bn_funs 
-  then ([], [], [], [], lthy)
-  else 
-    let
-      val (_, lthy1) = Function.add_function raw_bn_funs raw_bn_eqs
-        Function_Common.default_config (pat_completeness_simp constr_thms) lthy
-
-      val (info, lthy2) = prove_termination size_thms (Local_Theory.restore lthy1)
-      val {fs, simps, inducts, ...} = info
-
-      val raw_bn_induct = (the inducts)
-      val raw_bn_eqs = the simps
-
-      val raw_bn_info = 
-        prep_bn_info lthy dt_names dts (map prop_of raw_bn_eqs)
-    in
-      (fs, raw_bn_eqs, raw_bn_info, raw_bn_induct, lthy2)
-    end
-*}
-
-ML {*
-fun define_raw_dts dts bn_funs bn_eqs binds lthy =
-let
-  val thy = Local_Theory.exit_global lthy
-  val thy_name = Context.theory_name thy
-
-  val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts
-  val dt_full_names = map (Long_Name.qualify thy_name) dt_names 
-  val dt_full_names' = add_raws dt_full_names
-  val dts_env = dt_full_names ~~ dt_full_names'
-
-  val cnstrs = get_cnstr_strs dts
-  val cnstrs_ty = get_typed_cnstrs dts
-  val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs
-  val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name 
-    (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty
-  val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names'
-
-  val bn_fun_strs = get_bn_fun_strs bn_funs
-  val bn_fun_strs' = add_raws bn_fun_strs
-  val bn_fun_env = bn_fun_strs ~~ bn_fun_strs'
-  val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name)) 
-    (bn_fun_strs ~~ bn_fun_strs')
-  
-  val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env
-  val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs 
-  val raw_bclauses = rawify_bclauses dts_env cnstrs_env bn_fun_full_env binds 
-
-  val (raw_dt_full_names, thy1) = 
-    Datatype.add_datatype Datatype.default_config raw_dt_names raw_dts thy
-
-  val lthy1 = Named_Target.theory_init thy1
-in
-  (raw_dt_full_names, raw_dts, raw_bclauses, raw_bn_funs, raw_bn_eqs, lthy1)
-end
-*}
-
-
-ML {*
-(* for testing porposes - to exit the procedure early *)
-exception TEST of Proof.context
-
-val (STEPS, STEPS_setup) = Attrib.config_int "STEPS" (K 100);
-
-fun get_STEPS ctxt = Config.get ctxt STEPS
-*}
-
-setup STEPS_setup
-
-ML {*
-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";
-  val (raw_dt_names, raw_dts, raw_bclauses, raw_bn_funs, raw_bn_eqs, lthy0) =
-    if get_STEPS lthy > 0 
-    then define_raw_dts dts bn_funs bn_eqs bclauses lthy
-    else raise TEST lthy
-
-  val dtinfo = Datatype.the_info (ProofContext.theory_of lthy0) (hd raw_dt_names)
-  val {descr, sorts, ...} = dtinfo
-
-  val raw_tys = all_dtyps descr sorts
-  val raw_full_ty_names = map (fst o dest_Type) raw_tys
-  val tvs = hd raw_tys
-    |> snd o dest_Type
-    |> map dest_TFree  
-
-  val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy0)) raw_full_ty_names  
- 
-  val raw_cns_info = all_dtyp_constrs_types descr sorts
-  val raw_constrs = flat (map (map (fn (c, _, _, _) => c)) raw_cns_info)
-
-  val raw_inject_thms = flat (map #inject dtinfos)
-  val raw_distinct_thms = flat (map #distinct dtinfos)
-  val raw_induct_thm = #induct dtinfo
-  val raw_induct_thms = #inducts dtinfo
-  val raw_exhaust_thms = map #exhaust dtinfos
-  val raw_size_trms = map size_const raw_tys
-  val raw_size_thms = Size.size_thms (ProofContext.theory_of lthy0) (hd raw_dt_names)
-    |> `(fn thms => (length thms) div 2)
-    |> uncurry drop
-  
-  (* definitions of raw permutations by primitive recursion *)
-  val _ = warning "Definition of raw permutations";
-  val ((raw_perm_funs, raw_perm_simps, raw_perm_laws), lthy2a) =
-    if get_STEPS lthy0 > 1 
-    then define_raw_perms raw_full_ty_names raw_tys tvs raw_constrs raw_induct_thm lthy0
-    else raise TEST lthy0
- 
-  (* noting the raw permutations as eqvt theorems *)
-  val (_, lthy3) = Local_Theory.note ((Binding.empty, [eqvt_attr]), raw_perm_simps) lthy2a
-
-  (* definition of raw fv_functions *)
-  val _ = warning "Definition of raw fv-functions";
-  val (raw_bns, raw_bn_defs, raw_bn_info, raw_bn_induct, lthy3a) =
-    if get_STEPS lthy3 > 2 
-    then define_raw_bns raw_full_ty_names raw_dts raw_bn_funs raw_bn_eqs 
-      (raw_inject_thms @ raw_distinct_thms) raw_size_thms lthy3
-    else raise TEST lthy3
-
-  val (raw_fvs, raw_fv_bns, raw_fv_defs, raw_fv_bns_induct, lthy3b) = 
-    if get_STEPS lthy3a > 3 
-    then define_raw_fvs raw_full_ty_names raw_tys raw_cns_info raw_bn_info raw_bclauses 
-      (raw_inject_thms @ raw_distinct_thms) raw_size_thms lthy3a
-    else raise TEST lthy3a
-
-  (* definition of raw alphas *)
-  val _ = warning "Definition of alphas";
-  val (alpha_trms, alpha_bn_trms, alpha_intros, alpha_cases, alpha_induct, lthy4) =
-    if get_STEPS lthy3b > 4 
-    then define_raw_alpha raw_full_ty_names raw_tys raw_cns_info raw_bn_info raw_bclauses raw_fvs lthy3b
-    else raise TEST lthy3b
-  val alpha_tys = map (domain_type o fastype_of) alpha_trms  
-
-  (* definition of alpha-distinct lemmas *)
-  val _ = warning "Distinct theorems";
-  val alpha_distincts = 
-    mk_alpha_distincts lthy4 alpha_cases raw_distinct_thms alpha_trms raw_tys
-
-  (* definition of alpha_eq_iff  lemmas *)
-  (* they have a funny shape for the simplifier ---- CHECK WHETHER NEEDED*)
-  val _ = warning "Eq-iff theorems";
