haftmann@31723: (*  Title:      HOL/Tools/old_primrec.ML
wenzelm@29266:     Author:     Norbert Voelker, FernUni Hagen
wenzelm@29266:     Author:     Stefan Berghofer, TU Muenchen
haftmann@25557: 
haftmann@25557: Package for defining functions on datatypes by primitive recursion.
haftmann@25557: *)
haftmann@25557: 
haftmann@31723: signature OLD_PRIMREC =
haftmann@25557: sig
haftmann@25557:   val unify_consts: theory -> term list -> term list -> term list * term list
haftmann@25557:   val add_primrec: string -> ((bstring * string) * Attrib.src list) list
haftmann@25557:     -> theory -> thm list * theory
haftmann@25557:   val add_primrec_unchecked: string -> ((bstring * string) * Attrib.src list) list
haftmann@25557:     -> theory -> thm list * theory
haftmann@25557:   val add_primrec_i: string -> ((bstring * term) * attribute list) list
haftmann@25557:     -> theory -> thm list * theory
haftmann@25557:   val add_primrec_unchecked_i: string -> ((bstring * term) * attribute list) list
haftmann@25557:     -> theory -> thm list * theory
haftmann@25557: end;
haftmann@25557: 
haftmann@31723: structure OldPrimrec : OLD_PRIMREC =
haftmann@25557: struct
haftmann@25557: 
haftmann@25557: open DatatypeAux;
haftmann@25557: 
haftmann@25557: exception RecError of string;
haftmann@25557: 
haftmann@25557: fun primrec_err s = error ("Primrec definition error:\n" ^ s);
haftmann@25557: fun primrec_eq_err thy s eq =
wenzelm@26939:   primrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq));
haftmann@25557: 
haftmann@25557: 
haftmann@25557: (*the following code ensures that each recursive set always has the
haftmann@25557:   same type in all introduction rules*)
haftmann@25557: fun unify_consts thy cs intr_ts =
haftmann@25557:   (let
wenzelm@33338:     fun varify t (i, ts) =
haftmann@25557:       let val t' = map_types (Logic.incr_tvar (i + 1)) (snd (Type.varify [] t))
haftmann@25557:       in (maxidx_of_term t', t'::ts) end;
wenzelm@33338:     val (i, cs') = fold_rev varify cs (~1, []);
wenzelm@33338:     val (i', intr_ts') = fold_rev varify intr_ts (i, []);
wenzelm@29290:     val rec_consts = fold Term.add_consts cs' [];
wenzelm@29290:     val intr_consts = fold Term.add_consts intr_ts' [];
haftmann@25557:     fun unify (cname, cT) =
haftmann@25557:       let val consts = map snd (filter (fn (c, _) => c = cname) intr_consts)
haftmann@25557:       in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
haftmann@25557:     val (env, _) = fold unify rec_consts (Vartab.empty, i');
wenzelm@33832:     val subst = Type.legacy_freeze o map_types (Envir.norm_type env)
haftmann@25557: 
haftmann@25557:   in (map subst cs', map subst intr_ts')
haftmann@25557:   end) handle Type.TUNIFY =>
haftmann@25557:     (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
haftmann@25557: 
haftmann@25557: 
haftmann@25557: (* preprocessing of equations *)
haftmann@25557: 
haftmann@25557: fun process_eqn thy eq rec_fns =
haftmann@25557:   let
haftmann@25557:     val (lhs, rhs) =
wenzelm@29266:       if null (Term.add_vars eq []) then
haftmann@25557:         HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
haftmann@25557:         handle TERM _ => raise RecError "not a proper equation"
haftmann@25557:       else raise RecError "illegal schematic variable(s)";
haftmann@25557: 
haftmann@25557:     val (recfun, args) = strip_comb lhs;
haftmann@25557:     val fnameT = dest_Const recfun handle TERM _ =>
haftmann@25557:       raise RecError "function is not declared as constant in theory";
haftmann@25557: 
haftmann@25557:     val (ls', rest)  = take_prefix is_Free args;
