(* Title: HOL/Tools/BNF/bnf_lfp_rec_sugar.ML
Author: Lorenz Panny, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Copyright 2013
New-style recursor sugar ("primrec").
*)
signature BNF_LFP_REC_SUGAR =
sig
datatype primrec_option = Nonexhaustive_Option
type basic_lfp_sugar =
{T: typ,
fp_res_index: int,
C: typ,
fun_arg_Tsss : typ list list list,
ctr_defs: thm list,
ctr_sugar: Ctr_Sugar.ctr_sugar,
recx: term,
rec_thms: thm list};
type lfp_rec_extension =
{nested_simps: thm list,
is_new_datatype: Proof.context -> string -> bool,
get_basic_lfp_sugars: binding list -> typ list -> term list ->
(term * term list list) list list -> local_theory ->
typ list * int list * basic_lfp_sugar list * thm list * thm list * thm * bool * local_theory,
rewrite_nested_rec_call: Proof.context -> (term -> bool) -> (string -> int) -> typ list ->
term -> term -> term -> term};
exception PRIMREC of string * term list;
val register_lfp_rec_extension: lfp_rec_extension -> theory -> theory
val add_primrec: (binding * typ option * mixfix) list ->
(Attrib.binding * term) list -> local_theory -> (term list * thm list list) * local_theory
val add_primrec_cmd: primrec_option list -> (binding * string option * mixfix) list ->
(Attrib.binding * string) list -> local_theory -> (term list * thm list list) * local_theory
val add_primrec_global: (binding * typ option * mixfix) list ->
(Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
val add_primrec_overloaded: (string * (string * typ) * bool) list ->
(binding * typ option * mixfix) list ->
(Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
local_theory -> (string list * (term list * (int list list * thm list list))) * local_theory
end;
structure BNF_LFP_Rec_Sugar : BNF_LFP_REC_SUGAR =
struct
open Ctr_Sugar
open Ctr_Sugar_Util
open Ctr_Sugar_General_Tactics
open BNF_FP_Rec_Sugar_Util
val inductN = "induct"
val simpsN = "simps"
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs;
exception OLD_PRIMREC of unit;
exception PRIMREC of string * term list;
datatype primrec_option = Nonexhaustive_Option;
datatype rec_call =
No_Rec of int * typ |
Mutual_Rec of (int * typ) * (int * typ) |
Nested_Rec of int * typ;
type rec_ctr_spec =
{ctr: term,
offset: int,
calls: rec_call list,
rec_thm: thm};
type rec_spec =
{recx: term,
fp_nesting_map_ident0s: thm list,
fp_nesting_map_comps: thm list,
ctr_specs: rec_ctr_spec list};
type basic_lfp_sugar =
{T: typ,
fp_res_index: int,
C: typ,
fun_arg_Tsss : typ list list list,
ctr_defs: thm list,
ctr_sugar: ctr_sugar,
recx: term,
rec_thms: thm list};
type lfp_rec_extension =
{nested_simps: thm list,
is_new_datatype: Proof.context -> string -> bool,
get_basic_lfp_sugars: binding list -> typ list -> term list ->
(term * term list list) list list -> local_theory ->
typ list * int list * basic_lfp_sugar list * thm list * thm list * thm * bool * local_theory,
rewrite_nested_rec_call: Proof.context -> (term -> bool) -> (string -> int) -> typ list ->
term -> term -> term -> term};
structure Data = Theory_Data
(
type T = lfp_rec_extension option;
val empty = NONE;
val extend = I;
val merge = merge_options;
);
val register_lfp_rec_extension = Data.put o SOME;
fun nested_simps ctxt =
(case Data.get (Proof_Context.theory_of ctxt) of
SOME {nested_simps, ...} => nested_simps
| NONE => []);
fun is_new_datatype ctxt =
(case Data.get (Proof_Context.theory_of ctxt) of
SOME {is_new_datatype, ...} => is_new_datatype ctxt
| NONE => K false);
fun get_basic_lfp_sugars bs arg_Ts callers callssss lthy =
(case Data.get (Proof_Context.theory_of lthy) of
SOME {get_basic_lfp_sugars, ...} => get_basic_lfp_sugars bs arg_Ts callers callssss lthy
| NONE => error "Functionality not loaded yet");
fun rewrite_nested_rec_call ctxt =
(case Data.get (Proof_Context.theory_of ctxt) of
SOME {rewrite_nested_rec_call, ...} => rewrite_nested_rec_call ctxt);
fun rec_specs_of bs arg_Ts res_Ts callers callssss0 lthy0 =
let
