src/HOL/Tools/inductive_codegen.ML
author wenzelm
Fri Aug 31 18:46:48 2001 +0200 (2001-08-31)
changeset 11539 0f17da240450
parent 11537 e007d35359c3
child 12453 806502073957
permissions -rw-r--r--
tuned headers;
     1 (*  Title:      Pure/HOL/inductive_codegen.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4     License:    GPL (GNU GENERAL PUBLIC LICENSE)
     5 
     6 Code generator for inductive predicates.
     7 *)
     8 
     9 signature INDUCTIVE_CODEGEN =
    10 sig
    11   val setup : (theory -> theory) list
    12 end;
    13 
    14 structure InductiveCodegen : INDUCTIVE_CODEGEN =
    15 struct
    16 
    17 open Codegen;
    18 
    19 exception Modes of (string * int list list) list * (string * int list list) list;
    20 
    21 datatype indprem = Prem of string * term list * term list
    22                  | Sidecond of term;
    23 
    24 fun prod_factors p (Const ("Pair", _) $ t $ u) =
    25       p :: prod_factors (1::p) t @ prod_factors (2::p) u
    26   | prod_factors p _ = [];
    27 
    28 fun split_prod p ps t = if p mem ps then (case t of
    29        Const ("Pair", _) $ t $ u =>
    30          split_prod (1::p) ps t @ split_prod (2::p) ps u
    31      | _ => error "Inconsistent use of products") else [t];
    32 
    33 fun string_of_factors p ps = if p mem ps then
    34     "(" ^ string_of_factors (1::p) ps ^ ", " ^ string_of_factors (2::p) ps ^ ")"
    35   else "_";
    36 
    37 (**** check if a term contains only constructor functions ****)
    38 
    39 fun is_constrt thy =
    40   let
    41     val cnstrs = flat (flat (map
    42       (map (fn (_, (_, _, cs)) => map (apsnd length) cs) o #descr o snd)
    43       (Symtab.dest (DatatypePackage.get_datatypes thy))));
    44     fun check t = (case strip_comb t of
    45         (Var _, []) => true
    46       | (Const (s, _), ts) => (case assoc (cnstrs, s) of
    47             None => false
    48           | Some i => length ts = i andalso forall check ts)
    49       | _ => false)
    50   in check end;
    51 
    52 (**** check if a type is an equality type (i.e. doesn't contain fun) ****)
    53 
    54 fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
    55   | is_eqT _ = true;
    56 
    57 (**** mode inference ****)
    58 
    59 val term_vs = map (fst o fst o dest_Var) o term_vars;
    60 val terms_vs = distinct o flat o (map term_vs);
    61 
    62 (** collect all Vars in a term (with duplicates!) **)
    63 fun term_vTs t = map (apfst fst o dest_Var)
    64   (filter is_Var (foldl_aterms (op :: o Library.swap) ([], t)));
    65 
    66 fun known_args _ _ [] = []
    67   | known_args vs i (t::ts) = if term_vs t subset vs then i::known_args vs (i+1) ts
    68       else known_args vs (i+1) ts;
    69 
    70 fun get_args _ _ [] = ([], [])
    71   | get_args is i (x::xs) = (if i mem is then apfst else apsnd) (cons x)
    72       (get_args is (i+1) xs);
    73 
    74 fun merge xs [] = xs
    75   | merge [] ys = ys
    76   | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
    77       else y::merge (x::xs) ys;
    78 
    79 fun subsets i j = if i <= j then
    80        let val is = subsets (i+1) j
    81        in merge (map (fn ks => i::ks) is) is end
    82      else [[]];
    83 
    84 fun select_mode_prem thy modes vs ps =
    85   find_first (is_some o snd) (ps ~~ map
    86     (fn Prem (s, us, args) => find_first (fn is =>
    87           let
    88             val (_, out_ts) = get_args is 1 us;
    89             val vTs = flat (map term_vTs out_ts);
    90             val dupTs = map snd (duplicates vTs) @
    91               mapfilter (curry assoc vTs) vs;