haftmann@25557:     val (middle, rs') = take_suffix is_Free rest;
haftmann@25557:     val rpos = length ls';
haftmann@25557: 
haftmann@25557:     val (constr, cargs') = if null middle then raise RecError "constructor missing"
haftmann@25557:       else strip_comb (hd middle);
haftmann@25557:     val (cname, T) = dest_Const constr
haftmann@25557:       handle TERM _ => raise RecError "ill-formed constructor";
haftmann@25557:     val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
haftmann@25557:       raise RecError "cannot determine datatype associated with function"
haftmann@25557: 
haftmann@25557:     val (ls, cargs, rs) =
haftmann@25557:       (map dest_Free ls', map dest_Free cargs', map dest_Free rs')
haftmann@25557:       handle TERM _ => raise RecError "illegal argument in pattern";
haftmann@25557:     val lfrees = ls @ rs @ cargs;
haftmann@25557: 
haftmann@25557:     fun check_vars _ [] = ()
haftmann@25557:       | check_vars s vars = raise RecError (s ^ commas_quote (map fst vars))
haftmann@25557:   in
haftmann@25557:     if length middle > 1 then
haftmann@25557:       raise RecError "more than one non-variable in pattern"
haftmann@25557:     else
haftmann@25557:      (check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
haftmann@25557:       check_vars "extra variables on rhs: "
haftmann@33040:         (subtract (op =) lfrees (map dest_Free (OldTerm.term_frees rhs)));
haftmann@25557:       case AList.lookup (op =) rec_fns fnameT of
haftmann@25557:         NONE =>
haftmann@25557:           (fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
haftmann@25557:       | SOME (_, rpos', eqns) =>
haftmann@25557:           if AList.defined (op =) eqns cname then
haftmann@25557:             raise RecError "constructor already occurred as pattern"
haftmann@25557:           else if rpos <> rpos' then
haftmann@25557:             raise RecError "position of recursive argument inconsistent"
haftmann@25557:           else
haftmann@25557:             AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns))
haftmann@25557:               rec_fns)
haftmann@25557:   end
haftmann@25557:   handle RecError s => primrec_eq_err thy s eq;
haftmann@25557: 
haftmann@25557: fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) =
haftmann@25557:   let
haftmann@25557:     val (_, (tname, _, constrs)) = List.nth (descr, i);
haftmann@25557: 
haftmann@25557:     (* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
haftmann@25557: 
haftmann@25557:     fun subst [] t fs = (t, fs)
haftmann@25557:       | subst subs (Abs (a, T, t)) fs =
haftmann@25557:           fs
haftmann@25557:           |> subst subs t
haftmann@25557:           |-> (fn t' => pair (Abs (a, T, t')))
haftmann@25557:       | subst subs (t as (_ $ _)) fs =
haftmann@25557:           let
haftmann@25557:             val (f, ts) = strip_comb t;
haftmann@25557:           in
haftmann@25557:             if is_Const f andalso dest_Const f mem map fst rec_eqns then
haftmann@25557:               let
haftmann@25557:                 val fnameT' as (fname', _) = dest_Const f;
haftmann@25557:                 val (_, rpos, _) = the (AList.lookup (op =) rec_eqns fnameT');
haftmann@33957:                 val ls = take rpos ts;
haftmann@33957:                 val rest = drop rpos ts;
haftmann@25557:                 val (x', rs) = (hd rest, tl rest)
haftmann@25557:                   handle Empty => raise RecError ("not enough arguments\
haftmann@25557:                    \ in recursive application\nof function " ^ quote fname' ^ " on rhs");
haftmann@25557:                 val (x, xs) = strip_comb x'
