src/HOL/BNF/Tools/bnf_fp_rec_sugar.ML
author blanchet
Mon Oct 14 09:31:42 2013 +0200 (2013-10-14)
changeset 54102 82ada0a92dde
parent 54101 94f2dc9aea7a
child 54106 e5f853482006
permissions -rw-r--r--
tuned names
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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 nitpick_attrs = @{attributes [nitpick_simp]};
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val simp_attrs = @{attributes [simp]};
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val code_nitpick_attrs = Code.add_default_eqn_attrib :: nitpick_attrs;
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val code_nitpick_simp_attrs = Code.add_default_eqn_attrib :: nitpick_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 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 mutual_calls nested_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_mutual_y' = AList.lookup (op =) mutual_calls y;
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          val maybe_nested_y' = AList.lookup (op =) nested_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_mutual_y', g_args)
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          else if is_some maybe_nested_y' then
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            (if has_call g' then t else y)
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            |> massage_nested_rec_call lthy has_call
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              (rewrite_map_arg get_ctr_pos) bound_Ts y (the maybe_nested_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 : 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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  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 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 n => n | Mutual_Rec (n, _) => n)));
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      val mutual_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn Mutual_Rec (_, n) => n)));
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      val nested_calls' = tag_list 0 calls
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        |> map_filter (try (apsnd (fn Nested_Rec n => n)));
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      fun make_mutual_type _ = 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_nested_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_nested_type T end))
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        | make_nested_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_mutual_type)))
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          mutual_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_nested_type)))
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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)) mutual_calls';
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      val nested_calls = map (apfst (nth ctr_args) o apsnd (nth args)) nested_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 mutual_calls nested_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 : 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.map_name Thm.def_name b, []), t))) bs mxs
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  end;
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blanchet@54001
   289
fun find_rec_calls has_call (eqn_data : eqn_data) =
blanchet@53303
   290
  let
blanchet@53303
   291
    fun find (Abs (_, _, b)) ctr_arg = find b ctr_arg
blanchet@53303
   292
      | find (t as _ $ _) ctr_arg =
blanchet@53303
   293
        let
blanchet@53303
   294
          val (f', args') = strip_comb t;
blanchet@53303
   295
          val n = find_index (equal ctr_arg) args';
blanchet@53303
   296
        in
blanchet@53303
   297
          if n < 0 then
blanchet@53303
   298
            find f' ctr_arg @ maps (fn x => find x ctr_arg) args'
blanchet@53303
   299
          else
blanchet@53303
   300
            let val (f, args) = chop n args' |>> curry list_comb f' in
panny@53358
   301
              if has_call f then
blanchet@53303
   302
                f :: maps (fn x => find x ctr_arg) args
blanchet@53303
   303
              else
blanchet@53303
   304
                find f ctr_arg @ maps (fn x => find x ctr_arg) args
blanchet@53303
   305
            end
blanchet@53303
   306
        end
blanchet@53303
   307
      | find _ _ = [];
blanchet@53303
   308
  in
blanchet@53303
   309
    map (find (#rhs_term eqn_data)) (#ctr_args eqn_data)
blanchet@53303
   310
    |> (fn [] => NONE | callss => SOME (#ctr eqn_data, callss))
blanchet@53303
   311
  end;
blanchet@53303
   312
traytel@54013
   313
fun prepare_primrec fixes specs lthy =
blanchet@53303
   314
  let
traytel@53352
   315
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   316
    val fun_names = map Binding.name_of bs;
traytel@54013
   317
    val eqns_data = map (dissect_eqn lthy fun_names) specs;
blanchet@53303
   318
    val funs_data = eqns_data
blanchet@53303
   319
      |> partition_eq ((op =) o pairself #fun_name)
blanchet@53303
   320
      |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
blanchet@53303
   321
      |> map (fn (x, y) => the_single y handle List.Empty =>
blanchet@53303
   322
          primrec_error ("missing equations for function " ^ quote x));
blanchet@53303
   323
panny@53358
   324
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
blanchet@53303
   325
    val arg_Ts = map (#rec_type o hd) funs_data;
blanchet@53303
   326
    val res_Ts = map (#res_type o hd) funs_data;
blanchet@53303
   327
    val callssss = funs_data
blanchet@53303
   328
      |> map (partition_eq ((op =) o pairself #ctr))
panny@53358
   329
      |> map (maps (map_filter (find_rec_calls has_call)));
blanchet@53303
   330
blanchet@53830
   331
    val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =
blanchet@53794
   332
      rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53303
   333
blanchet@53303
   334
    val actual_nn = length funs_data;
blanchet@53303
   335
blanchet@53303
   336
    val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
blanchet@53303
   337
      map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
blanchet@53303
   338
        primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
blanchet@53303
   339
          " is not a constructor in left-hand side") user_eqn) eqns_data end;
