src/HOL/BNF/Tools/bnf_fp_rec_sugar.ML
author panny
Thu Sep 19 00:32:33 2013 +0200 (2013-09-19)
changeset 53722 e176d6d3345f
parent 53720 03fac7082137
child 53725 9e64151359e8
permissions -rw-r--r--
generate more theorems (e.g. for types with only one constructor)
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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_cmd: (binding * string option * mixfix) list ->
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    (Attrib.binding * string) list -> local_theory -> local_theory;
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  val add_primcorec_cmd: bool ->
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    (binding * string option * mixfix) list * (Attrib.binding * string) list -> Proof.context ->
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    Proof.state
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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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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 mk_not @{const True} = @{const False}
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  | mk_not @{const False} = @{const True}
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  | mk_not (@{const Not} $ t) = t
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  | mk_not (@{const Trueprop} $ t) = @{const Trueprop} $ mk_not t
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  | mk_not t = HOLogic.mk_not t
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val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
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val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
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fun invert_prems [t] = map mk_not (HOLogic.disjuncts t)
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  | invert_prems ts = [mk_disjs (map mk_not ts)];
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fun invert_prems_disj [t] = map mk_not (HOLogic.disjuncts t)
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  | invert_prems_disj ts = [mk_disjs (map (mk_conjs o map mk_not o HOLogic.disjuncts) ts)];
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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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val simp_attrs = @{attributes [simp]};
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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 _ = length nonfrees = 1 orelse if length 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 if d = SOME ~1 andalso const_name u = SOME @{const_name comp} then
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            list_comb (map_types (K dummyT) u, map2 subst [NONE, d] vs)
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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 direct_calls indirect_calls t =
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  let
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    fun subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
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      | subst bound_Ts (t as g' $ y) =
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        let
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          val maybe_direct_y' = AList.lookup (op =) direct_calls y;
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          val maybe_indirect_y' = AList.lookup (op =) indirect_calls y;
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          val (g, g_args) = strip_comb g';
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          val ctr_pos = try (get_ctr_pos o the) (free_name g) |> the_default ~1;
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          val _ = ctr_pos < 0 orelse length g_args >= ctr_pos orelse
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            primrec_error_eqn "too few arguments in recursive call" t;
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        in
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          if not (member (op =) ctr_args y) then
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            pairself (subst bound_Ts) (g', y) |> (op $)
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          else if ctr_pos >= 0 then
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            list_comb (the maybe_direct_y', g_args)
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          else if is_some maybe_indirect_y' then
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            (if has_call g' then t else y)
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            |> massage_indirect_rec_call lthy has_call
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              (rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_indirect_y')
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            |> (if has_call g' then I else curry (op $) g')
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          else
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            t
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        end
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      | subst _ t = t
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  in
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    subst [] t
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    |> tap (fn u => has_call u andalso (* 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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  end;
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fun build_rec_arg lthy funs_data has_call ctr_spec maybe_eqn_data =
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  if is_none maybe_eqn_data then undef_const else
