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(* Title: HOL/Tools/BNF/bnf_lfp_rec_sugar.ML
Author: Lorenz Panny, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Copyright 2013
Recursor sugar ("primrec").
*)
signature BNF_LFP_REC_SUGAR =
sig
datatype rec_option =
Plugins_Option of Proof.context -> Plugin_Name.filter |
Nonexhaustive_Option |
Transfer_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,
fp_nesting_pred_maps: 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_sugar: Ctr_Sugar.ctr_sugar,
recx: term,
rec_thms: thm list};
type lfp_rec_extension =
{nested_simps: thm list,
special_endgame_tac: Proof.context -> thm list -> thm list -> thm list -> tactic,
is_new_datatype: Proof.context -> string -> bool,
basic_lfp_sugars_of: 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 list * thm
* Token.src list * bool * local_theory,
rewrite_nested_rec_call: (Proof.context -> (term -> bool) -> (string -> int) -> typ list ->
term -> term -> term -> term) option};
val register_lfp_rec_extension: lfp_rec_extension -> theory -> theory
val default_basic_lfp_sugars_of: 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 list * thm
* Token.src list * bool * local_theory
val rec_specs_of: binding list -> typ list -> typ list -> term list ->
(term * term list list) list list -> local_theory ->
(bool * rec_spec list * typ list * thm * thm list * Token.src list * typ list) * local_theory
val lfp_rec_sugar_interpretation: string ->
(BNF_FP_Rec_Sugar_Util.fp_rec_sugar -> local_theory -> local_theory) -> theory -> theory
val primrec: bool -> rec_option list -> (binding * typ option * mixfix) list ->
Specification.multi_specs -> local_theory ->
(term list * thm list * thm list list) * local_theory
val primrec_cmd: bool -> rec_option list -> (binding * string option * mixfix) list ->
Specification.multi_specs_cmd -> local_theory ->
(term list * thm list * thm list list) * local_theory
val primrec_global: bool -> rec_option list -> (binding * typ option * mixfix) list ->
Specification.multi_specs -> theory -> (term list * thm list * thm list list) * theory
val primrec_overloaded: bool -> rec_option list -> (string * (string * typ) * bool) list ->
(binding * typ option * mixfix) list ->
Specification.multi_specs -> theory -> (term list * thm list * thm list list) * theory
val primrec_simple: bool -> ((binding * typ) * mixfix) list -> term list -> local_theory ->
((string list * (binding -> binding) list)
* (term list * thm 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 nitpicksimp_simp_attrs = nitpicksimp_attrs @ simp_attrs;
exception OLD_PRIMREC of unit;
datatype rec_option =
Plugins_Option of Proof.context -> Plugin_Name.filter |
Nonexhaustive_Option |
Transfer_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,
fp_nesting_pred_maps: 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_sugar: ctr_sugar,
recx: term,
rec_thms: thm list};
type lfp_rec_extension =
{nested_simps: thm list,
special_endgame_tac: Proof.context -> thm list -> thm list -> thm list -> tactic,
is_new_datatype: Proof.context -> string -> bool,
basic_lfp_sugars_of: 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 list * thm
* Token.src list * bool * local_theory,
rewrite_nested_rec_call: (Proof.context -> (term -> bool) -> (string -> int) -> typ list ->
term -> term -> term -> term) option};
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 special_endgame_tac ctxt =