haftmann@25557:               in case AList.lookup (op =) subs x
haftmann@25557:                of NONE =>
haftmann@25557:                     fs
haftmann@25557:                     |> fold_map (subst subs) ts
haftmann@25557:                     |-> (fn ts' => pair (list_comb (f, ts')))
haftmann@25557:                 | SOME (i', y) =>
haftmann@25557:                     fs
haftmann@25557:                     |> fold_map (subst subs) (xs @ ls @ rs)
haftmann@25557:                     ||> process_fun thy descr rec_eqns (i', fnameT')
haftmann@25557:                     |-> (fn ts' => pair (list_comb (y, ts')))
haftmann@25557:               end
haftmann@25557:             else
haftmann@25557:               fs
haftmann@25557:               |> fold_map (subst subs) (f :: ts)
haftmann@25557:               |-> (fn (f'::ts') => pair (list_comb (f', ts')))
haftmann@25557:           end
haftmann@25557:       | subst _ t fs = (t, fs);
haftmann@25557: 
haftmann@25557:     (* translate rec equations into function arguments suitable for rec comb *)
haftmann@25557: 
haftmann@25557:     fun trans eqns (cname, cargs) (fnameTs', fnss', fns) =
haftmann@25557:       (case AList.lookup (op =) eqns cname of
haftmann@25557:           NONE => (warning ("No equation for constructor " ^ quote cname ^
haftmann@25557:             "\nin definition of function " ^ quote fname);
haftmann@25557:               (fnameTs', fnss', (Const ("HOL.undefined", dummyT))::fns))
haftmann@25557:         | SOME (ls, cargs', rs, rhs, eq) =>
haftmann@25557:             let
haftmann@25557:               val recs = filter (is_rec_type o snd) (cargs' ~~ cargs);
haftmann@25557:               val rargs = map fst recs;
haftmann@25557:               val subs = map (rpair dummyT o fst)
wenzelm@29276:                 (rev (Term.rename_wrt_term rhs rargs));
haftmann@25557:               val (rhs', (fnameTs'', fnss'')) =
haftmann@25557:                   (subst (map (fn ((x, y), z) =>
haftmann@25557:                                (Free x, (body_index y, Free z)))
haftmann@25557:                           (recs ~~ subs)) rhs (fnameTs', fnss'))
haftmann@25557:                   handle RecError s => primrec_eq_err thy s eq
haftmann@25557:             in (fnameTs'', fnss'',
haftmann@25557:                 (list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns)
haftmann@25557:             end)
haftmann@25557: 
haftmann@25557:   in (case AList.lookup (op =) fnameTs i of
haftmann@25557:       NONE =>
haftmann@25557:         if exists (equal fnameT o snd) fnameTs then
haftmann@25557:           raise RecError ("inconsistent functions for datatype " ^ quote tname)
haftmann@25557:         else
haftmann@25557:           let
haftmann@25557:             val (_, _, eqns) = the (AList.lookup (op =) rec_eqns fnameT);
haftmann@25557:             val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs
haftmann@25557:               ((i, fnameT)::fnameTs, fnss, [])
haftmann@25557:           in
haftmann@25557:             (fnameTs', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
haftmann@25557:           end
haftmann@25557:     | SOME fnameT' =>
haftmann@25557:         if fnameT = fnameT' then (fnameTs, fnss)
haftmann@25557:         else raise RecError ("inconsistent functions for datatype " ^ quote tname))
haftmann@25557:   end;
haftmann@25557: 
haftmann@25557: 
haftmann@25557: (* prepare functions needed for definitions *)
haftmann@25557: 
haftmann@25557: fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) =
haftmann@25557:   case AList.lookup (op =) fns i of