    92           in
    93             is subset known_args vs 1 us andalso
    94             forall (is_constrt thy) (snd (get_args is 1 us)) andalso
    95             terms_vs args subset vs andalso
    96             forall is_eqT dupTs
    97           end)
    98             (the (assoc (modes, s)))
    99       | Sidecond t => if term_vs t subset vs then Some [] else None) ps);
   100 
   101 fun check_mode_clause thy arg_vs modes mode (ts, ps) =
   102   let
   103     fun check_mode_prems vs [] = Some vs
   104       | check_mode_prems vs ps = (case select_mode_prem thy modes vs ps of
   105           None => None
   106         | Some (x, _) => check_mode_prems
   107             (case x of Prem (_, us, _) => vs union terms_vs us | _ => vs)
   108             (filter_out (equal x) ps));
   109     val (in_ts', _) = get_args mode 1 ts;
   110     val in_ts = filter (is_constrt thy) in_ts';
   111     val in_vs = terms_vs in_ts;
   112     val concl_vs = terms_vs ts
   113   in
   114     forall is_eqT (map snd (duplicates (flat (map term_vTs in_ts')))) andalso
   115     (case check_mode_prems (arg_vs union in_vs) ps of
   116        None => false
   117      | Some vs => concl_vs subset vs)
   118   end;
   119 
   120 fun check_modes_pred thy arg_vs preds modes (p, ms) =
   121   let val Some rs = assoc (preds, p)
   122   in (p, filter (fn m => forall (check_mode_clause thy arg_vs modes m) rs) ms) end
   123 
   124 fun fixp f x =
   125   let val y = f x
   126   in if x = y then x else fixp f y end;
   127 
   128 fun infer_modes thy extra_modes arg_vs preds = fixp (fn modes =>
   129   map (check_modes_pred thy arg_vs preds (modes @ extra_modes)) modes)
   130     (map (fn (s, (ts, _)::_) => (s, subsets 1 (length ts))) preds);
   131 
   132 (**** code generation ****)
   133 
   134 fun mk_eq (x::xs) =
   135   let fun mk_eqs _ [] = []
   136         | mk_eqs a (b::cs) = Pretty.str (a ^ " = " ^ b) :: mk_eqs b cs
   137   in mk_eqs x xs end;
   138 
   139 fun mk_tuple xs = Pretty.block (Pretty.str "(" ::
   140   flat (separate [Pretty.str ",", Pretty.brk 1] (map single xs)) @
   141   [Pretty.str ")"]);
   142 
   143 fun mk_v ((names, vs), s) = (case assoc (vs, s) of
   144       None => ((names, (s, [s])::vs), s)
   145     | Some xs => let val s' = variant names s in
   146         ((s'::names, overwrite (vs, (s, s'::xs))), s') end);
   147 
   148 fun distinct_v (nvs, Var ((s, 0), T)) =
   149       apsnd (Var o rpair T o rpair 0) (mk_v (nvs, s))
   150   | distinct_v (nvs, t $ u) =
   151       let
   152         val (nvs', t') = distinct_v (nvs, t);
   153         val (nvs'', u') = distinct_v (nvs', u);
   154       in (nvs'', t' $ u') end
   155   | distinct_v x = x;
   156 
   157 fun compile_match nvs eq_ps out_ps success_p fail_p =
   158   let val eqs = flat (separate [Pretty.str " andalso", Pretty.brk 1]
   159     (map single (flat (map (mk_eq o snd) nvs) @ eq_ps)));
   160   in
   161     Pretty.block
   162      ([Pretty.str "(fn ", mk_tuple out_ps, Pretty.str " =>", Pretty.brk 1] @
   163       (Pretty.block ((if eqs=[] then [] else Pretty.str "if " ::
   164          [Pretty.block eqs, Pretty.brk 1, Pretty.str "then "]) @
   165          (success_p ::
   166           (if eqs=[] then [] else [Pretty.brk 1, Pretty.str "else ", fail_p]))) ::
   167        [Pretty.brk 1, Pretty.str "| _ => ", fail_p, Pretty.str ")"]))
   168   end;
   169 
   170 fun modename thy s mode = space_implode "_"
   171   (mk_const_id (sign_of thy) s :: map string_of_int mode);
   172 
   173 fun compile_clause thy gr dep all_vs arg_vs modes mode (ts, ps) =
   174   let