(case Data.get (Proof_Context.theory_of ctxt) of
SOME {special_endgame_tac, ...} => special_endgame_tac ctxt
| NONE => K (K (K no_tac)));
fun is_new_datatype ctxt =
(case Data.get (Proof_Context.theory_of ctxt) of
SOME {is_new_datatype, ...} => is_new_datatype ctxt
| NONE => K true);
fun default_basic_lfp_sugars_of _ [Type (arg_T_name, _)] _ _ ctxt =
let
val ctr_sugar as {T, ctrs, casex, case_thms, ...} =
(case ctr_sugar_of ctxt arg_T_name of
SOME ctr_sugar => ctr_sugar
| NONE => error ("Unsupported type " ^ quote arg_T_name ^ " at this stage"));
val C = body_type (fastype_of casex);
val fun_arg_Tsss = map (map single o binder_types o fastype_of) ctrs;
val basic_lfp_sugar =
{T = T, fp_res_index = 0, C = C, fun_arg_Tsss = fun_arg_Tsss, ctr_sugar = ctr_sugar,
recx = casex, rec_thms = case_thms};
in
([], [0], [basic_lfp_sugar], [], [], [], TrueI (*dummy*), [], false, ctxt)
end
| default_basic_lfp_sugars_of _ [T] _ _ ctxt =
error ("Cannot recurse through type " ^ quote (Syntax.string_of_typ ctxt T))
| default_basic_lfp_sugars_of _ _ _ _ _ = error "Unsupported mutual recursion at this stage";
fun basic_lfp_sugars_of bs arg_Ts callers callssss lthy =
(case Data.get (Proof_Context.theory_of lthy) of
SOME {basic_lfp_sugars_of, ...} => basic_lfp_sugars_of
| NONE => default_basic_lfp_sugars_of) bs arg_Ts callers callssss lthy;
fun rewrite_nested_rec_call ctxt =
(case Data.get (Proof_Context.theory_of ctxt) of
SOME {rewrite_nested_rec_call = SOME f, ...} => f ctxt
| _ => error "Unsupported nested recursion");
structure LFP_Rec_Sugar_Plugin = Plugin(type T = fp_rec_sugar);
fun lfp_rec_sugar_interpretation name f =
LFP_Rec_Sugar_Plugin.interpretation name (fn fp_rec_sugar => fn lthy =>
f (transfer_fp_rec_sugar (Proof_Context.theory_of lthy) fp_rec_sugar) lthy);
val interpret_lfp_rec_sugar = LFP_Rec_Sugar_Plugin.data;
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,
fp_nesting_pred_maps, common_induct, induct_attrs, n2m, lthy) =
basic_lfp_sugars_of bs arg_Ts callers callssss0 lthy0;
val perm_basic_lfp_sugars = sort (int_ord o apply2 #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_fpTs = map #T perm_basic_lfp_sugars;
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 fpTs = unpermute perm_fpTs;
val Cs = unpermute perm_Cs;
val ctr_offsets = unpermute perm_ctr_offsets;
val As_rho = tvar_subst thy (take nn0 fpTs) 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 =
@{map 4} 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 perm_Cs' (substAT T) recx,
fp_nesting_map_ident0s = fp_nesting_map_ident0s, fp_nesting_map_comps = fp_nesting_map_comps,
fp_nesting_pred_maps = fp_nesting_pred_maps,
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,
induct_attrs, map #T basic_lfp_sugars), lthy)
end;
val undef_const = Const (\<^const_name>\<open>undefined\<close>, 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 ctxt fun_names eqn0 =
let
val eqn = drop_all eqn0 |> HOLogic.dest_Trueprop
handle TERM _ => ill_formed_equation_lhs_rhs ctxt [eqn0];
val (lhs, rhs) = HOLogic.dest_eq eqn
handle TERM _ => ill_formed_equation_lhs_rhs ctxt [eqn];
val (fun_name, args) = strip_comb lhs
|>> (fn x => if is_Free x then fst (dest_Free x) else ill_formed_equation_head ctxt [eqn]);
val (left_args, rest) = chop_prefix is_Free args;
val (nonfrees, right_args) = chop_suffix is_Free rest;
val num_nonfrees = length nonfrees;