val thy = Proof_Context.theory_of lthy0;
val (missing_arg_Ts, perm0_kks, basic_lfp_sugars, fp_nesting_map_ident0s, fp_nesting_map_comps,
common_induct, n2m, lthy) =
get_basic_lfp_sugars bs arg_Ts callers callssss0 lthy0;
val perm_basic_lfp_sugars = sort (int_ord o pairself #fp_res_index) basic_lfp_sugars;
val indices = map #fp_res_index basic_lfp_sugars;
val perm_indices = map #fp_res_index perm_basic_lfp_sugars;
val perm_ctrss = map (#ctrs o #ctr_sugar) perm_basic_lfp_sugars;
val nn0 = length arg_Ts;
val nn = length perm_ctrss;
val kks = 0 upto nn - 1;
val perm_ctr_offsets = map (fn kk => Integer.sum (map length (take kk perm_ctrss))) kks;
val perm_lfpTs = map (body_type o fastype_of o hd) perm_ctrss;
val perm_Cs = map #C perm_basic_lfp_sugars;
val perm_fun_arg_Tssss = map #fun_arg_Tsss perm_basic_lfp_sugars;
fun unpermute0 perm0_xs = permute_like_unique (op =) perm0_kks kks perm0_xs;
fun unpermute perm_xs = permute_like_unique (op =) perm_indices indices perm_xs;
val inducts = unpermute0 (conj_dests nn common_induct);
val lfpTs = unpermute perm_lfpTs;
val Cs = unpermute perm_Cs;
val ctr_offsets = unpermute perm_ctr_offsets;
val As_rho = tvar_subst thy (take nn0 lfpTs) arg_Ts;
val Cs_rho = map (fst o dest_TVar) Cs ~~ pad_list HOLogic.unitT nn res_Ts;
val substA = Term.subst_TVars As_rho;
val substAT = Term.typ_subst_TVars As_rho;
val substCT = Term.typ_subst_TVars Cs_rho;
val substACT = substAT o substCT;
val perm_Cs' = map substCT perm_Cs;
fun call_of [i] [T] = (if exists_subtype_in Cs T then Nested_Rec else No_Rec) (i, substACT T)
| call_of [i, i'] [T, T'] = Mutual_Rec ((i, substACT T), (i', substACT T'));
fun mk_ctr_spec ctr offset fun_arg_Tss rec_thm =
let
val (fun_arg_hss, _) = indexedd fun_arg_Tss 0;
val fun_arg_hs = flat_rec_arg_args fun_arg_hss;
val fun_arg_iss = map (map (find_index_eq fun_arg_hs)) fun_arg_hss;
in
{ctr = substA ctr, offset = offset, calls = map2 call_of fun_arg_iss fun_arg_Tss,
rec_thm = rec_thm}
end;
fun mk_ctr_specs fp_res_index k ctrs rec_thms =
map4 mk_ctr_spec ctrs (k upto k + length ctrs - 1) (nth perm_fun_arg_Tssss fp_res_index)
rec_thms;
fun mk_spec ctr_offset
({T, fp_res_index, ctr_sugar = {ctrs, ...}, recx, rec_thms, ...} : basic_lfp_sugar) =
{recx = mk_co_rec thy Least_FP (substAT T) perm_Cs' recx,
fp_nesting_map_ident0s = fp_nesting_map_ident0s, fp_nesting_map_comps = fp_nesting_map_comps,
ctr_specs = mk_ctr_specs fp_res_index ctr_offset ctrs rec_thms};
in
((n2m, map2 mk_spec ctr_offsets basic_lfp_sugars, missing_arg_Ts, common_induct, inducts), lthy)
end;
val undef_const = Const (@{const_name undefined}, dummyT);
type eqn_data = {
fun_name: string,
rec_type: typ,
ctr: term,
ctr_args: term list,
left_args: term list,
right_args: term list,
res_type: typ,
rhs_term: term,
user_eqn: term
};
fun dissect_eqn lthy fun_names eqn' =
let
val eqn = drop_all eqn' |> HOLogic.dest_Trueprop
handle TERM _ =>
raise PRIMREC ("malformed function equation (expected \"lhs = rhs\")", [eqn']);
val (lhs, rhs) = HOLogic.dest_eq eqn
handle TERM _ =>
raise PRIMREC ("malformed function equation (expected \"lhs = rhs\")", [eqn']);
val (fun_name, args) = strip_comb lhs
|>> (fn x => if is_Free x then fst (dest_Free x)
else raise PRIMREC ("malformed function equation (does not start with free)", [eqn]));
val (left_args, rest) = take_prefix is_Free args;
val (nonfrees, right_args) = take_suffix is_Free rest;
val num_nonfrees = length nonfrees;
val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then
raise PRIMREC ("constructor pattern missing in left-hand side", [eqn]) else
raise PRIMREC ("more than one non-variable argument in left-hand side", [eqn]);
val _ = member (op =) fun_names fun_name orelse
raise PRIMREC ("malformed function equation (does not start with function name)", [eqn]);
val (ctr, ctr_args) = strip_comb (the_single nonfrees);
val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
raise PRIMREC ("partially applied constructor in pattern", [eqn]);
