src/HOL/Tools/primrec.ML
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Thu, 08 Jul 2010 16:19:24 +0200
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(*  Title:      HOL/Tools/primrec.ML
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    Author:     Stefan Berghofer, TU Muenchen; Norbert Voelker, FernUni Hagen;
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                Florian Haftmann, TU Muenchen
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Package for defining functions on datatypes by primitive recursion.
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*)
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signature PRIMREC =
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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) * 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) * 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) * 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) * theory
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  val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
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    local_theory -> (string * (term list * thm list)) * local_theory
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end;
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structure Primrec : PRIMREC =
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struct
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open Datatype_Aux;
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exception PrimrecError of string * term option;
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fun primrec_error msg = raise PrimrecError (msg, NONE);
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fun primrec_error_eqn msg eqn = raise PrimrecError (msg, SOME eqn);
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fun message s = if ! Toplevel.debug then tracing s else ();
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997e5fe47532 Function unify_consts moved from OldInductivePackage to PrimrecPackage.
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(* preprocessing of equations *)
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fun process_eqn is_fixed spec rec_fns =
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  let
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    val (vs, Ts) = split_list (strip_qnt_vars "all" spec);
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    val body = strip_qnt_body "all" spec;
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    val (vs', _) = Name.variants vs (Name.make_context (fold_aterms
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      (fn Free (v, _) => insert (op =) v | _ => I) body []));
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    val eqn = curry subst_bounds (map2 (curry Free) vs' Ts |> rev) body;
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    val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eqn)
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      handle TERM _ => primrec_error "not a proper equation";
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    val (recfun, args) = strip_comb lhs;
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    val fname = case recfun of Free (v, _) => if is_fixed v then v
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          else primrec_error "illegal head of function equation"
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      | _ => primrec_error "illegal head of function equation";
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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 primrec_error "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 _ => primrec_error "ill-formed constructor";
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    val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
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      primrec_error "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 _ => primrec_error "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 = primrec_error (s ^ commas_quote (map fst vars)) eqn;
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  in
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    if length middle > 1 then
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      primrec_error "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 (OldTerm.term_frees rhs) |> subtract (op =) lfrees
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          |> filter_out (is_fixed o fst));
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      case AList.lookup (op =) rec_fns fname of
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        NONE =>
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          (fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eqn))]))::rec_fns
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      | SOME (_, rpos', eqns) =>
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          if AList.defined (op =) eqns cname then
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            primrec_error "constructor already occurred as pattern"
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          else if rpos <> rpos' then
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            primrec_error "position of recursive argument inconsistent"
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          else
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            AList.update (op =)
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              (fname, (tname, rpos, (cname, (ls, cargs, rs, rhs, eqn))::eqns))
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              rec_fns)
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  end handle PrimrecError (msg, NONE) => primrec_error_eqn msg spec;
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fun process_fun descr eqns (i, fname) (fnames, fnss) =
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  let
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    val (_, (tname, _, constrs)) = 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_Free f
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              andalso member (fn ((v, _), (w, _)) => v = w) eqns (dest_Free f) then
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              let
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                val (fname', _) = dest_Free f;
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                val (_, rpos, _) = the (AList.lookup (op =) eqns fname');
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                val (ls, rs) = chop rpos ts
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                val (x', rs') = case rs
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                 of x' :: rs => (x', rs)
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                  | [] => primrec_error ("not enough arguments in recursive application\n"
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                      ^ "of 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 descr eqns (i', fname')
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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) (fnames', 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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              (fnames', 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 (Term.rename_wrt_term rhs rargs));
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              val (rhs', (fnames'', fnss'')) = subst (map2 (fn (x, y) => fn z =>
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                (Free x, (body_index y, Free z))) recs subs) rhs (fnames', fnss')
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                  handle PrimrecError (s, NONE) => primrec_error_eqn 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 AList.lookup (op =) fnames i of
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      NONE =>
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        if exists (fn (_, v) => fname = v) fnames then
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          primrec_error ("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 =) eqns fname);
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            val (fnames', fnss', fns) = fold_rev (trans eqns) constrs
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              ((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 primrec_error ("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 (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 ctxt fixes fs (fname, ls, rec_name, tname) =
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  let
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    val SOME (var, varT) = get_first (fn ((b, T), mx) =>
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      if Binding.name_of b = fname then SOME ((b, mx), T) else NONE) fixes;
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    val def_name = Thm.def_name (Long_Name.base_name fname);
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    val raw_rhs = fold_rev (fn T => fn t => Abs ("", T, t)) (map snd ls @ [dummyT])
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      (list_comb (Const (rec_name, dummyT), fs @ map Bound (0 :: (length ls downto 1))))
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    val rhs = singleton (Syntax.check_terms ctxt)
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      (Type_Infer.constrain varT raw_rhs);
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  in (var, ((Binding.conceal (Binding.name def_name), []), rhs)) end;
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(* find datatypes which contain all datatypes in tnames' *)
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fun find_dts (dt_info : 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_error (quote tname ^ " is not a datatype")
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        | SOME dt =>