val _ = num_nonfrees = 1 orelse
(if num_nonfrees = 0 then missing_pattern ctxt [eqn]
else more_than_one_nonvar_in_lhs ctxt [eqn]);
val _ = member (op =) fun_names fun_name orelse raise ill_formed_equation_head ctxt [eqn];
val (ctr, ctr_args) = strip_comb (the_single nonfrees);
val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
partially_applied_ctr_in_pattern ctxt [eqn];
val _ = check_duplicate_variables_in_lhs ctxt [eqn] (left_args @ ctr_args @ right_args)
val _ = forall is_Free ctr_args orelse nonprimitive_pattern_in_lhs ctxt [eqn];
val _ =
let
val bads =
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 ctxt v)) then
cons x
else
I
| _ => I) rhs [];
in
null bads orelse extra_variable_in_rhs ctxt [eqn] (hd bads)
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 = eqn0}
end;
fun subst_rec_calls ctxt 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 ctxt has_call get_ctr_pos bound_Ts y y' t);
fun subst bound_Ts (t as g' $ y) =
let
fun subst_comb (h $ z) = subst bound_Ts h $ subst bound_Ts z
| subst_comb t = t;
val y_head = head_of y;
in
if not (member (op =) ctr_args y_head) then
subst_comb t
else
(case try_nested_rec bound_Ts y_head t of
SOME t' => subst_comb t'
| NONE =>
let val (g, g_args) = strip_comb g' in
(case try (get_ctr_pos o fst o dest_Free) g of
SOME ~1 => subst_comb t
| SOME ctr_pos =>
(length g_args >= ctr_pos orelse too_few_args_in_rec_call ctxt [] t;
(case AList.lookup (op =) mutual_calls y of
SOME y' => list_comb (y', map (subst bound_Ts) g_args)
| NONE => subst_comb t))
| NONE => subst_comb t)
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 rec_call_not_apply_to_ctr_arg ctxt [] t
else try_nested_rec [] (head_of t) t |> the_default t;
in
subst' o subst []
end;
fun build_rec_arg ctxt (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 ctxt get_ctr_pos has_call ctr_args mutual_calls nested_calls
|> fold_rev lambda (args @ left_args @ right_args)
end);
fun build_defs ctxt nonexhaustives 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' =
maps (fn ((xs, ys), z) =>
let
val zs = replicate (length xs) z;
val (b, c) = finds (fn ((x, _), y) => #ctr x = #ctr y) (xs ~~ zs) ys;
val _ = null c orelse excess_equations ctxt (map #rhs_term c);
in b end) (map #ctr_specs (take n_funs rec_specs) ~~ funs_data ~~ nonexhaustives);
val (_ : unit list) = ctr_spec_eqn_data_list' |> map (fn (({ctr, ...}, nonexhaustive), x) =>
if length x > 1 then
multiple_equations_for_ctr ctxt (map #user_eqn x)
else if length x = 1 orelse nonexhaustive orelse not (Context_Position.is_visible ctxt) then
()
else
no_equation_for_ctr_warning ctxt [] ctr);
val ctr_spec_eqn_data_list =
map (apfst fst) 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 apply2 (#offset o fst) |> make_ord)
|> map (uncurry (build_rec_arg ctxt funs_data has_call) o apsnd (try the_single));
val ctr_poss = map (fn x =>
if length (distinct (op = o apply2 (length o #left_args)) x) <> 1 then
inconstant_pattern_pos_for_fun ctxt [] (#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 ctxt
|> @{map 3} (fn b => fn mx => fn t =>
((b, mx), ((Binding.concealed (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 fp_nesting_map_ident0s fp_nesting_map_comps
fp_nesting_pred_maps fun_defs recx =
unfold_thms_tac ctxt fun_defs THEN
HEADGOAL (rtac ctxt (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