val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
raise PRIMREC ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
"\" in left-hand side", [eqn]) end;
val _ = forall is_Free ctr_args orelse
raise PRIMREC ("non-primitive pattern in left-hand side", [eqn]);
val _ =
let val b = fold_aterms (fn x as Free (v, _) =>
if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
not (member (op =) fun_names v) andalso
not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
in
null b orelse
raise PRIMREC ("extra variable(s) in right-hand side: " ^
commas (map (Syntax.string_of_term lthy) b), [eqn])
end;
in
{fun_name = fun_name,
rec_type = body_type (type_of ctr),
ctr = ctr,
ctr_args = ctr_args,
left_args = left_args,
right_args = right_args,
res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
rhs_term = rhs,
user_eqn = eqn'}
end;
fun subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls =
let
fun try_nested_rec bound_Ts y t =
AList.lookup (op =) nested_calls y
|> Option.map (fn y' => rewrite_nested_rec_call lthy has_call get_ctr_pos bound_Ts y y' t);
fun subst bound_Ts (t as g' $ y) =
let
fun subst_rec () = subst bound_Ts g' $ subst bound_Ts y;
val y_head = head_of y;
in
if not (member (op =) ctr_args y_head) then
subst_rec ()
else
(case try_nested_rec bound_Ts y_head t of
SOME t' => t'
| NONE =>
let val (g, g_args) = strip_comb g' in
(case try (get_ctr_pos o fst o dest_Free) g of
SOME ctr_pos =>
(length g_args >= ctr_pos orelse
raise PRIMREC ("too few arguments in recursive call", [t]);
(case AList.lookup (op =) mutual_calls y of
SOME y' => list_comb (y', g_args)
| NONE => subst_rec ()))
| NONE => subst_rec ())
end)
end
| subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
| subst _ t = t
fun subst' t =
if has_call t then
(* FIXME detect this case earlier? *)
raise PRIMREC ("recursive call not directly applied to constructor argument", [t])
else
try_nested_rec [] (head_of t) t |> the_default t
in
subst' o subst []
end;
fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec)
(eqn_data_opt : eqn_data option) =
(case eqn_data_opt of
NONE => undef_const
| SOME {ctr_args, left_args, right_args, rhs_term = t, ...} =>
let
val calls = #calls ctr_spec;
val n_args = fold (Integer.add o (fn Mutual_Rec _ => 2 | _ => 1)) calls 0;
val no_calls' = tag_list 0 calls
|> map_filter (try (apsnd (fn No_Rec p => p | Mutual_Rec (p, _) => p)));
val mutual_calls' = tag_list 0 calls
|> map_filter (try (apsnd (fn Mutual_Rec (_, p) => p)));
val nested_calls' = tag_list 0 calls
|> map_filter (try (apsnd (fn Nested_Rec p => p)));
fun ensure_unique frees t =
if member (op =) frees t then Free (the_single (Term.variant_frees t [dest_Free t])) else t;
val args = replicate n_args ("", dummyT)
|> Term.rename_wrt_term t
|> map Free
|> fold (fn (ctr_arg_idx, (arg_idx, _)) =>
nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
no_calls'
|> fold (fn (ctr_arg_idx, (arg_idx, T)) => fn xs =>
nth_map arg_idx (K (ensure_unique xs
(retype_const_or_free T (nth ctr_args ctr_arg_idx)))) xs)
mutual_calls'
|> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
nth_map arg_idx (K (retype_const_or_free T (nth ctr_args ctr_arg_idx))))
nested_calls';
val fun_name_ctr_pos_list =
map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
val mutual_calls = map (map_prod (nth ctr_args) (nth args o fst)) mutual_calls';
val nested_calls = map (map_prod (nth ctr_args) (nth args o fst)) nested_calls';
in
t
|> subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls
|> fold_rev lambda (args @ left_args @ right_args)
end);
fun build_defs lthy nonexhaustive bs mxs (funs_data : eqn_data list list)
(rec_specs : rec_spec list) has_call =
let
val n_funs = length funs_data;
val ctr_spec_eqn_data_list' =
(take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
|> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
##> (fn x => null x orelse