blanchet@53303
   340
panny@53358
   341
    val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
blanchet@53303
   342
traytel@54013
   343
    fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec)
traytel@54013
   344
        (fun_data : eqn_data list) =
blanchet@53303
   345
      let
blanchet@53303
   346
        val def_thms = map (snd o snd) def_thms';
traytel@54013
   347
        val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
blanchet@53303
   348
          |> fst
blanchet@53303
   349
          |> map_filter (try (fn (x, [y]) =>
blanchet@53303
   350
            (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
blanchet@53303
   351
          |> map (fn (user_eqn, num_extra_args, rec_thm) =>
blanchet@53329
   352
            mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
traytel@54013
   353
            |> K |> Goal.prove lthy [] [] user_eqn);
traytel@54013
   354
        val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data;
traytel@54013
   355
      in
traytel@54013
   356
        (poss, simp_thmss)
traytel@54013
   357
      end;
blanchet@53303
   358
traytel@54013
   359
    val notes =
traytel@54013
   360
      (if n2m then map2 (fn name => fn thm =>
traytel@54013
   361
        (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else [])
traytel@54013
   362
      |> map (fn (prefix, thmN, thms, attrs) =>
traytel@54013
   363
        ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   364
blanchet@53303
   365
    val common_name = mk_common_name fun_names;
blanchet@53303
   366
blanchet@53303
   367
    val common_notes =
traytel@54013
   368
      (if n2m then [(inductN, [induct_thm], [])] else [])
blanchet@53303
   369
      |> map (fn (thmN, thms, attrs) =>
blanchet@53303
   370
        ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   371
  in
traytel@54013
   372
    (((fun_names, defs),
traytel@54013
   373
      fn lthy => fn defs =>
traytel@54013
   374
        split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),
traytel@54013
   375
      lthy' |> Local_Theory.notes (notes @ common_notes) |> snd)
blanchet@53303
   376
  end;
blanchet@53303
   377
traytel@54013
   378
(* primrec definition *)
traytel@54013
   379
traytel@54013
   380
fun add_primrec_simple fixes ts lthy =
blanchet@53303
   381
  let
traytel@54013
   382
    val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy
traytel@54013
   383
      handle ERROR str => primrec_error str;
blanchet@53303
   384
  in
traytel@54013
   385
    lthy
traytel@54013
   386
    |> fold_map Local_Theory.define defs
traytel@54013
   387
    |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))
blanchet@53303
   388
  end
blanchet@53303
   389
  handle Primrec_Error (str, eqns) =>
blanchet@53303
   390
    if null eqns
blanchet@53303
   391
    then error ("primrec_new error:\n  " ^ str)
blanchet@53303
   392
    else error ("primrec_new error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
   393
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
blanchet@53303
   394
traytel@54013
   395
local
traytel@54013
   396
traytel@54028
   397
fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy =
traytel@54013
   398
  let
traytel@54013
   399
    val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)
traytel@54013
   400
    val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d);
traytel@54013
   401
traytel@54013
   402
    val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy);
traytel@54013
   403
traytel@54013
   404
    val mk_notes =
traytel@54013
   405
      flat ooo map3 (fn poss => fn prefix => fn thms =>
traytel@54013
   406
        let
traytel@54013
   407
          val (bs, attrss) = map_split (fst o nth specs) poss;
traytel@54013
   408
          val notes =
traytel@54013
   409
            map3 (fn b => fn attrs => fn thm =>
traytel@54013
   410
              ((Binding.qualify false prefix b, code_nitpick_simp_attrs @ attrs), [([thm], [])]))
traytel@54013
   411
            bs attrss thms;
traytel@54013
   412
        in
traytel@54013
   413
          ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes
traytel@54013
   414
        end);
traytel@54013
   415
  in
traytel@54013
   416
    lthy
traytel@54013
   417
    |> add_primrec_simple fixes (map snd specs)
traytel@54013
   418
    |-> (fn (names, (ts, (posss, simpss))) =>
traytel@54013
   419
      Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)
traytel@54013
   420
      #> Local_Theory.notes (mk_notes posss names simpss)
traytel@54013
   421
      #>> pair ts o map snd)
traytel@54013
   422
  end;
traytel@54013
   423
traytel@54013
   424
in
traytel@54013
   425
traytel@54013
   426
val add_primrec = gen_primrec Specification.check_spec;
traytel@54013
   427
val add_primrec_cmd = gen_primrec Specification.read_spec;
traytel@54013
   428
traytel@54013
   429
end;
traytel@54013
   430
traytel@54013
   431
fun add_primrec_global fixes specs thy =
traytel@54013
   432
  let
traytel@54013
   433
    val lthy = Named_Target.theory_init thy;
traytel@54013
   434
    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
traytel@54013
   435
    val simps' = burrow (Proof_Context.export lthy' lthy) simps;
traytel@54013
   436
  in ((ts, simps'), Local_Theory.exit_global lthy') end;
traytel@54013
   437
traytel@54013
   438
fun add_primrec_overloaded ops fixes specs thy =
traytel@54013
   439
  let
traytel@54013
   440
    val lthy = Overloading.overloading ops thy;
traytel@54013
   441
    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
traytel@54013
   442
    val simps' = burrow (Proof_Context.export lthy' lthy) simps;
traytel@54013
   443
  in ((ts, simps'), Local_Theory.exit_global lthy') end;
traytel@54013
   444
blanchet@53303
   445
blanchet@53303
   446
blanchet@53310
   447
(* Primcorec *)
blanchet@53303
   448
panny@53341
   449
type co_eqn_data_disc = {
blanchet@53303
   450
  fun_name: string,
panny@53720
   451
  fun_T: typ,
panny@53401
   452
  fun_args: term list,
panny@53720
   453
  ctr: term,
panny@53341
   454
  ctr_no: int, (*###*)
panny@53720
   455
  disc: term,
panny@53654
   456
  prems: term list,
panny@53822
   457
  auto_gen: bool,
panny@54097
   458
  maybe_ctr_rhs: term option,
panny@54097
   459
  maybe_code_rhs: term option,
blanchet@53303
   460
  user_eqn: term
blanchet@53303
   461
};
blanchet@54001
   462
panny@53341
   463