-  val (alpha_eq_iff_simps, alpha_eq_iff) = 
-    if get_STEPS lthy > 5
-    then mk_alpha_eq_iff lthy4 alpha_intros raw_distinct_thms raw_inject_thms alpha_cases
-    else raise TEST lthy4
-
-  (* proving equivariance lemmas for bns, fvs, size and alpha *)
-  val _ = warning "Proving equivariance";
-  val raw_bn_eqvt = 
-    if get_STEPS lthy > 6
-    then raw_prove_eqvt raw_bns raw_bn_induct (raw_bn_defs @ raw_perm_simps) lthy4
-    else raise TEST lthy4
-
-  (* noting the raw_bn_eqvt lemmas in a temprorary theory *)
-  val lthy_tmp = snd (Local_Theory.note ((Binding.empty, [eqvt_attr]), raw_bn_eqvt) lthy4)
-
-  val raw_fv_eqvt = 
-    if get_STEPS lthy > 7
-    then raw_prove_eqvt (raw_fvs @ raw_fv_bns) raw_fv_bns_induct (raw_fv_defs @ raw_perm_simps) 
-      (Local_Theory.restore lthy_tmp)
-    else raise TEST lthy4
-
-  val raw_size_eqvt = 
-    if get_STEPS lthy > 8
-    then raw_prove_eqvt raw_size_trms raw_induct_thms (raw_size_thms @ raw_perm_simps) 
-      (Local_Theory.restore lthy_tmp)
-      |> map (rewrite_rule @{thms permute_nat_def[THEN eq_reflection]})
-      |> map (fn thm => thm RS @{thm sym})
-    else raise TEST lthy4
- 
-  val lthy5 = snd (Local_Theory.note ((Binding.empty, [eqvt_attr]), raw_fv_eqvt) lthy_tmp)
-
-  val (alpha_eqvt, lthy6) =
-    if get_STEPS lthy > 9
-    then Nominal_Eqvt.equivariance true (alpha_trms @ alpha_bn_trms) alpha_induct alpha_intros lthy5
-    else raise TEST lthy4
-
-  (* proving alpha equivalence *)
-  val _ = warning "Proving equivalence"
-
-  val alpha_refl_thms = 
-    if get_STEPS lthy > 10
-    then raw_prove_refl alpha_trms alpha_bn_trms alpha_intros raw_induct_thm lthy6 
-    else raise TEST lthy6
-
-  val alpha_sym_thms = 
-    if get_STEPS lthy > 11
-    then raw_prove_sym (alpha_trms @ alpha_bn_trms) alpha_intros alpha_induct lthy6 
-    else raise TEST lthy6
-
-  val alpha_trans_thms = 
-    if get_STEPS lthy > 12
-    then raw_prove_trans (alpha_trms @ alpha_bn_trms) (raw_distinct_thms @ raw_inject_thms) 
-           alpha_intros alpha_induct alpha_cases lthy6
-    else raise TEST lthy6
-
-  val (alpha_equivp_thms, alpha_bn_equivp_thms) = 
-    if get_STEPS lthy > 13
-    then raw_prove_equivp alpha_trms alpha_bn_trms alpha_refl_thms alpha_sym_thms 
-       alpha_trans_thms lthy6
-    else raise TEST lthy6
-
-  (* proving alpha implies alpha_bn *)
-  val _ = warning "Proving alpha implies bn"
-
-  val alpha_bn_imp_thms = 
-    if get_STEPS lthy > 14
-    then raw_prove_bn_imp alpha_trms alpha_bn_trms alpha_intros alpha_induct lthy6 
-    else raise TEST lthy6
-  
-  (* respectfulness proofs *)
-  val raw_funs_rsp_aux = 
-    if get_STEPS lthy > 15
-    then raw_fv_bn_rsp_aux alpha_trms alpha_bn_trms raw_fvs 
-      raw_bns raw_fv_bns alpha_induct (raw_bn_defs @ raw_fv_defs) lthy6
-    else raise TEST lthy6 
-  
-  val raw_funs_rsp = 
-    if get_STEPS lthy > 16
-    then map mk_funs_rsp raw_funs_rsp_aux
-    else raise TEST lthy6 
-
-  val raw_size_rsp = 
-    if get_STEPS lthy > 17
-    then
-      raw_size_rsp_aux (alpha_trms @ alpha_bn_trms) alpha_induct 
-      (raw_size_thms @ raw_size_eqvt) lthy6
-      |> map mk_funs_rsp
-    else raise TEST lthy6 
-
-  val raw_constrs_rsp = 
-    if get_STEPS lthy > 18
-    then raw_constrs_rsp raw_constrs alpha_trms alpha_intros
-      (alpha_bn_imp_thms @ raw_funs_rsp_aux) lthy6 
-    else raise TEST lthy6 
-
-  val alpha_permute_rsp = 
-    if get_STEPS lthy > 19
-    then map mk_alpha_permute_rsp alpha_eqvt
-    else raise TEST lthy6 
-
-  val alpha_bn_rsp = 
-    if get_STEPS lthy > 20
-    then raw_alpha_bn_rsp alpha_bn_trms alpha_bn_equivp_thms alpha_bn_imp_thms
-    else raise TEST lthy6 
-
-  (* noting the quot_respects lemmas *)
-  val (_, lthy6a) = 
-    if get_STEPS lthy > 21
-    then Local_Theory.note ((Binding.empty, [rsp_attr]),
-      raw_constrs_rsp @ raw_funs_rsp @ raw_size_rsp @ alpha_permute_rsp @ alpha_bn_rsp) lthy6
-    else raise TEST lthy6
-
-  (* defining the quotient type *)
-  val _ = warning "Declaring the quotient types"
-  val qty_descr = map (fn (vs, bind, mx, _) => (vs, bind, mx)) dts
-     
-  val (qty_infos, lthy7) = 
-    if get_STEPS lthy > 22
-    then define_qtypes qty_descr alpha_tys alpha_trms alpha_equivp_thms lthy6a
-    else raise TEST lthy6a
-
-  val qtys = map #qtyp qty_infos
-  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 = 
-    flat (map (fn (_, _, _, cs) => map (fn (b, _, mx) => (Name.of_binding b, mx)) cs) dts)
-    |> map2 (fn t => fn (b, mx) => (b, t, mx)) raw_constrs
-
-  val qbns_descr =
-    map2 (fn (b, _, mx) => fn t => (Name.of_binding b, t, mx)) bn_funs raw_bns
-
-  val qfvs_descr = 
-    map2 (fn n => fn t => ("fv_" ^ n, t, NoSyn)) qty_names raw_fvs
-
-  val qfv_bns_descr = 
-    map2 (fn (b, _, _) => fn t => ("fv_" ^ Name.of_binding b, t, NoSyn)) bn_funs raw_fv_bns
-
-  val qalpha_bns_descr = 
-    map2 (fn (b, _, _) => fn t => ("alpha_" ^ Name.of_binding b, t, NoSyn)) bn_funs  alpha_bn_trms
-
-  val qperm_descr =
-    map2 (fn n => fn t => ("permute_" ^ n, Type.legacy_freeze t, NoSyn)) qty_names raw_perm_funs
-
-  val qsize_descr =
-    map2 (fn n => fn t => ("size_" ^ n, t, NoSyn)) qty_names raw_size_trms
-
-  val (((((qconstrs_info, qbns_info), qfvs_info), qfv_bns_info), qalpha_bns_info), lthy8) = 
-    if get_STEPS lthy > 23
-    then 
