src/HOL/Tools/primrec_package.ML
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prove_goal' -> Goal.simple_prove_goal_cterm
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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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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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) * Args.src list) list
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    -> theory -> theory * thm list
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  val add_primrec_i: string -> ((bstring * term) * theory attribute list) list
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    -> theory -> theory * thm list
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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 sign s eq =
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  primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term sign 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 sign (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 (fname, _) = 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) = (map dest_Free ls', 
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			   map dest_Free cargs', 
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			   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 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 assoc (rec_fns, fname) of
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        None =>
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          (fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
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      | Some (_, rpos', eqns) =>
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          if is_some (assoc (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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            overwrite (rec_fns, 
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		       (fname, 
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			(tname, rpos,
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			 (cname, (ls, cargs, rs, rhs, eq))::eqns))))
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  end
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  handle RecError s => primrec_eq_err sign s eq;
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fun process_fun sign descr rec_eqns ((i, fname), (fnames, fnss)) =
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  let
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    val (_, (tname, _, constrs)) = nth_elem (i, descr);
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    (* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
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    fun subst [] x = x
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      | subst subs (fs, Abs (a, T, t)) =
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          let val (fs', t') = subst subs (fs, t)
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          in (fs', Abs (a, T, t')) end
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      | subst subs (fs, t as (_ $ _)) =
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          let val (f, ts) = strip_comb t;
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          in
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            if is_Const f andalso (fst (dest_Const f)) mem (map fst rec_eqns) then
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              let
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                val (fname', _) = dest_Const f;
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                val (_, rpos, _) = the (assoc (rec_eqns, fname'));
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                val ls = take (rpos, ts);
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                val rest = drop (rpos, ts);
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                val (x', rs) = (hd rest, tl rest)
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                  handle LIST _ => 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 
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                (case assoc (subs, x) of
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                    None =>
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                      let
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                        val (fs', ts') = foldl_map (subst subs) (fs, ts)
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                      in (fs', list_comb (f, ts')) end
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                  | Some (i', y) =>
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                      let
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                        val (fs', ts') = foldl_map (subst subs) (fs, xs @ ls @ rs);
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                        val fs'' = process_fun sign descr rec_eqns ((i', fname'), fs')
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                      in (fs'', list_comb (y, ts'))
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                      end)
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              end
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            else
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              let
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                val (fs', f'::ts') = foldl_map (subst subs) (fs, f::ts)
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              in (fs', list_comb (f', ts')) end
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          end
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      | subst _ x = x;
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    (* translate rec equations into function arguments suitable for rec comb *)
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    fun trans eqns ((cname, cargs), (fnames', fnss', fns)) =
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      (case assoc (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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              (fnames', fnss', (Const ("arbitrary", 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 ((fnames'', fnss''), rhs') = 
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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))
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		   ((fnames', fnss'), rhs))
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                  handle RecError s => primrec_eq_err sign s eq
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            in (fnames'', 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 assoc (fnames, i) of
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      None =>
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        if exists (equal fname o snd) fnames 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 (assoc (rec_eqns, fname));
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            val (fnames', fnss', fns) = foldr (trans eqns)
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              (constrs, ((i, fname)::fnames, fnss, []))
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          in
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            (fnames', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
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          end
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    | Some fname' =>
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        if fname = fname' then (fnames, 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, (tname, _, constrs)), rec_name), (fs, defs)) =
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  case assoc (fns, i) of
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     None =>
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       let
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         val dummy_fns = map (fn (_, cargs) => Const ("arbitrary",
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           replicate ((length cargs) + (length (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 sign fs (fname, ls, rec_name, tname) =
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  let
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    val rhs = foldr (fn (T, 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 defpair = (Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def",
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		   Logic.mk_equals (Const (fname, dummyT), rhs))
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  in Theory.inferT_axm sign defpair 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 = Library.assocs (flat (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 (flat (map (map #1 o #3 o #2) descr)))
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    |> RuleCases.save induction
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  end;
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fun add_primrec_i 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 sg = Theory.sign_of thy;
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    val dt_info = DatatypePackage.get_datatypes thy;
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    val rec_eqns = foldr (process_eqn sg) (map snd eqns, []);
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    val tnames = distinct (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 (the (find_first (fn f => #1 (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 ^ 
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			 "\nare not mutually recursive")
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	else snd (hd dts);
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    val (fnames, fnss) = foldr (process_fun sg descr rec_eqns)
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	                       (main_fns, ([], []));
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    val (fs, defs) = foldr (get_fns fnss) (descr ~~ rec_names, ([], []));
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    val defs' = map (make_def sg fs) defs;
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    val names1 = map snd fnames;
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    val names2 = map fst rec_eqns;
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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 (thy', defs_thms') = thy |> Theory.add_path primrec_name |>
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      (if eq_set (names1, names2) then (PureThy.add_defs_i false o map Thm.no_attributes) defs'
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       else primrec_err ("functions " ^ commas_quote names2 ^
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         "\nare not mutually recursive"));
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    val rewrites = (map mk_meta_eq rec_rewrites) @ defs_thms';
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    val _ = message ("Proving equations for primrec function(s) " ^ commas_quote names1 ^ " ...");
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    val simps = map (fn (_, t) => prove_goalw_cterm rewrites (cterm_of (Theory.sign_of thy') t)
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        (fn _ => [rtac refl 1])) eqns;
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    val (thy'', simps') = PureThy.add_thms ((map fst eqns ~~ simps) ~~ atts) thy';
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    val thy''' = thy''
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      |> (#1 o PureThy.add_thmss [(("simps", simps'), [Simplifier.simp_add_global, RecfunCodegen.add])])
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      |> (#1 o PureThy.add_thms [(("induct", prepare_induct (#2 (hd dts)) rec_eqns), [])])
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      |> Theory.parent_path
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  in
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    (thy''', simps')
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  end;
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fun add_primrec alt_name eqns thy =
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  let
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    val sign = Theory.sign_of thy;
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    val ((names, strings), srcss) = apfst split_list (split_list eqns);
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    val atts = map (map (Attrib.global_attribute thy)) srcss;
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    val eqn_ts = map (term_of o Thm.read_cterm sign o rpair propT) 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 sign "not a proper equation" eq) eqn_ts;
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    val (_, eqn_ts') = InductivePackage.unify_consts (sign_of thy) rec_ts eqn_ts
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  in
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    add_primrec_i alt_name (names ~~ eqn_ts' ~~ atts) thy
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  end;
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(* outer syntax *)
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local structure P = OuterParse and K = OuterSyntax.Keyword in
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val primrec_decl =
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  Scan.optional (P.$$$ "(" |-- P.name --| P.$$$ ")") "" --
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    Scan.repeat1 (P.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 (alt_name, eqns) =>
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      Toplevel.theory (#1 o add_primrec alt_name (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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eed1273c9146 local open OuterParse;
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end;