raise PRIMREC ("excess equations in definition", map #rhs_term x)) #> fst);
val _ = ctr_spec_eqn_data_list' |> map (fn ({ctr, ...}, x) =>
if length x > 1 then raise PRIMREC ("multiple equations for constructor", map #user_eqn x)
else if length x = 1 orelse nonexhaustive then ()
else warning ("no equation for constructor " ^ Syntax.string_of_term lthy ctr));
val ctr_spec_eqn_data_list =
ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
val recs = take n_funs rec_specs |> map #recx;
val rec_args = ctr_spec_eqn_data_list
|> sort ((op <) o pairself (#offset o fst) |> make_ord)
|> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
val ctr_poss = map (fn x =>
if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
raise PRIMREC ("inconstant constructor pattern position for function " ^
quote (#fun_name (hd x)), [])
else
hd x |> #left_args |> length) funs_data;
in
(recs, ctr_poss)
|-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
|> Syntax.check_terms lthy
|> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
bs mxs
end;
fun find_rec_calls has_call ({ctr, ctr_args, rhs_term, ...} : eqn_data) =
let
fun find bound_Ts (Abs (_, T, b)) ctr_arg = find (T :: bound_Ts) b ctr_arg
| find bound_Ts (t as _ $ _) ctr_arg =
let
val typof = curry fastype_of1 bound_Ts;
val (f', args') = strip_comb t;
val n = find_index (equal ctr_arg o head_of) args';
in
if n < 0 then
find bound_Ts f' ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args'
else
let
val (f, args as arg :: _) = chop n args' |>> curry list_comb f'
val (arg_head, arg_args) = Term.strip_comb arg;
in
if has_call f then
mk_partial_compN (length arg_args) (typof arg_head) f ::
maps (fn x => find bound_Ts x ctr_arg) args
else
find bound_Ts f ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args
end
end
| find _ _ _ = [];
in
map (find [] rhs_term) ctr_args
|> (fn [] => NONE | callss => SOME (ctr, callss))
end;
fun mk_primrec_tac ctxt num_extra_args map_ident0s map_comps fun_defs recx =
unfold_thms_tac ctxt fun_defs THEN
HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
unfold_thms_tac ctxt (nested_simps ctxt @ map_ident0s @ map_comps) THEN
HEADGOAL (rtac refl);
fun prepare_primrec nonexhaustive fixes specs lthy0 =
let
val thy = Proof_Context.theory_of lthy0;
val (bs, mxs) = map_split (apfst fst) fixes;
val fun_names = map Binding.name_of bs;
val eqns_data = map (dissect_eqn lthy0 fun_names) specs;
val funs_data = eqns_data
|> partition_eq ((op =) o pairself #fun_name)
|> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
|> map (fn (x, y) => the_single y
handle List.Empty => raise PRIMREC ("missing equations for function " ^ quote x, []));
val frees = map (fst #>> Binding.name_of #> Free) fixes;
val has_call = exists_subterm (member (op =) frees);
val arg_Ts = map (#rec_type o hd) funs_data;
val res_Ts = map (#res_type o hd) funs_data;
val callssss = funs_data
|> map (partition_eq ((op =) o pairself #ctr))
|> map (maps (map_filter (find_rec_calls has_call)));
fun is_only_old_datatype (Type (s, _)) =
is_some (Datatype_Data.get_info thy s) andalso not (is_new_datatype lthy0 s)
| is_only_old_datatype _ = false;
val _ = if exists is_only_old_datatype arg_Ts then raise OLD_PRIMREC () else ();
val _ = (case filter_out (fn (_, T) => Sign.of_sort thy (T, @{sort type})) (bs ~~ res_Ts) of
[] => ()
| (b, _) :: _ => raise PRIMREC ("type of " ^ Binding.print b ^ " contains top sort", []));
val ((n2m, rec_specs, _, common_induct, inducts), lthy) =
rec_specs_of bs arg_Ts res_Ts frees callssss lthy0;
val actual_nn = length funs_data;
val ctrs = maps (map #ctr o #ctr_specs) rec_specs;
val _ =
map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
raise PRIMREC ("argument " ^ quote (Syntax.string_of_term lthy ctr) ^
" is not a constructor in left-hand side", [user_eqn])) eqns_data;
val defs = build_defs lthy nonexhaustive bs mxs funs_data rec_specs has_call;
fun prove lthy' def_thms' ({ctr_specs, fp_nesting_map_ident0s, fp_nesting_map_comps, ...}