-      lthy7
-      |> define_qconsts qtys qconstrs_descr 
-      ||>> define_qconsts qtys qbns_descr 
-      ||>> define_qconsts qtys qfvs_descr
-      ||>> define_qconsts qtys qfv_bns_descr
-      ||>> define_qconsts qtys qalpha_bns_descr
-    else raise TEST lthy7
-
-  (* definition of the quotient permfunctions and pt-class *)
-  val lthy9 = 
-    if get_STEPS lthy > 24
-    then define_qperms qtys qty_full_names tvs qperm_descr raw_perm_laws lthy8 
-    else raise TEST lthy8
-  
-  val lthy9a = 
-    if get_STEPS lthy > 25
-    then define_qsizes qtys qty_full_names tvs qsize_descr lthy9
-    else raise TEST lthy9
-
-  val qtrms = map #qconst qconstrs_info
-  val qbns = map #qconst qbns_info
-  val qfvs = map #qconst qfvs_info
-  val qfv_bns = map #qconst qfv_bns_info
-  val qalpha_bns = map #qconst qalpha_bns_info
-
-  (* lifting of the theorems *)
-  val _ = warning "Lifting of Theorems"
-  
-  val eq_iff_simps = @{thms alphas permute_prod.simps prod_fv.simps prod_alpha_def prod_rel.simps
-    prod.cases} 
-
-  val ((((((qdistincts, qeq_iffs), qfv_defs), qbn_defs), qperm_simps), qfv_qbn_eqvts), lthyA) = 
-    if get_STEPS lthy > 26
-    then 
-      lthy9a    
-      |> lift_thms qtys [] alpha_distincts  
-      ||>> lift_thms qtys eq_iff_simps alpha_eq_iff       
-      ||>> lift_thms qtys [] raw_fv_defs
-      ||>> lift_thms qtys [] raw_bn_defs
-      ||>> lift_thms qtys [] raw_perm_simps
-      ||>> lift_thms qtys [] (raw_fv_eqvt @ raw_bn_eqvt)
-    else raise TEST lthy9a
-
-  val (((qsize_eqvt, [qinduct]), qexhausts), lthyB) = 
-    if get_STEPS lthy > 27
-    then
-      lthyA 
-      |> lift_thms qtys [] raw_size_eqvt
-      ||>> lift_thms qtys [] [raw_induct_thm]
-      ||>> lift_thms qtys [] raw_exhaust_thms
-    else raise TEST lthyA
-
-  (* supports lemmas *) 
-  val qsupports_thms =
-    if get_STEPS lthy > 28
-    then prove_supports lthyB qperm_simps qtrms
-    else raise TEST lthyB
-
-  (* finite supp lemmas *)
-  val qfsupp_thms =
-    if get_STEPS lthy > 29
-    then prove_fsupp lthyB qtys qinduct qsupports_thms
-    else raise TEST lthyB
-
-  (* fs instances *)
-  val lthyC =
-    if get_STEPS lthy > 30
-    then fs_instance qtys qty_full_names tvs qfsupp_thms lthyB
-    else raise TEST lthyB
-
-  (* 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') = lthyC
-     |> 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", [eqvt_attr, simp_attr]), 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)
-     ||>> Local_Theory.note ((thms_suffix "supports", []), qsupports_thms)
-     ||>> Local_Theory.note ((thms_suffix "fsupp", []), qfsupp_thms)
-in
-  (0, lthy9')
-end handle TEST ctxt => (0, ctxt)
-*}
-
-section {* Preparing and parsing of the specification *}
-
-ML {* 
-(* generates the parsed datatypes and 
-   declares the constructors 
-*)
-fun prepare_dts dt_strs thy = 
-let
-  fun inter_fs_sort thy (a, S) = 
-    (a, Type.inter_sort (Sign.tsig_of thy) (@{sort fs}, S)) 
-
-  fun mk_type tname sorts (cname, cargs, mx) =
-  let
-    val full_tname = Sign.full_name thy tname
-    val ty = Type (full_tname, map (TFree o inter_fs_sort thy) sorts)
-  in
-    (cname, cargs ---> ty, mx)
-  end
-
-  fun prep_constr (cname, cargs, mx, _) (constrs, sorts) =
-  let 
-    val (cargs', sorts') = 
-      fold_map (Datatype.read_typ thy) (map snd cargs) sorts
-      |>> map (map_type_tfree (TFree o inter_fs_sort thy)) 
-  in 
-    (constrs @ [(cname, cargs', mx)], sorts') 
-  end
-  
-  fun prep_dts (tvs, tname, mx, constrs) (constr_trms, dts, sorts) =
-  let 
-    val (constrs', sorts') = 
-      fold prep_constr constrs ([], sorts)
-
-    val constr_trms' = 
-      map (mk_type tname (rev sorts')) constrs'
-  in 
-    (constr_trms @ constr_trms', dts @ [(tvs, tname, mx, constrs')], sorts') 
-  end
-
-  val (constr_trms, dts, sorts) = fold prep_dts dt_strs ([], [], []);
-in
-  thy
-  |> Sign.add_consts_i constr_trms
-  |> pair dts
-end
-*}
-
-ML {*
-(* parsing the binding function specification and *)
-(* declaring the functions in the local theory    *)
-fun prepare_bn_funs bn_fun_strs bn_eq_strs thy =
-let
-  val lthy = Named_Target.theory_init thy
-
-  val ((bn_funs, bn_eqs), lthy') = 
-    Specification.read_spec bn_fun_strs bn_eq_strs lthy
-
-  fun prep_bn_fun ((bn, T), mx) = (bn, T, mx) 
-  
-  val bn_funs' = map prep_bn_fun bn_funs
-in
-  (Local_Theory.exit_global lthy')
-  |> Sign.add_consts_i bn_funs'
-  |> pair (bn_funs', bn_eqs) 
-end 
-*}
-
-text {* associates every SOME with the index in the list; drops NONEs *}
-ML {*
-fun indexify xs =
-let
-  fun mapp _ [] = []
-    | mapp i (NONE :: xs) = mapp (i + 1) xs
-    | mapp i (SOME x :: xs) = (x, i) :: mapp (i + 1) xs
-in 
-  mapp 0 xs 
-end
-
-fun index_lookup xs x =
-  case AList.lookup (op=) xs x of
-    SOME x => x
-  | NONE => error ("Cannot find " ^ x ^ " as argument annotation.");
-*}
-
-ML {*
-fun prepare_bclauses dt_strs thy = 
-let
-  val annos_bclauses =
-    get_cnstrs dt_strs
-    |> map (map (fn (_, antys, _, bns) => (map fst antys, bns)))
-
-  fun prep_binder env bn_str =
-    case (Syntax.read_term_global thy bn_str) of
-      Free (x, _) => (NONE, index_lookup env x)
-    | Const (a, T) $ Free (x, _) => (SOME (Const (a, T)), index_lookup env x)
-    | _ => error ("The term " ^ bn_str ^ " is not allowed as binding function.")