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    let
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      val eqn_data = the maybe_eqn_data;
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      val t = #rhs_term eqn_data;
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      val ctr_args = #ctr_args eqn_data;
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      val calls = #calls ctr_spec;
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      val n_args = fold (curry (op +) o (fn Direct_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 n => n | Direct_Rec (n, _) => n)));
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      val direct_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn Direct_Rec (_, n) => n)));
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      val indirect_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn Indirect_Rec n => n)));
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      fun make_direct_type T = dummyT; (* FIXME? *)
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      val rec_res_type_list = map (fn (x :: _) => (#rec_type x, #res_type x)) funs_data;
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      fun make_indirect_type (Type (Tname, Ts)) = Type (Tname, Ts |> map (fn T =>
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        let val maybe_res_type = AList.lookup (op =) rec_res_type_list T in
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          if is_some maybe_res_type
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          then HOLogic.mk_prodT (T, the maybe_res_type)
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          else make_indirect_type T end))
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        | make_indirect_type T = T;
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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) =>
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            nth_map arg_idx (K (nth ctr_args ctr_arg_idx |> map_types make_direct_type)))
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          direct_calls'
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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 |> map_types make_indirect_type)))
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          indirect_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 direct_calls = map (apfst (nth ctr_args) o apsnd (nth args)) direct_calls';
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      val indirect_calls = map (apfst (nth ctr_args) o apsnd (nth args)) indirect_calls';
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      val abstractions = args @ #left_args eqn_data @ #right_args eqn_data;
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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 direct_calls indirect_calls
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      |> fold_rev lambda abstractions
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    end;
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fun build_defs lthy bs mxs funs_data rec_specs 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.map_name Thm.def_name b, []), t))) bs mxs
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  end;
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fun find_rec_calls has_call eqn_data =
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  let
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    fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
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      | find (t as _ $ _) ctr_arg =
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        let
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          val (f', args') = strip_comb t;
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          val n = find_index (equal ctr_arg) args';
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        in
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          if n < 0 then
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            find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
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          else
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            let val (f, args) = chop n args' |>> curry list_comb f' in
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              if has_call f then
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                f :: maps (fn x => find x ctr_arg) args
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              else
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                find f ctr_arg @ maps (fn x => find x ctr_arg) args
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            end
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        end
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      | find _ _ = [];
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  in
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    map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
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   293
    |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
blanchet@53303
   294
  end;
blanchet@53303
   295
blanchet@53303
   296
fun add_primrec fixes specs lthy =
blanchet@53303
   297
  let
traytel@53352
   298
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   299
    val fun_names = map Binding.name_of bs;
blanchet@53303
   300
    val eqns_data = map (snd #> dissect_eqn lthy fun_names) specs;
blanchet@53303
   301
    val funs_data = eqns_data
blanchet@53303
   302
      |> partition_eq ((op =) o pairself #fun_name)
blanchet@53303
   303
