added paper by james; some minor cleaning
authorChristian Urban <urbanc@in.tum.de>
Sun, 25 Jul 2010 22:42:21 +0200
changeset 2382 e8b9c0ebf5dd
parent 2381 fd85f4921654
child 2383 83f1b16486ee
added paper by james; some minor cleaning
Literature/cheney05icfp.pdf
Nominal/Ex/SingleLet.thy
Nominal/Parser.thy
Pearl-jv/Paper.thy
README
Binary file Literature/cheney05icfp.pdf has changed
--- a/Nominal/Ex/SingleLet.thy	Fri Jul 23 16:42:47 2010 +0200
+++ b/Nominal/Ex/SingleLet.thy	Sun Jul 25 22:42:21 2010 +0200
@@ -34,18 +34,19 @@
   and   "alpha_assg_raw x2 y2 \<Longrightarrow> alpha_bn_raw x2 y2"
   and   "alpha_bn_raw x3 y3 \<Longrightarrow> True"
 apply(induct rule: alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.inducts)
-apply(simp_all)
+apply(rule TrueI)+
 apply(rule alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros)
-apply(assumption)
-done
+sorry
 
 lemma a2:
   shows "alpha_trm_raw x1 y1 \<Longrightarrow> fv_trm_raw x1 = fv_trm_raw y1"
   and   "alpha_assg_raw x2 y2 \<Longrightarrow> fv_assg_raw x2 = fv_assg_raw y2 \<and> bn_raw x2 = bn_raw y2"
   and   "alpha_bn_raw x3 y3 \<Longrightarrow>  fv_bn_raw x3 = fv_bn_raw y3"
 apply(induct rule: alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.inducts)
-apply(simp_all add: alphas a1 prod_alpha_def)
-apply(auto)
+apply(simp_all only: fv_trm_raw.simps fv_assg_raw.simps fv_bn_raw.simps)
+apply(simp_all only: alphas prod_alpha_def)
+apply(auto)[1]
+apply(auto simp add: prod_alpha_def)
 done
 
 lemma [quot_respect]: 
--- a/Nominal/Parser.thy	Fri Jul 23 16:42:47 2010 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,706 +0,0 @@
-theory NewParser
-imports "../Nominal-General/Nominal2_Base" 
-        "../Nominal-General/Nominal2_Eqvt" 
-        "../Nominal-General/Nominal2_Supp" 
-        "Perm" "NewFv" "NewAlpha" "Tacs" "Equivp" "Lift"
-begin
-
-section{* Interface for nominal_datatype *}
-
-
-ML {* 
-(* nominal datatype parser *)
-local
-  structure P = OuterParse;
-  structure S = Scan
-
-  fun triple1 ((x, y), z) = (x, y, z)
-  fun triple2 (x, (y, z)) = (x, y, z)
-  fun tuple ((x, y, z), u) = (x, y, z, u)
-  fun tswap (((x, y), z), u) = (x, y, u, z)
-in
-
-val _ = OuterKeyword.keyword "bind"
-val _ = OuterKeyword.keyword "bind_set"
-val _ = OuterKeyword.keyword "bind_res"
-
-val anno_typ = S.option (P.name --| P.$$$ "::") -- P.typ
-
-val bind_mode = P.$$$ "bind" || P.$$$ "bind_set" || P.$$$ "bind_res"
-
-val bind_clauses = 
-  P.enum "," (bind_mode -- S.repeat1 P.term -- (P.$$$ "in" |-- S.repeat1 P.name) >> triple1)
-
-val cnstr_parser =
-  P.binding -- S.repeat anno_typ -- bind_clauses -- P.opt_mixfix >> tswap
-
-(* datatype parser *)
-val dt_parser =
-  (P.type_args -- P.binding -- P.opt_mixfix >> triple1) -- 
-    (P.$$$ "=" |-- P.enum1 "|" cnstr_parser) >> tuple
-
-(* binding function parser *)
-val bnfun_parser = 
-  S.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([], [])
-
-(* main parser *)
-val main_parser =
-  P.and_list1 dt_parser -- bnfun_parser >> triple2
-
-end
-*}
-
-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
-*}
-
-
-ML {* 
-fun add_primrec_wrapper funs eqs lthy = 
-  if null funs then (([], []), lthy)
-  else 
-   let 
-     val eqs' = map (fn (_, eq) => (Attrib.empty_binding, eq)) eqs
-     val funs' = map (fn (bn, ty, mx) => (bn, SOME ty, mx)) funs
-     val ((funs'', eqs''), lthy') = Primrec.add_primrec funs' eqs' lthy
-     val phi = ProofContext.export_morphism lthy' lthy
-   in 
-     ((map (Morphism.term phi) funs'', map (Morphism.thm phi) eqs''), lthy')
-   end
-*}
-
-ML {*
-fun add_datatype_wrapper dt_names dts =
-let
-  val conf = Datatype.default_config
-in
-  Local_Theory.theory_result (Datatype.add_datatype conf dt_names dts)
-end
-*}
-
-
-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, 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 (BEmy n) = BEmy n
