--- /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
+
+
+