src/HOL/BNF/Tools/bnf_fp_rec_sugar.ML
author blanchet
Sun Oct 06 20:24:06 2013 +0200 (2013-10-06)
changeset 54068 447354985f6a
parent 54067 7be49e2bfccc
child 54074 43cdae9524bf
permissions -rw-r--r--
generate optimized DNF formula
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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 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 : 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 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 _ = 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 : 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) =
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   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,
blanchet@53303
   458
  user_eqn: term
blanchet@53303
   459
};
blanchet@54001
   460
panny@53341
   461
type co_eqn_data_sel = {
blanchet@53303
   462
  fun_name: string,
panny@53720
   463
  fun_T: typ,
panny@53401
   464
  fun_args: term list,
panny@53341
   465
  ctr: term,
panny@53341
   466
  sel: term,
blanchet@53303
   467
  rhs_term: term,
blanchet@53303
   468
  user_eqn: term
blanchet@53303
   469
};
blanchet@54001
   470
blanchet@53303
   471
datatype co_eqn_data =
panny@53341
   472
  Disc of co_eqn_data_disc |
panny@53341
   473
  Sel of co_eqn_data_sel;
blanchet@53303
   474
panny@54065
   475
fun co_dissect_eqn_disc seq fun_names (corec_specs : corec_spec list) prems' concl
blanchet@54002
   476
    matchedsss =
blanchet@53303
   477
  let
blanchet@53303
   478
    fun find_subterm p = let (* FIXME \<exists>? *)
panny@53401
   479
      fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
blanchet@53303
   480
        | f t = if p t then SOME t else NONE
blanchet@53303
   481
      in f end;
blanchet@53303
   482
panny@53654
   483
    val applied_fun = concl
panny@53654
   484
      |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
panny@53654
   485
      |> the
panny@53654
   486
      handle Option.Option => primrec_error_eqn "malformed discriminator equation" concl;
panny@53720
   487
    val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
panny@53720
   488
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
blanchet@53303
   489
panny@53720
   490
    val discs = map #disc ctr_specs;
panny@53720
   491
    val ctrs = map #ctr ctr_specs;
panny@53654
   492
    val not_disc = head_of concl = @{term Not};
panny@53401
   493
    val _ = not_disc andalso length ctrs <> 2 andalso
panny@53654
   494
      primrec_error_eqn "\<not>ed discriminator for a type with \<noteq> 2 constructors" concl;
panny@53654
   495
    val disc = find_subterm (member (op =) discs o head_of) concl;
panny@53654
   496
    val eq_ctr0 = concl |> perhaps (try (HOLogic.dest_not)) |> try (HOLogic.dest_eq #> snd)
blanchet@53303
   497
        |> (fn SOME t => let val n = find_index (equal t) ctrs in
blanchet@53303
   498
          if n >= 0 then SOME n else NONE end | _ => NONE);
blanchet@53303
   499
    val _ = is_some disc orelse is_some eq_ctr0 orelse
panny@53654
   500
      primrec_error_eqn "no discriminator in equation" concl;
blanchet@53303
   501
    val ctr_no' =
blanchet@53303
   502
      if is_none disc then the eq_ctr0 else find_index (equal (head_of (the disc))) discs;
blanchet@53303
   503
    val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
panny@53720
   504
    val ctr = #ctr (nth ctr_specs ctr_no);
panny@53654
   505
panny@53654
   506
    val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
panny@53720
   507
    val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
panny@53720
   508
    val prems = map (abstract (List.rev fun_args)) prems';
panny@53720
   509
    val real_prems =
blanchet@54067
   510
      (if catch_all orelse seq then maps s_not_conj matchedss else []) @
panny@53654
   511
      (if catch_all then [] else prems);
blanchet@53303
   512
panny@53720
   513
    val matchedsss' = AList.delete (op =) fun_name matchedsss
panny@54065
   514
      |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
blanchet@53303
   515
panny@53654
   516
    val user_eqn =
panny@53720
   517
      (real_prems, betapply (#disc (nth ctr_specs ctr_no), applied_fun))
panny@53654
   518
      |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop
panny@53654
