src/HOL/BNF/Tools/bnf_fp_rec_sugar.ML
author blanchet
Sat Oct 26 13:01:41 2013 +0200 (2013-10-26)
changeset 54209 16723c834406
parent 54208 513e91175170
child 54215 ab0595cb9fe9
permissions -rw-r--r--
tuning
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(*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar.ML
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    Author:     Lorenz Panny, TU Muenchen
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    Copyright   2013
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Recursor and corecursor sugar.
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*)
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signature BNF_FP_REC_SUGAR =
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sig
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  val add_primrec: (binding * typ option * mixfix) list ->
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    (Attrib.binding * term) list -> local_theory -> (term list * thm list list) * local_theory
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  val add_primrec_cmd: (binding * string option * mixfix) list ->
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    (Attrib.binding * string) list -> local_theory -> (term list * thm list list) * local_theory
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  val add_primrec_global: (binding * typ option * mixfix) list ->
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    (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
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  val add_primrec_overloaded: (string * (string * typ) * bool) list ->
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    (binding * typ option * mixfix) list ->
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    (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
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  val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
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    local_theory -> (string list * (term list * (int list list * thm list list))) * local_theory
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  val add_primcorecursive_cmd: bool ->
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    (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
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    Proof.context -> Proof.state
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  val add_primcorec_cmd: bool ->
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    (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
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    local_theory -> local_theory
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end;
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structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
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struct
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open BNF_Util
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open BNF_FP_Util
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open BNF_FP_Rec_Sugar_Util
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open BNF_FP_Rec_Sugar_Tactics
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val codeN = "code";
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val ctrN = "ctr";
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val discN = "disc";
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val selN = "sel";
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val nitpicksimp_attrs = @{attributes [nitpick_simp]};
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val simp_attrs = @{attributes [simp]};
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val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
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val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs;
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exception Primrec_Error of string * term list;
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fun primrec_error str = raise Primrec_Error (str, []);
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fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
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fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
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fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
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val free_name = try (fn Free (v, _) => v);
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val const_name = try (fn Const (v, _) => v);
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val undef_const = Const (@{const_name undefined}, dummyT);
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fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
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  |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n);
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val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
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fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,
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  strip_qnt_body @{const_name all} t)
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fun abstract vs =
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  let fun a n (t $ u) = a n t $ a n u
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        | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
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        | a n t = let val idx = find_index (equal t) vs in
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            if idx < 0 then t else Bound (n + idx) end
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  in a 0 end;
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fun mk_prod1 Ts (t, u) = HOLogic.pair_const (fastype_of1 (Ts, t)) (fastype_of1 (Ts, u)) $ t $ u;
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fun mk_tuple1 Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 Ts));
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fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes
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  |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
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  |> map_filter I;
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(* Primrec *)
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type eqn_data = {
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  fun_name: string,
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  rec_type: typ,
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  ctr: term,
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  ctr_args: term list,
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  left_args: term list,
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  right_args: term list,
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  res_type: typ,
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  rhs_term: term,
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  user_eqn: term
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};
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fun dissect_eqn lthy fun_names eqn' =
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  let
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    val eqn = drop_All eqn' |> HOLogic.dest_Trueprop
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      handle TERM _ =>
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        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
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    val (lhs, rhs) = HOLogic.dest_eq eqn
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        handle TERM _ =>
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          primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
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    val (fun_name, args) = strip_comb lhs
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      |>> (fn x => if is_Free x then fst (dest_Free x)
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          else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
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    val (left_args, rest) = take_prefix is_Free args;
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    val (nonfrees, right_args) = take_suffix is_Free rest;
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    val num_nonfrees = length nonfrees;
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    val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then
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      primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
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      primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
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    val _ = member (op =) fun_names fun_name orelse
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      primrec_error_eqn "malformed function equation (does not start with function name)" eqn
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    val (ctr, ctr_args) = strip_comb (the_single nonfrees);