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            if subset (op =) (tnames', 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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(* distill primitive definition(s) from primrec specification *)
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fun distill lthy fixes eqs = 
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  let
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    val eqns = fold_rev (process_eqn (fn v => Variable.is_fixed lthy v
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      orelse exists (fn ((w, _), _) => v = Binding.name_of w) fixes)) eqs [];
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    val tnames = distinct (op =) (map (#1 o snd) eqns);
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    val dts = find_dts (Datatype_Data.get_all (ProofContext.theory_of lthy)) tnames tnames;
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    val main_fns = map (fn (tname, {index, ...}) =>
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      (index, (fst o the o find_first (fn (_, x) => #1 x = tname)) eqns)) dts;
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    val {descr, rec_names, rec_rewrites, ...} =
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      if null dts then primrec_error
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        ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
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      else snd (hd dts);
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    val (fnames, fnss) = fold_rev (process_fun descr eqns) main_fns ([], []);
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    val (fs, raw_defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
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    val defs = map (make_def lthy fixes fs) raw_defs;
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    val names = map snd fnames;
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    val names_eqns = map fst eqns;
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    val _ = if eq_set (op =) (names, names_eqns) then ()
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      else primrec_error ("functions " ^ commas_quote names_eqns ^
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        "\nare not mutually recursive");
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    val rec_rewrites' = map mk_meta_eq rec_rewrites;
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    val prefix = space_implode "_" (map (Long_Name.base_name o #1) raw_defs);
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    fun prove lthy defs =
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      let
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        val frees = (fold o Term.fold_aterms) (fn Free (x, _) =>
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          if Variable.is_fixed lthy x then I else insert (op =) x | _ => I) eqs [];
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        val rewrites = rec_rewrites' @ map (snd o snd) defs;
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        fun tac _ = EVERY [rewrite_goals_tac rewrites, rtac refl 1];
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        val _ = message ("Proving equations for primrec function(s) " ^ commas_quote names);
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      in map (fn eq => Goal.prove lthy frees [] eq tac) eqs end;
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  in ((prefix, (fs, defs)), prove) end
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  handle PrimrecError (msg, some_eqn) =>
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    error ("Primrec definition error:\n" ^ msg ^ (case some_eqn
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     of SOME eqn => "\nin\n" ^ quote (Syntax.string_of_term lthy eqn)
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      | NONE => ""));
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(* primrec definition *)
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fun add_primrec_simple fixes ts lthy =
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  let
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    val ((prefix, (fs, defs)), prove) = distill lthy fixes ts;
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  in
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    lthy
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    |> fold_map Local_Theory.define defs
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    |-> (fn defs => `(fn lthy => (prefix, (map fst defs, prove lthy defs))))
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  end;
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local
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fun gen_primrec prep_spec raw_fixes raw_spec lthy =
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  let
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    val (fixes, spec) = fst (prep_spec raw_fixes raw_spec lthy);
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    fun attr_bindings prefix = map (fn ((b, attrs), _) =>
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      (Binding.qualify false prefix b, Code.add_default_eqn_attrib :: attrs)) spec;
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    fun simp_attr_binding prefix =
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      (Binding.qualify true prefix (Binding.name "simps"),
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        map (Attrib.internal o K) [Simplifier.simp_add, Nitpick_Simps.add]);
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  in
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    lthy
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    |> add_primrec_simple fixes (map snd spec)
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    |-> (fn (prefix, (ts, simps)) =>
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      Spec_Rules.add Spec_Rules.Equational (ts, simps)
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      #> fold_map Local_Theory.note (attr_bindings prefix ~~ map single simps)
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      #-> (fn simps' => Local_Theory.note (simp_attr_binding prefix, maps snd simps')
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      #>> (fn (_, simps'') => (ts, simps''))))
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  end;
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in
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val add_primrec = gen_primrec Specification.check_spec;
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val add_primrec_cmd = gen_primrec Specification.read_spec;
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end;
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fun add_primrec_global fixes specs thy =
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  let
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    val lthy = Theory_Target.init NONE thy;
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    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
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    val simps' = ProofContext.export lthy' lthy simps;
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  in ((ts, simps'), Local_Theory.exit_global lthy') end;
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fun add_primrec_overloaded ops fixes specs thy =
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  let
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    val lthy = Theory_Target.overloading ops thy;
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    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
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    val simps' = ProofContext.export lthy' lthy simps;
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  in ((ts, simps'), Local_Theory.exit_global lthy') end;
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(* outer syntax *)
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val opt_unchecked_name =
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  Scan.optional (Parse.$$$ "(" |-- Parse.!!!
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    (((Parse.$$$ "unchecked" >> K true) -- Scan.optional Parse.name "" ||
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      Parse.name >> pair false) --| Parse.$$$ ")")) (false, "");
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val old_primrec_decl =
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  opt_unchecked_name --
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    Scan.repeat1 ((Parse_Spec.opt_thm_name ":" >> apfst Binding.name_of) -- Parse.prop);
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val primrec_decl = Parse.opt_target -- Parse.fixes -- Parse_Spec.where_alt_specs;
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val _ =
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  Outer_Syntax.command "primrec" "define primitive recursive functions on datatypes"
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  Keyword.thy_decl
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    ((primrec_decl >> (fn ((opt_target, fixes), specs) =>
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      Toplevel.local_theory opt_target (add_primrec_cmd fixes specs #> snd)))
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    || (old_primrec_decl >> (fn ((unchecked, alt_name), eqns) =>
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      Toplevel.theory (snd o
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        (if unchecked then OldPrimrec.add_primrec_unchecked else OldPrimrec.add_primrec)
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          alt_name (map Parse.triple_swap eqns) o
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        tap (fn _ => legacy_feature "Old variant of 'primrec' command -- use new syntax instead")))));
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end;