- 
-  fun prep_body env bn_str = index_lookup env bn_str
-
-  fun prep_bclause env (mode, binders, bodies) = 
-  let
-    val binders' = map (prep_binder env) binders
-    val bodies' = map (prep_body env) bodies
-  in  
-    BC (mode, binders', bodies')
-  end
-
-  fun prep_bclauses (annos, bclause_strs) = 
-  let
-    val env = indexify annos (* for every label, associate the index *)
-  in
-    map (prep_bclause env) bclause_strs
-  end
-in
-  (map (map prep_bclauses) annos_bclauses, thy)
-end
-*}
-
-text {* 
-  adds an empty binding clause for every argument
-  that is not already part of a binding clause
-*}
-
-ML {*
-fun included i bcs = 
-let
-  fun incl (BC (_, bns, bds)) = 
-    member (op =) (map snd bns) i orelse member (op =) bds i
-in
-  exists incl bcs 
-end
-*}
-
-ML {* 
-fun complete dt_strs bclauses = 
-let
-  val args = 
-    get_cnstrs dt_strs
-    |> map (map (fn (_, antys, _, _) => length antys))
-
-  fun complt n bcs = 
-  let
-    fun add bcs i = (if included i bcs then [] else [BC (Lst, [], [i])]) 
-  in
-    bcs @ (flat (map_range (add bcs) n))
-  end
-in
-  map2 (map2 complt) args bclauses
-end
-*}
-
-ML {*
-fun nominal_datatype2_cmd (opt_thms_name, dt_strs, bn_fun_strs, bn_eq_strs) lthy = 
-let
-  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  
-  val tmp_thy = Theory.copy thy 
-
-  val (((dts, (bn_funs, bn_eqs)), bclauses), tmp_thy') = 
-    tmp_thy
-    |> Sign.add_types pre_typs
-    |> prepare_dts dt_strs 
-    ||>> prepare_bn_funs bn_fun_strs bn_eq_strs 
-    ||>> prepare_bclauses dt_strs 
-
-  val bclauses' = complete dt_strs bclauses
-in
-  timeit (fn () => nominal_datatype2 opt_thms_name dts bn_funs bn_eqs bclauses' lthy |> snd)
-end
-*}
-
-ML {* 
-(* nominal datatype parser *)
-local
-  structure P = Parse;
-  structure S = Scan
-
-  fun triple ((x, y), z) = (x, y, z)
-  fun tuple1 ((x, y, z), u) = (x, y, z, u)
-  fun tuple2 (((x, y), z), u) = (x, y, u, z)
-  fun tuple3 ((x, y), (z, u)) = (x, y, z, u)
-in
-
-val _ = Keyword.keyword "bind"
-
-val opt_name = Scan.option (P.binding --| Args.colon)
-
-val anno_typ = S.option (P.name --| P.$$$ "::") -- P.typ
-
-val bind_mode = P.$$$ "bind" |--
-  S.optional (Args.parens 
-    (Args.$$$ "list" >> K Lst || Args.$$$ "set" >> K Set || Args.$$$ "res" >> K Res)) Lst
-
-val bind_clauses = 
-  P.enum "," (bind_mode -- S.repeat1 P.term -- (P.$$$ "in" |-- S.repeat1 P.name) >> triple)
-
-val cnstr_parser =
-  P.binding -- S.repeat anno_typ -- bind_clauses -- P.opt_mixfix >> tuple2
-
-(* datatype parser *)
-val dt_parser =
-  (P.type_args -- P.binding -- P.opt_mixfix >> triple) -- 
-    (P.$$$ "=" |-- P.enum1 "|" cnstr_parser) >> tuple1
-
-(* binding function parser *)
-val bnfun_parser = 
-  S.optional (P.$$$ "binder" |-- P.fixes -- Parse_Spec.where_alt_specs) ([], [])
-
-(* main parser *)
-val main_parser =
-  opt_name -- P.and_list1 dt_parser -- bnfun_parser >> tuple3
-
-end
-
-(* Command Keyword *)
-val _ = Outer_Syntax.local_theory "nominal_datatype" "test" Keyword.thy_decl
-  (main_parser >> nominal_datatype2_cmd)
-*}
-
-
-end
-
-
-
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/Nominal2.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/Nominal2.thy	Sun Aug 29 13:36:03 2010 +0800
@@ -0,0 +1,811 @@
+theory Nominal2
+imports 
+  "../Nominal-General/Nominal2_Base" 
+  "../Nominal-General/Nominal2_Eqvt" 
+  "../Nominal-General/Nominal2_Supp" 
+  "Nominal2_FSet"
+  "Abs"
+uses ("nominal_dt_rawperm.ML")
+     ("nominal_dt_rawfuns.ML")
+     ("nominal_dt_alpha.ML")
+     ("nominal_dt_quot.ML")
+     ("nominal_dt_supp.ML")
+begin
+
+use "nominal_dt_rawperm.ML"
+ML {* open Nominal_Dt_RawPerm *}
+
+use "nominal_dt_rawfuns.ML"
+ML {* open Nominal_Dt_RawFuns *}
+
+use "nominal_dt_alpha.ML"
+ML {* open Nominal_Dt_Alpha *}
+
+use "nominal_dt_quot.ML"
+ML {* open Nominal_Dt_Quot *}
+
+use "nominal_dt_supp.ML"
+ML {* open Nominal_Dt_Supp *}
+
+section{* Interface for nominal_datatype *}
+
+ML {*
+(* attributes *)
+val eqvt_attr = Attrib.internal (K Nominal_ThmDecls.eqvt_add)
+val rsp_attr = Attrib.internal (K Quotient_Info.rsp_rules_add)
+val simp_attr = Attrib.internal (K Simplifier.simp_add)
+
+*}
+
+ML {* print_depth 50 *}
+
+ML {*
+fun get_cnstrs dts =
+  map (fn (_, _, _, constrs) => constrs) dts
+
+fun get_typed_cnstrs dts =
+  flat (map (fn (_, bn, _, constrs) => 
+   (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)
+
+fun get_cnstr_strs dts =
+  map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts))
+
+fun get_bn_fun_strs bn_funs =
+  map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs
+*}
+
+
+text {* Infrastructure for adding "_raw" to types and terms *}
+
+ML {*
+fun add_raw s = s ^ "_raw"
+fun add_raws ss = map add_raw ss
+fun raw_bind bn = Binding.suffix_name "_raw" bn
+
+fun replace_str ss s = 
+  case (AList.lookup (op=) ss s) of 
+     SOME s' => s'
+   | NONE => s
+
+fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)
+  | replace_typ ty_ss T = T  
+
+fun raw_dts ty_ss dts =
+let
+  fun raw_dts_aux1 (bind, tys, mx) =
+    (raw_bind bind, map (replace_typ ty_ss) tys, mx)
+
+  fun raw_dts_aux2 (ty_args, bind, mx, constrs) =
+    (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)
+in
+  map raw_dts_aux2 dts
+end
+
+fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)
+  | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)
+  | replace_aterm trm_ss trm = trm
+
+fun replace_term trm_ss ty_ss trm =
+  trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) 
+*}
+
+ML {*
+fun rawify_dts dt_names dts dts_env =
+let
+  val raw_dts = raw_dts dts_env dts
+  val raw_dt_names = add_raws dt_names
+in
+  (raw_dt_names, raw_dts)
+end 
