src/HOL/Tools/old_primrec_package.ML
changeset 25557 ea6b11021e79
child 25561 d955e1d01e6a
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/old_primrec_package.ML	Thu Dec 06 15:10:09 2007 +0100
@@ -0,0 +1,362 @@
+(*  Title:      HOL/Tools/primrec_package.ML
+    ID:         $Id$
+    Author:     Stefan Berghofer, TU Muenchen and Norbert Voelker, FernUni Hagen
+
+Package for defining functions on datatypes by primitive recursion.
+*)
+
+signature OLD_PRIMREC_PACKAGE =
+sig
+  val quiet_mode: bool ref
+  val unify_consts: theory -> term list -> term list -> term list * term list
+  val add_primrec: string -> ((bstring * string) * Attrib.src list) list
+    -> theory -> thm list * theory
+  val add_primrec_unchecked: string -> ((bstring * string) * Attrib.src list) list
+    -> theory -> thm list * theory
+  val add_primrec_i: string -> ((bstring * term) * attribute list) list
+    -> theory -> thm list * theory
+  val add_primrec_unchecked_i: string -> ((bstring * term) * attribute list) list
+    -> theory -> thm list * theory
+  (* FIXME !? *)
+  val gen_primrec: ((bstring * attribute list) * thm list -> theory -> (bstring * thm list) * theory)
+    -> ((bstring * attribute list) * term -> theory -> (bstring * thm) * theory)
+    -> string -> ((bstring * attribute list) * term) list
+    -> theory -> thm list * theory;
+end;
+
+structure OldPrimrecPackage : OLD_PRIMREC_PACKAGE =
+struct
+
+open DatatypeAux;
+
+exception RecError of string;
+
+fun primrec_err s = error ("Primrec definition error:\n" ^ s);
+fun primrec_eq_err thy s eq =
+  primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq));
+
+
+(* messages *)
+
+val quiet_mode = ref false;
+fun message s = if ! quiet_mode then () else writeln s;
+
+
+(*the following code ensures that each recursive set always has the
+  same type in all introduction rules*)
+fun unify_consts thy cs intr_ts =
+  (let
+    val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
+    fun varify (t, (i, ts)) =
+      let val t' = map_types (Logic.incr_tvar (i + 1)) (snd (Type.varify [] t))
+      in (maxidx_of_term t', t'::ts) end;
+    val (i, cs') = foldr varify (~1, []) cs;
+    val (i', intr_ts') = foldr varify (i, []) intr_ts;
+    val rec_consts = fold add_term_consts_2 cs' [];
+    val intr_consts = fold add_term_consts_2 intr_ts' [];
+    fun unify (cname, cT) =
+      let val consts = map snd (filter (fn (c, _) => c = cname) intr_consts)
+      in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
+    val (env, _) = fold unify rec_consts (Vartab.empty, i');
+    val subst = Type.freeze o map_types (Envir.norm_type env)
+
+  in (map subst cs', map subst intr_ts')
+  end) handle Type.TUNIFY =>
+    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
+
+
+(* preprocessing of equations *)
+
+fun process_eqn thy eq rec_fns =
+  let
+    val (lhs, rhs) =
+      if null (term_vars eq) then
+        HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
+        handle TERM _ => raise RecError "not a proper equation"
+      else raise RecError "illegal schematic variable(s)";
+
+    val (recfun, args) = strip_comb lhs;
+    val fnameT = dest_Const recfun handle TERM _ =>
+      raise RecError "function is not declared as constant in theory";
+
+    val (ls', rest)  = take_prefix is_Free args;
+    val (middle, rs') = take_suffix is_Free rest;
+    val rpos = length ls';
+
+    val (constr, cargs') = if null middle then raise RecError "constructor missing"
+      else strip_comb (hd middle);
+    val (cname, T) = dest_Const constr
+      handle TERM _ => raise RecError "ill-formed constructor";
+    val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
+      raise RecError "cannot determine datatype associated with function"
+
+    val (ls, cargs, rs) =
+      (map dest_Free ls', map dest_Free cargs', map dest_Free rs')
+      handle TERM _ => raise RecError "illegal argument in pattern";
+    val lfrees = ls @ rs @ cargs;
+
+    fun check_vars _ [] = ()
+      | check_vars s vars = raise RecError (s ^ commas_quote (map fst vars))
+  in
+    if length middle > 1 then
+      raise RecError "more than one non-variable in pattern"
+    else
+     (check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
+      check_vars "extra variables on rhs: "
+        (map dest_Free (term_frees rhs) \\ lfrees);
+      case AList.lookup (op =) rec_fns fnameT of
+        NONE =>
+          (fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
+      | SOME (_, rpos', eqns) =>
+          if AList.defined (op =) eqns cname then
+            raise RecError "constructor already occurred as pattern"
+          else if rpos <> rpos' then
+            raise RecError "position of recursive argument inconsistent"
+          else
+            AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns))
+              rec_fns)
+  end
+  handle RecError s => primrec_eq_err thy s eq;
+
+fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) =
+  let
+    val (_, (tname, _, constrs)) = List.nth (descr, i);
+
+    (* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
+
+    fun subst [] t fs = (t, fs)
+      | subst subs (Abs (a, T, t)) fs =
+          fs
+          |> subst subs t
+          |-> (fn t' => pair (Abs (a, T, t')))
+      | subst subs (t as (_ $ _)) fs =
+          let
+            val (f, ts) = strip_comb t;
+          in
+            if is_Const f andalso dest_Const f mem map fst rec_eqns then
+              let
+                val fnameT' as (fname', _) = dest_Const f;
+                val (_, rpos, _) = the (AList.lookup (op =) rec_eqns fnameT');
+                val ls = Library.take (rpos, ts);
+                val rest = Library.drop (rpos, ts);
+                val (x', rs) = (hd rest, tl rest)
+                  handle Empty => raise RecError ("not enough arguments\
+                   \ in recursive application\nof function " ^ quote fname' ^ " on rhs");
+                val (x, xs) = strip_comb x'
+              in case AList.lookup (op =) subs x
+               of NONE =>
+                    fs
+                    |> fold_map (subst subs) ts
+                    |-> (fn ts' => pair (list_comb (f, ts')))
+                | SOME (i', y) =>
+                    fs
+                    |> fold_map (subst subs) (xs @ ls @ rs)
+                    ||> process_fun thy descr rec_eqns (i', fnameT')
+                    |-> (fn ts' => pair (list_comb (y, ts')))
+              end
+            else
+              fs
+              |> fold_map (subst subs) (f :: ts)
+              |-> (fn (f'::ts') => pair (list_comb (f', ts')))
+          end
+      | subst _ t fs = (t, fs);
+
+    (* translate rec equations into function arguments suitable for rec comb *)
+
+    fun trans eqns (cname, cargs) (fnameTs', fnss', fns) =
+      (case AList.lookup (op =) eqns cname of
+          NONE => (warning ("No equation for constructor " ^ quote cname ^
+            "\nin definition of function " ^ quote fname);
+              (fnameTs', fnss', (Const ("HOL.undefined", dummyT))::fns))
+        | SOME (ls, cargs', rs, rhs, eq) =>
+            let
+              val recs = filter (is_rec_type o snd) (cargs' ~~ cargs);
+              val rargs = map fst recs;
+              val subs = map (rpair dummyT o fst)
+                (rev (rename_wrt_term rhs rargs));
+              val (rhs', (fnameTs'', fnss'')) =
+                  (subst (map (fn ((x, y), z) =>
+                               (Free x, (body_index y, Free z)))
+                          (recs ~~ subs)) rhs (fnameTs', fnss'))
+                  handle RecError s => primrec_eq_err thy s eq
+            in (fnameTs'', fnss'',
+                (list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns)
+            end)
+
+  in (case AList.lookup (op =) fnameTs i of
+      NONE =>
+        if exists (equal fnameT o snd) fnameTs then
+          raise RecError ("inconsistent functions for datatype " ^ quote tname)
+        else
+          let
+            val (_, _, eqns) = the (AList.lookup (op =) rec_eqns fnameT);
+            val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs
+              ((i, fnameT)::fnameTs, fnss, [])
+          in
+            (fnameTs', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
+          end
+    | SOME fnameT' =>
+        if fnameT = fnameT' then (fnameTs, fnss)
+        else raise RecError ("inconsistent functions for datatype " ^ quote tname))
+  end;
+
+
+(* prepare functions needed for definitions *)
+
+fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) =
+  case AList.lookup (op =) fns i of
+     NONE =>
+       let
+         val dummy_fns = map (fn (_, cargs) => Const ("HOL.undefined",
+           replicate ((length cargs) + (length (List.filter is_rec_type cargs)))
+             dummyT ---> HOLogic.unitT)) constrs;
+         val _ = warning ("No function definition for datatype " ^ quote tname)
+       in
+         (dummy_fns @ fs, defs)
+       end
+   | SOME (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname) :: defs);
+
+
+(* make definition *)
+
+fun make_def thy fs (fname, ls, rec_name, tname) =
+  let
+    val rhs = fold_rev (fn T => fn t => Abs ("", T, t))
+                    ((map snd ls) @ [dummyT])
+                    (list_comb (Const (rec_name, dummyT),
+                                fs @ map Bound (0 ::(length ls downto 1))))
+    val def_name = Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def";
+    val def_prop =
+      singleton (Syntax.check_terms (ProofContext.init thy))
+        (Logic.mk_equals (Const (fname, dummyT), rhs));
+  in (def_name, def_prop) end;
+
+
+(* find datatypes which contain all datatypes in tnames' *)
+
+fun find_dts (dt_info : datatype_info Symtab.table) _ [] = []
+  | find_dts dt_info tnames' (tname::tnames) =