type co_eqn_data_sel = {
blanchet@53303
   464
  fun_name: string,
panny@53720
   465
  fun_T: typ,
panny@53401
   466
  fun_args: term list,
panny@53341
   467
  ctr: term,
panny@53341
   468
  sel: term,
blanchet@53303
   469
  rhs_term: term,
blanchet@53303
   470
  user_eqn: term
blanchet@53303
   471
};
blanchet@54001
   472
blanchet@53303
   473
datatype co_eqn_data =
panny@53341
   474
  Disc of co_eqn_data_disc |
panny@53341
   475
  Sel of co_eqn_data_sel;
blanchet@53303
   476
panny@54097
   477
fun co_dissect_eqn_disc seq fun_names (corec_specs : corec_spec list) maybe_ctr_rhs maybe_code_rhs
panny@54097
   478
    prems' concl matchedsss =
blanchet@53303
   479
  let
blanchet@53303
   480
    fun find_subterm p = let (* FIXME \<exists>? *)
panny@53401
   481
      fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
blanchet@53303
   482
        | f t = if p t then SOME t else NONE
blanchet@53303
   483
      in f end;
blanchet@53303
   484
panny@53654
   485
    val applied_fun = concl
panny@53654
   486
      |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
panny@53654
   487
      |> the
panny@53654
   488
      handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
panny@53720
   489
    val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
panny@53720
   490
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
blanchet@53303
   491
panny@53720
   492
    val discs = map #disc ctr_specs;
panny@53720
   493
    val ctrs = map #ctr ctr_specs;
panny@53654
   494
    val not_disc = head_of concl = @{term Not};
panny@53401
   495
    val _ = not_disc andalso length ctrs <> 2 andalso
panny@53654
   496
      primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
panny@53654
   497
    val disc = find_subterm (member (op =) discs o head_of) concl;
panny@53654
   498
    val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
blanchet@53303
   499
        |> (fn SOME t => let val n = find_index (equal t) ctrs in
blanchet@53303
   500
          if n >= 0 then SOME n else NONE end | _ => NONE);
blanchet@53303
   501
    val _ = is_some disc orelse is_some eq_ctr0 orelse
panny@53654
   502
      primrec_error_eqn "no discriminator in equation" concl;
blanchet@53303
   503
    val ctr_no' =
blanchet@53303
   504
      if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
blanchet@53303
   505
    val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
panny@53720
   506
    val ctr = #ctr (nth ctr_specs ctr_no);
panny@53654
   507
panny@53654
   508
    val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
panny@53720
   509
    val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
panny@53720
   510
    val prems = map (abstract (List.rev fun_args)) prems';
panny@53720
   511
    val real_prems =
blanchet@54067
   512
      (if catch_all orelse seq then maps s_not_conj matchedss else []) @
panny@53654
   513
      (if catch_all then [] else prems);
blanchet@53303
   514
panny@53720
   515
    val matchedsss' = AList.delete (op =) fun_name matchedsss
panny@54065
   516
      |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
blanchet@53303
   517
panny@53654
   518
    val user_eqn =
panny@54097
   519
      (real_prems, concl)
panny@54097
   520
      |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
panny@54097
   521
      |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
blanchet@53303
   522
  in
panny@53341
   523
    (Disc {
blanchet@53303
   524
      fun_name = fun_name,
panny@53720
   525
      fun_T = fun_T,
panny@53401
   526
      fun_args = fun_args,
panny@53720
   527
      ctr = ctr,
blanchet@53303
   528
      ctr_no = ctr_no,
panny@53720
   529
      disc = #disc (nth ctr_specs ctr_no),
panny@53654
   530
      prems = real_prems,
panny@53822
   531
      auto_gen = catch_all,
panny@54097
   532
      maybe_ctr_rhs = maybe_ctr_rhs,
panny@54097
   533
      maybe_code_rhs = maybe_code_rhs,
panny@53654
   534
      user_eqn = user_eqn
panny@53720
   535
    }, matchedsss')
blanchet@53303
   536
  end;
blanchet@53303
   537
blanchet@54002
   538
fun co_dissect_eqn_sel fun_names (corec_specs : corec_spec list) eqn' of_spec eqn =
blanchet@53303
   539
  let
blanchet@53303
   540
    val (lhs, rhs) = HOLogic.dest_eq eqn
blanchet@53303
   541
      handle TERM _ =>
blanchet@53303
   542
        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
blanchet@53303
   543
    val sel = head_of lhs;
panny@53720
   544
    val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
blanchet@53303
   545
      handle TERM _ =>
blanchet@53303
   546
        primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@53654
   547
    val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
blanchet@53303
   548
      handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@53831
   549
    val ctr_spec =
panny@53831
   550
      if is_some of_spec
panny@53831
   551
      then the (find_first (equal (the of_spec) o #ctr) (#ctr_specs corec_spec))
panny@53831
   552
      else #ctr_specs corec_spec |> filter (exists (equal sel) o #sels) |> the_single
panny@53831
   553
        handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn;
panny@53654
   554
    val user_eqn = drop_All eqn';
blanchet@53303
   555
  in
panny@53341
   556
    Sel {
blanchet@53303
   557
      fun_name = fun_name,
panny@53720
   558
      fun_T = fun_T,
panny@53401
   559
      fun_args = fun_args,
panny@53341
   560
      ctr = #ctr ctr_spec,
panny@53341
   561
      sel = sel,
blanchet@53303
   562
      rhs_term = rhs,
panny@53654
   563
      user_eqn = user_eqn
blanchet@53303
   564
    }
blanchet@53303
   565
  end;
blanchet@53303
   566
panny@54097
   567
fun co_dissect_eqn_ctr seq fun_names (corec_specs : corec_spec list) eqn' maybe_code_rhs
panny@54097
   568
    prems concl matchedsss =
blanchet@53910
   569
  let
panny@54065
   570
    val (lhs, rhs) = HOLogic.dest_eq concl;
panny@54097
   571
    val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
panny@53720
   572
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
blanchet@54074
   573
    val (ctr, ctr_args) = strip_comb (unfold_let rhs);
panny@53720
   574
    val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs)
blanchet@53303
   575
      handle Option.Option => primrec_error_eqn "not a constructor" ctr;
panny@53341
   576
panny@54065
   577
    val disc_concl = betapply (disc, lhs);
panny@53720