   519
      |> Logic.list_implies;
blanchet@53303
   520
  in
panny@53341
   521
    (Disc {
blanchet@53303
   522
      fun_name = fun_name,
panny@53720
   523
      fun_T = fun_T,
panny@53401
   524
      fun_args = fun_args,
panny@53720
   525
      ctr = ctr,
blanchet@53303
   526
      ctr_no = ctr_no,
panny@53720
   527
      disc = #disc (nth ctr_specs ctr_no),
panny@53654
   528
      prems = real_prems,
panny@53822
   529
      auto_gen = catch_all,
panny@53654
   530
      user_eqn = user_eqn
panny@53720
   531
    }, matchedsss')
blanchet@53303
   532
  end;
blanchet@53303
   533
blanchet@54002
   534
fun co_dissect_eqn_sel fun_names (corec_specs : corec_spec list) eqn' of_spec eqn =
blanchet@53303
   535
  let
blanchet@53303
   536
    val (lhs, rhs) = HOLogic.dest_eq eqn
blanchet@53303
   537
      handle TERM _ =>
blanchet@53303
   538
        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
blanchet@53303
   539
    val sel = head_of lhs;
panny@53720
   540
    val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
blanchet@53303
   541
      handle TERM _ =>
blanchet@53303
   542
        primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@53654
   543
    val corec_spec = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name)
blanchet@53303
   544
      handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@53831
   545
    val ctr_spec =
panny@53831
   546
      if is_some of_spec
panny@53831
   547
      then the (find_first (equal (the of_spec) o #ctr) (#ctr_specs corec_spec))
panny@53831
   548
      else #ctr_specs corec_spec |> filter (exists (equal sel) o #sels) |> the_single
panny@53831
   549
        handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn;
panny@53654
   550
    val user_eqn = drop_All eqn';
blanchet@53303
   551
  in
panny@53341
   552
    Sel {
blanchet@53303
   553
      fun_name = fun_name,
panny@53720
   554
      fun_T = fun_T,
panny@53401
   555
      fun_args = fun_args,
panny@53341
   556
      ctr = #ctr ctr_spec,
panny@53341
   557
      sel = sel,
blanchet@53303
   558
      rhs_term = rhs,
panny@53654
   559
      user_eqn = user_eqn
blanchet@53303
   560
    }
blanchet@53303
   561
  end;
blanchet@53303
   562
panny@54065
   563
fun co_dissect_eqn_ctr seq fun_names (corec_specs : corec_spec list) eqn' prems concl
blanchet@54002
   564
    matchedsss =
blanchet@53910
   565
  let
panny@54065
   566
    val (lhs, rhs) = HOLogic.dest_eq concl;
blanchet@53303
   567
    val fun_name = head_of lhs |> fst o dest_Free;
panny@53720
   568
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
blanchet@53303
   569
    val (ctr, ctr_args) = strip_comb rhs;
panny@53720
   570
    val {disc, sels, ...} = the (find_first (equal ctr o #ctr) ctr_specs)
blanchet@53303
   571
      handle Option.Option => primrec_error_eqn "not a constructor" ctr;
panny@53341
   572
panny@54065
   573
    val disc_concl = betapply (disc, lhs);
panny@53720
   574
    val (maybe_eqn_data_disc, matchedsss') = if length ctr_specs = 1
panny@53720
   575
      then (NONE, matchedsss)
panny@53341
   576
      else apfst SOME (co_dissect_eqn_disc
panny@54065
   577
          seq fun_names corec_specs prems disc_concl matchedsss);
blanchet@53303
   578
panny@54065
   579
    val sel_concls = (sels ~~ ctr_args)
blanchet@53303
   580
      |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
blanchet@53303
   581
blanchet@53856
   582
(*
panny@54065
   583
val _ = tracing ("reduced\n    " ^ Syntax.string_of_term @{context} concl ^ "\nto\n    \<cdot> " ^
panny@54065
   584
 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n    \<cdot> ")) "" ^
panny@54065
   585
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls));
blanchet@53856
   586
*)
blanchet@53303
   587
panny@54065
   588
    val eqns_data_sel = map (co_dissect_eqn_sel fun_names corec_specs eqn' (SOME ctr)) sel_concls;
blanchet@53303
   589
  in
panny@53720
   590
    (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
blanchet@53303
   591
  end;
blanchet@53303
   592
panny@54065
   593
fun co_dissect_eqn_code lthy has_call fun_names corec_specs eqn' concl matchedsss =
panny@54065
   594
  let
panny@54065
   595
    val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
panny@54065
   596