+      (case Symtab.lookup dt_info tname of
+          NONE => primrec_err (quote tname ^ " is not a datatype")
+        | SOME dt =>
+            if tnames' subset (map (#1 o snd) (#descr dt)) then
+              (tname, dt)::(find_dts dt_info tnames' tnames)
+            else find_dts dt_info tnames' tnames);
+
+fun prepare_induct ({descr, induction, ...}: datatype_info) rec_eqns =
+  let
+    fun constrs_of (_, (_, _, cs)) =
+      map (fn (cname:string, (_, cargs, _, _, _)) => (cname, map fst cargs)) cs;
+    val params_of = these o AList.lookup (op =) (List.concat (map constrs_of rec_eqns));
+  in
+    induction
+    |> RuleCases.rename_params (map params_of (List.concat (map (map #1 o #3 o #2) descr)))
+    |> RuleCases.save induction
+  end;
+
+local
+
+fun gen_primrec_i note def alt_name eqns_atts thy =
+  let
+    val (eqns, atts) = split_list eqns_atts;
+    val dt_info = DatatypePackage.get_datatypes thy;
+    val rec_eqns = fold_rev (process_eqn thy o snd) eqns [] ;
+    val tnames = distinct (op =) (map (#1 o snd) rec_eqns);
+    val dts = find_dts dt_info tnames tnames;
+    val main_fns =
+      map (fn (tname, {index, ...}) =>
+        (index,
+          (fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns))
+      dts;
+    val {descr, rec_names, rec_rewrites, ...} =
+      if null dts then
+        primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
+      else snd (hd dts);
+    val (fnameTs, fnss) =
+      fold_rev (process_fun thy descr rec_eqns) main_fns ([], []);
+    val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
+    val defs' = map (make_def thy fs) defs;
+    val nameTs1 = map snd fnameTs;
+    val nameTs2 = map fst rec_eqns;
+    val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then ()
+            else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^
+              "\nare not mutually recursive");
+    val primrec_name =
+      if alt_name = "" then (space_implode "_" (map (Sign.base_name o #1) defs)) else alt_name;
+    val (defs_thms', thy') =
+      thy
+      |> Sign.add_path primrec_name
+      |> fold_map def (map (fn (name, t) => ((name, []), t)) defs');
+    val rewrites = (map mk_meta_eq rec_rewrites) @ map snd defs_thms';
+    val _ = message ("Proving equations for primrec function(s) " ^
+      commas_quote (map fst nameTs1) ^ " ...");
+    val simps = map (fn (_, t) => Goal.prove_global thy' [] [] t
+        (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
+    val (simps', thy'') =
+      thy'
+      |> fold_map note ((map fst eqns ~~ atts) ~~ map single simps);
+    val simps'' = maps snd simps';
+  in
+    thy''
+    |> note (("simps", [Simplifier.simp_add, RecfunCodegen.add_default]), simps'')
+    |> snd
+    |> note (("induct", []), [prepare_induct (#2 (hd dts)) rec_eqns])
+    |> snd
+    |> Sign.parent_path
+    |> pair simps''
+  end;
+
+fun gen_primrec note def alt_name eqns thy =
+  let
+    val ((names, strings), srcss) = apfst split_list (split_list eqns);
+    val atts = map (map (Attrib.attribute thy)) srcss;
+    val eqn_ts = map (fn s => Syntax.read_prop_global thy s
+      handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings;
+    val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop eq)))
+      handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts;
+    val (_, eqn_ts') = unify_consts thy rec_ts eqn_ts
+  in
+    gen_primrec_i note def alt_name (names ~~ eqn_ts' ~~ atts) thy
+  end;
+
+fun thy_note ((name, atts), thms) =
+  PureThy.add_thmss [((name, thms), atts)] #-> (fn [thms] => pair (name, thms));
+fun thy_def false ((name, atts), t) =
+      PureThy.add_defs_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm))
+  | thy_def true ((name, atts), t) =
+      PureThy.add_defs_unchecked_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm));
+
+in
+
+val add_primrec = gen_primrec thy_note (thy_def false);
+val add_primrec_unchecked = gen_primrec thy_note (thy_def true);
+val add_primrec_i = gen_primrec_i thy_note (thy_def false);
+val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true);
+fun gen_primrec note def alt_name specs =
+  gen_primrec_i note def alt_name (map (fn ((name, t), atts) => ((name, atts), t)) specs);
+
+end;
+
+
+(* see primrecr_package.ML (* outer syntax *)
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val opt_unchecked_name =
+  Scan.optional (P.$$$ "(" |-- P.!!!
+    (((P.$$$ "unchecked" >> K true) -- Scan.optional P.name "" ||
+      P.name >> pair false) --| P.$$$ ")")) (false, "");
+
+val primrec_decl =
+  opt_unchecked_name -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop);
+
+val _ =
+  OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl
+    (primrec_decl >> (fn ((unchecked, alt_name), eqns) =>
+      Toplevel.theory (snd o
+        (if unchecked then add_primrec_unchecked else add_primrec) alt_name
+          (map P.triple_swap eqns))));
+
+end;*)
+
+end;