+*}
+
+ML {*
+fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs =
+let
+  val bn_funs' = map (fn (bn, ty, mx) => 
+    (raw_bind bn, SOME (replace_typ dts_env ty), mx)) bn_funs
+  
+  val bn_eqs' = map (fn (attr, trm) => 
+    (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs
+in
+  (bn_funs', bn_eqs') 
+end 
+*}
+
+ML {* 
+fun rawify_bclauses dts_env cnstrs_env bn_fun_env bclauses =
+let
+  fun rawify_bnds bnds = 
+    map (apfst (Option.map (replace_term (cnstrs_env @ bn_fun_env) dts_env))) bnds
+
+  fun rawify_bclause (BC (mode, bnds, bdys)) = BC (mode, rawify_bnds bnds, bdys)
+in
+  map (map (map rawify_bclause)) bclauses
+end
+*}
+
+(* strip_bn_fun takes a rhs of a bn function: this can only contain unions or
+   appends of elements; in case of recursive calls it retruns also the applied
+   bn function *)
+ML {*
+fun strip_bn_fun lthy args t =
+let 
+  fun aux t =
+    case t of
+      Const (@{const_name sup}, _) $ l $ r => aux l @ aux r
+    | Const (@{const_name append}, _) $ l $ r => aux l @ aux r
+    | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ (x as Var _)) $ y =>
+        (find_index (equal x) args, NONE) :: aux y
+    | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ (x as Var _)) $ y =>
+        (find_index (equal x) args, NONE) :: aux y
+    | Const (@{const_name bot}, _) => []
+    | Const (@{const_name Nil}, _) => []
+    | (f as Const _) $ (x as Var _) => [(find_index (equal x) args, SOME f)]
+    | _ => error ("Unsupported binding function: " ^ (Syntax.string_of_term lthy t))
+in
+  aux t
+end  
+*}
+
+ML {*
+(** definition of the raw binding functions **)
+
+(* TODO: needs cleaning *)
+fun find [] _ = error ("cannot find element")
+  | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y
+
+fun prep_bn_info lthy dt_names dts eqs = 
+let
+  fun aux eq = 
+  let
+    val (lhs, rhs) = eq
+      |> HOLogic.dest_Trueprop
+      |> HOLogic.dest_eq
+    val (bn_fun, [cnstr]) = strip_comb lhs
+    val (_, ty) = dest_Const bn_fun
+    val (ty_name, _) = dest_Type (domain_type ty)
+    val dt_index = find_index (fn x => x = ty_name) dt_names
+    val (cnstr_head, cnstr_args) = strip_comb cnstr    
+    val rhs_elements = strip_bn_fun lthy cnstr_args rhs
+  in
+    (dt_index, (bn_fun, (cnstr_head, rhs_elements)))
+  end
+  fun order dts i ts = 
+  let
+    val dt = nth dts i
+    val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt)
+    val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts
+  in
+    map (find ts') cts
+  end
+
+  val unordered = AList.group (op=) (map aux eqs)
+  val unordered' = map (fn (x, y) =>  (x, AList.group (op=) y)) unordered
+  val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered' 
+  val ordered' = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) ordered)
+
+  (*val _ = tracing ("eqs\n" ^ cat_lines (map (Syntax.string_of_term lthy) eqs))*)
+  (*val _ = tracing ("map eqs\n" ^ @{make_string} (map aux2 eqs))*)
+  (*val _ = tracing ("ordered'\n" ^ @{make_string} ordered')*)
+in
+  ordered'
+end
+
+
+fun define_raw_bns dt_names dts raw_bn_funs raw_bn_eqs constr_thms size_thms lthy =
+  if null raw_bn_funs 
+  then ([], [], [], [], lthy)
+  else 
+    let
+      val (_, lthy1) = Function.add_function raw_bn_funs raw_bn_eqs
+        Function_Common.default_config (pat_completeness_simp constr_thms) lthy
+
+      val (info, lthy2) = prove_termination size_thms (Local_Theory.restore lthy1)
+      val {fs, simps, inducts, ...} = info
+
+      val raw_bn_induct = (the inducts)
+      val raw_bn_eqs = the simps
+
+      val raw_bn_info = 
+        prep_bn_info lthy dt_names dts (map prop_of raw_bn_eqs)
+    in
+      (fs, raw_bn_eqs, raw_bn_info, raw_bn_induct, lthy2)
+    end
+*}
+
+ML {*
+fun define_raw_dts dts bn_funs bn_eqs binds lthy =
+let
+  val thy = Local_Theory.exit_global lthy
+  val thy_name = Context.theory_name thy
+
+  val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts
+  val dt_full_names = map (Long_Name.qualify thy_name) dt_names 
+  val dt_full_names' = add_raws dt_full_names
+  val dts_env = dt_full_names ~~ dt_full_names'
+
+  val cnstrs = get_cnstr_strs dts
+  val cnstrs_ty = get_typed_cnstrs dts
+  val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs
+  val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name 
+    (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty
+  val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names'
+
+  val bn_fun_strs = get_bn_fun_strs bn_funs
+  val bn_fun_strs' = add_raws bn_fun_strs
+  val bn_fun_env = bn_fun_strs ~~ bn_fun_strs'
+  val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name)) 
+    (bn_fun_strs ~~ bn_fun_strs')
+  
+  val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env
+  val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs 
+  val raw_bclauses = rawify_bclauses dts_env cnstrs_env bn_fun_full_env binds 
+
+  val (raw_dt_full_names, thy1) = 
+    Datatype.add_datatype Datatype.default_config raw_dt_names raw_dts thy
+
+  val lthy1 = Named_Target.theory_init thy1
+in
+  (raw_dt_full_names, raw_dts, raw_bclauses, raw_bn_funs, raw_bn_eqs, lthy1)
+end
+*}
+
+
+ML {*
+(* for testing porposes - to exit the procedure early *)
+exception TEST of Proof.context
+
+val (STEPS, STEPS_setup) = Attrib.config_int "STEPS" (K 100);
+
+fun get_STEPS ctxt = Config.get ctxt STEPS
+*}
+
+setup STEPS_setup
+
+ML {*
+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";
+  val (raw_dt_names, raw_dts, raw_bclauses, raw_bn_funs, raw_bn_eqs, lthy0) =
+    if get_STEPS lthy > 0 
+    then define_raw_dts dts bn_funs bn_eqs bclauses lthy
+    else raise TEST lthy
+