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    val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
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      primrec_error_eqn "partially applied constructor in pattern" eqn;
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    val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
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      primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
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        "\" in left-hand side") eqn end;
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    val _ = forall is_Free ctr_args orelse
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      primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
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    val _ =
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      let val b = fold_aterms (fn x as Free (v, _) =>
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        if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
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        not (member (op =) fun_names v) andalso
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        not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
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      in
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        null b orelse
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        primrec_error_eqn ("extra variable(s) in right-hand side: " ^
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          commas (map (Syntax.string_of_term lthy) b)) eqn
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      end;
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  in
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    {fun_name = fun_name,
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     rec_type = body_type (type_of ctr),
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     ctr = ctr,
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     ctr_args = ctr_args,
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     left_args = left_args,
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     right_args = right_args,
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     res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
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     rhs_term = rhs,
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     user_eqn = eqn'}
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  end;
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fun rewrite_map_arg get_ctr_pos rec_type res_type =
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  let
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    val pT = HOLogic.mk_prodT (rec_type, res_type);
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    val maybe_suc = Option.map (fn x => x + 1);
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    fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)
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      | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)
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      | subst d t =
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        let
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          val (u, vs) = strip_comb t;
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          val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1;
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        in
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          if ctr_pos >= 0 then
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            if d = SOME ~1 andalso length vs = ctr_pos then
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              list_comb (permute_args ctr_pos (snd_const pT), vs)
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            else if length vs > ctr_pos andalso is_some d
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                andalso d = try (fn Bound n => n) (nth vs ctr_pos) then
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              list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
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            else
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              primrec_error_eqn ("recursive call not directly applied to constructor argument") t
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          else
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            list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
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        end
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  in
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    subst (SOME ~1)
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  end;
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fun subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls =
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  let
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    fun try_nested_rec bound_Ts y t =
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      AList.lookup (op =) nested_calls y
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      |> Option.map (fn y' =>
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        massage_nested_rec_call lthy has_call (rewrite_map_arg get_ctr_pos) bound_Ts y y' t);
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    fun subst bound_Ts (t as g' $ y) =
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        let
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          fun subst_rec () = subst bound_Ts g' $ subst bound_Ts y;
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          val y_head = head_of y;
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        in
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          if not (member (op =) ctr_args y_head) then
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            subst_rec ()
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          else
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            (case try_nested_rec bound_Ts y_head t of
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              SOME t' => t'
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            | NONE =>
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              let val (g, g_args) = strip_comb g' in
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                (case try (get_ctr_pos o the) (free_name g) of
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                  SOME ctr_pos =>
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                  (length g_args >= ctr_pos orelse
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                   primrec_error_eqn "too few arguments in recursive call" t;
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                   (case AList.lookup (op =) mutual_calls y of
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                     SOME y' => list_comb (y', g_args)
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                   | NONE => subst_rec ()))
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                | NONE => subst_rec ())
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              end)
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        end
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      | subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
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      | subst _ t = t
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    fun subst' t =
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      if has_call t then
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        (* FIXME detect this case earlier? *)
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        primrec_error_eqn "recursive call not directly applied to constructor argument" t
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      else
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        try_nested_rec [] (head_of t) t |> the_default t
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  in
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    subst' o subst []
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  end;
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fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec)
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    (maybe_eqn_data : eqn_data option) =
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  (case maybe_eqn_data of
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    NONE => undef_const
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  | SOME {ctr_args, left_args, right_args, rhs_term = t, ...} =>
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    let
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      val calls = #calls ctr_spec;
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      val n_args = fold (Integer.add o (fn Mutual_Rec _ => 2 | _ => 1)) calls 0;
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      val no_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn No_Rec p => p | Mutual_Rec (p, _) => p)));