unfold_thms_tac ctxt (nested_simps ctxt @ fp_nesting_map_ident0s @ fp_nesting_map_comps @
fp_nesting_pred_maps) THEN
REPEAT_DETERM (HEADGOAL (rtac ctxt refl) ORELSE
special_endgame_tac ctxt fp_nesting_map_ident0s fp_nesting_map_comps fp_nesting_pred_maps);
fun prepare_primrec plugins nonexhaustives transfers 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 qualifys = map (fold_rev (uncurry Binding.qualify o swap) o Binding.path_of) bs;
val eqns_data = map (dissect_eqn lthy0 fun_names) specs;
val funs_data = eqns_data
|> partition_eq (op = o apply2 #fun_name)
|> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
|> map (fn (x, y) => the_single y
handle List.Empty => missing_equations_for_fun 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 apply2 #ctr))
|> map (maps (map_filter (find_rec_calls has_call)));
fun is_only_old_datatype (Type (s, _)) =
is_some (Old_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 _ = List.app (uncurry (check_top_sort lthy0)) (bs ~~ res_Ts);
val ((n2m, rec_specs, _, common_induct, inducts, induct_attrs, Ts), 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 _ = List.app (fn {ctr, user_eqn, ...} =>
ignore (member (op =) ctrs ctr orelse not_constructor_in_pattern lthy0 [user_eqn] ctr))
eqns_data;
val defs = build_defs lthy nonexhaustives bs mxs funs_data rec_specs has_call;
fun prove def_thms ({ctr_specs, fp_nesting_map_ident0s, fp_nesting_map_comps,
fp_nesting_pred_maps, ...} : rec_spec) (fun_data : eqn_data list) lthy' =
let
val js =
find_indices (op = o apply2 (fn {fun_name, ctr, ...} => (fun_name, ctr)))
fun_data eqns_data;
val simps = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
|> fst
|> map_filter (try (fn (x, [y]) =>
(#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
|> map (fn (user_eqn, num_extra_args, rec_thm) =>
Goal.prove_sorry lthy' [] [] user_eqn
(fn {context = ctxt, prems = _} =>
mk_primrec_tac ctxt num_extra_args fp_nesting_map_ident0s fp_nesting_map_comps
fp_nesting_pred_maps def_thms rec_thm)
|> Thm.close_derivation \<^here>);
in
((js, simps), lthy')
end;
val notes =
(if n2m then
@{map 3} (fn name => fn qualify => fn thm => (name, qualify, inductN, [thm], induct_attrs))
fun_names qualifys (take actual_nn inducts)
else
[])
|> map (fn (prefix, qualify, thmN, thms, attrs) =>
((qualify (Binding.qualify true prefix (Binding.name thmN)), attrs), [(thms, [])]));
val common_name = mk_common_name fun_names;
val common_qualify = fold_rev I qualifys;
val common_notes =
(if n2m then [(inductN, [common_induct], [])] else [])
|> map (fn (thmN, thms, attrs) =>
((common_qualify (Binding.qualify true common_name (Binding.name thmN)), attrs),
[(thms, [])]));
in
(((fun_names, qualifys, arg_Ts, defs),
fn lthy => fn defs =>
let
val def_thms = map (snd o snd) defs;
val ts = map fst defs;
val phi = Local_Theory.target_morphism lthy;
val fp_rec_sugar =
{transfers = transfers, fun_names = fun_names, funs = map (Morphism.term phi) ts,
fun_defs = Morphism.fact phi def_thms, fpTs = take actual_nn Ts};
in
map_prod split_list (interpret_lfp_rec_sugar plugins fp_rec_sugar)
(@{fold_map 2} (prove (map (snd o snd) defs)) (take actual_nn rec_specs) funs_data lthy)
end),
lthy |> Local_Theory.notes (notes @ common_notes) |> snd)
end;
fun primrec_simple0 int plugins nonexhaustive transfer fixes ts lthy =
let
val _ = check_duplicate_const_names (map (fst o fst) fixes);
val actual_nn = length fixes;