   175     fun check_constrt ((names, eqs), t) =
   176       if is_constrt thy t then ((names, eqs), t) else
   177         let val s = variant names "x";
   178         in ((s::names, (s, t)::eqs), Var ((s, 0), fastype_of t)) end;
   179 
   180     val (in_ts, out_ts) = get_args mode 1 ts;
   181     val ((all_vs', eqs), in_ts') =
   182       foldl_map check_constrt ((all_vs, []), in_ts);
   183 
   184     fun compile_prems out_ts' vs names gr [] =
   185           let
   186             val (gr2, out_ps) = foldl_map (fn (gr, t) =>
   187               invoke_codegen thy gr dep false t) (gr, out_ts);
   188             val (gr3, eq_ps) = foldl_map (fn (gr, (s, t)) =>
   189               apsnd (Pretty.block o cons (Pretty.str (s ^ " = ")) o single)
   190                 (invoke_codegen thy gr dep false t)) (gr2, eqs);
   191             val (nvs, out_ts'') = foldl_map distinct_v
   192               ((names, map (fn x => (x, [x])) vs), out_ts');
   193             val (gr4, out_ps') = foldl_map (fn (gr, t) =>
   194               invoke_codegen thy gr dep false t) (gr3, out_ts'');
   195           in
   196             (gr4, compile_match (snd nvs) eq_ps out_ps'
   197               (Pretty.block [Pretty.str "Seq.single", Pretty.brk 1, mk_tuple out_ps])
   198               (Pretty.str "Seq.empty"))
   199           end
   200       | compile_prems out_ts vs names gr ps =
   201           let
   202             val vs' = distinct (flat (vs :: map term_vs out_ts));
   203             val Some (p, Some mode') =
   204               select_mode_prem thy modes (arg_vs union vs') ps;
   205             val ps' = filter_out (equal p) ps;
   206           in
   207             (case p of
   208                Prem (s, us, args) =>
   209                  let
   210                    val (in_ts, out_ts') = get_args mode' 1 us;
   211                    val (gr1, in_ps) = foldl_map (fn (gr, t) =>
   212                      invoke_codegen thy gr dep false t) (gr, in_ts);
   213                    val (gr2, arg_ps) = foldl_map (fn (gr, t) =>
   214                      invoke_codegen thy gr dep true t) (gr1, args);
   215                    val (nvs, out_ts'') = foldl_map distinct_v
   216                      ((names, map (fn x => (x, [x])) vs), out_ts);
   217                    val (gr3, out_ps) = foldl_map (fn (gr, t) =>
   218                      invoke_codegen thy gr dep false t) (gr2, out_ts'')
   219                    val (gr4, rest) = compile_prems out_ts' vs' (fst nvs) gr3 ps';
   220                  in
   221                    (gr4, compile_match (snd nvs) [] out_ps
   222                       (Pretty.block (separate (Pretty.brk 1)
   223                         (Pretty.str (modename thy s mode') :: arg_ps) @
   224                          [Pretty.brk 1, mk_tuple in_ps,
   225                           Pretty.str " :->", Pretty.brk 1, rest]))
   226                       (Pretty.str "Seq.empty"))
   227                  end
   228              | Sidecond t =>
   229                  let
   230                    val (gr1, side_p) = invoke_codegen thy gr dep true t;
   231                    val (nvs, out_ts') = foldl_map distinct_v
   232                      ((names, map (fn x => (x, [x])) vs), out_ts);
   233                    val (gr2, out_ps) = foldl_map (fn (gr, t) =>
   234                      invoke_codegen thy gr dep false t) (gr1, out_ts')
   235                    val (gr3, rest) = compile_prems [] vs' (fst nvs) gr2 ps';
   236                  in
   237                    (gr3, compile_match (snd nvs) [] out_ps
   238                       (Pretty.block [Pretty.str "?? ", side_p,