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      val mutual_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn Mutual_Rec (_, p) => p)));
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      val nested_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn Nested_Rec p => p)));
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      val args = replicate n_args ("", dummyT)
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        |> Term.rename_wrt_term t
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        |> map Free
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        |> fold (fn (ctr_arg_idx, (arg_idx, _)) =>
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            nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
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          no_calls'
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        |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
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            nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))
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          mutual_calls'
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        |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
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            nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))
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          nested_calls';
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      val fun_name_ctr_pos_list =
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        map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
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      val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
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      val mutual_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) mutual_calls';
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      val nested_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) nested_calls';
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    in
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      t
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      |> subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls
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      |> fold_rev lambda (args @ left_args @ right_args)
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    end);
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fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call =
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  let
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    val n_funs = length funs_data;
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    val ctr_spec_eqn_data_list' =
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      (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
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      |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
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          ##> (fn x => null x orelse
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            primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
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    val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
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      primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
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    val ctr_spec_eqn_data_list =
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      ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
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    val recs = take n_funs rec_specs |> map #recx;
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    val rec_args = ctr_spec_eqn_data_list
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      |> sort ((op <) o pairself (#offset o fst) |> make_ord)
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      |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
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    val ctr_poss = map (fn x =>
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      if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
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        primrec_error ("inconstant constructor pattern position for function " ^
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          quote (#fun_name (hd x)))
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      else
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        hd x |> #left_args |> length) funs_data;
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  in
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    (recs, ctr_poss)
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    |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
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    |> Syntax.check_terms lthy
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    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
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      bs mxs
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  end;
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fun massage_comp ctxt has_call bound_Ts t =
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  massage_nested_corec_call ctxt has_call (K (K (K I))) bound_Ts (fastype_of1 (bound_Ts, t)) t;
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fun find_rec_calls ctxt has_call (eqn_data : eqn_data) =
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  let
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    fun find bound_Ts (Abs (_, T, b)) ctr_arg = find (T :: bound_Ts) b ctr_arg
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      | find bound_Ts (t as _ $ _) ctr_arg =
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        let
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   292
          val typof = curry fastype_of1 bound_Ts;
blanchet@53303
   293
          val (f', args') = strip_comb t;
blanchet@54202
   294
          val n = find_index (equal ctr_arg o head_of) args';
blanchet@53303
   295
        in
blanchet@53303
   296
          if n < 0 then
blanchet@54202
   297
            find bound_Ts f' ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args'
blanchet@53303
   298
          else
blanchet@54202
   299
            let
blanchet@54202
   300
              val (f, args as arg :: _) = chop n args' |>> curry list_comb f'
blanchet@54202
   301
              val (arg_head, arg_args) = Term.strip_comb arg;
blanchet@54202
   302
            in
panny@53358
   303
              if has_call f then
blanchet@54202
   304
                mk_partial_compN (length arg_args) (typof f) (typof arg_head) f ::
blanchet@54202
   305
                maps (fn x => find bound_Ts x ctr_arg) args
blanchet@53303
   306
              else
blanchet@54202
   307
                find bound_Ts f ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args
blanchet@53303
   308
            end
blanchet@53303
   309
        end
blanchet@54202
   310
      | find _ _ _ = [];
blanchet@53303
   311
  in
blanchet@54202
   312
    map (find [] (#rhs_term eqn_data)) (#ctr_args eqn_data)
blanchet@53303
   313
    |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
blanchet@53303
   314
  end;
blanchet@53303
   315
traytel@54013
   316
fun prepare_primrec fixes specs lthy =
blanchet@53303
   317
  let
traytel@53352
   318
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   319
    val fun_names = map Binding.name_of bs;
traytel@54013
   320
    val eqns_data = map (dissect_eqn lthy fun_names) specs;
blanchet@53303
   321
    val funs_data = eqns_data
blanchet@53303
   322
      |> partition_eq ((op =) o pairself #fun_name)
blanchet@53303
   323
      |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
blanchet@53303
   324
      |> map (fn (x, y) => the_single y handle List.Empty =>
blanchet@53303
   325
          primrec_error ("missing equations for function " ^ quote x));
blanchet@53303
   326
panny@53358
   327
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
blanchet@53303
   328
    val arg_Ts = map (#rec_type o hd) funs_data;
blanchet@53303
   329
    val res_Ts = map (#res_type o hd) funs_data;
blanchet@53303
   330
    val callssss = funs_data
blanchet@53303
   331
      |> map (partition_eq ((op =) o pairself #ctr))
blanchet@54202
   332
      |> map (maps (map_filter (find_rec_calls lthy has_call)));
blanchet@53303
   333
blanchet@53830
   334
    val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =
blanchet@53794
   335
      rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53303
   336
blanchet@53303
   337
    val actual_nn = length funs_data;
blanchet@53303
   338
blanchet@53303
   339
    val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
blanchet@53303
   340
      map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
blanchet@53303
   341
        primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
blanchet@53303
   342
          " is not a constructor in left-hand side") user_eqn) eqns_data end;
blanchet@53303
   343
panny@53358
   344
    val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
blanchet@53303
   345
traytel@54013
   346
    fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec)
traytel@54013
   347
        (fun_data : eqn_data list) =
blanchet@53303
   348
      let
blanchet@53303
   349
        val def_thms = map (snd o snd) def_thms';
traytel@54013
   350
        val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
blanchet@53303
   351
          |> fst
blanchet@53303
   352
          |> map_filter (try (fn (x, [y]) =>
blanchet@53303
   353
            (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
blanchet@53303
   354
          |> map (fn (user_eqn, num_extra_args, rec_thm) =>
blanchet@53329
   355
            mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
blanchet@54176
   356
            |> K |> Goal.prove lthy [] [] user_eqn
blanchet@54176
   357
            |> Thm.close_derivation);
traytel@54013
   358
        val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data;
traytel@54013
   359
      in
traytel@54013
   360
        (poss, simp_thmss)
traytel@54013
   361
      end;
blanchet@53303
   362
traytel@54013
   363
    val notes =
traytel@54013
   364
      (if n2m then map2 (fn name => fn thm =>
traytel@54013
   365
        (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else [])
traytel@54013
   366
      |> map (fn (prefix, thmN, thms, attrs) =>
traytel@54013
   367
        ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   368
blanchet@53303
   369
    val common_name = mk_common_name fun_names;
blanchet@53303
   370
blanchet@53303
   371
    val common_notes =
traytel@54013
   372
      (if n2m then [(inductN, [induct_thm], [])] else [])
blanchet@53303
   373
      |> map (fn (thmN, thms, attrs) =>
blanchet@53303
   374
        ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   375
  in
traytel@54013
   376
    (((fun_names, defs),
traytel@54013
   377
      fn lthy => fn defs =>
traytel@54013
   378
        split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),
traytel@54013
   379
      lthy' |> Local_Theory.notes (notes @ common_notes) |> snd)
blanchet@53303
   380
  end;
blanchet@53303
   381
traytel@54013
   382
(* primrec definition *)
traytel@54013
   383
traytel@54013
   384
fun add_primrec_simple fixes ts lthy =
blanchet@53303
   385
  let
traytel@54013
   386
    val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy
traytel@54013
   387
      handle ERROR str => primrec_error str;
blanchet@53303
   388
  in
traytel@54013
   389
    lthy
traytel@54013
   390
    |> fold_map Local_Theory.define defs
traytel@54013
   391
    |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))
blanchet@53303
   392
  end
blanchet@53303
   393
  handle Primrec_Error (str, eqns) =>
blanchet@53303
   394
    if null eqns
blanchet@53303
   395
    then error ("primrec_new error:\n  " ^ str)
blanchet@53303
   396
    else error ("primrec_new error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
   397
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
blanchet@53303
   398
traytel@54013
   399
local
traytel@54013
   400
traytel@54028
   401
fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy =
traytel@54013
   402
  let
traytel@54013
   403
    val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)
traytel@54013
   404
    val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d);
traytel@54013
   405
traytel@54013
   406
    val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy);
traytel@54013
   407
traytel@54013
   408
    val mk_notes =
traytel@54013
   409
      flat ooo map3 (fn poss => fn prefix => fn thms =>
traytel@54013
   410
        let
traytel@54013
   411
          val (bs, attrss) = map_split (fst o nth specs) poss;
traytel@54013
   412
          val notes =
traytel@54013
   413
            map3 (fn b => fn attrs => fn thm =>
blanchet@54145
   414
              ((Binding.qualify false prefix b, code_nitpicksimp_simp_attrs @ attrs), [([thm], [])]))
traytel@54013
   415
            bs attrss thms;
traytel@54013
   416
        in
traytel@54013
   417
          ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes
traytel@54013
   418
        end);
traytel@54013
   419
  in
traytel@54013
   420
    lthy
traytel@54013
   421
    |> add_primrec_simple fixes (map snd specs)
traytel@54013
   422
    |-> (fn (names, (ts, (posss, simpss))) =>
traytel@54013
   423
      Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)
traytel@54013
   424
      #> Local_Theory.notes (mk_notes posss names simpss)
traytel@54013
   425
      #>> pair ts o map snd)
traytel@54013
   426
  end;
traytel@54013
   427
traytel@54013
   428
in
traytel@54013
   429
traytel@54013
   430
val add_primrec = gen_primrec Specification.check_spec;
traytel@54013
   431
val add_primrec_cmd = gen_primrec Specification.read_spec;
traytel@54013
   432
traytel@54013
   433
end;
traytel@54013
   434
traytel@54013
   435
fun add_primrec_global fixes specs thy =
traytel@54013
   436
  let
traytel@54013
   437
    val lthy = Named_Target.theory_init thy;
traytel@54013
   438
    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
traytel@54013
   439
    val simps' = burrow (Proof_Context.export lthy' lthy) simps;
traytel@54013
   440
  in ((ts, simps'), Local_Theory.exit_global lthy') end;
traytel@54013
   441
traytel@54013
   442
fun add_primrec_overloaded ops fixes specs thy =
traytel@54013
   443
  let
traytel@54013
   444
    val lthy = Overloading.overloading ops thy;
traytel@54013
   445
    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
traytel@54013
   446
    val simps' = burrow (Proof_Context.export lthy' lthy) simps;
traytel@54013
   447
  in ((ts, simps'), Local_Theory.exit_global lthy') end;
traytel@54013
   448
blanchet@53303
   449
blanchet@53303
   450
blanchet@53310
   451
(* Primcorec *)
blanchet@53303
   452
blanchet@54153
   453
type coeqn_data_disc = {
blanchet@53303
   454
  fun_name: string,
panny@53720
   455
  fun_T: typ,
panny@53401
   456
  fun_args: term list,
panny@53720
   457
  ctr: term,
panny@53341
   458
  ctr_no: int, (*###*)
panny@53720
   459
  disc: term,
panny@53654
   460
  prems: term list,
panny@53822
   461
  auto_gen: bool,
panny@54097
   462
  maybe_ctr_rhs: term option,
panny@54097
   463
  maybe_code_rhs: term option,
blanchet@53303
   464
  user_eqn: term
blanchet@53303
   465
};
blanchet@54001
   466
blanchet@54153
   467
type coeqn_data_sel = {
blanchet@53303
   468
  fun_name: string,
panny@53720
   469
  fun_T: typ,
panny@53401
   470
  fun_args: term list,
panny@53341
   471
  ctr: term,
panny@53341
   472
  sel: term,
blanchet@53303
   473
  rhs_term: term,
blanchet@53303
   474
  user_eqn: term
blanchet@53303
   475
};
blanchet@54001
   476
blanchet@54153
   477
datatype coeqn_data =
blanchet@54153
   478
  Disc of coeqn_data_disc |
blanchet@54153
   479
  Sel of coeqn_data_sel;
blanchet@53303
   480
panny@54160
   481
fun dissect_coeqn_disc seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
panny@54160
   482
    maybe_ctr_rhs maybe_code_rhs prems' concl matchedsss =
blanchet@53303
   483
  let
blanchet@53303
   484
    fun find_subterm p = let (* FIXME \<exists>? *)
panny@53401
   485
      fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
blanchet@53303
   486
        | f t = if p t then SOME t else NONE
blanchet@53303
   487
      in f end;
blanchet@53303
   488
panny@53654
   489
    val applied_fun = concl
panny@53654
   490
      |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
panny@53654
   491
      |> the
blanchet@54204
   492
      handle Option.Option => primrec_error_eqn "malformed discriminator formula" concl;
panny@53720
   493
    val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
blanchet@54209
   494
    val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
blanchet@53303
   495
panny@54160
   496
    val discs = map #disc basic_ctr_specs;
panny@54160
   497
    val ctrs = map #ctr basic_ctr_specs;
panny@53654
   498
    val not_disc = head_of concl = @{term Not};
panny@53401
   499
    val _ = not_disc andalso length ctrs <> 2 andalso
blanchet@54209
   500
      primrec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl;
panny@54160
   501
    val disc' = find_subterm (member (op =) discs o head_of) concl;
blanchet@54209
   502
    val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd)
blanchet@53303
   503
        |> (fn SOME t => let val n = find_index (equal t) ctrs in
blanchet@53303
   504
          if n >= 0 then SOME n else NONE end | _ => NONE);
panny@54160
   505
    val _ = is_some disc' orelse is_some eq_ctr0 orelse
panny@53654
   506
      primrec_error_eqn "no discriminator in equation" concl;
blanchet@53303
   507
    val ctr_no' =
panny@54160
   508
      if is_none disc' then the eq_ctr0 else find_index (equal (head_of (the disc'))) discs;
blanchet@53303
   509
    val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
panny@54160
   510
    val {ctr, disc, ...} = nth basic_ctr_specs ctr_no;
panny@53654
   511
panny@53654
   512
    val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
panny@53720
   513
    val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
panny@53720
   514
    val prems = map (abstract (List.rev fun_args)) prems';
panny@53720
   515
    val real_prems =
blanchet@54067
   516
      (if catch_all orelse seq then maps s_not_conj matchedss else []) @
panny@53654
   517
      (if catch_all then [] else prems);
blanchet@53303
   518
panny@53720
   519