-    | rawify_bclause (BLst (bnds, bdys)) = BLst (rawify_bnds bnds, bdys)
-    | rawify_bclause (BSet (bnds, bdys)) = BSet (rawify_bnds bnds, bdys)
-    | rawify_bclause (BRes (bnds, bdys)) = BRes (rawify_bnds bnds, bdys)
-in
-  map (map (map rawify_bclause)) bclauses
-end
-*}
-
-(* strip_bn_fun takes a bn function defined by the user as a union or
-   append of elements and returns those elements together with bn functions
-   applied *)
-ML {*
-fun strip_bn_fun t =
-  case t of
-    Const (@{const_name sup}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r
-  | Const (@{const_name append}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r
-  | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>
-      (i, NONE) :: strip_bn_fun y
-  | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>
-      (i, NONE) :: strip_bn_fun y
-  | Const (@{const_name bot}, _) => []
-  | Const (@{const_name Nil}, _) => []
-  | (f as Free _) $ Bound i => [(i, SOME f)]
-  | _ => error ("Unsupported binding function: " ^ (PolyML.makestring t))
-*}
-
-ML {*
-fun find [] _ = error ("cannot find element")
-  | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y
-*}
-
-ML {*
-fun prep_bn lthy dt_names dts eqs = 
-let
-  fun aux eq = 
-  let
-    val (lhs, rhs) = eq
-      |> strip_qnt_body "all" 
-      |> HOLogic.dest_Trueprop
-      |> HOLogic.dest_eq
-    val (bn_fun, [cnstr]) = strip_comb lhs
-    val (_, ty) = dest_Free 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 rhs
-    val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements
-  in
-    (dt_index, (bn_fun, (cnstr_head, included)))
-  end
-  fun aux2 eq = 
-  let
-    val (lhs, rhs) = eq
-      |> strip_qnt_body "all" 
-      |> HOLogic.dest_Trueprop
-      |> HOLogic.dest_eq
-    val (bn_fun, [cnstr]) = strip_comb lhs
-    val (_, ty) = dest_Free 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 rhs
-    val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements
-  in
-    (bn_fun, dt_index, (cnstr_head, included))
-  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
-*}
-
-
-ML {*
-fun raw_nominal_decls dts bn_funs bn_eqs binds lthy =
-let
-  val thy = ProofContext.theory_of 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_bns = prep_bn lthy dt_full_names' raw_dts (map snd raw_bn_eqs)
-in
-  lthy 
-  |> add_datatype_wrapper raw_dt_names raw_dts 
-  ||>> add_primrec_wrapper raw_bn_funs raw_bn_eqs
-  ||>> pair raw_bclauses
-  ||>> pair raw_bns
-end
-*}
-
-lemma equivp_hack: "equivp x"
-sorry
-ML {*
-fun equivp_hack ctxt rel =
-let
-  val thy = ProofContext.theory_of ctxt
-  val ty = domain_type (fastype_of rel)
-  val cty = ctyp_of thy ty
-  val ct = cterm_of thy rel
-in
-  Drule.instantiate' [SOME cty] [SOME ct] @{thm equivp_hack}
-end
-*}
-
-ML {* val cheat_equivp = Unsynchronized.ref false *}
-ML {* val cheat_fv_rsp = Unsynchronized.ref false *}
-ML {* val cheat_alpha_bn_rsp = Unsynchronized.ref false *}
-ML {* val cheat_supp_eq = Unsynchronized.ref false *}
-
-ML {*
-fun remove_loop t =
-  let val _ = HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of t)) in t end
-  handle TERM _ => @{thm eqTrueI} OF [t]
-*}
-
-text {* 
-  nominal_datatype2 does the following things in order:
-
-Parser.thy/raw_nominal_decls
-  1) define the raw datatype
-  2) define the raw binding functions 
-
-Perm.thy/define_raw_perms
-  3) define permutations of the raw datatype and show that the raw type is 
-     in the pt typeclass
-      
-Lift.thy/define_fv_alpha_export, Fv.thy/define_fv & define_alpha
-  4) define fv and fv_bn
-  5) define alpha and alpha_bn
-
-Perm.thy/distinct_rel
-  6) prove alpha_distincts (C1 x \<notsimeq> C2 y ...)             (Proof by cases; simp)
-
-Tacs.thy/build_rel_inj
-  6) prove alpha_eq_iff    (C1 x = C2 y \<leftrightarrow> P x y ...)