    val fun_name = head_of lhs |> fst o dest_Free;
panny@54065
   597
    val {ctr_specs, ...} = the (AList.lookup (op =) (fun_names ~~ corec_specs) fun_name);
panny@54065
   598
panny@54065
   599
    val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
panny@54065
   600
        if member ((op =) o apsnd #ctr) ctr_specs ctr
panny@54065
   601
        then cons (ctr, cs)
panny@54065
   602
        else primrec_error_eqn "not a constructor" ctr) [] rhs' []
panny@54065
   603
      |> AList.group (op =);
panny@54065
   604
blanchet@54068
   605
    val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
panny@54065
   606
    val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
panny@54065
   607
        binder_types (fastype_of ctr)
panny@54065
   608
        |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
panny@54065
   609
          if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
panny@54065
   610
        |> curry list_comb ctr
panny@54065
   611
        |> curry HOLogic.mk_eq lhs);
panny@54065
   612
  in
panny@54065
   613
    fold_map2 (co_dissect_eqn_ctr false fun_names corec_specs eqn') ctr_premss ctr_concls matchedsss
panny@54065
   614
  end;
panny@54065
   615
panny@54065
   616
fun co_dissect_eqn lthy has_call seq fun_names (corec_specs : corec_spec list) eqn' of_spec
panny@54065
   617
    matchedsss =
blanchet@53303
   618
  let
panny@53654
   619
    val eqn = drop_All eqn'
panny@53654
   620
      handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
panny@54065
   621
    val (prems, concl) = Logic.strip_horn eqn
panny@53341
   622
      |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
blanchet@53303
   623
panny@54065
   624
    val head = concl
blanchet@53303
   625
      |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
blanchet@53303
   626
      |> head_of;
blanchet@53303
   627
panny@54065
   628
    val maybe_rhs = concl |> perhaps (try (HOLogic.dest_not)) |> try (snd o HOLogic.dest_eq);
blanchet@53303
   629
panny@53654
   630
    val discs = maps #ctr_specs corec_specs |> map #disc;
panny@53654
   631
    val sels = maps #ctr_specs corec_specs |> maps #sels;
panny@53654
   632
    val ctrs = maps #ctr_specs corec_specs |> map #ctr;
blanchet@53303
   633
  in
blanchet@53303
   634
    if member (op =) discs head orelse
blanchet@53303
   635
      is_some maybe_rhs andalso
blanchet@53303
   636
        member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
panny@54065
   637
      co_dissect_eqn_disc seq fun_names corec_specs prems concl matchedsss
blanchet@53303
   638
      |>> single
blanchet@53303
   639
    else if member (op =) sels head then
panny@54065
   640
      ([co_dissect_eqn_sel fun_names corec_specs eqn' of_spec concl], matchedsss)
panny@54065
   641
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
panny@54065
   642
      member (op =) ctrs (head_of (the maybe_rhs)) then
panny@54065
   643
      co_dissect_eqn_ctr seq fun_names corec_specs eqn' prems concl matchedsss
panny@54065
   644
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
panny@54065
   645
      null prems then
panny@54065
   646
      co_dissect_eqn_code lthy has_call fun_names corec_specs eqn' concl matchedsss
panny@54065
   647
      |>> flat
blanchet@53303
   648
    else
blanchet@53303
   649
      primrec_error_eqn "malformed function equation" eqn
blanchet@53303
   650
  end;
blanchet@53303
   651
blanchet@54002
   652
fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
blanchet@54002
   653
    ({fun_args, ctr_no, prems, ...} : co_eqn_data_disc) =
panny@53654
   654
  if is_none (#pred (nth ctr_specs ctr_no)) then I else
blanchet@54068
   655
    s_conjs prems
panny@53654
   656
    |> curry subst_bounds (List.rev fun_args)
panny@53654
   657
    |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
panny@53654
   658
    |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
blanchet@53303
   659
blanchet@54002
   660
fun build_corec_arg_no_call (sel_eqns : co_eqn_data_sel list) sel =
panny@53720
   661
  find_first (equal sel o #sel) sel_eqns
panny@53720
   662
  |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
panny@53720
   663
  |> the_default undef_const
panny@53411
   664
  |> K;
panny@53360
   665
blanchet@54002
   666