    val matchedsss' = AList.delete (op =) fun_name matchedsss
panny@54065
   520
      |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
blanchet@53303
   521
panny@53654
   522
    val user_eqn =
panny@54097
   523
      (real_prems, concl)
panny@54097
   524
      |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
panny@54097
   525
      |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
blanchet@53303
   526
  in
panny@53341
   527
    (Disc {
blanchet@53303
   528
      fun_name = fun_name,
panny@53720
   529
      fun_T = fun_T,
panny@53401
   530
      fun_args = fun_args,
panny@53720
   531
      ctr = ctr,
blanchet@53303
   532
      ctr_no = ctr_no,
panny@54160
   533
      disc = disc,
panny@53654
   534
      prems = real_prems,
panny@53822
   535
      auto_gen = catch_all,
panny@54097
   536
      maybe_ctr_rhs = maybe_ctr_rhs,
panny@54097
   537
      maybe_code_rhs = maybe_code_rhs,
panny@53654
   538
      user_eqn = user_eqn
panny@53720
   539
    }, matchedsss')
blanchet@53303
   540
  end;
blanchet@53303
   541
blanchet@54209
   542
fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
blanchet@54209
   543
    maybe_of_spec eqn =
blanchet@53303
   544
  let
blanchet@53303
   545
    val (lhs, rhs) = HOLogic.dest_eq eqn
blanchet@53303
   546
      handle TERM _ =>
blanchet@53303
   547
        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
blanchet@53303
   548
    val sel = head_of lhs;
panny@53720
   549
    val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
blanchet@53303
   550
      handle TERM _ =>
blanchet@53303
   551
        primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@54160
   552
    val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
blanchet@53303
   553
      handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@54160
   554
    val {ctr, ...} =
blanchet@54209
   555
      (case maybe_of_spec of
blanchet@54209
   556
        SOME of_spec => the (find_first (equal of_spec o #ctr) basic_ctr_specs)
blanchet@54209
   557
      | NONE => filter (exists (equal sel) o #sels) basic_ctr_specs |> the_single
blanchet@54209
   558
          handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn);
panny@53654
   559
    val user_eqn = drop_All eqn';
blanchet@53303
   560
  in
panny@53341
   561
    Sel {
blanchet@53303
   562
      fun_name = fun_name,
panny@53720
   563
      fun_T = fun_T,
panny@53401
   564
      fun_args = fun_args,
panny@54160
   565
      ctr = ctr,
panny@53341
   566
      sel = sel,
blanchet@53303
   567
      rhs_term = rhs,
panny@53654
   568
      user_eqn = user_eqn
blanchet@53303
   569
    }
blanchet@53303
   570
  end;
blanchet@53303
   571
panny@54160
   572
fun dissect_coeqn_ctr seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
panny@54160
   573
    maybe_code_rhs prems concl matchedsss =
blanchet@53910
   574
  let
panny@54065
   575
    val (lhs, rhs) = HOLogic.dest_eq concl;
panny@54097
   576
    val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
blanchet@54209
   577
    val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
blanchet@54074
   578
    val (ctr, ctr_args) = strip_comb (unfold_let rhs);
panny@54160
   579
    val {disc, sels, ...} = the (find_first (equal ctr o #ctr) basic_ctr_specs)
blanchet@53303
   580
      handle Option.Option => primrec_error_eqn "not a constructor" ctr;
panny@53341
   581
panny@54065
   582
    val disc_concl = betapply (disc, lhs);
panny@54160
   583
    val (maybe_eqn_data_disc, matchedsss') = if length basic_ctr_specs = 1
panny@53720
   584
      then (NONE, matchedsss)
panny@54160
   585
      else apfst SOME (dissect_coeqn_disc seq fun_names basic_ctr_specss
panny@54097
   586
          (SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
blanchet@53303
   587
blanchet@54159
   588
    val sel_concls = sels ~~ ctr_args
blanchet@53303
   589
      |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
blanchet@53303
   590
blanchet@53856
   591
(*
panny@54065
   592
val _ = tracing ("reduced\n    " ^ Syntax.string_of_term @{context} concl ^ "\nto\n    \<cdot> " ^
panny@54065
   593
 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n    \<cdot> ")) "" ^
panny@54097
   594
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
panny@54097
   595
 "\nfor premise(s)\n    \<cdot> " ^
panny@54097
   596
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) prems));
blanchet@53856
   597
*)
blanchet@53303
   598
panny@54160
   599
    val eqns_data_sel =
panny@54160
   600
      map (dissect_coeqn_sel fun_names basic_ctr_specss eqn' (SOME ctr)) sel_concls;
blanchet@53303
   601
  in
panny@53720
   602
    (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
blanchet@53303
   603
  end;
blanchet@53303
   604
panny@54160
   605
fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss =
panny@54065
   606
  let
panny@54065
   607
    val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
panny@54097
   608
    val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
blanchet@54209
   609
    val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
panny@54065
   610
panny@54065
   611
    val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
panny@54160
   612
        if member ((op =) o apsnd #ctr) basic_ctr_specs ctr
panny@54065
   613
        then cons (ctr, cs)
panny@54065
   614
        else primrec_error_eqn "not a constructor" ctr) [] rhs' []
panny@54065
   615
      |> AList.group (op =);
panny@54065
   616
blanchet@54068
   617
    val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
panny@54065
   618
    val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
panny@54065
   619
        binder_types (fastype_of ctr)
panny@54065
   620
        |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
panny@54065
   621
          if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
panny@54065
   622
        |> curry list_comb ctr
panny@54065
   623
        |> curry HOLogic.mk_eq lhs);
panny@54065
   624
  in
panny@54160
   625
    fold_map2 (dissect_coeqn_ctr false fun_names basic_ctr_specss eqn'
panny@54097
   626
        (SOME (abstract (List.rev fun_args) rhs)))
panny@54097
   627
      ctr_premss ctr_concls matchedsss
panny@54065
   628
  end;
panny@54065
   629
panny@54160
   630
fun dissect_coeqn lthy seq has_call fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
blanchet@54209
   631
    eqn' maybe_of_spec matchedsss =
blanchet@53303
   632
  let
panny@53654
   633
    val eqn = drop_All eqn'
panny@53654
   634
      handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
panny@54065
   635
    val (prems, concl) = Logic.strip_horn eqn
panny@53341
   636
      |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
blanchet@53303
   637
panny@54065
   638
    val head = concl
blanchet@53303
   639
      |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
blanchet@53303
   640
      |> head_of;
blanchet@53303
   641
blanchet@54209
   642
    val maybe_rhs = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq);
blanchet@53303
   643
panny@54160
   644
    val discs = maps (map #disc) basic_ctr_specss;
panny@54160
   645
    val sels = maps (maps #sels) basic_ctr_specss;
panny@54160
   646
    val ctrs = maps (map #ctr) basic_ctr_specss;
blanchet@53303
   647
  in
blanchet@53303
   648
    if member (op =) discs head orelse
blanchet@53303
   649
      is_some maybe_rhs andalso
blanchet@53303
   650
        member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
panny@54160
   651
      dissect_coeqn_disc seq fun_names basic_ctr_specss NONE NONE prems concl matchedsss
blanchet@53303
   652
      |>> single
blanchet@53303
   653
    else if member (op =) sels head then
blanchet@54209
   654
      ([dissect_coeqn_sel fun_names basic_ctr_specss eqn' maybe_of_spec concl], matchedsss)
panny@54065
   655
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
blanchet@54074
   656
      member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
panny@54160
   657
      dissect_coeqn_ctr seq fun_names basic_ctr_specss eqn' NONE prems concl matchedsss
panny@54065
   658
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
panny@54065
   659
      null prems then
panny@54160
   660
      dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss
panny@54065
   661
      |>> flat
blanchet@53303
   662
    else
blanchet@53303
   663
      primrec_error_eqn "malformed function equation" eqn
blanchet@53303
   664
  end;
blanchet@53303
   665
blanchet@54002
   666
fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
blanchet@54153
   667
    ({fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
panny@53654
   668
  if is_none (#pred (nth ctr_specs ctr_no)) then I else
blanchet@54068
   669
    s_conjs prems
panny@53654
   670
    |> curry subst_bounds (List.rev fun_args)
panny@53654
   671
    |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
panny@53654
   672
    |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
blanchet@53303
   673
blanchet@54153
   674
fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel =
panny@53720
   675
  find_first (equal sel o #sel) sel_eqns
panny@53720
   676
  |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
panny@53720
   677
  |> the_default undef_const
panny@53411
   678
  |> K;
panny@53360
   679
blanchet@54153
   680
fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
blanchet@54208
   681