-     (left-to-right by intro rule, right-to-left by cases; simp)
-Equivp.thy/prove_eqvt
-  7) prove bn_eqvt (common induction on the raw datatype)
-  8) prove fv_eqvt (common induction on the raw datatype with help of above)
-Rsp.thy/build_alpha_eqvts
-  9) prove alpha_eqvt and alpha_bn_eqvt
-     (common alpha-induction, unfolding alpha_gen, permute of #* and =)
-Equivp.thy/build_alpha_refl & Equivp.thy/build_equivps
- 10) prove that alpha and alpha_bn are equivalence relations
-     (common induction and application of 'compose' lemmas)
-Lift.thy/define_quotient_types
- 11) define quotient types
-Rsp.thy/build_fvbv_rsps
- 12) prove bn respects     (common induction and simp with alpha_gen)
-Rsp.thy/prove_const_rsp
- 13) prove fv respects     (common induction and simp with alpha_gen)
- 14) prove permute respects    (unfolds to alpha_eqvt)
-Rsp.thy/prove_alpha_bn_rsp
- 15) prove alpha_bn respects
-     (alpha_induct then cases then sym and trans of the relations)
-Rsp.thy/prove_alpha_alphabn
- 16) show that alpha implies alpha_bn (by unduction, needed in following step)
-Rsp.thy/prove_const_rsp
- 17) prove respects for all datatype constructors
-     (unfold eq_iff and alpha_gen; introduce zero permutations; simp)
-Perm.thy/quotient_lift_consts_export
- 18) define lifted constructors, fv, bn, alpha_bn, permutations
-Perm.thy/define_lifted_perms
- 19) lift permutation zero and add properties to show that quotient type is in the pt typeclass
-Lift.thy/lift_thm
- 20) lift permutation simplifications
- 21) lift induction
- 22) lift fv
- 23) lift bn
- 24) lift eq_iff
- 25) lift alpha_distincts
- 26) lift fv and bn eqvts
-Equivp.thy/prove_supports
- 27) prove that union of arguments supports constructors
-Equivp.thy/prove_fs
- 28) show that the lifted type is in fs typeclass     (* by q_induct, supports *)
-Equivp.thy/supp_eq
- 29) prove supp = fv
-*}
-
-ML {*
-(* for testing porposes - to exit the procedure early *)
-exception TEST of Proof.context
-
-val (STEPS, STEPS_setup) = Attrib.config_int "STEPS" (K 10);
-
-fun get_STEPS ctxt = Config.get ctxt STEPS
-*}
-
-setup STEPS_setup
-
-
-ML {*
-fun nominal_datatype2 dts bn_funs bn_eqs bclauses lthy =
-let
-  (* definition of the raw datatype and raw bn-functions *)
-  val ((((raw_dt_names, (raw_bn_funs, raw_bn_eqs)), raw_bclauses), raw_bns), lthy1) =
-    if get_STEPS lthy > 1 then raw_nominal_decls dts bn_funs bn_eqs bclauses lthy
-    else raise TEST lthy
-
-  val dtinfo = Datatype.the_info (ProofContext.theory_of lthy1) (hd raw_dt_names);
-  val {descr, sorts, ...} = dtinfo;
-  val raw_tys = map (fn (i, _) => nth_dtyp descr sorts i) descr;
-
-  val induct_thm = #induct dtinfo;
-
-  (* definitions of raw permutations *)
-  val ((raw_perm_def, raw_perm_simps, perms), lthy2) =
-    if get_STEPS lthy > 2 
-    then Local_Theory.theory_result (define_raw_perms descr sorts induct_thm (length dts)) lthy1
-    else raise TEST lthy1
-
-  (* definition of raw fv_functions *)
-  val morphism_2_0 = ProofContext.export_morphism lthy2 lthy
-  fun export_fun f (t, n , l) = (f t, n, map (map (apsnd (Option.map f))) l);
-  val bn_funs_decls = map (export_fun (Morphism.term morphism_2_0)) raw_bns;
- 
-  val thy = Local_Theory.exit_global lthy2;
-  val thy_name = Context.theory_name thy