   578
    val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1
panny@53720
   579
      then (NONE, matchedsss)
panny@54097
   580
      else apfst SOME (co_dissect_eqn_disc seq fun_names corec_specs
panny@54097
   581
          (SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
blanchet@53303
   582
panny@54065
   583
    val sel_concls = (sels ~~ ctr_args)
blanchet@53303
   584
      |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
blanchet@53303
   585
blanchet@53856
   586
(*
panny@54065
   587
val _ = tracing ("reduced\n    " ^ Syntax.string_of_term @{context} concl ^ "\nto\n    \<cdot> " ^
panny@54065
   588
 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n    \<cdot> ")) "" ^
panny@54097
   589
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
panny@54097
   590
 "\nfor premise(s)\n    \<cdot> " ^
panny@54097
   591
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) prems));
blanchet@53856
   592
*)
blanchet@53303
   593
panny@54065
   594
    val eqns_data_sel = map (co_dissect_eqn_sel fun_names corec_specs eqn' (SOME ctr)) sel_concls;
blanchet@53303
   595
  in
panny@53720
   596
    (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
blanchet@53303
   597
  end;
blanchet@53303
   598
panny@54065
   599
fun co_dissect_eqn_code lthy has_call fun_names corec_specs eqn' concl matchedsss =
panny@54065
   600
  let
panny@54065
   601
    val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
panny@54097
   602
    val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
panny@54065
   603
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
panny@54065
   604
panny@54065
   605
    val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
panny@54065
   606
        if member ((op =) o apsnd #ctr) ctr_specs ctr
panny@54065
   607
        then cons (ctr, cs)
panny@54065
   608
        else primrec_error_eqn "not a constructor" ctr) [] rhs' []
panny@54065
   609
      |> AList.group (op =);
panny@54065
   610
blanchet@54068
   611
    val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
panny@54065
   612
    val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
panny@54065
   613
        binder_types (fastype_of ctr)
panny@54065
   614
        |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
panny@54065
   615
          if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
panny@54065
   616
        |> curry list_comb ctr
panny@54065
   617
        |> curry HOLogic.mk_eq lhs);
panny@54065
   618
  in
panny@54097
   619
    fold_map2 (co_dissect_eqn_ctr false fun_names corec_specs eqn'
panny@54097
   620
        (SOME (abstract (List.rev fun_args) rhs)))
panny@54097
   621
      ctr_premss ctr_concls matchedsss
panny@54065
   622
  end;
panny@54065
   623
panny@54097
   624
fun co_dissect_eqn lthy seq has_call fun_names (corec_specs : corec_spec list) eqn' of_spec
panny@54065
   625
    matchedsss =
blanchet@53303
   626
  let
panny@53654
   627
    val eqn = drop_All eqn'
panny@53654
   628
      handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
panny@54065
   629
    val (prems, concl) = Logic.strip_horn eqn
panny@53341
   630
      |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
blanchet@53303
   631
panny@54065
   632
    val head = concl
blanchet@53303
   633
      |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
blanchet@53303
   634
      |> head_of;
blanchet@53303
   635
panny@54065
   636
    val maybe_rhs = concl |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
blanchet@53303
   637
panny@53654
   638
    val discs = maps #ctr_specs corec_specs |> map #disc;
panny@53654
   639
    val sels = maps #ctr_specs corec_specs |> maps #sels;
panny@53654
   640
    val ctrs = maps #ctr_specs corec_specs |> map #ctr;
blanchet@53303
   641
  in
blanchet@53303
   642
    if member (op =) discs head orelse
blanchet@53303
   643
      is_some maybe_rhs andalso
blanchet@53303
   644
        member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
panny@54097
   645
      co_dissect_eqn_disc seq fun_names corec_specs NONE NONE prems concl matchedsss
blanchet@53303
   646
      |>> single
blanchet@53303
   647
    else if member (op =) sels head then
panny@54065
   648
      ([co_dissect_eqn_sel fun_names corec_specs eqn' of_spec concl], matchedsss)
panny@54065
   649
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
blanchet@54074
   650
      member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
panny@54097
   651
      co_dissect_eqn_ctr seq fun_names corec_specs eqn' NONE prems concl matchedsss
panny@54065
   652
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
panny@54065
   653
      null prems then
panny@54065
   654
      co_dissect_eqn_code lthy has_call fun_names corec_specs eqn' concl matchedsss
panny@54065
   655
      |>> flat
blanchet@53303
   656
    else
blanchet@53303
   657
      primrec_error_eqn "malformed function equation" eqn
blanchet@53303
   658
  end;
blanchet@53303
   659
blanchet@54002
   660
fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
blanchet@54002
   661
    ({fun_args, ctr_no, prems, ...} : co_eqn_data_disc) =
panny@53654
   662
  if is_none (#pred (nth ctr_specs ctr_no)) then I else
blanchet@54068
   663
    s_conjs prems
panny@53654
   664
    |> curry subst_bounds (List.rev fun_args)
panny@53654
   665
    |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
panny@53654
   666
    |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
blanchet@53303
   667
blanchet@54002
   668
fun build_corec_arg_no_call (sel_eqns : co_eqn_data_sel list) sel =
panny@53720
   669
  find_first (equal sel o #sel) sel_eqns
panny@53720
   670
  |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
panny@53720
   671
  |> the_default undef_const
panny@53411
   672
  |> K;
panny@53360
   673
blanchet@54102
   674
fun build_corec_args_mutual_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel =
panny@53360
   675
  let
panny@53411
   676
    val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
panny@53360
   677
  in
panny@53876
   678
    if is_none maybe_sel_eqn then (I, I, I) else
panny@53876
   679
    let
panny@53876
   680
      val {fun_args, rhs_term, ... } = the maybe_sel_eqn;
panny@54097
   681
      val bound_Ts = List.rev (map fastype_of fun_args);
blanchet@53890
   682
      fun rewrite_q _ t = if has_call t then @{term False} else @{term True};