      |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
blanchet@53303
   304
      |> map (fn (x, y) => the_single y handle List.Empty =>
blanchet@53303
   305
          primrec_error ("missing equations for function " ^ quote x));
blanchet@53303
   306
panny@53358
   307
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
blanchet@53303
   308
    val arg_Ts = map (#rec_type o hd) funs_data;
blanchet@53303
   309
    val res_Ts = map (#res_type o hd) funs_data;
blanchet@53303
   310
    val callssss = funs_data
blanchet@53303
   311
      |> map (partition_eq ((op =) o pairself #ctr))
panny@53358
   312
      |> map (maps (map_filter (find_rec_calls has_call)));
blanchet@53303
   313
panny@53358
   314
    fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
panny@53358
   315
      |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
panny@53358
   316
      |> map_filter I;
blanchet@53303
   317
    val ((nontriv, rec_specs, _, induct_thm, induct_thms), lthy') =
blanchet@53303
   318
      rec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
blanchet@53303
   319
blanchet@53303
   320
    val actual_nn = length funs_data;
blanchet@53303
   321
blanchet@53303
   322
    val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
blanchet@53303
   323
      map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
blanchet@53303
   324
        primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
blanchet@53303
   325
          " is not a constructor in left-hand side") user_eqn) eqns_data end;
blanchet@53303
   326
panny@53358
   327
    val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
blanchet@53303
   328
blanchet@53329
   329
    fun prove def_thms' {ctr_specs, nested_map_idents, nested_map_comps, ...} induct_thm fun_data
blanchet@53303
   330
        lthy =
blanchet@53303
   331
      let
blanchet@53303
   332
        val fun_name = #fun_name (hd fun_data);
blanchet@53303
   333
        val def_thms = map (snd o snd) def_thms';
blanchet@53303
   334
        val simp_thms = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
blanchet@53303
   335
          |> fst
blanchet@53303
   336
          |> map_filter (try (fn (x, [y]) =>
blanchet@53303
   337
            (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
blanchet@53303
   338
          |> map (fn (user_eqn, num_extra_args, rec_thm) =>
blanchet@53329
   339
            mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
blanchet@53303
   340
            |> K |> Goal.prove lthy [] [] user_eqn)
blanchet@53303
   341
blanchet@53303
   342
        val notes =
blanchet@53303
   343
          [(inductN, if actual_nn > 1 then [induct_thm] else [], []),
blanchet@53303
   344
           (simpsN, simp_thms, simp_attrs)]
blanchet@53303
   345
          |> filter_out (null o #2)
blanchet@53303
   346
          |> map (fn (thmN, thms, attrs) =>
blanchet@53303
   347
            ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   348
      in
blanchet@53303
   349
        lthy |> Local_Theory.notes notes
blanchet@53303
   350
      end;
blanchet@53303
   351
blanchet@53303
   352
    val common_name = mk_common_name fun_names;
blanchet@53303
   353
blanchet@53303
   354
    val common_notes =
blanchet@53303
   355
      [(inductN, if nontriv andalso actual_nn > 1 then [induct_thm] else [], [])]
blanchet@53303
   356
      |> filter_out (null o #2)
blanchet@53303
   357
      |> map (fn (thmN, thms, attrs) =>
blanchet@53303
   358
        ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   359
  in
blanchet@53303
   360
    lthy'
blanchet@53303
   361
    |> fold_map Local_Theory.define defs
panny@53654
   362
    |-> snd oo (fn def_thms' => fold_map3 (prove def_thms') (take actual_nn rec_specs)
blanchet@53303
   363
      (take actual_nn induct_thms) funs_data)
panny@53654
   364
    |> snd o Local_Theory.notes common_notes
blanchet@53303
   365
  end;
blanchet@53303
   366
blanchet@53303
   367
fun add_primrec_cmd raw_fixes raw_specs lthy =
blanchet@53303
   368
  let
blanchet@53303
   369
    val _ = let val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes) in null d orelse
blanchet@53303
   370
      primrec_error ("duplicate function name(s): " ^ commas d) end;
blanchet@53303
   371
    val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
blanchet@53303
   372
  in
blanchet@53303
   373
    add_primrec fixes specs lthy
blanchet@53303
   374
      handle ERROR str => primrec_error str
blanchet@53303
   375
  end
blanchet@53303
   376
  handle Primrec_Error (str, eqns) =>
blanchet@53303
   377
    if null eqns
blanchet@53303
   378
    then error ("primrec_new error:\n  " ^ str)
blanchet@53303
   379
    else error ("primrec_new error:\n  " ^ str ^ "\nin\n  " ^
blanchet@53303
   380
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns))
blanchet@53303
   381
blanchet@53303
   382
blanchet@53303
   383
blanchet@53310
   384
(* Primcorec *)
blanchet@53303
   385
panny@53341
   386
type co_eqn_data_disc = {
blanchet@53303
   387
  fun_name: string,
panny@53720
   388
  fun_T: typ,
panny@53401
   389
  fun_args: term list,
panny@53720
   390
  ctr: term,
panny@53341
   391
  ctr_no: int, (*###*)
panny@53720
   392
  disc: term,
panny@53654
   393
  prems: term list,
blanchet@53303
   394
  user_eqn: term
blanchet@53303
   395
};
panny@53341
   396
type co_eqn_data_sel = {
blanchet@53303
   397
  fun_name: string,
panny@53720
   398
  fun_T: typ,
panny@53401
   399
  fun_args: term list,
panny@53341
   400
  ctr: term,
panny@53341
   401
  sel: term,
blanchet@53303
   402
  rhs_term: term,
blanchet@53303
   403
  user_eqn: term
blanchet@53303
   404
};
blanchet@53303
   405
datatype co_eqn_data =
panny@53341
   406
  Disc of co_eqn_data_disc |
panny@53341
   407
  Sel of co_eqn_data_sel;
blanchet@53303
   408