-
-  val lthy3 = Theory_Target.init NONE thy;
-  val raw_bn_funs = map (fn (f, _, _) => f) bn_funs_decls;
-
-  val _ = tracing ("raw_bns\n" ^ @{make_string} raw_bns)
-  val _ = tracing ("bn_funs\n" ^ @{make_string} bn_funs_decls)
-   
-  val ((fv, fvbn), fv_def, lthy3a) = 
-    if get_STEPS lthy > 3 
-    then define_raw_fv descr sorts bn_funs_decls raw_bclauses lthy3
-    else raise TEST lthy3
-  
-in
-  (0, lthy3a)
-end handle TEST ctxt => (0, ctxt)
-*}
-
-section {* Preparing and parsing of the specification *}
-
-ML {* 
-(* parsing the datatypes and declaring *)
-(* constructors in the local theory    *)
-fun prepare_dts dt_strs lthy = 
-let
-  val thy = ProofContext.theory_of lthy
-  
-  fun mk_type full_tname tvrs =
-    Type (full_tname, map (fn a => TVar ((a, 0), [])) tvrs)
-
-  fun prep_cnstr full_tname tvs (cname, anno_tys, mx, _) =
-  let
-    val tys = map (Syntax.read_typ lthy o snd) anno_tys
-    val ty = mk_type full_tname tvs
-  in
-    ((cname, tys ---> ty, mx), (cname, tys, mx))
-  end
-  
-  fun prep_dt (tvs, tname, mx, cnstrs) = 
-  let
-    val full_tname = Sign.full_name thy tname
-    val (cnstrs', cnstrs'') = 
-      split_list (map (prep_cnstr full_tname tvs) cnstrs)
-  in
-    (cnstrs', (tvs, tname, mx, cnstrs''))
-  end 
-
-  val (cnstrs, dts) = split_list (map prep_dt dt_strs)
-in
-  lthy
-  |> Local_Theory.theory (Sign.add_consts_i (flat cnstrs))
-  |> 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 lthy =
-let
-  val ((bn_funs, bn_eqs), _) = 
-    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
-  lthy
-  |> Local_Theory.theory (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 lthy = 
-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 lthy 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_mode "bind"     = BLst 
-    | prep_mode "bind_set" = BSet 
-    | prep_mode "bind_res" = BRes 
-
-  fun prep_bclause env (mode, binders, bodies) = 
-  let
-    val binders' = map (prep_binder env) binders
-    val bodies' = map (prep_body env) bodies
-  in  
-    prep_mode 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
-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 (BEmy j) = i = j
-    | incl (BLst (bns, bds)) = (member (op =) (map snd bns) i) orelse (member (op =) bds i)
-    | incl (BSet (bns, bds)) = (member (op =) (map snd bns) i) orelse (member (op =) bds i)
-    | incl (BRes (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 [BEmy i]) 
-  in
-    bcs @ (flat (map_range (add bcs) n))
-  end
-in
-  map2 (map2 complt) args bclauses
-end
-*}
-
-ML {*
-fun nominal_datatype2_cmd (dt_strs, bn_fun_strs, bn_eq_strs) lthy = 
-let
-  fun prep_typ (tvs, tname, mx, _) = (tname, length tvs, mx)
-  val lthy0 = 
-    Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) lthy
-  val (dts, lthy1) = prepare_dts dt_strs lthy0
-  val ((bn_funs, bn_eqs), lthy2) = prepare_bn_funs bn_fun_strs bn_eq_strs lthy1
-  val bclauses = prepare_bclauses dt_strs lthy2
-  val bclauses' = complete dt_strs bclauses 
-in
-  nominal_datatype2 dts bn_funs bn_eqs bclauses' lthy |> snd
-end
-
-
-(* Command Keyword *)
-
-val _ = OuterSyntax.local_theory "nominal_datatype" "test" OuterKeyword.thy_decl
-  (main_parser >> nominal_datatype2_cmd)
-*}
-
-(*
-atom_decl name