: rec_spec) (fun_data : eqn_data list) =
let
val js =
find_indices (op = o pairself (fn {fun_name, ctr, ...} => (fun_name, ctr)))
fun_data eqns_data;
val def_thms = map (snd o snd) def_thms';
val simp_thms = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
|> fst
|> map_filter (try (fn (x, [y]) =>
(#fun_name x, #user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
|> map2 (fn j => fn (fun_name, user_eqn, num_extra_args, rec_thm) =>
mk_primrec_tac lthy' num_extra_args fp_nesting_map_ident0s fp_nesting_map_comps
def_thms rec_thm
|> K |> Goal.prove_sorry lthy' [] [] user_eqn
(* for code extraction from proof terms: *)
|> singleton (Proof_Context.export lthy' lthy)
|> Thm.name_derivation (Sign.full_name thy (Binding.name fun_name) ^
Long_Name.separator ^ simpsN ^
(if js = [0] then "" else "_" ^ string_of_int (j + 1))))
js;
in
(js, simp_thms)
end;
val notes =
(if n2m then
map2 (fn name => fn thm => (name, inductN, [thm], [])) fun_names (take actual_nn inducts)
else
[])
|> map (fn (prefix, thmN, thms, attrs) =>
((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));
val common_name = mk_common_name fun_names;
val common_notes =
(if n2m then [(inductN, [common_induct], [])] else [])
|> map (fn (thmN, thms, attrs) =>
((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
in
(((fun_names, defs),
fn lthy => fn defs =>
split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),
lthy |> Local_Theory.notes (notes @ common_notes) |> snd)
end;
fun add_primrec_simple' opts fixes ts lthy =
let
val nonexhaustive = member (op =) opts Nonexhaustive_Option;
val (((names, defs), prove), lthy') = prepare_primrec nonexhaustive fixes ts lthy
handle ERROR str => raise PRIMREC (str, []);
in
lthy'
|> fold_map Local_Theory.define defs
|-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))
end
handle PRIMREC (str, eqns) =>
if null eqns then
error ("primrec error:\n " ^ str)
else
error ("primrec error:\n " ^ str ^ "\nin\n " ^
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
val add_primrec_simple = add_primrec_simple' [];
fun gen_primrec old_primrec prep_spec opts
(raw_fixes : (binding * 'a option * mixfix) list) raw_specs lthy =
let
val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)
val _ = null d orelse raise PRIMREC ("duplicate function name(s): " ^ commas d, []);
val (fixes, specs) = fst (prep_spec raw_fixes raw_specs lthy);
val mk_notes =
flat ooo map3 (fn js => fn prefix => fn thms =>
let
val (bs, attrss) = map_split (fst o nth specs) js;
val notes =
map3 (fn b => fn attrs => fn thm =>
((Binding.qualify false prefix b, code_nitpicksimp_simp_attrs @ attrs),
[([thm], [])]))
bs attrss thms;
in
((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes
end);
in
lthy
|> add_primrec_simple' opts fixes (map snd specs)
|-> (fn (names, (ts, (jss, simpss))) =>
Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)
#> Local_Theory.notes (mk_notes jss names simpss)
#>> pair ts o map snd)
end
handle OLD_PRIMREC () => old_primrec raw_fixes raw_specs lthy |>> apsnd single;
val add_primrec = gen_primrec Primrec.add_primrec Specification.check_spec [];
val add_primrec_cmd = gen_primrec Primrec.add_primrec_cmd Specification.read_spec;
fun add_primrec_global fixes specs =
Named_Target.theory_init
#> add_primrec fixes specs
##> Local_Theory.exit_global;
fun add_primrec_overloaded ops fixes specs =
Overloading.overloading ops
#> add_primrec fixes specs
##> Local_Theory.exit_global;
val primrec_option_parser = Parse.group (fn () => "option")
(Parse.reserved "nonexhaustive" >> K Nonexhaustive_Option)
val _ = Outer_Syntax.local_theory @{command_spec "primrec"}
"define primitive recursive functions"
((Scan.optional (@{keyword "("} |--
Parse.!!! (Parse.list1 primrec_option_parser) --| @{keyword ")"}) []) --
(Parse.fixes -- Parse_Spec.where_alt_specs)
>> (fn (opts, (fixes, specs)) => snd o add_primrec_cmd opts fixes specs));
end;