blanchet@53890
   683
      fun rewrite_g _ t = if has_call t then undef_const else t;
panny@53899
   684
      fun rewrite_h bound_Ts t =
panny@53899
   685
        if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
blanchet@54102
   686
      fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
panny@54097
   687
        |> abs_tuple fun_args;
panny@53876
   688
    in
panny@53876
   689
      (massage rewrite_q,
panny@53876
   690
       massage rewrite_g,
panny@53876
   691
       massage rewrite_h)
panny@53876
   692
    end
panny@53360
   693
  end;
panny@53360
   694
blanchet@54102
   695
fun build_corec_arg_nested_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel =
panny@53411
   696
  let
panny@53411
   697
    val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
panny@53899
   698
  in
panny@53899
   699
    if is_none maybe_sel_eqn then I else
panny@53899
   700
    let
panny@53899
   701
      val {fun_args, rhs_term, ...} = the maybe_sel_eqn;
panny@54097
   702
      val bound_Ts = List.rev (map fastype_of fun_args);
panny@53899
   703
      fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
panny@53899
   704
        | rewrite bound_Ts U T (t as _ $ _) =
panny@53899
   705
          let val (u, vs) = strip_comb t in
panny@53899
   706
            if is_Free u andalso has_call u then
panny@53899
   707
              Inr_const U T $ mk_tuple1 bound_Ts vs
panny@53899
   708
            else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
panny@53899
   709
              map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
panny@53899
   710
            else
panny@53899
   711
              list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
panny@53899
   712
          end
panny@53899
   713
        | rewrite _ U T t =
panny@53899
   714
          if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
panny@53899
   715
      fun massage t =
panny@54097
   716
        rhs_term
blanchet@54102
   717
        |> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
panny@53735
   718
        |> abs_tuple fun_args;
panny@53899
   719
    in
panny@53899
   720
      massage
panny@53899
   721
    end
panny@53411
   722
  end;
panny@53360
   723
blanchet@54002
   724
fun build_corec_args_sel lthy has_call (all_sel_eqns : co_eqn_data_sel list)
blanchet@54002
   725
    (ctr_spec : corec_ctr_spec) =
panny@53341
   726
  let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
panny@53341
   727
    if null sel_eqns then I else
panny@53341
   728
      let
panny@53341
   729
        val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
panny@53341
   730
panny@53341
   731
        val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
blanchet@54102
   732
        val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
blanchet@54102
   733
        val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
panny@53341
   734
      in
panny@53360
   735
        I
panny@53735
   736
        #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
panny@53360
   737
        #> fold (fn (sel, (q, g, h)) =>
blanchet@54102
   738
          let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in
blanchet@54102
   739
            nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
panny@53360
   740
        #> fold (fn (sel, n) => nth_map n
blanchet@54102
   741
          (build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls'
panny@53341
   742
      end
blanchet@53303
   743
  end;
blanchet@53303
   744
blanchet@54002
   745
fun co_build_defs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
blanchet@54002
   746
    (disc_eqnss : co_eqn_data_disc list list) (sel_eqnss : co_eqn_data_sel list list) =
panny@53654
   747
  let
panny@53654
   748
    val corec_specs' = take (length bs) corec_specs;
panny@53654
   749
    val corecs = map #corec corec_specs';
panny@53654
   750
    val ctr_specss = map #ctr_specs corec_specs';
panny@53360
   751
    val corec_args = hd corecs
panny@53360
   752
      |> fst o split_last o binder_types o fastype_of
panny@53360
   753
      |> map (Const o pair @{const_name undefined})
panny@53720
   754
      |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
panny@53360
   755
      |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
panny@53735
   756
    fun currys [] t = t
panny@53735
   757
      | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
panny@53735
   758
          |> fold_rev (Term.abs o pair Name.uu) Ts;
panny@53401
   759
blanchet@53856
   760
(*
panny@53360
   761
val _ = tracing ("corecursor arguments:\n    \<cdot> " ^
panny@53411
   762
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
blanchet@53856
   763
*)
blanchet@53303
   764
panny@53654
   765
    val exclss' =
panny@53720
   766
      disc_eqnss
panny@53822
   767
      |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
panny@53654
   768
        #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
panny@53654
   769
        #> maps (uncurry (map o pair)
panny@53822
   770
          #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
blanchet@54068
   771
              ((c, c', a orelse a'), (x, s_not (s_conjs y)))
panny@53654
   772
            ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
panny@53654
   773
            ||> Logic.list_implies
panny@53654
   774
            ||> curry Logic.list_all (map dest_Free fun_args))))
blanchet@53303
   775
  in
blanchet@53303
   776
    map (list_comb o rpair corec_args) corecs
blanchet@53303
   777
    |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
blanchet@53303
   778
    |> map2 currys arg_Tss
blanchet@53303
   779
    |> Syntax.check_terms lthy
traytel@53352
   780
    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
panny@53654
   781
    |> rpair exclss'
blanchet@53303
   782
  end;
blanchet@53303
   783
blanchet@54002
   784
fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
blanchet@54002
   785
    (sel_eqns : co_eqn_data_sel list) (disc_eqns : co_eqn_data_disc list) =
panny@53720
   786
  if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
panny@53720
   787
    let
panny@53720
   788
      val n = 0 upto length ctr_specs
panny@53720
   789
        |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
panny@53722
   790
      val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
panny@53722
   791