fun build_corec_args_direct_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel =
panny@53360
   667
  let
panny@53411
   668
    val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
panny@53360
   669
  in
panny@53876
   670
    if is_none maybe_sel_eqn then (I, I, I) else
panny@53876
   671
    let
panny@53876
   672
      val {fun_args, rhs_term, ... } = the maybe_sel_eqn;
blanchet@53890
   673
      fun rewrite_q _ t = if has_call t then @{term False} else @{term True};
blanchet@53890
   674
      fun rewrite_g _ t = if has_call t then undef_const else t;
panny@53899
   675
      fun rewrite_h bound_Ts t =
panny@53899
   676
        if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
panny@54065
   677
      fun massage f _ = massage_direct_corec_call lthy has_call f [] rhs_term |> abs_tuple fun_args;
panny@53876
   678
    in
panny@53876
   679
      (massage rewrite_q,
panny@53876
   680
       massage rewrite_g,
panny@53876
   681
       massage rewrite_h)
panny@53876
   682
    end
panny@53360
   683
  end;
panny@53360
   684
blanchet@54002
   685
fun build_corec_arg_indirect_call lthy has_call (sel_eqns : co_eqn_data_sel list) sel =
panny@53411
   686
  let
panny@53411
   687
    val maybe_sel_eqn = find_first (equal sel o #sel) sel_eqns;
panny@53899
   688
  in
panny@53899
   689
    if is_none maybe_sel_eqn then I else
panny@53899
   690
    let
panny@53899
   691
      val {fun_args, rhs_term, ...} = the maybe_sel_eqn;
panny@53899
   692
      fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
panny@53899
   693
        | rewrite bound_Ts U T (t as _ $ _) =
panny@53899
   694
          let val (u, vs) = strip_comb t in
panny@53899
   695
            if is_Free u andalso has_call u then
panny@53899
   696
              Inr_const U T $ mk_tuple1 bound_Ts vs
panny@53899
   697
            else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
panny@53899
   698
              map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
panny@53899
   699
            else
panny@53899
   700
              list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
panny@53899
   701
          end
panny@53899
   702
        | rewrite _ U T t =
panny@53899
   703
          if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
panny@53899
   704
      fun massage t =
blanchet@53890
   705
        massage_indirect_corec_call lthy has_call rewrite [] (range_type (fastype_of t)) rhs_term
panny@53735
   706
        |> abs_tuple fun_args;
panny@53899
   707
    in
panny@53899
   708
      massage
panny@53899
   709
    end
panny@53411
   710
  end;
panny@53360
   711
blanchet@54002
   712
fun build_corec_args_sel lthy has_call (all_sel_eqns : co_eqn_data_sel list)
blanchet@54002
   713
    (ctr_spec : corec_ctr_spec) =
panny@53341
   714
  let val sel_eqns = filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns in
panny@53341
   715
    if null sel_eqns then I else
panny@53341
   716
      let
panny@53341
   717
        val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
panny@53341
   718
panny@53341
   719
        val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
panny@53341
   720
        val direct_calls' = map_filter (try (apsnd (fn Direct_Corec n => n))) sel_call_list;
panny@53341
   721
        val indirect_calls' = map_filter (try (apsnd (fn Indirect_Corec n => n))) sel_call_list;
panny@53341
   722
      in
panny@53360
   723
        I
panny@53735
   724
        #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
panny@53360
   725
        #> fold (fn (sel, (q, g, h)) =>
panny@53735
   726
          let val (fq, fg, fh) = build_corec_args_direct_call lthy has_call sel_eqns sel in
panny@53735
   727
            nth_map q fq o nth_map g fg o nth_map h fh end) direct_calls'
panny@53360
   728
        #> fold (fn (sel, n) => nth_map n
panny@53411
   729
          (build_corec_arg_indirect_call lthy has_call sel_eqns sel)) indirect_calls'
panny@53341
   730
      end
blanchet@53303
   731
  end;
blanchet@53303
   732
blanchet@54002
   733
fun co_build_defs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
blanchet@54002
   734
    (disc_eqnss : co_eqn_data_disc list list) (sel_eqnss : co_eqn_data_sel list list) =
panny@53654
   735
  let
panny@53654
   736
    val corec_specs' = take (length bs) corec_specs;