val nonexhaustives = replicate actual_nn nonexhaustive;
val transfers = replicate actual_nn transfer;
val (((names, qualifys, arg_Ts, defs), prove), lthy') =
prepare_primrec plugins nonexhaustives transfers fixes ts lthy;
in
lthy'
|> fold_map Local_Theory.define defs
|> tap (uncurry (print_def_consts int))
|-> (fn defs => fn lthy =>
let
val ((jss, simpss), lthy) = prove lthy defs;
val res =
{prefix = (names, qualifys),
types = map (#1 o dest_Type) arg_Ts,
result = (map fst defs, map (snd o snd) defs, (jss, simpss))};
in (res, lthy) end)
end;
fun primrec_simple int fixes ts lthy =
primrec_simple0 int Plugin_Name.default_filter false false fixes ts lthy
|>> (fn {prefix, result, ...} => (prefix, result))
handle OLD_PRIMREC () =>
Old_Primrec.primrec_simple int fixes ts lthy
|>> (fn {prefix, result = (ts, thms), ...} =>
(map_split (rpair I) [prefix], (ts, [], ([], [thms]))))
fun gen_primrec old_primrec prep_spec int opts raw_fixes raw_specs lthy =
let
val plugins = get_first (fn Plugins_Option f => SOME (f lthy) | _ => NONE) (rev opts)
|> the_default Plugin_Name.default_filter;
val nonexhaustive = exists (can (fn Nonexhaustive_Option => ())) opts;
val transfer = exists (can (fn Transfer_Option => ())) opts;
val (fixes, specs) = fst (prep_spec raw_fixes raw_specs lthy);
val spec_name = Binding.conglomerate (map (#1 o #1) fixes);
val mk_notes =
flat oooo @{map 4} (fn js => fn prefix => fn qualify => fn thms =>
let
val (bs, attrss) = map_split (fst o nth specs) js;
val notes =
@{map 3} (fn b => fn attrs => fn thm =>
((Binding.qualify false prefix b, nitpicksimp_simp_attrs @ attrs),
[([thm], [])]))
bs attrss thms;
in
((qualify (Binding.qualify true prefix (Binding.name simpsN)), []), [(thms, [])]) :: notes
end);
in
lthy
|> primrec_simple0 int plugins nonexhaustive transfer fixes (map snd specs)
|-> (fn {prefix = (names, qualifys), types, result = (ts, defs, (jss, simpss))} =>
Spec_Rules.add spec_name (Spec_Rules.equational_primrec types) ts (flat simpss)
#> Local_Theory.notes (mk_notes jss names qualifys simpss)
#-> (fn notes =>
plugins code_plugin ? Code.declare_default_eqns (map (rpair true) (maps snd notes))
#> pair (ts, defs, map_filter (fn ("", _) => NONE | (_, thms) => SOME thms) notes)))
end
handle OLD_PRIMREC () =>
old_primrec int raw_fixes raw_specs lthy
|>> (fn {result = (ts, thms), ...} => (ts, [], [thms]));
val primrec = gen_primrec Old_Primrec.primrec Specification.check_multi_specs;
val primrec_cmd = gen_primrec Old_Primrec.primrec_cmd Specification.read_multi_specs;
fun primrec_global int opts fixes specs =
Named_Target.theory_init
#> primrec int opts fixes specs
##> Local_Theory.exit_global;
fun primrec_overloaded int opts ops fixes specs =
Overloading.overloading ops
#> primrec int opts fixes specs
##> Local_Theory.exit_global;
val rec_option_parser = Parse.group (K "option")
(Plugin_Name.parse_filter >> Plugins_Option
|| Parse.reserved "nonexhaustive" >> K Nonexhaustive_Option
|| Parse.reserved "transfer" >> K Transfer_Option);
val _ = Outer_Syntax.local_theory \<^command_keyword>\<open>primrec\<close>
"define primitive recursive functions"
((Scan.optional (\<^keyword>\<open>(\<close> |-- Parse.!!! (Parse.list1 rec_option_parser)
--| \<^keyword>\<open>)\<close>) []) -- Parse_Spec.specification
>> (fn (opts, (fixes, specs)) => snd o primrec_cmd true opts fixes specs));
end;
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