panny@53720
   409
fun co_dissect_eqn_disc sequential fun_names corec_specs prems' concl matchedsss =
blanchet@53303
   410
  let
blanchet@53303
   411
    fun find_subterm p = let (* FIXME \<exists>? *)
panny@53401
   412
      fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
blanchet@53303
   413
        | f t = if p t then SOME t else NONE
blanchet@53303
   414
      in f end;
blanchet@53303
   415
panny@53654
   416
    val applied_fun = concl
panny@53654
   417
      |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
panny@53654
   418
      |> the
panny@53654
   419
      handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
panny@53720
   420
    val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
panny@53720
   421
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
blanchet@53303
   422
panny@53720
   423
    val discs = map #disc ctr_specs;
panny@53720
   424
    val ctrs = map #ctr ctr_specs;
panny@53654
   425
    val not_disc = head_of concl = @{term Not};
panny@53401
   426
    val _ = not_disc andalso length ctrs <> 2 andalso
panny@53654
   427
      primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
panny@53654
   428
    val disc = find_subterm (member (op =) discs o head_of) concl;
panny@53654
   429
    val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
blanchet@53303
   430
        |> (fn SOME t => let val n = find_index (equal t) ctrs in
blanchet@53303
   431
          if n >= 0 then SOME n else NONE end | _ => NONE);
blanchet@53303
   432
    val _ = is_some disc orelse is_some eq_ctr0 orelse
panny@53654
   433
      primrec_error_eqn "no discriminator in equation" concl;
blanchet@53303
   434
    val ctr_no' =
blanchet@53303
   435
      if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
blanchet@53303
   436
    val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
panny@53720
   437
    val ctr = #ctr (nth ctr_specs ctr_no);
panny@53654
   438
panny@53654
   439
    val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
panny@53720
   440
    val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
panny@53720
   441
    val prems = map (abstract (List.rev fun_args)) prems';
panny@53720
   442
    val real_prems =
panny@53720
   443
      (if catch_all orelse sequential then maps invert_prems_disj matchedss else []) @
panny@53654
   444
      (if catch_all then [] else prems);
blanchet@53303
   445
panny@53720
   446
    val matchedsss' = AList.delete (op =) fun_name matchedsss
panny@53720
   447
      |> cons (fun_name, if sequential then matchedss @ [prems] else matchedss @ [real_prems]);
blanchet@53303
   448
panny@53654
   449
    val user_eqn =
panny@53720
   450
      (real_prems, betapply (#disc (nth ctr_specs ctr_no), applied_fun))
panny@53654
   451
      |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop
panny@53654
   452
      |> Logic.list_implies;
blanchet@53303
   453
  in
panny@53341
   454
    (Disc {
blanchet@53303
   455
      fun_name = fun_name,
panny@53720
   456
      fun_T = fun_T,
panny@53401
   457
      fun_args = fun_args,
panny@53720
   458
      ctr = ctr,
blanchet@53303
   459
      ctr_no = ctr_no,
panny@53720
   460
      disc = #disc (nth ctr_specs ctr_no),
panny@53654
   461
      prems = real_prems,
panny@53654
   462
      user_eqn = user_eqn
panny@53720
   463
    }, matchedsss')
blanchet@53303
   464
  end;
blanchet@53303
   465
panny@53654
   466
fun co_dissect_eqn_sel fun_names corec_specs eqn' eqn =
blanchet@53303
   467
  let
blanchet@53303
   468
    val (lhs, rhs) = HOLogic.dest_eq eqn
blanchet@53303
   469
      handle TERM _ =>
blanchet@53303
   470
        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
blanchet@53303
   471
    val sel = head_of lhs;
panny@53720
   472
    val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
blanchet@53303
   473
      handle TERM _ =>
blanchet@53303
   474
        primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@53654
   475
    val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
blanchet@53303
   476
      handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@53341
   477
    val (ctr_spec, sel) = #ctr_specs corec_spec
blanchet@53303
   478
      |> the o get_index (try (the o find_first (equal sel) o #sels))
panny@53341
   479
      |>> nth (#ctr_specs corec_spec);
panny@53654
   480
    val user_eqn = drop_All eqn';
blanchet@53303
   481
  in
panny@53341
   482
    Sel {
blanchet@53303
   483
      fun_name = fun_name,
panny@53720
   484
      fun_T = fun_T,
panny@53401
   485
      fun_args = fun_args,
panny@53341
   486
      ctr = #ctr ctr_spec,
panny@53341
   487
      sel = sel,
blanchet@53303
   488
      rhs_term = rhs,
panny@53654
   489
      user_eqn = user_eqn
blanchet@53303
   490
    }
blanchet@53303
   491
  end;
blanchet@53303
   492
panny@53720
   493
fun co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss =
blanchet@53303
   494
  let 
blanchet@53303
   495
    val (lhs, rhs) = HOLogic.dest_eq imp_rhs;
blanchet@53303
   496
    val fun_name = head_of lhs |> fst o dest_Free;
panny@53720
   497
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
blanchet@53303
   498
    val (ctr, ctr_args) = strip_comb rhs;
panny@53720
   499
    val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs)
blanchet@53303
   500
      handle Option.Option => primrec_error_eqn "not a constructor" ctr;
panny@53341
   501
panny@53720
   502
    val disc_imp_rhs = betapply (disc, lhs);
panny@53720
   503
    val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1
panny@53720
   504
      then (NONE, matchedsss)
panny@53341
   505
      else apfst SOME (co_dissect_eqn_disc
panny@53720
   506
          sequential fun_names corec_specs imp_prems disc_imp_rhs matchedsss);
blanchet@53303
   507
panny@53720
   508