  (case find_first (equal sel o #sel) sel_eqns of
blanchet@54208
   682
    NONE => (I, I, I)
blanchet@54208
   683
  | SOME {fun_args, rhs_term, ... } =>
panny@53876
   684
    let
panny@54097
   685
      val bound_Ts = List.rev (map fastype_of fun_args);
blanchet@54207
   686
      fun rewrite_stop _ t = if has_call t then @{term False} else @{term True};
blanchet@54207
   687
      fun rewrite_end _ t = if has_call t then undef_const else t;
blanchet@54207
   688
      fun rewrite_cont bound_Ts t =
panny@53899
   689
        if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
blanchet@54102
   690
      fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
panny@54097
   691
        |> abs_tuple fun_args;
panny@53876
   692
    in
blanchet@54207
   693
      (massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
blanchet@54208
   694
    end);
panny@53360
   695
blanchet@54153
   696
fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
blanchet@54208
   697
  (case find_first (equal sel o #sel) sel_eqns of
blanchet@54208
   698
    NONE => I
blanchet@54208
   699
  | SOME {fun_args, rhs_term, ...} =>
panny@53899
   700
    let
panny@54097
   701
      val bound_Ts = List.rev (map fastype_of fun_args);
panny@53899
   702
      fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
panny@53899
   703
        | rewrite bound_Ts U T (t as _ $ _) =
panny@53899
   704
          let val (u, vs) = strip_comb t in
panny@53899
   705
            if is_Free u andalso has_call u then
panny@53899
   706
              Inr_const U T $ mk_tuple1 bound_Ts vs
panny@53899
   707
            else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
panny@53899
   708
              map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
panny@53899
   709
            else
panny@53899
   710
              list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
panny@53899
   711
          end
panny@53899
   712
        | rewrite _ U T t =
panny@53899
   713
          if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
panny@53899
   714
      fun massage t =
panny@54097
   715
        rhs_term
blanchet@54102
   716
        |> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
panny@53735
   717
        |> abs_tuple fun_args;
panny@53899
   718
    in
panny@53899
   719
      massage
blanchet@54208
   720
    end);
panny@53360
   721
blanchet@54153
   722
fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list)
blanchet@54002
   723
    (ctr_spec : corec_ctr_spec) =
blanchet@54208
   724
  (case filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns of
blanchet@54208
   725
    [] => I
blanchet@54208
   726
  | sel_eqns =>
blanchet@54208
   727
    let
blanchet@54208
   728
      val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
blanchet@54208
   729
      val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
blanchet@54208
   730
      val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
blanchet@54208
   731
      val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
blanchet@54208
   732
    in
blanchet@54208
   733
      I
blanchet@54208
   734
      #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
blanchet@54208
   735
      #> fold (fn (sel, (q, g, h)) =>
blanchet@54208
   736
        let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in
blanchet@54208
   737
          nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
blanchet@54208
   738
      #> fold (fn (sel, n) => nth_map n
blanchet@54208
   739
        (build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls'
blanchet@54208
   740
    end);
blanchet@53303
   741
blanchet@54153
   742
fun build_codefs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
blanchet@54153
   743
    (disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) =
panny@53654
   744
  let
panny@54160
   745
    val corecs = map #corec corec_specs;
panny@54160
   746
    val ctr_specss = map #ctr_specs corec_specs;
panny@53360
   747
    val corec_args = hd corecs
panny@53360
   748
      |> fst o split_last o binder_types o fastype_of
panny@53360
   749
      |> map (Const o pair @{const_name undefined})
panny@53720
   750
      |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
panny@53360
   751
      |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
panny@53735
   752
    fun currys [] t = t
panny@53735
   753
      | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
panny@53735
   754
          |> fold_rev (Term.abs o pair Name.uu) Ts;
panny@53401
   755
blanchet@53856
   756
(*
panny@53360
   757
val _ = tracing ("corecursor arguments:\n    \<cdot> " ^
panny@53411
   758
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
blanchet@53856
   759
*)
blanchet@53303
   760
panny@53654
   761
    val exclss' =
panny@53720
   762
      disc_eqnss
panny@53822
   763
      |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
panny@53654
   764
        #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
panny@53654
   765
        #> maps (uncurry (map o pair)
panny@53822
   766
          #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
blanchet@54068
   767
              ((c, c', a orelse a'), (x, s_not (s_conjs y)))
panny@53654
   768
            ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
panny@53654
   769
            ||> Logic.list_implies
panny@53654
   770
            ||> curry Logic.list_all (map dest_Free fun_args))))
blanchet@53303
   771
  in
blanchet@53303
   772
    map (list_comb o rpair corec_args) corecs
blanchet@53303
   773
    |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
blanchet@53303
   774
    |> map2 currys arg_Tss
blanchet@53303
   775
    |> Syntax.check_terms lthy
blanchet@54155
   776
    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
blanchet@54155
   777
      bs mxs
panny@53654
   778
    |> rpair exclss'
blanchet@53303
   779
  end;
blanchet@53303
   780
blanchet@54002
   781
fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
blanchet@54153
   782
    (sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
panny@53720
   783
  if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
panny@53720
   784
    let
panny@53720
   785
      val n = 0 upto length ctr_specs
panny@53720
   786
        |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
panny@53722
   787
      val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
panny@53722
   788
        |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
panny@53720
   789
      val extra_disc_eqn = {
panny@53720
   790
        fun_name = Binding.name_of fun_binding,
panny@53720
   791
        fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
panny@53722
   792
        fun_args = fun_args,
panny@53720
   793
        ctr = #ctr (nth ctr_specs n),
panny@53720
   794
        ctr_no = n,
panny@53720
   795
        disc = #disc (nth ctr_specs n),
blanchet@54067
   796
        prems = maps (s_not_conj o #prems) disc_eqns,
panny@53822
   797
        auto_gen = true,
panny@54097
   798
        maybe_ctr_rhs = NONE,
panny@54097
   799
        maybe_code_rhs = NONE,
panny@53720
   800
        user_eqn = undef_const};
panny@53720
   801
    in
panny@53720
   802
      chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
panny@53720
   803
    end;
panny@53720
   804
panny@54160
   805
fun find_corec_calls has_call basic_ctr_specs {ctr, sel, rhs_term, ...} =
panny@54160
   806
  let
panny@54160
   807
    val sel_no = find_first (equal ctr o #ctr) basic_ctr_specs
panny@54160
   808
      |> find_index (equal sel) o #sels o the;
panny@54160
   809
    fun find (Abs (_, _, b)) = find b
panny@54160
   810
      | find (t as _ $ _) = strip_comb t |>> find ||> maps find |> (op @)
panny@54160
   811
      | find f = if is_Free f andalso has_call f then [f] else [];
panny@54160
   812
  in
panny@54160
   813
    find rhs_term
panny@54160
   814
    |> K |> nth_map sel_no |> AList.map_entry (op =) ctr
panny@54160
   815
  end;
panny@54160
   816
blanchet@54209
   817
fun add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy =
blanchet@53303
   818
  let
traytel@53352
   819
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   820
    val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
blanchet@53303
   821
panny@54160
   822
    val fun_names = map Binding.name_of bs;
panny@54160
   823
    val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
panny@54160
   824
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
panny@54160
   825
    val eqns_data =
panny@54160
   826
      fold_map2 (dissect_coeqn lthy seq has_call fun_names basic_ctr_specss) (map snd specs)
blanchet@54209
   827
        maybe_of_specs []
panny@54160
   828
      |> flat o fst;
panny@54160
   829
panny@54160
   830
    val callssss =
panny@54160
   831
      map_filter (try (fn Sel x => x)) eqns_data
panny@54160
   832
      |> partition_eq ((op =) o pairself #fun_name)
panny@54160
   833
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@54161
   834
      |> map (flat o snd)
panny@54161
   835
      |> map2 (fold o find_corec_calls has_call) basic_ctr_specss
panny@54160
   836
      |> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} =>
panny@54160
   837
        (ctr, map (K []) sels))) basic_ctr_specss);
panny@54160
   838
panny@54160
   839
(*
panny@54160
   840
val _ = tracing ("callssss = " ^ @{make_string} callssss);
panny@54160
   841
*)
blanchet@53303