+  val dtinfo = Datatype.the_info (ProofContext.theory_of lthy0) (hd raw_dt_names)
+  val {descr, sorts, ...} = dtinfo
+
+  val raw_tys = all_dtyps descr sorts
+  val raw_full_ty_names = map (fst o dest_Type) raw_tys
+  val tvs = hd raw_tys
+    |> snd o dest_Type
+    |> map dest_TFree  
+
+  val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy0)) raw_full_ty_names  
+ 
+  val raw_cns_info = all_dtyp_constrs_types descr sorts
+  val raw_constrs = flat (map (map (fn (c, _, _, _) => c)) raw_cns_info)
+
+  val raw_inject_thms = flat (map #inject dtinfos)
+  val raw_distinct_thms = flat (map #distinct dtinfos)
+  val raw_induct_thm = #induct dtinfo
+  val raw_induct_thms = #inducts dtinfo
+  val raw_exhaust_thms = map #exhaust dtinfos
+  val raw_size_trms = map size_const raw_tys
+  val raw_size_thms = Size.size_thms (ProofContext.theory_of lthy0) (hd raw_dt_names)
+    |> `(fn thms => (length thms) div 2)
+    |> uncurry drop
+  
+  (* definitions of raw permutations by primitive recursion *)
+  val _ = warning "Definition of raw permutations";
+  val ((raw_perm_funs, raw_perm_simps, raw_perm_laws), lthy2a) =
+    if get_STEPS lthy0 > 1 
+    then define_raw_perms raw_full_ty_names raw_tys tvs raw_constrs raw_induct_thm lthy0
+    else raise TEST lthy0
+ 
+  (* noting the raw permutations as eqvt theorems *)
+  val (_, lthy3) = Local_Theory.note ((Binding.empty, [eqvt_attr]), raw_perm_simps) lthy2a
+
+  (* definition of raw fv_functions *)
+  val _ = warning "Definition of raw fv-functions";
+  val (raw_bns, raw_bn_defs, raw_bn_info, raw_bn_induct, lthy3a) =
+    if get_STEPS lthy3 > 2 
+    then define_raw_bns raw_full_ty_names raw_dts raw_bn_funs raw_bn_eqs 
+      (raw_inject_thms @ raw_distinct_thms) raw_size_thms lthy3
+    else raise TEST lthy3
+
+  val (raw_fvs, raw_fv_bns, raw_fv_defs, raw_fv_bns_induct, lthy3b) = 
+    if get_STEPS lthy3a > 3 
+    then define_raw_fvs raw_full_ty_names raw_tys raw_cns_info raw_bn_info raw_bclauses 
+      (raw_inject_thms @ raw_distinct_thms) raw_size_thms lthy3a
+    else raise TEST lthy3a
+
+  (* definition of raw alphas *)
+  val _ = warning "Definition of alphas";
+  val (alpha_trms, alpha_bn_trms, alpha_intros, alpha_cases, alpha_induct, lthy4) =
+    if get_STEPS lthy3b > 4 
+    then define_raw_alpha raw_full_ty_names raw_tys raw_cns_info raw_bn_info raw_bclauses raw_fvs lthy3b
+    else raise TEST lthy3b
+  val alpha_tys = map (domain_type o fastype_of) alpha_trms  
+
+  (* definition of alpha-distinct lemmas *)
+  val _ = warning "Distinct theorems";
+  val alpha_distincts = 
+    mk_alpha_distincts lthy4 alpha_cases raw_distinct_thms alpha_trms raw_tys
+
+  (* definition of alpha_eq_iff  lemmas *)
+  (* they have a funny shape for the simplifier ---- CHECK WHETHER NEEDED*)
+  val _ = warning "Eq-iff theorems";
+  val (alpha_eq_iff_simps, alpha_eq_iff) = 
+    if get_STEPS lthy > 5
+    then mk_alpha_eq_iff lthy4 alpha_intros raw_distinct_thms raw_inject_thms alpha_cases
+    else raise TEST lthy4
+
+  (* proving equivariance lemmas for bns, fvs, size and alpha *)
+  val _ = warning "Proving equivariance";
+  val raw_bn_eqvt = 
+    if get_STEPS lthy > 6
+    then raw_prove_eqvt raw_bns raw_bn_induct (raw_bn_defs @ raw_perm_simps) lthy4
+    else raise TEST lthy4
+
+  (* noting the raw_bn_eqvt lemmas in a temprorary theory *)
+  val lthy_tmp = snd (Local_Theory.note ((Binding.empty, [eqvt_attr]), raw_bn_eqvt) lthy4)
+
+  val raw_fv_eqvt = 
+    if get_STEPS lthy > 7
+    then raw_prove_eqvt (raw_fvs @ raw_fv_bns) raw_fv_bns_induct (raw_fv_defs @ raw_perm_simps) 
+      (Local_Theory.restore lthy_tmp)
+    else raise TEST lthy4
+
+  val raw_size_eqvt = 
+    if get_STEPS lthy > 8
+    then raw_prove_eqvt raw_size_trms raw_induct_thms (raw_size_thms @ raw_perm_simps) 
+      (Local_Theory.restore lthy_tmp)
+      |> map (rewrite_rule @{thms permute_nat_def[THEN eq_reflection]})
+      |> map (fn thm => thm RS @{thm sym})
+    else raise TEST lthy4
+ 
+  val lthy5 = snd (Local_Theory.note ((Binding.empty, [eqvt_attr]), raw_fv_eqvt) lthy_tmp)
+
+  val (alpha_eqvt, lthy6) =
+    if get_STEPS lthy > 9
+    then Nominal_Eqvt.equivariance true (alpha_trms @ alpha_bn_trms) alpha_induct alpha_intros lthy5
+    else raise TEST lthy4
+
+  (* proving alpha equivalence *)
+  val _ = warning "Proving equivalence"
+
+  val alpha_refl_thms = 
+    if get_STEPS lthy > 10
+    then raw_prove_refl alpha_trms alpha_bn_trms alpha_intros raw_induct_thm lthy6 
+    else raise TEST lthy6
+
+  val alpha_sym_thms = 
+    if get_STEPS lthy > 11
+    then raw_prove_sym (alpha_trms @ alpha_bn_trms) alpha_intros alpha_induct lthy6 
+    else raise TEST lthy6
+
+  val alpha_trans_thms = 
+    if get_STEPS lthy > 12
+    then raw_prove_trans (alpha_trms @ alpha_bn_trms) (raw_distinct_thms @ raw_inject_thms) 
+           alpha_intros alpha_induct alpha_cases lthy6
+    else raise TEST lthy6
+
+  val (alpha_equivp_thms, alpha_bn_equivp_thms) = 
+    if get_STEPS lthy > 13
+    then raw_prove_equivp alpha_trms alpha_bn_trms alpha_refl_thms alpha_sym_thms 
+       alpha_trans_thms lthy6
+    else raise TEST lthy6
+
+  (* proving alpha implies alpha_bn *)
+  val _ = warning "Proving alpha implies bn"
+
+  val alpha_bn_imp_thms = 
+    if get_STEPS lthy > 14
+    then raw_prove_bn_imp alpha_trms alpha_bn_trms alpha_intros alpha_induct lthy6 
+    else raise TEST lthy6
+  
+  (* respectfulness proofs *)
+  val raw_funs_rsp_aux = 
+    if get_STEPS lthy > 15
+    then raw_fv_bn_rsp_aux alpha_trms alpha_bn_trms raw_fvs 
+      raw_bns raw_fv_bns alpha_induct (raw_bn_defs @ raw_fv_defs) lthy6
+    else raise TEST lthy6 
+  
+  val raw_funs_rsp = 