        |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
panny@53720
   792
      val extra_disc_eqn = {
panny@53720
   793
        fun_name = Binding.name_of fun_binding,
panny@53720
   794
        fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
panny@53722
   795
        fun_args = fun_args,
panny@53720
   796
        ctr = #ctr (nth ctr_specs n),
panny@53720
   797
        ctr_no = n,
panny@53720
   798
        disc = #disc (nth ctr_specs n),
blanchet@54067
   799
        prems = maps (s_not_conj o #prems) disc_eqns,
panny@53822
   800
        auto_gen = true,
panny@54097
   801
        maybe_ctr_rhs = NONE,
panny@54097
   802
        maybe_code_rhs = NONE,
panny@53720
   803
        user_eqn = undef_const};
panny@53720
   804
    in
panny@53720
   805
      chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
panny@53720
   806
    end;
panny@53720
   807
panny@54065
   808
fun add_primcorec simple seq fixes specs of_specs lthy =
blanchet@53303
   809
  let
traytel@53352
   810
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   811
    val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
blanchet@53303
   812
blanchet@53303
   813
    val callssss = []; (* FIXME *)
blanchet@53303
   814
blanchet@53830
   815
    val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
blanchet@53797
   816
          strong_coinduct_thms), lthy') =
blanchet@53794
   817
      corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53303
   818
blanchet@53830
   819
    val actual_nn = length bs;
blanchet@53303
   820
    val fun_names = map Binding.name_of bs;
blanchet@53830
   821
    val corec_specs = take actual_nn corec_specs'; (*###*)
blanchet@53303
   822
panny@54065
   823
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
panny@53831
   824
    val eqns_data =
panny@54097
   825
      fold_map2 (co_dissect_eqn lthy seq has_call fun_names corec_specs)
panny@54065
   826
        (map snd specs) of_specs []
panny@53831
   827
      |> flat o fst;
blanchet@53303
   828
panny@53720
   829
    val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
panny@53654
   830
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   831
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   832
      |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
panny@53720
   833
    val _ = disc_eqnss' |> map (fn x =>
panny@53720
   834
      let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
panny@53720
   835
        primrec_error_eqns "excess discriminator equations in definition"
panny@53720
   836
          (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
panny@53654
   837
panny@53654
   838
    val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
panny@53654
   839
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   840
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   841
      |> map (flat o snd);
panny@53654
   842
panny@53360
   843
    val arg_Tss = map (binder_types o snd o fst) fixes;
panny@53722
   844
    val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
panny@53654
   845
    val (defs, exclss') =
panny@53654
   846
      co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
panny@53654
   847
blanchet@53923
   848
    fun excl_tac (c, c', a) =
panny@54065
   849
      if a orelse c = c' orelse seq then
blanchet@54044
   850
        SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
blanchet@54044
   851
      else if simple then
blanchet@54044
   852
        SOME (K (auto_tac lthy))
blanchet@54044
   853
      else
blanchet@54044
   854
        NONE;
panny@53822
   855
blanchet@53856
   856
(*
panny@53822
   857
val _ = tracing ("exclusiveness properties:\n    \<cdot> " ^
panny@53822
   858
 space_implode "\n    \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
blanchet@53856
   859
*)
panny@53822
   860
panny@53822
   861
    val exclss'' = exclss' |> map (map (fn (idx, t) =>
blanchet@53923
   862
      (idx, (Option.map (Goal.prove lthy [] [] t) (excl_tac idx), t))));
panny@53654
   863
    val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
panny@53654
   864
    val (obligation_idxss, obligationss) = exclss''
panny@53654
   865
      |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
panny@53654
   866
      |> split_list o map split_list;
panny@53654
   867
panny@53654
   868
    fun prove thmss' def_thms' lthy =
panny@53654
   869
      let
panny@53654
   870
        val def_thms = map (snd o snd) def_thms';
panny@53654
   871
panny@53654
   872
        val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
panny@53654
   873
        fun mk_exclsss excls n =
panny@53654
   874
          (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
panny@53822
   875
          |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
panny@53654
   876
        val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
panny@53654
   877
          |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
panny@53654
   878
blanchet@54002
   879
        fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
blanchet@54002
   880
            ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : co_eqn_data_disc) =
panny@53722
   881
          if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
panny@53720
   882
            let
panny@53722
   883
              val {disc_corec, ...} = nth ctr_specs ctr_no;
panny@53720
   884
              val k = 1 + ctr_no;
panny@53720
   885
              val m = length prems;
panny@53720
   886
              val t =
panny@53720
   887
                list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   888
                |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
panny@53720
   889
                |> HOLogic.mk_Trueprop
panny@53720
   890
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   891
                |> curry Logic.list_all (map dest_Free fun_args);
panny@53720
   892
            in
panny@54097
   893
              if prems = [@{term False}] then [] else
panny@53720
   894
              mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
panny@53720
   895
              |> K |> Goal.prove lthy [] [] t
panny@53720
   896
              |> pair (#disc (nth ctr_specs ctr_no))
panny@53720
   897
              |> single
panny@53720
   898
            end;
panny@53720
   899
blanchet@54002
   900
        fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
blanchet@54002
   901