   239                         Pretty.str " :->", Pretty.brk 1, rest])
   240                       (Pretty.str "Seq.empty"))
   241                  end)
   242           end;
   243 
   244     val (gr', prem_p) = compile_prems in_ts' [] all_vs' gr ps;
   245   in
   246     (gr', Pretty.block [Pretty.str "Seq.single inp :->", Pretty.brk 1, prem_p])
   247   end;
   248 
   249 fun compile_pred thy gr dep prfx all_vs arg_vs modes s cls mode =
   250   let val (gr', cl_ps) = foldl_map (fn (gr, cl) =>
   251     compile_clause thy gr dep all_vs arg_vs modes mode cl) (gr, cls)
   252   in
   253     ((gr', "and "), Pretty.block
   254       ([Pretty.block (separate (Pretty.brk 1)
   255          (Pretty.str (prfx ^ modename thy s mode) :: map Pretty.str arg_vs) @
   256          [Pretty.str " inp ="]),
   257         Pretty.brk 1] @
   258        flat (separate [Pretty.str " ++", Pretty.brk 1] (map single cl_ps))))
   259   end;
   260 
   261 fun compile_preds thy gr dep all_vs arg_vs modes preds =
   262   let val ((gr', _), prs) = foldl_map (fn ((gr, prfx), (s, cls)) =>
   263     foldl_map (fn ((gr', prfx'), mode) =>
   264       compile_pred thy gr' dep prfx' all_vs arg_vs modes s cls mode)
   265         ((gr, prfx), the (assoc (modes, s)))) ((gr, "fun "), preds)
   266   in
   267     (gr', space_implode "\n\n" (map Pretty.string_of (flat prs)) ^ ";\n\n")
   268   end;
   269 
   270 (**** processing of introduction rules ****)
   271 
   272 val string_of_mode = enclose "[" "]" o commas o map string_of_int;
   273 
   274 fun print_modes modes = message ("Inferred modes:\n" ^
   275   space_implode "\n" (map (fn (s, ms) => s ^ ": " ^ commas (map
   276     string_of_mode ms)) modes));
   277 
   278 fun print_factors factors = message ("Factors:\n" ^
   279   space_implode "\n" (map (fn (s, fs) => s ^ ": " ^ string_of_factors [] fs) factors));
   280   
   281 fun get_modes (Some (Modes x), _) = x
   282   | get_modes _ = ([], []);
   283 
   284 fun mk_ind_def thy gr dep names intrs =
   285   let val ids = map (mk_const_id (sign_of thy)) names
   286   in Graph.add_edge (hd ids, dep) gr handle Graph.UNDEF _ =>
   287     let
   288       fun process_prem factors (gr, t' as _ $ (Const ("op :", _) $ t $ u)) =
   289             (case strip_comb u of
   290                (Const (name, _), args) =>
   291                   (case InductivePackage.get_inductive thy name of
   292                      None => (gr, Sidecond t')
   293                    | Some ({names=names', ...}, {intrs=intrs', ...}) =>
   294                        (if names = names' then gr
   295                           else mk_ind_def thy gr (hd ids) names' intrs',
   296                         Prem (name, split_prod []
   297                           (the (assoc (factors, name))) t, args)))
   298              | _ => (gr, Sidecond t'))
   299         | process_prem factors (gr, _ $ (Const ("op =", _) $ t $ u)) =
   300             (gr, Prem ("eq", [t, u], []))
   301         | process_prem factors (gr, _ $ t) = (gr, Sidecond t);
   302 
   303       fun add_clause factors ((clauses, gr), intr) =
   304         let
   305           val _ $ (_ $ t $ u) = Logic.strip_imp_concl intr;
   306           val (Const (name, _), args) = strip_comb u;
   307           val (gr', prems) = foldl_map (process_prem factors)
   308             (gr, Logic.strip_imp_prems intr);
   309         in
   310           (overwrite (clauses, (name, if_none (assoc (clauses, name)) [] @
   311              [(split_prod [] (the (assoc (factors, name))) t, prems)])), gr')
   312         end;
   313 
   314       fun add_prod_factors (fs, x as _ $ (Const ("op :", _) $ t $ u)) =