+    if get_STEPS lthy > 16
+    then map mk_funs_rsp raw_funs_rsp_aux
+    else raise TEST lthy6 
+
+  val raw_size_rsp = 
+    if get_STEPS lthy > 17
+    then
+      raw_size_rsp_aux (alpha_trms @ alpha_bn_trms) alpha_induct 
+      (raw_size_thms @ raw_size_eqvt) lthy6
+      |> map mk_funs_rsp
+    else raise TEST lthy6 
+
+  val raw_constrs_rsp = 
+    if get_STEPS lthy > 18
+    then raw_constrs_rsp raw_constrs alpha_trms alpha_intros
+      (alpha_bn_imp_thms @ raw_funs_rsp_aux) lthy6 
+    else raise TEST lthy6 
+
+  val alpha_permute_rsp = 
+    if get_STEPS lthy > 19
+    then map mk_alpha_permute_rsp alpha_eqvt
+    else raise TEST lthy6 
+
+  val alpha_bn_rsp = 
+    if get_STEPS lthy > 20
+    then raw_alpha_bn_rsp alpha_bn_trms alpha_bn_equivp_thms alpha_bn_imp_thms
+    else raise TEST lthy6 
+
+  (* noting the quot_respects lemmas *)
+  val (_, lthy6a) = 
+    if get_STEPS lthy > 21
+    then Local_Theory.note ((Binding.empty, [rsp_attr]),
+      raw_constrs_rsp @ raw_funs_rsp @ raw_size_rsp @ alpha_permute_rsp @ alpha_bn_rsp) lthy6
+    else raise TEST lthy6
+
+  (* defining the quotient type *)
+  val _ = warning "Declaring the quotient types"
+  val qty_descr = map (fn (vs, bind, mx, _) => (vs, bind, mx)) dts
+     
+  val (qty_infos, lthy7) = 
+    if get_STEPS lthy > 22
+    then define_qtypes qty_descr alpha_tys alpha_trms alpha_equivp_thms lthy6a
+    else raise TEST lthy6a
+
+  val qtys = map #qtyp qty_infos
+  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 = 
+    flat (map (fn (_, _, _, cs) => map (fn (b, _, mx) => (Name.of_binding b, mx)) cs) dts)
+    |> map2 (fn t => fn (b, mx) => (b, t, mx)) raw_constrs
+
+  val qbns_descr =
+    map2 (fn (b, _, mx) => fn t => (Name.of_binding b, t, mx)) bn_funs raw_bns
+
+  val qfvs_descr = 
+    map2 (fn n => fn t => ("fv_" ^ n, t, NoSyn)) qty_names raw_fvs
+
+  val qfv_bns_descr = 
+    map2 (fn (b, _, _) => fn t => ("fv_" ^ Name.of_binding b, t, NoSyn)) bn_funs raw_fv_bns
+
+  val qalpha_bns_descr = 
+    map2 (fn (b, _, _) => fn t => ("alpha_" ^ Name.of_binding b, t, NoSyn)) bn_funs  alpha_bn_trms
+
+  val qperm_descr =
+    map2 (fn n => fn t => ("permute_" ^ n, Type.legacy_freeze t, NoSyn)) qty_names raw_perm_funs
+
+  val qsize_descr =
+    map2 (fn n => fn t => ("size_" ^ n, t, NoSyn)) qty_names raw_size_trms
+
+  val (((((qconstrs_info, qbns_info), qfvs_info), qfv_bns_info), qalpha_bns_info), lthy8) = 
+    if get_STEPS lthy > 23
+    then 
+      lthy7
+      |> define_qconsts qtys qconstrs_descr 
+      ||>> define_qconsts qtys qbns_descr 
+      ||>> define_qconsts qtys qfvs_descr
+      ||>> define_qconsts qtys qfv_bns_descr
+      ||>> define_qconsts qtys qalpha_bns_descr
+    else raise TEST lthy7
+
+  (* definition of the quotient permfunctions and pt-class *)
+  val lthy9 = 
+    if get_STEPS lthy > 24
+    then define_qperms qtys qty_full_names tvs qperm_descr raw_perm_laws lthy8 
+    else raise TEST lthy8
+  
+  val lthy9a = 
+    if get_STEPS lthy > 25
+    then define_qsizes qtys qty_full_names tvs qsize_descr lthy9
+    else raise TEST lthy9
+
+  val qtrms = map #qconst qconstrs_info
+  val qbns = map #qconst qbns_info
+  val qfvs = map #qconst qfvs_info
+  val qfv_bns = map #qconst qfv_bns_info
+  val qalpha_bns = map #qconst qalpha_bns_info
+
+  (* lifting of the theorems *)
+  val _ = warning "Lifting of Theorems"
+  
+  val eq_iff_simps = @{thms alphas permute_prod.simps prod_fv.simps prod_alpha_def prod_rel.simps
+    prod.cases} 
+
+  val ((((((qdistincts, qeq_iffs), qfv_defs), qbn_defs), qperm_simps), qfv_qbn_eqvts), lthyA) = 
+    if get_STEPS lthy > 26
+    then 
+      lthy9a    
+      |> lift_thms qtys [] alpha_distincts  
+      ||>> lift_thms qtys eq_iff_simps alpha_eq_iff       
+      ||>> lift_thms qtys [] raw_fv_defs
+      ||>> lift_thms qtys [] raw_bn_defs
+      ||>> lift_thms qtys [] raw_perm_simps
+      ||>> lift_thms qtys [] (raw_fv_eqvt @ raw_bn_eqvt)
+    else raise TEST lthy9a
+
+  val (((qsize_eqvt, [qinduct]), qexhausts), lthyB) = 
+    if get_STEPS lthy > 27
+    then
+      lthyA 
+      |> lift_thms qtys [] raw_size_eqvt
+      ||>> lift_thms qtys [] [raw_induct_thm]
+      ||>> lift_thms qtys [] raw_exhaust_thms
+    else raise TEST lthyA
+
+  (* supports lemmas *) 
+  val qsupports_thms =
+    if get_STEPS lthy > 28
+    then prove_supports lthyB qperm_simps qtrms
+    else raise TEST lthyB
+
+  (* finite supp lemmas *)
+  val qfsupp_thms =
+    if get_STEPS lthy > 29
+    then prove_fsupp lthyB qtys qinduct qsupports_thms
+    else raise TEST lthyB
+
+  (* fs instances *)
+  val lthyC =
+    if get_STEPS lthy > 30
+    then fs_instance qtys qty_full_names tvs qfsupp_thms lthyB
+    else raise TEST lthyB
+
+  (* 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') = lthyC
+     |> 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", [eqvt_attr, simp_attr]), 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)
+     ||>> Local_Theory.note ((thms_suffix "supports", []), qsupports_thms)
+     ||>> Local_Theory.note ((thms_suffix "fsupp", []), qfsupp_thms)
+in
+  (0, lthy9')
+end handle TEST ctxt => (0, ctxt)
+*}
+
+section {* Preparing and parsing of the specification *}
+
+ML {* 
+(* generates the parsed datatypes and 
+   declares the constructors 
+*)
+fun prepare_dts dt_strs thy = 
+let
+  fun inter_fs_sort thy (a, S) = 
+    (a, Type.inter_sort (Sign.tsig_of thy) (@{sort fs}, S)) 
+
+  fun mk_type tname sorts (cname, cargs, mx) =
+  let
+    val full_tname = Sign.full_name thy tname
+    val ty = Type (full_tname, map (TFree o inter_fs_sort thy) sorts)
+  in
+    (cname, cargs ---> ty, mx)
+  end
+