            : corec_spec) (disc_eqns : co_eqn_data_disc list) exclsss
blanchet@54002
   902
            ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : co_eqn_data_sel) =
panny@53654
   903
          let
blanchet@53909
   904
            val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
panny@53720
   905
            val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
blanchet@54067
   906
            val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
panny@53720
   907
                (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
panny@53720
   908
            val sel_corec = find_index (equal sel) (#sels ctr_spec)
panny@53720
   909
              |> nth (#sel_corecs ctr_spec);
panny@53654
   910
            val k = 1 + ctr_no;
panny@53654
   911
            val m = length prems;
panny@53654
   912
            val t =
panny@53720
   913
              list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   914
              |> curry betapply sel
panny@53720
   915
              |> rpair (abstract (List.rev fun_args) rhs_term)
panny@53720
   916
              |> HOLogic.mk_Trueprop o HOLogic.mk_eq
panny@53654
   917
              |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   918
              |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53925
   919
            val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
panny@53654
   920
          in
blanchet@53918
   921
            mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
blanchet@53910
   922
              nested_map_idents nested_map_comps sel_corec k m exclsss
panny@53654
   923
            |> K |> Goal.prove lthy [] [] t
panny@53720
   924
            |> pair sel
panny@53654
   925
          end;
panny@53654
   926
blanchet@54002
   927
        fun prove_ctr disc_alist sel_alist (disc_eqns : co_eqn_data_disc list)
blanchet@54002
   928
            (sel_eqns : co_eqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
panny@54097
   929
          (* don't try to prove theorems when some sel_eqns are missing *)
panny@53720
   930
          if not (exists (equal ctr o #ctr) disc_eqns)
panny@53722
   931
              andalso not (exists (equal ctr o #ctr) sel_eqns)
panny@54097
   932
            orelse
panny@53720
   933
              filter (equal ctr o #ctr) sel_eqns
panny@53720
   934
              |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   935
              |> exists (null o snd)
panny@53720
   936
          then [] else
panny@53720
   937
            let
panny@54097
   938
              val (fun_name, fun_T, fun_args, prems, maybe_rhs) =
panny@53722
   939
                (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
panny@54097
   940
                |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
panny@54097
   941
                  #maybe_ctr_rhs x))
panny@54097
   942
                ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
panny@53722
   943
                |> the o merge_options;
panny@53720
   944
              val m = length prems;
panny@54097
   945
              val t = (if is_some maybe_rhs then the maybe_rhs else
panny@54097
   946
                  filter (equal ctr o #ctr) sel_eqns
panny@54097
   947
                  |> fst o finds ((op =) o apsnd #sel) sels
panny@54097
   948
                  |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
panny@54097
   949
                  |> curry list_comb ctr)
panny@53720
   950
                |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
panny@53720
   951
                  map Bound (length fun_args - 1 downto 0)))
panny@53720
   952
                |> HOLogic.mk_Trueprop
panny@53720
   953
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   954
                |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53791
   955
              val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
blanchet@53791
   956
              val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
panny@53720
   957
            in
panny@54097
   958
              if prems = [@{term False}] then [] else
panny@54097
   959
                mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
panny@54097
   960
                |> K |> Goal.prove lthy [] [] t
panny@54097
   961
                |> pair ctr
panny@54097
   962
                |> single
panny@53876
   963
            end;
panny@53720
   964
panny@54098
   965
        fun prove_code disc_eqns sel_eqns ctr_alist {ctr_specs, ...} =
panny@54098
   966
          let
panny@54097
   967
            val (fun_name, fun_T, fun_args, maybe_rhs) =
panny@54097
   968
              (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
panny@54097
   969
               find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
panny@54097
   970
              |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x))
panny@54097
   971
              ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
panny@54097
   972
              |> the o merge_options;
panny@54097
   973
panny@54097
   974
            val maybe_rhs' = if is_some maybe_rhs then maybe_rhs else
panny@54097
   975
              let
panny@54098
   976
                fun prove_code_ctr {ctr, sels, ...} =
panny@54097
   977
                  if not (exists (equal ctr o fst) ctr_alist) then NONE else
panny@54097
   978
                    let
panny@54099
   979
                      val prems = find_first (equal ctr o #ctr) disc_eqns
panny@54099
   980
                        |> Option.map #prems |> the_default [];
panny@54097
   981
                      val t =
panny@54097
   982
                        filter (equal ctr o #ctr) sel_eqns
panny@54097
   983
                        |> fst o finds ((op =) o apsnd #sel) sels
panny@54097
   984
                        |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
panny@54097
   985
                        |> curry list_comb ctr;
panny@54097
   986
                    in
panny@54097
   987
                      SOME (prems, t)
panny@54097
   988
                    end;
panny@54097
   989
                val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
panny@54097
   990
              in
panny@54097
   991
                if exists is_none maybe_ctr_conds_argss then NONE else
panny@54097
   992
                  fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
panny@54097