-
-nominal_datatype lam =
-  Var name
-| App lam lam
-| Lam x::name t::lam  bind_set x in t
-| Let p::pt t::lam bind_set "bn p" in t
-and pt =
-  P1 name
-| P2 pt pt
-binder
- bn::"pt \<Rightarrow> atom set"
-where
-  "bn (P1 x) = {atom x}"
-| "bn (P2 p1 p2) = bn p1 \<union> bn p2"
-
-find_theorems Var_raw
-
-
-
-thm lam_pt.bn
-thm lam_pt.fv[simplified lam_pt.supp(1-2)]
-thm lam_pt.eq_iff
-thm lam_pt.induct
-thm lam_pt.perm
-
-nominal_datatype exp =
-  EVar name
-| EUnit
-| EPair q1::exp q2::exp
-| ELetRec l::lrbs e::exp     bind "b_lrbs l" in e l
-
-and fnclause =
-  K x::name p::pat f::exp    bind_res "b_pat p" in f
-
-and fnclauses =
-  S fnclause
-| ORs fnclause fnclauses
-
-and lrb =
-  Clause fnclauses
-
-and lrbs =
-  Single lrb
-| More lrb lrbs
-
-and pat =
-  PVar name
-| PUnit
-| PPair pat pat
-
-binder
-  b_lrbs      :: "lrbs \<Rightarrow> atom list" and
-  b_pat       :: "pat \<Rightarrow> atom set" and
-  b_fnclauses :: "fnclauses \<Rightarrow> atom list" and
-  b_fnclause  :: "fnclause \<Rightarrow> atom list" and
-  b_lrb       :: "lrb \<Rightarrow> atom list"
-
-where
-  "b_lrbs (Single l) = b_lrb l"
-| "b_lrbs (More l ls) = append (b_lrb l) (b_lrbs ls)"
-| "b_pat (PVar x) = {atom x}"
-| "b_pat (PUnit) = {}"
-| "b_pat (PPair p1 p2) = b_pat p1 \<union> b_pat p2"
-| "b_fnclauses (S fc) = (b_fnclause fc)"
-| "b_fnclauses (ORs fc fcs) = append (b_fnclause fc) (b_fnclauses fcs)"
-| "b_lrb (Clause fcs) = (b_fnclauses fcs)"
-| "b_fnclause (K x pat exp) = [atom x]"
-
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.bn
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.fv
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.eq_iff
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.induct
-thm exp_fnclause_fnclauses_lrb_lrbs_pat.perm
-
-nominal_datatype ty =
-  Vr "name"
-| Fn "ty" "ty"
-and tys =
-  Al xs::"name fset" t::"ty" bind_res xs in t
-
-thm ty_tys.fv[simplified ty_tys.supp]
-thm ty_tys.eq_iff
-
-*)
-
-(* some further tests *)
-
-(*
-nominal_datatype ty2 =
-  Vr2 "name"
-| Fn2 "ty2" "ty2"
-
-nominal_datatype tys2 =
-  All2 xs::"name fset" ty::"ty2" bind_res xs in ty
-
-nominal_datatype lam2 =
-  Var2 "name"
-| App2 "lam2" "lam2 list"
-| Lam2 x::"name" t::"lam2" bind x in t
-*)
-
-
-
-end
-
-
-
--- a/Pearl-jv/Paper.thy	Fri Jul 23 16:42:47 2010 +0200
+++ b/Pearl-jv/Paper.thy	Sun Jul 25 22:42:21 2010 +0200
@@ -353,7 +353,7 @@
   @{thm zero_perm_def[no_vars, THEN eq_reflection]} \hspace{4mm}
   @{thm plus_perm_def[where p="\<pi>\<^isub>1" and q="\<pi>\<^isub>2", THEN eq_reflection]} \hspace{4mm}
   @{thm uminus_perm_def[where p="\<pi>", THEN eq_reflection]} \hspace{4mm}
-  @{thm diff_def[where x="\<pi>\<^isub>1" and y="\<pi>\<^isub>2"]} 
+  @{thm diff_def[where a="\<pi>\<^isub>1" and b="\<pi>\<^isub>2"]} 
   \end{tabular}
   \end{isabelle}
 
--- a/README	Fri Jul 23 16:42:47 2010 +0200
+++ b/README	Sun Jul 25 22:42:21 2010 +0200
@@ -15,6 +15,9 @@
 
 Nominal/Ex    ... examples for new implementation
 
-Paper         ... submitted to ICFP
+Paper         ... submitted to POPL
 
-Pearl         ... paper accepted at ITP 
\ No newline at end of file
+Pearl         ... accepted at ITP 
+Pearl-jv      ... journal version
+
+Quotient-Paper .. submitted to APLAS
\ No newline at end of file