src/HOL/Tools/primrec_package.ML
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proper ProofContext.infer_types;
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(*  Title:      HOL/Tools/primrec_package.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer, TU Muenchen and Norbert Voelker, FernUni Hagen
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Package for defining functions on datatypes by primitive recursion.
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*)
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signature PRIMREC_PACKAGE =
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sig
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  val quiet_mode: bool ref
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  val add_primrec: string -> ((bstring * string) * Attrib.src list) list
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    -> theory -> thm list * theory
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  val add_primrec_unchecked: string -> ((bstring * string) * Attrib.src list) list
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    -> theory -> thm list * theory
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  val add_primrec_i: string -> ((bstring * term) * attribute list) list
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    -> theory -> thm list * theory
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  val add_primrec_unchecked_i: string -> ((bstring * term) * attribute list) list
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    -> theory -> thm list * theory
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  (* FIXME !? *)
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  val gen_primrec: ((bstring * attribute list) * thm list -> theory -> (bstring * thm list) * theory)
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    -> ((bstring * attribute list) * term -> theory -> (bstring * thm) * theory)
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    -> string -> ((bstring * attribute list) * term) list
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    -> theory -> thm list * theory;
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end;
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structure PrimrecPackage : PRIMREC_PACKAGE =
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struct
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open DatatypeAux;
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exception RecError of string;
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fun primrec_err s = error ("Primrec definition error:\n" ^ s);
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fun primrec_eq_err thy s eq =
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  primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq));
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(* messages *)
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val quiet_mode = ref false;
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fun message s = if ! quiet_mode then () else writeln s;
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(* preprocessing of equations *)
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fun process_eqn thy eq rec_fns =
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  let
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    val (lhs, rhs) =
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      if null (term_vars eq) then
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        HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
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        handle TERM _ => raise RecError "not a proper equation"
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      else raise RecError "illegal schematic variable(s)";
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    val (recfun, args) = strip_comb lhs;
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    val fnameT = dest_Const recfun handle TERM _ =>
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      raise RecError "function is not declared as constant in theory";
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    val (ls', rest)  = take_prefix is_Free args;
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    val (middle, rs') = take_suffix is_Free rest;
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    val rpos = length ls';
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    val (constr, cargs') = if null middle then raise RecError "constructor missing"
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      else strip_comb (hd middle);
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    val (cname, T) = dest_Const constr
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      handle TERM _ => raise RecError "ill-formed constructor";
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    val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
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      raise RecError "cannot determine datatype associated with function"
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    val (ls, cargs, rs) =
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      (map dest_Free ls', map dest_Free cargs', map dest_Free rs')
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      handle TERM _ => raise RecError "illegal argument in pattern";
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    val lfrees = ls @ rs @ cargs;
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    fun check_vars _ [] = ()
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      | check_vars s vars = raise RecError (s ^ commas_quote (map fst vars))
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  in
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    if length middle > 1 then
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      raise RecError "more than one non-variable in pattern"
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    else
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     (check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
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      check_vars "extra variables on rhs: "
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        (map dest_Free (term_frees rhs) \\ lfrees);
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      case AList.lookup (op =) rec_fns fnameT of
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        NONE =>
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          (fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
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      | SOME (_, rpos', eqns) =>
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          if AList.defined (op =) eqns cname then
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            raise RecError "constructor already occurred as pattern"
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          else if rpos <> rpos' then
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            raise RecError "position of recursive argument inconsistent"
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          else
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            AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns))
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              rec_fns)
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  end
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  handle RecError s => primrec_eq_err thy s eq;
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fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) =
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  let
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    val (_, (tname, _, constrs)) = List.nth (descr, i);
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    (* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
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    fun subst [] t fs = (t, fs)
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      | subst subs (Abs (a, T, t)) fs =
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          fs
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          |> subst subs t
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          |-> (fn t' => pair (Abs (a, T, t')))
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      | subst subs (t as (_ $ _)) fs =
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          let
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            val (f, ts) = strip_comb t;
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          in
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            if is_Const f andalso dest_Const f mem map fst rec_eqns then
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              let
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                val fnameT' as (fname', _) = dest_Const f;
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                val (_, rpos, _) = the (AList.lookup (op =) rec_eqns fnameT');
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                val ls = Library.take (rpos, ts);
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                val rest = Library.drop (rpos, ts);
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                val (x', rs) = (hd rest, tl rest)
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                  handle Empty => raise RecError ("not enough arguments\