   842
blanchet@53830
   843
    val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
blanchet@53797
   844
          strong_coinduct_thms), lthy') =
blanchet@53794
   845
      corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53830
   846
    val actual_nn = length bs;
blanchet@53830
   847
    val corec_specs = take actual_nn corec_specs'; (*###*)
blanchet@54178
   848
    val ctr_specss = map #ctr_specs corec_specs;
blanchet@53303
   849
panny@53720
   850
    val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
panny@53654
   851
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   852
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   853
      |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
panny@53720
   854
    val _ = disc_eqnss' |> map (fn x =>
panny@53720
   855
      let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
blanchet@54204
   856
        primrec_error_eqns "excess discriminator formula in definition"
panny@53720
   857
          (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
panny@53654
   858
panny@53654
   859
    val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
panny@53654
   860
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   861
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   862
      |> map (flat o snd);
panny@53654
   863
panny@53360
   864
    val arg_Tss = map (binder_types o snd o fst) fixes;
panny@53722
   865
    val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
panny@53654
   866
    val (defs, exclss') =
blanchet@54153
   867
      build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
panny@53654
   868
blanchet@53923
   869
    fun excl_tac (c, c', a) =
blanchet@54177
   870
      if a orelse c = c' orelse seq then SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
blanchet@54177
   871
      else maybe_tac;
panny@53822
   872
blanchet@53856
   873
(*
panny@53822
   874
val _ = tracing ("exclusiveness properties:\n    \<cdot> " ^
panny@53822
   875
 space_implode "\n    \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
blanchet@53856
   876
*)
panny@53822
   877
panny@53822
   878
    val exclss'' = exclss' |> map (map (fn (idx, t) =>
blanchet@54177
   879
      (idx, (Option.map (Goal.prove lthy [] [] t #> Thm.close_derivation) (excl_tac idx), t))));
panny@53654
   880
    val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
blanchet@54180
   881
    val (goal_idxss, goalss) = exclss''
panny@53654
   882
      |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
panny@53654
   883
      |> split_list o map split_list;
panny@53654
   884
panny@53654
   885
    fun prove thmss' def_thms' lthy =
panny@53654
   886
      let
panny@53654
   887
        val def_thms = map (snd o snd) def_thms';
panny@53654
   888
blanchet@54180
   889
        val exclss' = map (op ~~) (goal_idxss ~~ thmss');
panny@53654
   890
        fun mk_exclsss excls n =
panny@53654
   891
          (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
panny@53822
   892
          |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
panny@53654
   893
        val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
panny@53654
   894
          |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
panny@53654
   895
blanchet@54002
   896
        fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
blanchet@54153
   897
            ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
panny@53722
   898
          if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
panny@53720
   899
            let
panny@53722
   900
              val {disc_corec, ...} = nth ctr_specs ctr_no;
panny@53720
   901
              val k = 1 + ctr_no;
panny@53720
   902
              val m = length prems;
panny@53720
   903
              val t =
panny@53720
   904
                list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   905
                |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
panny@53720
   906
                |> HOLogic.mk_Trueprop
panny@53720
   907
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   908
                |> curry Logic.list_all (map dest_Free fun_args);
panny@53720
   909
            in
panny@54097
   910
              if prems = [@{term False}] then [] else
panny@53720
   911
              mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
panny@53720
   912
              |> K |> Goal.prove lthy [] [] t
blanchet@54176
   913
              |> Thm.close_derivation
panny@53720
   914
              |> pair (#disc (nth ctr_specs ctr_no))
panny@53720
   915
              |> single
panny@53720
   916
            end;
panny@53720
   917
blanchet@54002
   918
        fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
blanchet@54153
   919
            : corec_spec) (disc_eqns : coeqn_data_disc list) exclsss
blanchet@54153
   920
            ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : coeqn_data_sel) =
panny@53654
   921
          let
blanchet@53909
   922
            val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
panny@53720
   923
            val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
blanchet@54067
   924
            val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
panny@53720
   925
                (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
panny@53720
   926
            val sel_corec = find_index (equal sel) (#sels ctr_spec)
panny@53720
   927
              |> nth (#sel_corecs ctr_spec);
panny@53654
   928
            val k = 1 + ctr_no;
panny@53654
   929
            val m = length prems;
panny@53654
   930
            val t =
panny@53720
   931
              list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   932
              |> curry betapply sel
panny@53720
   933
              |> rpair (abstract (List.rev fun_args) rhs_term)
panny@53720
   934
              |> HOLogic.mk_Trueprop o HOLogic.mk_eq
panny@53654
   935
              |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   936
              |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53925
   937
            val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
panny@53654
   938
          in
blanchet@53918
   939
            mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
blanchet@53910
   940
              nested_map_idents nested_map_comps sel_corec k m exclsss
panny@53654
   941
            |> K |> Goal.prove lthy [] [] t
blanchet@54176
   942
            |> Thm.close_derivation
panny@53720
   943
            |> pair sel
panny@53654
   944
          end;
panny@53654
   945
blanchet@54153
   946
        fun prove_ctr disc_alist sel_alist (disc_eqns : coeqn_data_disc list)
blanchet@54153
   947
            (sel_eqns : coeqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
panny@54097
   948
          (* don't try to prove theorems when some sel_eqns are missing *)
panny@53720
   949
          if not (exists (equal ctr o #ctr) disc_eqns)
panny@53722
   950
              andalso not (exists (equal ctr o #ctr) sel_eqns)
panny@54097
   951
            orelse
panny@53720
   952
              filter (equal ctr o #ctr) sel_eqns
panny@53720
   953
              |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   954
              |> exists (null o snd)
panny@53720
   955
          then [] else
panny@53720
   956
            let
panny@54097
   957
              val (fun_name, fun_T, fun_args, prems, maybe_rhs) =
panny@53722
   958
                (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
panny@54097
   959
                |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
panny@54097
   960
                  #maybe_ctr_rhs x))
panny@54097
   961
                ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
panny@53722
   962
                |> the o merge_options;
panny@53720
   963
              val m = length prems;
panny@54097
   964
              val t = (if is_some maybe_rhs then the maybe_rhs else
panny@54097
   965
                  filter (equal ctr o #ctr) sel_eqns
panny@54097
   966
                  |> fst o finds ((op =) o apsnd #sel) sels
panny@54097
   967
                  |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
panny@54097
   968
                  |> curry list_comb ctr)
panny@53720
   969
                |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
panny@53720
   970
                  map Bound (length fun_args - 1 downto 0)))
panny@53720
   971
                |> HOLogic.mk_Trueprop
panny@53720
   972
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   973
                |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53791
   974
              val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
blanchet@53791
   975
              val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
panny@53720
   976
            in
panny@54097
   977
              if prems = [@{term False}] then [] else
panny@54097
   978
                mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
panny@54097
   979
                |> K |> Goal.prove lthy [] [] t
blanchet@54176
   980
                |> Thm.close_derivation
panny@54097
   981
                |> pair ctr
panny@54097
   982
                |> single
panny@53876
   983
            end;
panny@53720
   984
blanchet@54178
   985
        fun prove_code disc_eqns sel_eqns ctr_alist ctr_specs =
panny@54098
   986
          let