+  fun prep_constr (cname, cargs, mx, _) (constrs, sorts) =
+  let 
+    val (cargs', sorts') = 
+      fold_map (Datatype.read_typ thy) (map snd cargs) sorts
+      |>> map (map_type_tfree (TFree o inter_fs_sort thy)) 
+  in 
+    (constrs @ [(cname, cargs', mx)], sorts') 
+  end
+  
+  fun prep_dts (tvs, tname, mx, constrs) (constr_trms, dts, sorts) =
+  let 
+    val (constrs', sorts') = 
+      fold prep_constr constrs ([], sorts)
+
+    val constr_trms' = 
+      map (mk_type tname (rev sorts')) constrs'
+  in 
+    (constr_trms @ constr_trms', dts @ [(tvs, tname, mx, constrs')], sorts') 
+  end
+
+  val (constr_trms, dts, sorts) = fold prep_dts dt_strs ([], [], []);
+in
+  thy
+  |> Sign.add_consts_i constr_trms
+  |> pair dts
+end
+*}
+
+ML {*
+(* parsing the binding function specification and *)
+(* declaring the functions in the local theory    *)
+fun prepare_bn_funs bn_fun_strs bn_eq_strs thy =
+let
+  val lthy = Named_Target.theory_init thy
+
+  val ((bn_funs, bn_eqs), lthy') = 
+    Specification.read_spec bn_fun_strs bn_eq_strs lthy
+
+  fun prep_bn_fun ((bn, T), mx) = (bn, T, mx) 
+  
+  val bn_funs' = map prep_bn_fun bn_funs
+in
+  (Local_Theory.exit_global lthy')
+  |> Sign.add_consts_i bn_funs'
+  |> pair (bn_funs', bn_eqs) 
+end 
+*}
+
+text {* associates every SOME with the index in the list; drops NONEs *}
+ML {*
+fun indexify xs =
+let
+  fun mapp _ [] = []
+    | mapp i (NONE :: xs) = mapp (i + 1) xs
+    | mapp i (SOME x :: xs) = (x, i) :: mapp (i + 1) xs
+in 
+  mapp 0 xs 
+end
+
+fun index_lookup xs x =
+  case AList.lookup (op=) xs x of
+    SOME x => x
+  | NONE => error ("Cannot find " ^ x ^ " as argument annotation.");
+*}
+
+ML {*
+fun prepare_bclauses dt_strs thy = 
+let
+  val annos_bclauses =
+    get_cnstrs dt_strs
+    |> map (map (fn (_, antys, _, bns) => (map fst antys, bns)))
+
+  fun prep_binder env bn_str =
+    case (Syntax.read_term_global thy bn_str) of
+      Free (x, _) => (NONE, index_lookup env x)
+    | Const (a, T) $ Free (x, _) => (SOME (Const (a, T)), index_lookup env x)
+    | _ => error ("The term " ^ bn_str ^ " is not allowed as binding function.")
+ 
+  fun prep_body env bn_str = index_lookup env bn_str
+
+  fun prep_bclause env (mode, binders, bodies) = 
+  let
+    val binders' = map (prep_binder env) binders
+    val bodies' = map (prep_body env) bodies
+  in  
+    BC (mode, binders', bodies')
+  end
+
+  fun prep_bclauses (annos, bclause_strs) = 
+  let
+    val env = indexify annos (* for every label, associate the index *)
+  in
+    map (prep_bclause env) bclause_strs
+  end
+in
+  (map (map prep_bclauses) annos_bclauses, thy)
+end
+*}
+
+text {* 
+  adds an empty binding clause for every argument
+  that is not already part of a binding clause
+*}
+
+ML {*
+fun included i bcs = 
+let
+  fun incl (BC (_, bns, bds)) = 
+    member (op =) (map snd bns) i orelse member (op =) bds i
+in
+  exists incl bcs 
+end
+*}
+
+ML {* 
+fun complete dt_strs bclauses = 
+let
+  val args = 
+    get_cnstrs dt_strs
+    |> map (map (fn (_, antys, _, _) => length antys))
+
+  fun complt n bcs = 
+  let
+    fun add bcs i = (if included i bcs then [] else [BC (Lst, [], [i])]) 
+  in
+    bcs @ (flat (map_range (add bcs) n))
+  end
+in
+  map2 (map2 complt) args bclauses
+end
+*}
+
+ML {*
+fun nominal_datatype2_cmd (opt_thms_name, dt_strs, bn_fun_strs, bn_eq_strs) lthy = 
+let
+  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  
+  val tmp_thy = Theory.copy thy 
+
+  val (((dts, (bn_funs, bn_eqs)), bclauses), tmp_thy') = 
+    tmp_thy
+    |> Sign.add_types pre_typs
+    |> prepare_dts dt_strs 
+    ||>> prepare_bn_funs bn_fun_strs bn_eq_strs 
+    ||>> prepare_bclauses dt_strs 
+
+  val bclauses' = complete dt_strs bclauses
+in
+  timeit (fn () => nominal_datatype2 opt_thms_name dts bn_funs bn_eqs bclauses' lthy |> snd)
+end
+*}
+
+ML {* 
+(* nominal datatype parser *)
+local
+  structure P = Parse;
+  structure S = Scan
+
+  fun triple ((x, y), z) = (x, y, z)
+  fun tuple1 ((x, y, z), u) = (x, y, z, u)
+  fun tuple2 (((x, y), z), u) = (x, y, u, z)
+  fun tuple3 ((x, y), (z, u)) = (x, y, z, u)
+in
+
+val _ = Keyword.keyword "bind"
+
+val opt_name = Scan.option (P.binding --| Args.colon)
+
+val anno_typ = S.option (P.name --| P.$$$ "::") -- P.typ
+
+val bind_mode = P.$$$ "bind" |--
+  S.optional (Args.parens 
+    (Args.$$$ "list" >> K Lst || Args.$$$ "set" >> K Set || Args.$$$ "res" >> K Res)) Lst
+
+val bind_clauses = 
+  P.enum "," (bind_mode -- S.repeat1 P.term -- (P.$$$ "in" |-- S.repeat1 P.name) >> triple)
+
+val cnstr_parser =
+  P.binding -- S.repeat anno_typ -- bind_clauses -- P.opt_mixfix >> tuple2
+
+(* datatype parser *)
+val dt_parser =
+  (P.type_args -- P.binding -- P.opt_mixfix >> triple) -- 
+    (P.$$$ "=" |-- P.enum1 "|" cnstr_parser) >> tuple1
+
+(* binding function parser *)
+val bnfun_parser = 
+  S.optional (P.$$$ "binder" |-- P.fixes -- Parse_Spec.where_alt_specs) ([], [])
+
+(* main parser *)
+val main_parser =
+  opt_name -- P.and_list1 dt_parser -- bnfun_parser >> tuple3
+
+end
+
+(* Command Keyword *)
+val _ = Outer_Syntax.local_theory "nominal_datatype" "test" Keyword.thy_decl
+  (main_parser >> nominal_datatype2_cmd)
+*}
+
+
+end
+
+
+
diff -r 2f47291b6ff9 -r 9ffee4eb1ae1 Nominal/ROOT.ML
--- a/Nominal/ROOT.ML	Sun Aug 29 12:17:25 2010 +0800
+++ b/Nominal/ROOT.ML	Sun Aug 29 13:36:03 2010 +0800
@@ -3,6 +3,7 @@
 no_document use_thys
    ["Ex/Classical",    
     "Ex/CoreHaskell",
+    "Ex/Ex1",
     "Ex/ExPS3",
     "Ex/ExPS7",
     "Ex/ExPS8",
@@ -12,6 +13,7 @@
     "Ex/LetPat",
     "Ex/LetRec",
     "Ex/LetRec2",
+    "Ex/LetFun",
     "Ex/Modules",
     "Ex/SingleLet",
     "Ex/TypeSchemes",