    val sel_imp_rhss = (sels ~~ ctr_args)
blanchet@53303
   509
      |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
blanchet@53303
   510
panny@53360
   511
val _ = tracing ("reduced\n    " ^ Syntax.string_of_term @{context} imp_rhs ^ "\nto\n    \<cdot> " ^
panny@53341
   512
 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_imp_rhs ^ "\n    \<cdot> ")) "" ^
blanchet@53303
   513
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) sel_imp_rhss));
blanchet@53303
   514
blanchet@53303
   515
    val eqns_data_sel =
panny@53654
   516
      map (co_dissect_eqn_sel fun_names corec_specs eqn') sel_imp_rhss;
blanchet@53303
   517
  in
panny@53720
   518
    (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
blanchet@53303
   519
  end;
blanchet@53303
   520
panny@53720
   521
fun co_dissect_eqn sequential fun_names corec_specs eqn' matchedsss =
blanchet@53303
   522
  let
panny@53654
   523
    val eqn = drop_All eqn'
panny@53654
   524
      handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
panny@53654
   525
    val (imp_prems, imp_rhs) = Logic.strip_horn eqn
panny@53341
   526
      |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
blanchet@53303
   527
blanchet@53303
   528
    val head = imp_rhs
blanchet@53303
   529
      |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
blanchet@53303
   530
      |> head_of;
blanchet@53303
   531
blanchet@53303
   532
    val maybe_rhs = imp_rhs |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
blanchet@53303
   533
panny@53654
   534
    val discs = maps #ctr_specs corec_specs |> map #disc;
panny@53654
   535
    val sels = maps #ctr_specs corec_specs |> maps #sels;
panny@53654
   536
    val ctrs = maps #ctr_specs corec_specs |> map #ctr;
blanchet@53303
   537
  in
blanchet@53303
   538
    if member (op =) discs head orelse
blanchet@53303
   539
      is_some maybe_rhs andalso
blanchet@53303
   540
        member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
panny@53720
   541
      co_dissect_eqn_disc sequential fun_names corec_specs imp_prems imp_rhs matchedsss
blanchet@53303
   542
      |>> single
blanchet@53303
   543
    else if member (op =) sels head then
panny@53720
   544
      ([co_dissect_eqn_sel fun_names corec_specs eqn' imp_rhs], matchedsss)
blanchet@53303
   545
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then
panny@53720
   546
      co_dissect_eqn_ctr sequential fun_names corec_specs eqn' imp_prems imp_rhs matchedsss
blanchet@53303
   547
    else
blanchet@53303
   548
      primrec_error_eqn "malformed function equation" eqn
blanchet@53303
   549
  end;
blanchet@53303
   550
panny@53654
   551
fun build_corec_arg_disc ctr_specs {fun_args, ctr_no, prems, ...} =
panny@53654
   552
  if is_none (#pred (nth ctr_specs ctr_no)) then I else
panny@53654
   553
    mk_conjs prems
panny@53654
   554
    |> curry subst_bounds (List.rev fun_args)
panny@53654
   555
    |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
panny@53654
   556
    |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
blanchet@53303
   557
panny@53720
   558
fun build_corec_arg_no_call sel_eqns sel =
panny@53720
   559
  find_first (equal sel o #sel) sel_eqns
panny@53720
   560
  |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
panny@53720
   561
  |> the_default undef_const
panny@53411
   562
  |> K;
panny@53360
   563
panny@53360
   564
fun build_corec_arg_direct_call lthy has_call sel_eqns sel =
panny@53360
   565
  let
panny@53411
   566
    val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
panny@53654
   567
    fun rewrite is_end U _ t =
panny@53360
   568
      if U = @{typ bool} then @{term True} |> has_call t ? K @{term False} (* stop? *)
panny@53401
   569
      else if is_end = has_call t then undef_const
panny@53401
   570
      else if is_end then t (* end *)
panny@53360
   571
      else HOLogic.mk_tuple (snd (strip_comb t)); (* continue *)
panny@53401
   572
    fun massage rhs_term is_end t = massage_direct_corec_call
panny@53401
   573
      lthy has_call (rewrite is_end) [] (range_type (fastype_of t)) rhs_term;
panny@53360
   574
  in
panny@53401
   575
    if is_none maybe_sel_eqn then K I else
panny@53401
   576
      abs_tuple (#fun_args (the maybe_sel_eqn)) oo massage (#rhs_term (the maybe_sel_eqn))
panny@53360
   577
  end;
panny@53360
   578
panny@53411
   579
fun build_corec_arg_indirect_call lthy has_call sel_eqns sel =
panny@53411
   580
  let
panny@53411
   581
    val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
panny@53411
   582
    fun rewrite _ _ =
panny@53411
   583
      let
panny@53411
   584
        fun subst (Abs (v, T, b)) = Abs (v, T, subst b)
panny@53411
   585
          | subst (t as _ $ _) =
panny@53411
   586
            let val (u, vs) = strip_comb t in
panny@53411
   587
              if is_Free u andalso has_call u then
panny@53720
   588
                Const (@{const_name Inr}, dummyT) $
panny@53411
   589
                  (try (foldr1 (fn (x, y) => Const (@{const_name Pair}, dummyT) $ x $ y)) vs
panny@53411
   590
                    |> the_default (hd vs))
panny@53411
   591
              else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
panny@53411
   592
                list_comb (u |> map_types (K dummyT), map subst vs)
panny@53411
   593
              else
panny@53411
   594
                list_comb (subst u, map subst vs)
panny@53411
   595
            end
panny@53411
   596
          | subst t = t;
panny@53411
   597
      in
panny@53411
   598
        subst
panny@53411
   599
      end;
panny@53411
   600
    fun massage rhs_term t = massage_indirect_corec_call
panny@53720
   601
      lthy has_call rewrite [] (range_type (fastype_of t)) rhs_term;
panny@53411
   602
  in
panny@53411
   603
    if is_none maybe_sel_eqn then I else