panny@53654
   737
    val corecs = map #corec corec_specs';
panny@53654
   738
    val ctr_specss = map #ctr_specs corec_specs';
panny@53360
   739
    val corec_args = hd corecs
panny@53360
   740
      |> fst o split_last o binder_types o fastype_of
panny@53360
   741
      |> map (Const o pair @{const_name undefined})
panny@53720
   742
      |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
panny@53360
   743
      |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
panny@53735
   744
    fun currys [] t = t
panny@53735
   745
      | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
panny@53735
   746
          |> fold_rev (Term.abs o pair Name.uu) Ts;
panny@53401
   747
blanchet@53856
   748
(*
panny@53360
   749
val _ = tracing ("corecursor arguments:\n    \<cdot> " ^
panny@53411
   750
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
blanchet@53856
   751
*)
blanchet@53303
   752
panny@53654
   753
    val exclss' =
panny@53720
   754
      disc_eqnss
panny@53822
   755
      |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
panny@53654
   756
        #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
panny@53654
   757
        #> maps (uncurry (map o pair)
panny@53822
   758
          #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
blanchet@54068
   759
              ((c, c', a orelse a'), (x, s_not (s_conjs y)))
panny@53654
   760
            ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
panny@53654
   761
            ||> Logic.list_implies
panny@53654
   762
            ||> curry Logic.list_all (map dest_Free fun_args))))
blanchet@53303
   763
  in
blanchet@53303
   764
    map (list_comb o rpair corec_args) corecs
blanchet@53303
   765
    |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
blanchet@53303
   766
    |> map2 currys arg_Tss
blanchet@53303
   767
    |> Syntax.check_terms lthy
traytel@53352
   768
    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.map_name Thm.def_name b, []), t))) bs mxs
panny@53654
   769
    |> rpair exclss'
blanchet@53303
   770
  end;
blanchet@53303
   771
blanchet@54002
   772
fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
blanchet@54002
   773
    (sel_eqns : co_eqn_data_sel list) (disc_eqns : co_eqn_data_disc list) =
panny@53720
   774
  if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
panny@53720
   775
    let
panny@53720
   776
      val n = 0 upto length ctr_specs
panny@53720
   777
        |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
panny@53722
   778
      val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
panny@53722
   779
        |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
panny@53720
   780
      val extra_disc_eqn = {
panny@53720
   781
        fun_name = Binding.name_of fun_binding,
panny@53720
   782
        fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
panny@53722
   783
        fun_args = fun_args,
panny@53720
   784
        ctr = #ctr (nth ctr_specs n),
panny@53720
   785
        ctr_no = n,
panny@53720
   786
        disc = #disc (nth ctr_specs n),
blanchet@54067
   787
        prems = maps (s_not_conj o #prems) disc_eqns,
panny@53822
   788
        auto_gen = true,
panny@53720
   789
        user_eqn = undef_const};
panny@53720
   790
    in
panny@53720
   791
      chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
panny@53720
   792
    end;
panny@53720
   793
panny@54065
   794
fun add_primcorec simple seq fixes specs of_specs lthy =
blanchet@53303
   795
  let
traytel@53352
   796
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   797
    val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
blanchet@53303
   798
blanchet@53303
   799
    val callssss = []; (* FIXME *)
blanchet@53303
   800
blanchet@53830
   801
    val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
blanchet@53797
   802
          strong_coinduct_thms), lthy') =
blanchet@53794
   803
      corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53303
   804
blanchet@53830
   805
    val actual_nn = length bs;
blanchet@53303
   806
    val fun_names = map Binding.name_of bs;
blanchet@53830
   807
    val corec_specs = take actual_nn corec_specs'; (*###*)
blanchet@53303
   808
panny@54065
   809
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