   993
                    maybe_ctr_conds_argss (Const (@{const_name undefined}, body_type fun_T))
panny@54097
   994
                  |> SOME
panny@54097
   995
              end;
panny@54097
   996
          in
panny@54097
   997
            if is_none maybe_rhs' then [] else
panny@54097
   998
              let
panny@54097
   999
                val rhs = the maybe_rhs';
panny@54097
  1000
                val bound_Ts = List.rev (map fastype_of fun_args);
panny@54098
  1001
                val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
panny@54098
  1002
                val cond_ctrs =
panny@54098
  1003
                  fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
panny@54097
  1004
                val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
panny@54097
  1005
                val ms = map (Logic.count_prems o prop_of) ctr_thms;
panny@54098
  1006
                val (raw_t, t) = (raw_rhs, rhs)
panny@54097
  1007
                  |> pairself
panny@54097
  1008
                    (curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
panny@54097
  1009
                      map Bound (length fun_args - 1 downto 0)))
panny@54097
  1010
                    #> HOLogic.mk_Trueprop
panny@54097
  1011
                    #> curry Logic.list_all (map dest_Free fun_args));
panny@54098
  1012
                val (distincts, discIs, sel_splits, sel_split_asms) =
panny@54098
  1013
                  case_thms_of_term lthy bound_Ts raw_rhs;
panny@54098
  1014
panny@54098
  1015
                val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
panny@54097
  1016
                    sel_split_asms ms ctr_thms
panny@54098
  1017
                  |> K |> Goal.prove lthy [] [] raw_t;
panny@54097
  1018
              in
blanchet@54101
  1019
                mk_primcorec_code_of_raw_code_tac lthy sel_splits raw_code_thm
panny@54097
  1020
                |> K |> Goal.prove lthy [] [] t
panny@54097
  1021
                |> single
panny@54097
  1022
              end
panny@54098
  1023
          end;
panny@54097
  1024
blanchet@53791
  1025
        val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
blanchet@53791
  1026
        val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
blanchet@53791
  1027
        val disc_thmss = map (map snd) disc_alists;
blanchet@53791
  1028
        val sel_thmss = map (map snd) sel_alists;
panny@54097
  1029
panny@54097
  1030
        val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
blanchet@53744
  1031
          (map #ctr_specs corec_specs);
panny@54097
  1032
        val ctr_thmss = map (map snd) ctr_alists;
panny@54097
  1033
panny@54097
  1034
        val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists corec_specs;
blanchet@53791
  1035
blanchet@54030
  1036
        val simp_thmss = map2 append disc_thmss sel_thmss
blanchet@53795
  1037
blanchet@53797
  1038
        val common_name = mk_common_name fun_names;
blanchet@53797
  1039
blanchet@53791
  1040
        val notes =
blanchet@53830
  1041
          [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
panny@54097
  1042
           (codeN, code_thmss, code_nitpick_attrs),
blanchet@53797
  1043
           (ctrN, ctr_thmss, []),
blanchet@53791
  1044
           (discN, disc_thmss, simp_attrs),
blanchet@53795
  1045
           (selN, sel_thmss, simp_attrs),
blanchet@53797
  1046
           (simpsN, simp_thmss, []),
blanchet@53830
  1047
           (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
blanchet@53791
  1048
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@53791
  1049
            map2 (fn fun_name => fn thms =>
blanchet@53791
  1050
                ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
blanchet@53830
  1051
              fun_names (take actual_nn thmss))
blanchet@53791
  1052
          |> filter_out (null o fst o hd o snd);
blanchet@53797
  1053
blanchet@53797
  1054
        val common_notes =
blanchet@53830
  1055
          [(coinductN, if n2m then [coinduct_thm] else [], []),
blanchet@53830
  1056
           (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
blanchet@53797
  1057
          |> filter_out (null o #2)
blanchet@53797
  1058
          |> map (fn (thmN, thms, attrs) =>
blanchet@53797
  1059
            ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
panny@53654
  1060
      in
blanchet@54030
  1061
        lthy |> Local_Theory.notes (notes @ common_notes) |> snd
panny@53654
  1062
      end;
panny@53822
  1063
panny@53822
  1064
    fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
panny@53822
  1065
panny@53822
  1066
    val _ = if not simple orelse forall null obligationss then () else
panny@53822
  1067
      primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec";
blanchet@53303
  1068
  in
panny@53822
  1069
    if simple then
panny@53822
  1070
      lthy'
panny@53822
  1071
      |> after_qed (map (fn [] => []) obligationss)
panny@53822
  1072
      |> pair NONE o SOME
panny@53822
  1073
    else
panny@53822
  1074
      lthy'
panny@53822
  1075
      |> Proof.theorem NONE after_qed obligationss
panny@53822
  1076
      |> Proof.refine (Method.primitive_text I)
panny@53822
  1077
      |> Seq.hd
panny@53822
  1078
      |> rpair NONE o SOME
panny@53822
  1079
  end;
blanchet@53303
  1080
panny@53831
  1081
fun add_primcorec_ursive_cmd simple seq (raw_fixes, raw_specs') lthy =
blanchet@53303
  1082
  let
panny@53831
  1083
    val (raw_specs, of_specs) = split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
panny@53831
  1084
    val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
blanchet@53303
  1085
  in
panny@53831
  1086
    add_primcorec simple seq fixes specs of_specs lthy
blanchet@53303
  1087
    handle ERROR str => primrec_error str
blanchet@53303
  1088
  end
blanchet@53303
  1089
  handle Primrec_Error (str, eqns) =>
blanchet@53303
  1090
    if null eqns
blanchet@53303
  1091
    then error ("primcorec error:\n  " ^ str)
blanchet@53303
  1092
    else error ("primcorec error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
  1093
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
panny@53822
  1094
panny@53822
  1095
val add_primcorecursive_cmd = (the o fst) ooo add_primcorec_ursive_cmd false;
panny@53822
  1096
val add_primcorec_cmd = (the o snd) ooo add_primcorec_ursive_cmd true;
blanchet@53303
  1097
blanchet@53303
  1098
end;