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                   \ in recursive application\nof function " ^ quote fname' ^ " on rhs");
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                val (x, xs) = strip_comb x'
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              in case AList.lookup (op =) subs x
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               of NONE =>
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                    fs
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                    |> fold_map (subst subs) ts
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                    |-> (fn ts' => pair (list_comb (f, ts')))
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                | SOME (i', y) =>
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                    fs
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                    |> fold_map (subst subs) (xs @ ls @ rs)
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                    ||> process_fun thy descr rec_eqns (i', fnameT')
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                    |-> (fn ts' => pair (list_comb (y, ts')))
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              end
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            else
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              fs
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              |> fold_map (subst subs) (f :: ts)
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              |-> (fn (f'::ts') => pair (list_comb (f', ts')))
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          end
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      | subst _ t fs = (t, fs);
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    (* translate rec equations into function arguments suitable for rec comb *)
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    fun trans eqns (cname, cargs) (fnameTs', fnss', fns) =
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      (case AList.lookup (op =) eqns cname of
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          NONE => (warning ("No equation for constructor " ^ quote cname ^
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            "\nin definition of function " ^ quote fname);
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              (fnameTs', fnss', (Const ("HOL.undefined", dummyT))::fns))
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        | SOME (ls, cargs', rs, rhs, eq) =>
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            let
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              val recs = filter (is_rec_type o snd) (cargs' ~~ cargs);
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              val rargs = map fst recs;
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              val subs = map (rpair dummyT o fst)
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                (rev (rename_wrt_term rhs rargs));
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              val (rhs', (fnameTs'', fnss'')) =
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                  (subst (map (fn ((x, y), z) =>
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                               (Free x, (body_index y, Free z)))
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                          (recs ~~ subs)) rhs (fnameTs', fnss'))
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                  handle RecError s => primrec_eq_err thy s eq
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            in (fnameTs'', fnss'',
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                (list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns)
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            end)
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  in (case AList.lookup (op =) fnameTs i of
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      NONE =>
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        if exists (equal fnameT o snd) fnameTs then
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          raise RecError ("inconsistent functions for datatype " ^ quote tname)
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        else
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          let
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            val (_, _, eqns) = the (AList.lookup (op =) rec_eqns fnameT);
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            val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs
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              ((i, fnameT)::fnameTs, fnss, [])
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          in
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            (fnameTs', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
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          end
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    | SOME fnameT' =>
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        if fnameT = fnameT' then (fnameTs, fnss)
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        else raise RecError ("inconsistent functions for datatype " ^ quote tname))
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  end;
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(* prepare functions needed for definitions *)
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fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) =
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  case AList.lookup (op =) fns i of
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     NONE =>
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       let
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         val dummy_fns = map (fn (_, cargs) => Const ("HOL.undefined",
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           replicate ((length cargs) + (length (List.filter is_rec_type cargs)))
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             dummyT ---> HOLogic.unitT)) constrs;
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         val _ = warning ("No function definition for datatype " ^ quote tname)
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       in
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         (dummy_fns @ fs, defs)
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       end
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   | SOME (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname) :: defs);
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(* make definition *)
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fun make_def thy fs (fname, ls, rec_name, tname) =
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  let
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    val rhs = fold_rev (fn T => fn t => Abs ("", T, t))
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                    ((map snd ls) @ [dummyT])
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                    (list_comb (Const (rec_name, dummyT),
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                                fs @ map Bound (0 ::(length ls downto 1))))
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    val def_name = Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def";
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    val def_prop =
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      singleton (ProofContext.infer_types (ProofContext.init thy))
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        (Logic.mk_equals (Const (fname, dummyT), rhs), propT) |> #1;
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  in (def_name, def_prop) end;
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(* find datatypes which contain all datatypes in tnames' *)
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fun find_dts (dt_info : datatype_info Symtab.table) _ [] = []
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  | find_dts dt_info tnames' (tname::tnames) =
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      (case Symtab.lookup dt_info tname of
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          NONE => primrec_err (quote tname ^ " is not a datatype")
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        | SOME dt =>
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            if tnames' subset (map (#1 o snd) (#descr dt)) then
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              (tname, dt)::(find_dts dt_info tnames' tnames)
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            else find_dts dt_info tnames' tnames);
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fun prepare_induct ({descr, induction, ...}: datatype_info) rec_eqns =
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  let
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    fun constrs_of (_, (_, _, cs)) =
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      map (fn (cname:string, (_, cargs, _, _, _)) => (cname, map fst cargs)) cs;
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    val params_of = these o AList.lookup (op =) (List.concat (map constrs_of rec_eqns));
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  in