panny@53831
   810
    val eqns_data =
panny@54065
   811
      fold_map2 (co_dissect_eqn lthy has_call seq fun_names corec_specs)
panny@54065
   812
        (map snd specs) of_specs []
panny@53831
   813
      |> flat o fst;
blanchet@53303
   814
panny@53720
   815
    val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
panny@53654
   816
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   817
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   818
      |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
panny@53720
   819
    val _ = disc_eqnss' |> map (fn x =>
panny@53720
   820
      let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
panny@53720
   821
        primrec_error_eqns "excess discriminator equations in definition"
panny@53720
   822
          (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
panny@53654
   823
panny@53654
   824
    val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
panny@53654
   825
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   826
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   827
      |> map (flat o snd);
panny@53654
   828
panny@53360
   829
    val arg_Tss = map (binder_types o snd o fst) fixes;
panny@53722
   830
    val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
panny@53654
   831
    val (defs, exclss') =
panny@53654
   832
      co_build_defs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
panny@53654
   833
blanchet@53923
   834
    fun excl_tac (c, c', a) =
panny@54065
   835
      if a orelse c = c' orelse seq then
blanchet@54044
   836
        SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
blanchet@54044
   837
      else if simple then
blanchet@54044
   838
        SOME (K (auto_tac lthy))
blanchet@54044
   839
      else
blanchet@54044
   840
        NONE;
panny@53822
   841
blanchet@53856
   842
(*
panny@53822
   843
val _ = tracing ("exclusiveness properties:\n    \<cdot> " ^
panny@53822
   844
 space_implode "\n    \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
blanchet@53856
   845
*)
panny@53822
   846
panny@53822
   847
    val exclss'' = exclss' |> map (map (fn (idx, t) =>
blanchet@53923
   848
      (idx, (Option.map (Goal.prove lthy [] [] t) (excl_tac idx), t))));
panny@53654
   849
    val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
panny@53654
   850
    val (obligation_idxss, obligationss) = exclss''
panny@53654
   851
      |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
panny@53654
   852
      |> split_list o map split_list;
panny@53654
   853
panny@53654
   854
    fun prove thmss' def_thms' lthy =
panny@53654
   855
      let
panny@53654
   856
        val def_thms = map (snd o snd) def_thms';
panny@53654
   857
panny@53654
   858
        val exclss' = map (op ~~) (obligation_idxss ~~ thmss');
panny@53654
   859
        fun mk_exclsss excls n =
panny@53654
   860
          (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
panny@53822
   861
          |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
panny@53654
   862
        val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
panny@53654
   863
          |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
panny@53654
   864
blanchet@54002
   865
        fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
blanchet@54002
   866
            ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : co_eqn_data_disc) =
panny@53722
   867
          if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
panny@53720
   868
            let
panny@53722
   869
              val {disc_corec, ...} = nth ctr_specs ctr_no;
panny@53720
   870
              val k = 1 + ctr_no;
panny@53720
   871
              val m = length prems;
panny@53720
   872
              val t =
panny@53720
   873
                list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   874
                |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
panny@53720
   875
                |> HOLogic.mk_Trueprop
panny@53720
   876
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   877
                |> curry Logic.list_all (map dest_Free fun_args);
panny@53720
   878
            in
panny@53720
   879
              mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
panny@53720
   880