panny@54097
   987
            val (fun_name, fun_T, fun_args, maybe_rhs) =
panny@54097
   988
              (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
panny@54097
   989
               find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
panny@54097
   990
              |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x))
panny@54097
   991
              ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
panny@54097
   992
              |> the o merge_options;
panny@54097
   993
blanchet@54173
   994
            val bound_Ts = List.rev (map fastype_of fun_args);
blanchet@54173
   995
panny@54120
   996
            val lhs = list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
blanchet@54173
   997
            val maybe_rhs_info =
blanchet@54173
   998
              (case maybe_rhs of
blanchet@54173
   999
                SOME rhs =>
blanchet@54173
  1000
                let
blanchet@54173
  1001
                  val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
blanchet@54173
  1002
                  val cond_ctrs =
blanchet@54173
  1003
                    fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
blanchet@54173
  1004
                  val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
blanchet@54173
  1005
                in SOME (rhs, raw_rhs, ctr_thms) end
blanchet@54173
  1006
              | NONE =>
blanchet@54173
  1007
                let
blanchet@54173
  1008
                  fun prove_code_ctr {ctr, sels, ...} =
blanchet@54173
  1009
                    if not (exists (equal ctr o fst) ctr_alist) then NONE else
blanchet@54173
  1010
                      let
blanchet@54173
  1011
                        val prems = find_first (equal ctr o #ctr) disc_eqns
blanchet@54173
  1012
                          |> Option.map #prems |> the_default [];
blanchet@54173
  1013
                        val t =
blanchet@54173
  1014
                          filter (equal ctr o #ctr) sel_eqns
blanchet@54173
  1015
                          |> fst o finds ((op =) o apsnd #sel) sels
blanchet@54173
  1016
                          |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x))
blanchet@54173
  1017
                            #-> abstract)
blanchet@54173
  1018
                          |> curry list_comb ctr;
blanchet@54173
  1019
                      in
blanchet@54173
  1020
                        SOME (prems, t)
blanchet@54173
  1021
                      end;
blanchet@54173
  1022
                  val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
blanchet@54173
  1023
                in
blanchet@54173
  1024
                  if exists is_none maybe_ctr_conds_argss then NONE else
panny@54097
  1025
                    let
blanchet@54173
  1026
                      val rhs = fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
blanchet@54173
  1027
                        maybe_ctr_conds_argss
blanchet@54173
  1028
                        (Const (@{const_name Code.abort}, @{typ String.literal} -->
blanchet@54173
  1029
                            (@{typ unit} --> body_type fun_T) --> body_type fun_T) $
blanchet@54178
  1030
                          HOLogic.mk_literal fun_name $
blanchet@54173
  1031
                          absdummy @{typ unit} (incr_boundvars 1 lhs));
blanchet@54173
  1032
                    in SOME (rhs, rhs, map snd ctr_alist) end
blanchet@54173
  1033
                end);
panny@54097
  1034
          in
blanchet@54173
  1035
            (case maybe_rhs_info of
blanchet@54173
  1036
              NONE => []
blanchet@54173
  1037
            | SOME (rhs, raw_rhs, ctr_thms) =>
panny@54097
  1038
              let
panny@54097
  1039
                val ms = map (Logic.count_prems o prop_of) ctr_thms;
blanchet@54172
  1040
                val (raw_t, t) = (raw_rhs, rhs)
blanchet@54172
  1041
                  |> pairself
blanchet@54172
  1042
                    (curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
blanchet@54172
  1043
                      map Bound (length fun_args - 1 downto 0)))
blanchet@54172
  1044
                    #> HOLogic.mk_Trueprop
blanchet@54172
  1045
                    #> curry Logic.list_all (map dest_Free fun_args));
panny@54098
  1046
                val (distincts, discIs, sel_splits, sel_split_asms) =
blanchet@54172
  1047
                  case_thms_of_term lthy bound_Ts raw_rhs;
panny@54098
  1048
blanchet@54172
  1049
                val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
panny@54097
  1050
                    sel_split_asms ms ctr_thms
blanchet@54176
  1051
                  |> K |> Goal.prove lthy [] [] raw_t
blanchet@54176
  1052
                  |> Thm.close_derivation;
blanchet@54172
  1053
              in
blanchet@54174
  1054
                mk_primcorec_code_of_raw_code_tac lthy distincts sel_splits raw_code_thm
blanchet@54172
  1055
                |> K |> Goal.prove lthy [] [] t
blanchet@54176
  1056
                |> Thm.close_derivation
blanchet@54172
  1057
                |> single
blanchet@54173
  1058
              end)
blanchet@54173
  1059
          end;
panny@54097
  1060
blanchet@53791
  1061
        val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
blanchet@53791
  1062
        val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
blanchet@53791
  1063
        val disc_thmss = map (map snd) disc_alists;
blanchet@53791
  1064
        val sel_thmss = map (map snd) sel_alists;
panny@54097
  1065
panny@54097
  1066
        val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
blanchet@54178
  1067
          ctr_specss;
panny@54097
  1068
        val ctr_thmss = map (map snd) ctr_alists;
panny@54097
  1069
blanchet@54178
  1070
        val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists ctr_specss;
blanchet@53791
  1071
blanchet@54030
  1072
        val simp_thmss = map2 append disc_thmss sel_thmss
blanchet@53795
  1073
blanchet@53797
  1074
        val common_name = mk_common_name fun_names;
blanchet@53797
  1075
blanchet@53791
  1076
        val notes =
blanchet@53830
  1077
          [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
blanchet@54145
  1078
           (codeN, code_thmss, code_nitpicksimp_attrs),
blanchet@53797
  1079
           (ctrN, ctr_thmss, []),
blanchet@53791
  1080
           (discN, disc_thmss, simp_attrs),
blanchet@53795
  1081
           (selN, sel_thmss, simp_attrs),
blanchet@53797
  1082
           (simpsN, simp_thmss, []),
blanchet@53830
  1083
           (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
blanchet@53791
  1084
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@53791
  1085
            map2 (fn fun_name => fn thms =>
blanchet@53791
  1086
                ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
blanchet@53830
  1087
              fun_names (take actual_nn thmss))
blanchet@53791
  1088
          |> filter_out (null o fst o hd o snd);
blanchet@53797
  1089
blanchet@53797
  1090
        val common_notes =
blanchet@53830
  1091
          [(coinductN, if n2m then [coinduct_thm] else [], []),
blanchet@53830
  1092
           (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
blanchet@53797
  1093
          |> filter_out (null o #2)
blanchet@53797
  1094
          |> map (fn (thmN, thms, attrs) =>
blanchet@53797
  1095
            ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
panny@53654
  1096
      in
blanchet@54030
  1097
        lthy |> Local_Theory.notes (notes @ common_notes) |> snd
panny@53654
  1098
      end;
panny@53822
  1099
panny@53822
  1100
    fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
blanchet@53303
  1101
  in
blanchet@54177
  1102
    (goalss, after_qed, lthy')
panny@53822
  1103
  end;
blanchet@53303
  1104
blanchet@54177
  1105
fun add_primcorec_ursive_cmd maybe_tac seq (raw_fixes, raw_specs') lthy =
blanchet@53303
  1106
  let
blanchet@54209
  1107
    val (raw_specs, maybe_of_specs) =
blanchet@54209
  1108
      split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
panny@53831
  1109
    val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
blanchet@53303
  1110
  in
blanchet@54209
  1111
    add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy
blanchet@53303
  1112
    handle ERROR str => primrec_error str
blanchet@53303
  1113
  end
blanchet@53303
  1114
  handle Primrec_Error (str, eqns) =>
blanchet@53303
  1115
    if null eqns
blanchet@53303
  1116
    then error ("primcorec error:\n  " ^ str)
blanchet@53303
  1117
    else error ("primcorec error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
  1118
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
panny@53822
  1119
blanchet@54177
  1120
val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@54177
  1121
  lthy
blanchet@54177
  1122
  |> Proof.theorem NONE after_qed goalss
blanchet@54177
  1123
  |> Proof.refine (Method.primitive_text I)
blanchet@54177
  1124
  |> Seq.hd) ooo add_primcorec_ursive_cmd NONE;
blanchet@54177
  1125
blanchet@54177
  1126
val add_primcorec_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@54177
  1127
  lthy
blanchet@54177
  1128
  |> after_qed (map (fn [] => []
blanchet@54177
  1129
      | _ => primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec")
blanchet@54177
  1130
    goalss)) ooo add_primcorec_ursive_cmd (SOME (fn {context = ctxt, ...} => auto_tac ctxt));
blanchet@53303
  1131
blanchet@53303
  1132
end;