haftmann@25557:      NONE =>
haftmann@25557:        let
haftmann@25557:          val dummy_fns = map (fn (_, cargs) => Const ("HOL.undefined",
wenzelm@33317:            replicate (length cargs + length (filter is_rec_type cargs))
haftmann@25557:              dummyT ---> HOLogic.unitT)) constrs;
haftmann@25557:          val _ = warning ("No function definition for datatype " ^ quote tname)
haftmann@25557:        in
haftmann@25557:          (dummy_fns @ fs, defs)
haftmann@25557:        end
haftmann@25557:    | SOME (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname) :: defs);
haftmann@25557: 
haftmann@25557: 
haftmann@25557: (* make definition *)
haftmann@25557: 
haftmann@25557: fun make_def thy fs (fname, ls, rec_name, tname) =
haftmann@25557:   let
haftmann@25557:     val rhs = fold_rev (fn T => fn t => Abs ("", T, t))
haftmann@25557:                     ((map snd ls) @ [dummyT])
haftmann@25557:                     (list_comb (Const (rec_name, dummyT),
haftmann@25557:                                 fs @ map Bound (0 ::(length ls downto 1))))
wenzelm@30364:     val def_name = Long_Name.base_name fname ^ "_" ^ Long_Name.base_name tname ^ "_def";
haftmann@25557:     val def_prop =
haftmann@25557:       singleton (Syntax.check_terms (ProofContext.init thy))
haftmann@25557:         (Logic.mk_equals (Const (fname, dummyT), rhs));
haftmann@25557:   in (def_name, def_prop) end;
haftmann@25557: 
haftmann@25557: 
haftmann@25557: (* find datatypes which contain all datatypes in tnames' *)
haftmann@25557: 
haftmann@31737: fun find_dts (dt_info : info Symtab.table) _ [] = []
haftmann@25557:   | find_dts dt_info tnames' (tname::tnames) =
haftmann@25557:       (case Symtab.lookup dt_info tname of
haftmann@25557:           NONE => primrec_err (quote tname ^ " is not a datatype")
haftmann@25557:         | SOME dt =>
haftmann@33038:             if subset (op =) (tnames', map (#1 o snd) (#descr dt)) then
haftmann@25557:               (tname, dt)::(find_dts dt_info tnames' tnames)
haftmann@25557:             else find_dts dt_info tnames' tnames);
haftmann@25557: 
haftmann@32727: fun prepare_induct ({descr, induct, ...}: info) rec_eqns =
haftmann@25557:   let
haftmann@25557:     fun constrs_of (_, (_, _, cs)) =
haftmann@25557:       map (fn (cname:string, (_, cargs, _, _, _)) => (cname, map fst cargs)) cs;
haftmann@32712:     val params_of = these o AList.lookup (op =) (maps constrs_of rec_eqns);
haftmann@25557:   in
haftmann@32712:     induct
wenzelm@33368:     |> Rule_Cases.rename_params (map params_of (maps (map #1 o #3 o #2) descr))
wenzelm@33368:     |> Rule_Cases.save induct
haftmann@25557:   end;
haftmann@25557: 
haftmann@25557: local
haftmann@25557: 
haftmann@25557: fun gen_primrec_i note def alt_name eqns_atts thy =
haftmann@25557:   let
haftmann@25557:     val (eqns, atts) = split_list eqns_atts;
haftmann@31784:     val dt_info = Datatype.get_all thy;
haftmann@25557:     val rec_eqns = fold_rev (process_eqn thy o snd) eqns [] ;
haftmann@25557:     val tnames = distinct (op =) (map (#1 o snd) rec_eqns);
haftmann@25557:     val dts = find_dts dt_info tnames tnames;
haftmann@25557:     val main_fns =
haftmann@25557:       map (fn (tname, {index, ...}) =>
haftmann@25557:         (index,
haftmann@25557:           (fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns))
haftmann@25557:       dts;
haftmann@25557:     val {descr, rec_names, rec_rewrites, ...} =
haftmann@25557:       if null dts then
haftmann@25557:         primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
haftmann@25557:       else snd (hd dts);