              |> K |> Goal.prove lthy [] [] t
panny@53720
   881
              |> pair (#disc (nth ctr_specs ctr_no))
panny@53720
   882
              |> single
panny@53720
   883
            end;
panny@53720
   884
blanchet@54002
   885
        fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
blanchet@54002
   886
            : corec_spec) (disc_eqns : co_eqn_data_disc list) exclsss
blanchet@54002
   887
            ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : co_eqn_data_sel) =
panny@53654
   888
          let
blanchet@53909
   889
            val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
panny@53720
   890
            val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
blanchet@54067
   891
            val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
panny@53720
   892
                (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
panny@53720
   893
            val sel_corec = find_index (equal sel) (#sels ctr_spec)
panny@53720
   894
              |> nth (#sel_corecs ctr_spec);
panny@53654
   895
            val k = 1 + ctr_no;
panny@53654
   896
            val m = length prems;
panny@53654
   897
            val t =
panny@53720
   898
              list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   899
              |> curry betapply sel
panny@53720
   900
              |> rpair (abstract (List.rev fun_args) rhs_term)
panny@53720
   901
              |> HOLogic.mk_Trueprop o HOLogic.mk_eq
panny@53654
   902
              |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   903
              |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53925
   904
            val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
panny@53654
   905
          in
blanchet@53918
   906
            mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
blanchet@53910
   907
              nested_map_idents nested_map_comps sel_corec k m exclsss
panny@53654
   908
            |> K |> Goal.prove lthy [] [] t
panny@53720
   909
            |> pair sel
panny@53654
   910
          end;
panny@53654
   911
blanchet@54002
   912
        fun prove_ctr disc_alist sel_alist (disc_eqns : co_eqn_data_disc list)
blanchet@54002
   913
            (sel_eqns : co_eqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
panny@53720
   914
          if not (exists (equal ctr o #ctr) disc_eqns)
panny@53722
   915
              andalso not (exists (equal ctr o #ctr) sel_eqns)
panny@53722
   916
            orelse (* don't try to prove theorems when some sel_eqns are missing *)
panny@53720
   917
              filter (equal ctr o #ctr) sel_eqns
panny@53720
   918
              |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   919
              |> exists (null o snd)
panny@53720
   920
          then [] else
panny@53720
   921
            let
panny@53722
   922
              val (fun_name, fun_T, fun_args, prems) =
panny@53722
   923
                (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
panny@53722
   924
                |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x))
panny@53722
   925
                ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, []))
panny@53722
   926
                |> the o merge_options;
panny@53720
   927
              val m = length prems;
panny@53831
   928
              val t = filter (equal ctr o #ctr) sel_eqns
panny@53720
   929
                |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   930
                |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
panny@53720
   931
                |> curry list_comb ctr
panny@53720
   932
                |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
panny@53720
   933
                  map Bound (length fun_args - 1 downto 0)))
panny@53720
   934
                |> HOLogic.mk_Trueprop
panny@53720
   935
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   936
                |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53791
   937
              val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
blanchet@53791
   938
              val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
panny@53720
   939
            in
panny@53722
   940
              mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
panny@53720
   941