   315             (case strip_comb u of
   316                (Const (name, _), _) =>
   317                  let val f = prod_factors [] t
   318                  in overwrite (fs, (name, f inter if_none (assoc (fs, name)) f)) end
   319              | _ => fs)
   320         | add_prod_factors (fs, _) = fs;
   321 
   322       val intrs' = map (rename_term o #prop o rep_thm o standard) intrs;
   323       val factors = foldl add_prod_factors ([], flat (map (fn t =>
   324         Logic.strip_imp_concl t :: Logic.strip_imp_prems t) intrs'));
   325       val (clauses, gr') = foldl (add_clause factors) (([], Graph.add_edge (hd ids, dep)
   326         (Graph.new_node (hd ids, (None, "")) gr)), intrs');
   327       val _ $ (_ $ _ $ u) = Logic.strip_imp_concl (hd intrs');
   328       val (_, args) = strip_comb u;
   329       val arg_vs = flat (map term_vs args);
   330       val extra_modes = ("eq", [[1], [2], [1,2]]) :: (flat (map
   331         (fst o get_modes o Graph.get_node gr') (Graph.all_preds gr' [hd ids])));
   332       val modes = infer_modes thy extra_modes arg_vs clauses;
   333       val _ = print_modes modes;
   334       val _ = print_factors factors;
   335       val (gr'', s) = compile_preds thy gr' (hd ids) (terms_vs intrs') arg_vs
   336         (modes @ extra_modes) clauses;
   337     in
   338       (Graph.map_node (hd ids) (K (Some (Modes (modes, factors)), s)) gr'')
   339     end      
   340   end;
   341 
   342 fun mk_ind_call thy gr dep t u is_query = (case strip_comb u of
   343   (Const (s, _), args) => (case InductivePackage.get_inductive thy s of
   344        None => None
   345      | Some ({names, ...}, {intrs, ...}) =>
   346          let
   347           fun mk_mode (((ts, mode), i), Var _) = ((ts, mode), i+1)
   348             | mk_mode (((ts, mode), i), Free _) = ((ts, mode), i+1)
   349             | mk_mode (((ts, mode), i), t) = ((ts @ [t], mode @ [i]), i+1);
   350 
   351            val gr1 = mk_ind_def thy gr dep names intrs;
   352            val (modes, factors) = pairself flat (ListPair.unzip
   353              (map (get_modes o Graph.get_node gr1) (Graph.all_preds gr1 [dep])));
   354            val ts = split_prod [] (the (assoc (factors, s))) t;
   355            val (ts', mode) = if is_query then
   356                fst (foldl mk_mode ((([], []), 1), ts))
   357              else (ts, 1 upto length ts);
   358            val _ = if mode mem the (assoc (modes, s)) then () else
   359              error ("No such mode for " ^ s ^ ": " ^ string_of_mode mode);
   360            val (gr2, in_ps) = foldl_map (fn (gr, t) =>
   361              invoke_codegen thy gr dep false t) (gr1, ts');
   362            val (gr3, arg_ps) = foldl_map (fn (gr, t) =>
   363              invoke_codegen thy gr dep true t) (gr2, args);
   364          in
   365            Some (gr3, Pretty.block (separate (Pretty.brk 1)
   366              (Pretty.str (modename thy s mode) :: arg_ps @ [mk_tuple in_ps])))
   367          end)
   368   | _ => None);
   369 
   370 fun inductive_codegen thy gr dep brack (Const ("op :", _) $ t $ u) =
   371       (case mk_ind_call thy gr dep t u false of
   372          None => None
   373        | Some (gr', call_p) => Some (gr', (if brack then parens else I)
   374            (Pretty.block [Pretty.str "nonempty (", call_p, Pretty.str ")"])))
   375   | inductive_codegen thy gr dep brack (Free ("query", _) $ (Const ("op :", _) $ t $ u)) =
   376       mk_ind_call thy gr dep t u true
   377   | inductive_codegen thy gr dep brack _ = None;
   378 
   379 val setup = [add_codegen "inductive" inductive_codegen];
   380 
   381 end;