panny@53411
   604
      abs_tuple (#fun_args (the maybe_sel_eqn)) o massage (#rhs_term (the maybe_sel_eqn))
panny@53411
   605
  end;
panny@53360
   606
panny@53360
   607
fun build_corec_args_sel lthy has_call all_sel_eqns ctr_spec =
panny@53341
   608
  let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
panny@53341
   609
    if null sel_eqns then I else
panny@53341
   610
      let
panny@53341
   611
        val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
panny@53341
   612
panny@53341
   613
        val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
panny@53341
   614
        val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list;
panny@53341
   615
        val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list;
panny@53341
   616
      in
panny@53360
   617
        I
panny@53360
   618
        #> fold (fn (sel, n) => nth_map n
panny@53411
   619
          (build_corec_arg_no_call sel_eqns sel)) no_calls'
panny@53360
   620
        #> fold (fn (sel, (q, g, h)) =>
panny@53360
   621
          let val f = build_corec_arg_direct_call lthy has_call sel_eqns sel in
panny@53401
   622
            nth_map h (f false) o nth_map g (f true) o nth_map q (f true) end) direct_calls'
panny@53360
   623
        #> fold (fn (sel, n) => nth_map n
panny@53411
   624
          (build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls'
panny@53341
   625
      end
blanchet@53303
   626
  end;
blanchet@53303
   627
panny@53654
   628
fun co_build_defs lthy bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss =
panny@53654
   629
  let
panny@53654
   630
    val corec_specs' = take (length bs) corec_specs;
panny@53654
   631
    val corecs = map #corec corec_specs';
panny@53654
   632
    val ctr_specss = map #ctr_specs corec_specs';
panny@53360
   633
    val corec_args = hd corecs
panny@53360
   634
      |> fst o split_last o binder_types o fastype_of
panny@53360
   635
      |> map (Const o pair @{const_name undefined})
panny@53720
   636
      |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
panny@53360
   637
      |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
panny@53401
   638
    fun currys Ts t = if length Ts <= 1 then t else
panny@53401
   639
      t $ foldr1 (fn (u, v) => HOLogic.pair_const dummyT dummyT $ u $ v)
panny@53401
   640
        (length Ts - 1 downto 0 |> map Bound)
panny@53720
   641
      |> fold_rev (Term.abs o pair Name.uu) Ts;
panny@53401
   642
panny@53360
   643
val _ = tracing ("corecursor arguments:\n    \<cdot> " ^
panny@53411
   644
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
blanchet@53303
   645
panny@53654
   646
    val exclss' =
panny@53720
   647
      disc_eqnss
panny@53654
   648
      |> map (map (fn {fun_args, ctr_no, prems, ...} => (fun_args, ctr_no, prems))
panny@53654
   649
        #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
panny@53654
   650
        #> maps (uncurry (map o pair)
panny@53654
   651
          #> map (fn ((fun_args, c, x), (_, c', y)) => ((c, c'), (x, mk_not (mk_conjs y)))
panny@53654
   652
            ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
panny@53654
   653
            ||> Logic.list_implies
panny@53654
   654
            ||> curry Logic.list_all (map dest_Free fun_args))))
blanchet@53303
   655
  in
blanchet@53303
   656
    map (list_comb o rpair corec_args) corecs
blanchet@53303
   657
    |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
blanchet@53303
   658
    |> map2 currys arg_Tss
blanchet@53303
   659
    |> Syntax.check_terms lthy
traytel@53352
   660
    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
panny@53654
   661
    |> rpair exclss'
blanchet@53303
   662
  end;
blanchet@53303
   663
panny@53722
   664
fun mk_real_disc_eqns fun_binding arg_Ts {ctr_specs, ...} sel_eqns disc_eqns =
panny@53720
   665
  if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
panny@53720
   666
    let
panny@53720
   667
      val n = 0 upto length ctr_specs
panny@53720
   668
        |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
panny@53722
   669
      val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
panny@53722
   670
        |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
panny@53720
   671
      val extra_disc_eqn = {
panny@53720
   672
        fun_name = Binding.name_of fun_binding,
panny@53720
   673
        fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
panny@53722
   674
        fun_args = fun_args,
panny@53720
   675
        ctr = #ctr (nth ctr_specs n),
panny@53720
   676
        ctr_no = n,
panny@53720
   677
        disc = #disc (nth ctr_specs n),
panny@53720
   678
        prems = maps (invert_prems o #prems) disc_eqns,
panny@53720
   679
        user_eqn = undef_const};
panny@53720
   680
    in
panny@53720
   681
      chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
panny@53720
   682
    end;
panny@53720
   683
blanchet@53303
   684
fun add_primcorec sequential fixes specs lthy =
blanchet@53303
   685
  let
traytel@53352
   686
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   687
    val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
blanchet@53303
   688
blanchet@53303
   689
    (* copied from primrec_new *)
blanchet@53303
   690
    fun get_indices t = map (fst #>> Binding.name_of #> Free) fixes
blanchet@53303
   691
      |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
blanchet@53303
   692
      |> map_filter I;
blanchet@53303
   693
blanchet@53303
   694
    val callssss = []; (* FIXME *)
blanchet@53303
   695
panny@53654
   696
    val ((nontriv, corec_specs', _, coinduct_thm, strong_co_induct_thm, coinduct_thmss,
blanchet@53303
   697
          strong_coinduct_thmss), lthy') =
blanchet@53303
   698
      corec_specs_of bs arg_Ts res_Ts get_indices callssss lthy;