              |> K |> Goal.prove lthy [] [] t
panny@53720
   942
              |> single
panny@53876
   943
            end;
panny@53720
   944
blanchet@53791
   945
        val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
blanchet@53791
   946
        val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
blanchet@53744
   947
blanchet@53791
   948
        val disc_thmss = map (map snd) disc_alists;
blanchet@53791
   949
        val sel_thmss = map (map snd) sel_alists;
blanchet@53791
   950
        val ctr_thmss = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
blanchet@53744
   951
          (map #ctr_specs corec_specs);
blanchet@53791
   952
blanchet@54030
   953
        val simp_thmss = map2 append disc_thmss sel_thmss
blanchet@53795
   954
blanchet@53797
   955
        val common_name = mk_common_name fun_names;
blanchet@53797
   956
blanchet@53791
   957
        val notes =
blanchet@53830
   958
          [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
traytel@54013
   959
           (codeN, ctr_thmss(*FIXME*), code_nitpick_attrs),
blanchet@53797
   960
           (ctrN, ctr_thmss, []),
blanchet@53791
   961
           (discN, disc_thmss, simp_attrs),
blanchet@53795
   962
           (selN, sel_thmss, simp_attrs),
blanchet@53797
   963
           (simpsN, simp_thmss, []),
blanchet@53830
   964
           (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
blanchet@53791
   965
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@53791
   966
            map2 (fn fun_name => fn thms =>
blanchet@53791
   967
                ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
blanchet@53830
   968
              fun_names (take actual_nn thmss))
blanchet@53791
   969
          |> filter_out (null o fst o hd o snd);
blanchet@53797
   970
blanchet@53797
   971
        val common_notes =
blanchet@53830
   972
          [(coinductN, if n2m then [coinduct_thm] else [], []),
blanchet@53830
   973
           (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
blanchet@53797
   974
          |> filter_out (null o #2)
blanchet@53797
   975
          |> map (fn (thmN, thms, attrs) =>
blanchet@53797
   976
            ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
panny@53654
   977
      in
blanchet@54030
   978
        lthy |> Local_Theory.notes (notes @ common_notes) |> snd
panny@53654
   979
      end;
panny@53822
   980
panny@53822
   981
    fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
panny@53822
   982
panny@53822
   983
    val _ = if not simple orelse forall null obligationss then () else
panny@53822
   984
      primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec";
blanchet@53303
   985
  in
panny@53822
   986
    if simple then
panny@53822
   987
      lthy'
panny@53822
   988
      |> after_qed (map (fn [] => []) obligationss)
panny@53822
   989
      |> pair NONE o SOME
panny@53822
   990
    else
panny@53822
   991
      lthy'
panny@53822
   992
      |> Proof.theorem NONE after_qed obligationss
panny@53822
   993
      |> Proof.refine (Method.primitive_text I)
panny@53822
   994
      |> Seq.hd
panny@53822
   995
      |> rpair NONE o SOME
panny@53822
   996
  end;
blanchet@53303
   997
panny@53831
   998
fun add_primcorec_ursive_cmd simple seq (raw_fixes, raw_specs') lthy =
blanchet@53303
   999
  let
panny@53831
  1000
    val (raw_specs, of_specs) = split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
panny@53831
  1001
    val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
blanchet@53303
  1002
  in
panny@53831
  1003
    add_primcorec simple seq fixes specs of_specs lthy
blanchet@53303
  1004
    handle ERROR str => primrec_error str
blanchet@53303
  1005
  end
blanchet@53303
  1006
  handle Primrec_Error (str, eqns) =>
blanchet@53303
  1007
    if null eqns
blanchet@53303
  1008
    then error ("primcorec error:\n  " ^ str)
blanchet@53303
  1009
    else error ("primcorec error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
  1010
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
panny@53822
  1011
panny@53822
  1012
val add_primcorecursive_cmd = (the o fst) ooo add_primcorec_ursive_cmd false;
panny@53822
  1013
val add_primcorec_cmd = (the o snd) ooo add_primcorec_ursive_cmd true;
blanchet@53303
  1014
blanchet@53303
  1015
end;