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    induction
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    |> RuleCases.rename_params (map params_of (List.concat (map (map #1 o #3 o #2) descr)))
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    |> RuleCases.save induction
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  end;
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local
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fun gen_primrec_i note def alt_name eqns_atts thy =
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  let
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    val (eqns, atts) = split_list eqns_atts;
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    val dt_info = DatatypePackage.get_datatypes thy;
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    val rec_eqns = fold_rev (process_eqn thy o snd) eqns [] ;
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    val tnames = distinct (op =) (map (#1 o snd) rec_eqns);
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    val dts = find_dts dt_info tnames tnames;
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    val main_fns =
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      map (fn (tname, {index, ...}) =>
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        (index,
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          (fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns))
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      dts;
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    val {descr, rec_names, rec_rewrites, ...} =
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      if null dts then
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        primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
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      else snd (hd dts);
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    val (fnameTs, fnss) =
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      fold_rev (process_fun thy descr rec_eqns) main_fns ([], []);
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    val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
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    val defs' = map (make_def thy fs) defs;
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    val nameTs1 = map snd fnameTs;
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    val nameTs2 = map fst rec_eqns;
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    val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then ()
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            else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^
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              "\nare not mutually recursive");
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    val primrec_name =
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      if alt_name = "" then (space_implode "_" (map (Sign.base_name o #1) defs)) else alt_name;
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    val (defs_thms', thy') =
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      thy
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      |> Theory.add_path primrec_name
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      |> fold_map def (map (fn (name, t) => ((name, []), t)) defs');
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    val rewrites = (map mk_meta_eq rec_rewrites) @ map snd defs_thms';
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    val _ = message ("Proving equations for primrec function(s) " ^
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      commas_quote (map fst nameTs1) ^ " ...");
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    val simps = map (fn (_, t) => Goal.prove_global thy' [] [] t
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        (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
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    val (simps', thy'') =
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      thy'
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      |> fold_map note ((map fst eqns ~~ atts) ~~ map single simps);
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    val simps'' = maps snd simps';
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  in
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    thy''
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    |> note (("simps", [Simplifier.simp_add, RecfunCodegen.add NONE]), simps'')
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    |> snd
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    |> note (("induct", []), [prepare_induct (#2 (hd dts)) rec_eqns])
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    |> snd
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    |> Theory.parent_path
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    |> pair simps''
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  end;
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fun gen_primrec note def alt_name eqns thy =
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  let
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    val ((names, strings), srcss) = apfst split_list (split_list eqns);
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    val atts = map (map (Attrib.attribute thy)) srcss;
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    val eqn_ts = map (fn s => term_of (Thm.read_cterm thy (s, propT))
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      handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings;
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    val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop eq)))
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      handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts;
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    val (_, eqn_ts') = OldInductivePackage.unify_consts thy rec_ts eqn_ts
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  in
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    gen_primrec_i note def alt_name (names ~~ eqn_ts' ~~ atts) thy
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  end;
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fun thy_note ((name, atts), thms) =
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  PureThy.add_thmss [((name, thms), atts)] #-> (fn [thms] => pair (name, thms));
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fun thy_def false ((name, atts), t) =
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      PureThy.add_defs_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm))
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  | thy_def true ((name, atts), t) =
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      PureThy.add_defs_unchecked_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm));
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in
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val add_primrec = gen_primrec thy_note (thy_def false);
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val add_primrec_unchecked = gen_primrec thy_note (thy_def true);
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val add_primrec_i = gen_primrec_i thy_note (thy_def false);
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val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true);
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fun gen_primrec note def alt_name specs =
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  gen_primrec_i note def alt_name (map (fn ((name, t), atts) => ((name, atts), t)) specs);
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end;
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(* outer syntax *)
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0934ac31985f OuterKeyword;
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local structure P = OuterParse and K = OuterKeyword in
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val opt_unchecked_name =
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  Scan.optional (P.$$$ "(" |-- P.!!!
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    (((P.$$$ "unchecked" >> K true) -- Scan.optional P.name "" ||
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      P.name >> pair false) --| P.$$$ ")")) (false, "");
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val primrec_decl =
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  opt_unchecked_name -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop);
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val primrecP =
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  OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl
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    (primrec_decl >> (fn ((unchecked, alt_name), eqns) =>
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      Toplevel.theory (snd o
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        (if unchecked then add_primrec_unchecked else add_primrec) alt_name
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          (map P.triple_swap eqns))));
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val _ = OuterSyntax.add_parsers [primrecP];
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end;
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eed1273c9146 local open OuterParse;
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end;