blanchet@53303
   699
blanchet@53303
   700
    val fun_names = map Binding.name_of bs;
panny@53654
   701
    val corec_specs = take (length fun_names) corec_specs'; (*###*)
blanchet@53303
   702
blanchet@53303
   703
    val (eqns_data, _) =
panny@53654
   704
      fold_map (co_dissect_eqn sequential fun_names corec_specs) (map snd specs) []
blanchet@53303
   705
      |>> flat;
blanchet@53303
   706
panny@53720
   707
    val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
panny@53654
   708
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   709
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   710
      |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
panny@53720
   711
    val _ = disc_eqnss' |> map (fn x =>
panny@53720
   712
      let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
panny@53720
   713
        primrec_error_eqns "excess discriminator equations in definition"
panny@53720
   714
          (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
panny@53654
   715
panny@53654
   716
    val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
panny@53654
   717
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   718
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   719
      |> map (flat o snd);
panny@53654
   720
panny@53360
   721
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
panny@53360
   722
    val arg_Tss = map (binder_types o snd o fst) fixes;
panny@53722
   723
    val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
panny@53654
   724
    val (defs, exclss') =
panny@53654
   725
      co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
panny@53654
   726
panny@53654
   727
    (* try to prove (automatically generated) tautologies by ourselves *)
panny@53654
   728
    val exclss'' = exclss'
panny@53654
   729
      |> map (map (apsnd
blanchet@53699
   730
        (`(try (fn t => Goal.prove lthy [] [] t (mk_primcorec_assumption_tac lthy |> K))))));
panny@53654
   731
    val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
panny@53654
   732
    val (obligation_idxss, obligationss) = exclss''
panny@53654
   733
      |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
panny@53654
   734
      |> split_list o map split_list;
panny@53654
   735
panny@53654
   736
    fun prove thmss' def_thms' lthy =
panny@53654
   737
      let
panny@53654
   738
        val def_thms = map (snd o snd) def_thms';
panny@53654
   739
panny@53654
   740
        val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
panny@53654
   741
        fun mk_exclsss excls n =
panny@53654
   742
          (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
panny@53654
   743
          |-> fold (fn ((c, c'), thm) => nth_map c (nth_map c' (K [thm])));
panny@53654
   744
        val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
panny@53654
   745
          |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
panny@53654
   746
panny@53654
   747
        fun prove_disc {ctr_specs, ...} exclsss
panny@53720
   748
            {fun_name, fun_T, fun_args, ctr_no, prems, user_eqn, ...} =
panny@53722
   749
          if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
panny@53720
   750
            let
panny@53722
   751
              val {disc_corec, ...} = nth ctr_specs ctr_no;
panny@53720
   752
              val k = 1 + ctr_no;
panny@53720
   753
              val m = length prems;
panny@53720
   754
              val t =
panny@53720
   755
                list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   756
                |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
panny@53720
   757
                |> HOLogic.mk_Trueprop
panny@53720
   758
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   759
                |> curry Logic.list_all (map dest_Free fun_args);
panny@53720
   760
            in
panny@53720
   761
              mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
panny@53720
   762
              |> K |> Goal.prove lthy [] [] t
panny@53720
   763
              |> pair (#disc (nth ctr_specs ctr_no))
panny@53720
   764
              |> single
panny@53720
   765
            end;
panny@53720
   766
panny@53720
   767
        fun prove_sel {ctr_specs, nested_maps, nested_map_idents, nested_map_comps, ...}
panny@53720
   768
            disc_eqns exclsss {fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} =
panny@53654
   769
          let
panny@53720
   770
            val (SOME ctr_spec) = find_first (equal ctr o #ctr) ctr_specs;
panny@53720
   771
            val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
panny@53720
   772
            val prems = the_default (maps (invert_prems o #prems) disc_eqns)
panny@53720
   773
                (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
panny@53720
   774
            val sel_corec = find_index (equal sel) (#sels ctr_spec)
panny@53720
   775
              |> nth (#sel_corecs ctr_spec);
panny@53654
   776
            val k = 1 + ctr_no;
panny@53654
   777
            val m = length prems;
panny@53654
   778
            val t =
panny@53720
   779
              list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   780
              |> curry betapply sel
panny@53720
   781
              |> rpair (abstract (List.rev fun_args) rhs_term)
panny@53720
   782
              |> HOLogic.mk_Trueprop o HOLogic.mk_eq
panny@53654
   783
              |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   784
              |> curry Logic.list_all (map dest_Free fun_args);
panny@53654
   785
          in
blanchet@53692
   786
            mk_primcorec_ctr_or_sel_tac lthy def_thms sel_corec k m exclsss
panny@53654
   787
              nested_maps nested_map_idents nested_map_comps
panny@53654
   788