haftmann@25557:     val (fnameTs, fnss) =
haftmann@25557:       fold_rev (process_fun thy descr rec_eqns) main_fns ([], []);
haftmann@25557:     val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
haftmann@25557:     val defs' = map (make_def thy fs) defs;
haftmann@25557:     val nameTs1 = map snd fnameTs;
haftmann@25557:     val nameTs2 = map fst rec_eqns;
haftmann@33038:     val _ = if eq_set (op =) (nameTs1, nameTs2) then ()
haftmann@25557:             else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^
haftmann@25557:               "\nare not mutually recursive");
haftmann@25557:     val primrec_name =
wenzelm@30364:       if alt_name = "" then (space_implode "_" (map (Long_Name.base_name o #1) defs)) else alt_name;
haftmann@25557:     val (defs_thms', thy') =
haftmann@25557:       thy
haftmann@25557:       |> Sign.add_path primrec_name
haftmann@25557:       |> fold_map def (map (fn (name, t) => ((name, []), t)) defs');
haftmann@25557:     val rewrites = (map mk_meta_eq rec_rewrites) @ map snd defs_thms';
haftmann@25557:     val simps = map (fn (_, t) => Goal.prove_global thy' [] [] t
haftmann@25557:         (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
haftmann@25557:     val (simps', thy'') =
haftmann@25557:       thy'
haftmann@25557:       |> fold_map note ((map fst eqns ~~ atts) ~~ map single simps);
haftmann@25557:     val simps'' = maps snd simps';
haftmann@25557:   in
haftmann@25557:     thy''
wenzelm@31902:     |> note (("simps",
blanchet@33056:         [Simplifier.simp_add, Nitpick_Simps.add, Code.add_default_eqn_attribute]), simps'')
haftmann@25557:     |> snd
haftmann@25557:     |> note (("induct", []), [prepare_induct (#2 (hd dts)) rec_eqns])
haftmann@25557:     |> snd
haftmann@25557:     |> Sign.parent_path
haftmann@25557:     |> pair simps''
haftmann@25557:   end;
haftmann@25557: 
haftmann@25557: fun gen_primrec note def alt_name eqns thy =
haftmann@25557:   let
haftmann@25557:     val ((names, strings), srcss) = apfst split_list (split_list eqns);
haftmann@25557:     val atts = map (map (Attrib.attribute thy)) srcss;
haftmann@25557:     val eqn_ts = map (fn s => Syntax.read_prop_global thy s
haftmann@25557:       handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings;
haftmann@25557:     val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop eq)))
haftmann@25557:       handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts;
haftmann@25557:     val (_, eqn_ts') = unify_consts thy rec_ts eqn_ts
haftmann@25557:   in
haftmann@25557:     gen_primrec_i note def alt_name (names ~~ eqn_ts' ~~ atts) thy
haftmann@25557:   end;
haftmann@25557: 
haftmann@25557: fun thy_note ((name, atts), thms) =
haftmann@29579:   PureThy.add_thmss [((Binding.name name, thms), atts)] #-> (fn [thms] => pair (name, thms));
haftmann@25557: fun thy_def false ((name, atts), t) =
haftmann@29579:       PureThy.add_defs false [((Binding.name name, t), atts)] #-> (fn [thm] => pair (name, thm))
haftmann@25557:   | thy_def true ((name, atts), t) =
haftmann@29579:       PureThy.add_defs_unchecked false [((Binding.name name, t), atts)] #-> (fn [thm] => pair (name, thm));
haftmann@25557: 
haftmann@25557: in
haftmann@25557: 
haftmann@25557: val add_primrec = gen_primrec thy_note (thy_def false);
haftmann@25557: val add_primrec_unchecked = gen_primrec thy_note (thy_def true);
haftmann@25557: val add_primrec_i = gen_primrec_i thy_note (thy_def false);
haftmann@25557: val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true);
haftmann@25557: 
haftmann@25557: end;
haftmann@25557: 
haftmann@25557: end;