            |> K |> Goal.prove lthy [] [] t
panny@53720
   789
            |> pair sel
panny@53654
   790
          end;
panny@53654
   791
panny@53720
   792
        fun prove_ctr (_, disc_thms) (_, sel_thms') disc_eqns sel_eqns
panny@53720
   793
            {ctr, disc, sels, collapse, ...} =
panny@53722
   794
let val _ = tracing ("disc = " ^ @{make_string} disc); in
panny@53720
   795
          if not (exists (equal ctr o #ctr) disc_eqns)
panny@53722
   796
              andalso not (exists (equal ctr o #ctr) sel_eqns)
panny@53722
   797
andalso (warning ("no eqns for ctr " ^ Syntax.string_of_term lthy ctr); true)
panny@53722
   798
            orelse (* don't try to prove theorems when some sel_eqns are missing *)
panny@53720
   799
              filter (equal ctr o #ctr) sel_eqns
panny@53720
   800
              |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   801
              |> exists (null o snd)
panny@53720
   802
andalso (warning ("sel_eqn(s) missing for ctr " ^ Syntax.string_of_term lthy ctr); true)
panny@53720
   803
          then [] else
panny@53720
   804
            let
panny@53720
   805
val _ = tracing ("ctr = " ^ Syntax.string_of_term lthy ctr);
panny@53722
   806
val _ = tracing (the_default "NO disc_eqn" (Option.map (curry (op ^) "disc = " o Syntax.string_of_term lthy o #disc) (find_first (equal ctr o #ctr) disc_eqns)));
panny@53722
   807
              val (fun_name, fun_T, fun_args, prems) =
panny@53722
   808
                (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
panny@53722
   809
                |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x))
panny@53722
   810
                ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, []))
panny@53722
   811
                |> the o merge_options;
panny@53720
   812
              val m = length prems;
panny@53720
   813
              val t = sel_eqns
panny@53720
   814
                |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   815
                |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
panny@53720
   816
                |> curry list_comb ctr
panny@53720
   817
                |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
panny@53720
   818
                  map Bound (length fun_args - 1 downto 0)))
panny@53720
   819
                |> HOLogic.mk_Trueprop
panny@53720
   820
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   821
                |> curry Logic.list_all (map dest_Free fun_args);
panny@53722
   822
              val maybe_disc_thm = AList.lookup (op =) disc_thms disc;
panny@53720
   823
              val sel_thms = map snd (filter (member (op =) sels o fst) sel_thms');
panny@53720
   824
val _ = tracing ("t = " ^ Syntax.string_of_term lthy t);
panny@53720
   825
val _ = tracing ("m = " ^ @{make_string} m);
panny@53720
   826
val _ = tracing ("collapse = " ^ @{make_string} collapse);
panny@53722
   827
val _ = tracing ("maybe_disc_thm = " ^ @{make_string} maybe_disc_thm);
panny@53720
   828
val _ = tracing ("sel_thms = " ^ @{make_string} sel_thms);
panny@53720
   829
            in
panny@53722
   830
              mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
panny@53720
   831
              |> K |> Goal.prove lthy [] [] t
panny@53720
   832
              |> single
panny@53722
   833
(*handle ERROR x => (warning x; []))*)
panny@53722
   834
end
panny@53720
   835
          end;
panny@53720
   836
panny@53720
   837
        val (disc_notes, disc_thmss) =
panny@53720
   838
          fun_names ~~ map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss
panny@53720
   839
          |> `(map (fn (fun_name, thms) =>
panny@53720
   840
            ((Binding.qualify true fun_name (@{binding disc}), simp_attrs), [(map snd thms, [])])));
panny@53720
   841
        val (sel_notes, sel_thmss) =
panny@53720
   842
          fun_names ~~ map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss
panny@53720
   843
          |> `(map (fn (fun_name, thms) =>
panny@53720
   844
            ((Binding.qualify true fun_name (@{binding sel}), simp_attrs), [(map snd thms, [])])));
panny@53720
   845
        val ctr_notes =
panny@53720
   846
          fun_names ~~ map5 (maps oooo prove_ctr) disc_thmss sel_thmss
panny@53720
   847
            disc_eqnss sel_eqnss (map #ctr_specs corec_specs)
panny@53654
   848
          |> map (fn (fun_name, thms) =>
panny@53720
   849
            ((Binding.qualify true fun_name (@{binding ctr}), simp_attrs), [(thms, [])]));
panny@53654
   850
      in
panny@53720
   851
        lthy |> snd o Local_Theory.notes
panny@53720
   852
          (filter (not o null o fst o the_single o snd) (disc_notes @ sel_notes @ ctr_notes))
panny@53654
   853
      end;
blanchet@53303
   854
  in
blanchet@53303
   855
    lthy'
panny@53654
   856
    |> Proof.theorem NONE (curry (op #->) (fold_map Local_Theory.define defs) o prove) obligationss
blanchet@53303
   857
    |> Proof.refine (Method.primitive_text I)
blanchet@53303
   858
    |> Seq.hd
blanchet@53303
   859
  end
blanchet@53303
   860
blanchet@53303
   861
fun add_primcorec_cmd seq (raw_fixes, raw_specs) lthy =
blanchet@53303
   862
  let
blanchet@53303
   863
    val (fixes, specs) = fst (Specification.read_spec raw_fixes raw_specs lthy);
blanchet@53303
   864
  in
blanchet@53303
   865
    add_primcorec seq fixes specs lthy
blanchet@53303
   866
    handle ERROR str => primrec_error str
blanchet@53303
   867
  end
blanchet@53303
   868
  handle Primrec_Error (str, eqns) =>
blanchet@53303
   869
    if null eqns
blanchet@53303
   870
    then error ("primcorec error:\n  " ^ str)
blanchet@53303
   871
    else error ("primcorec error:\n  " ^ str ^ "\nin\n  " ^
blanchet@53303
   872
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns))
blanchet@53303
   873
blanchet@53303
   874
end;