src/HOL/Tools/Sledgehammer/sledgehammer_annotate.ML
author smolkas
Wed Nov 28 12:22:05 2012 +0100 (2012-11-28 ago)
changeset 50258 1c708d7728c7
child 50259 9c64a52ae499
permissions -rw-r--r--
put annotate in own structure
     1 signature SLEDGEHAMMER_ANNOTATE =
     2 sig
     3   val annotate_types : Proof.context -> term -> term
     4 end
     5 
     6 structure Sledgehammer_Annotate : SLEDGEHAMMER_ANNOTATE =
     7 struct
     8 
     9 (* Util *)
    10 fun post_traverse_term_type' f _ (t as Const (_, T)) s = f t T s
    11   | post_traverse_term_type' f _ (t as Free (_, T)) s = f t T s
    12   | post_traverse_term_type' f _ (t as Var (_, T)) s = f t T s
    13   | post_traverse_term_type' f env (t as Bound i) s = f t (nth env i) s
    14   | post_traverse_term_type' f env (Abs (x, T1, b)) s =
    15     let
    16       val ((b', s'), T2) = post_traverse_term_type' f (T1 :: env) b s
    17     in f (Abs (x, T1, b')) (T1 --> T2) s' end
    18   | post_traverse_term_type' f env (u $ v) s =
    19     let
    20       val ((u', s'), Type (_, [_, T])) = post_traverse_term_type' f env u s
    21       val ((v', s''), _) = post_traverse_term_type' f env v s'
    22     in f (u' $ v') T s'' end
    23 
    24 fun post_traverse_term_type f s t =
    25   post_traverse_term_type' (fn t => fn T => fn s => (f t T s, T)) [] t s |> fst
    26 fun post_fold_term_type f s t =
    27   post_traverse_term_type (fn t => fn T => fn s => (t, f t T s)) s t |> snd
    28 
    29 (* Data structures, orders *)
    30 val cost_ord = prod_ord int_ord (prod_ord int_ord int_ord)
    31 
    32 structure Var_Set_Tab = Table(
    33   type key = indexname list
    34   val ord = list_ord Term_Ord.fast_indexname_ord)
    35 
    36 (* (1) Generalize types *)
    37 fun generalize_types ctxt t =
    38   t |> map_types (fn _ => dummyT)
    39     |> Syntax.check_term
    40          (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)
    41 
    42 (* (2) Typing-spot table *)
    43 local
    44 fun key_of_atype (TVar (z, _)) =
    45     Ord_List.insert Term_Ord.fast_indexname_ord z
    46   | key_of_atype _ = I
    47 fun key_of_type T = fold_atyps key_of_atype T []
    48 fun update_tab t T (tab, pos) =
    49   (case key_of_type T of
    50      [] => tab
    51    | key =>
    52      let val cost = (size_of_typ T, (size_of_term t, pos)) in
    53        case Var_Set_Tab.lookup tab key of
    54          NONE => Var_Set_Tab.update_new (key, cost) tab
    55        | SOME old_cost =>
    56          (case cost_ord (cost, old_cost) of
    57             LESS => Var_Set_Tab.update (key, cost) tab
    58           | _ => tab)
    59      end,
    60    pos + 1)
    61 in
    62 val typing_spot_table =
    63   post_fold_term_type update_tab (Var_Set_Tab.empty, 0) #> fst
    64 end
    65 
    66 (* (3) Reverse-greedy *)
    67 fun reverse_greedy typing_spot_tab =
    68   let
    69     fun update_count z =
    70       fold (fn tvar => fn tab =>
    71         let val c = Vartab.lookup tab tvar |> the_default 0 in
    72           Vartab.update (tvar, c + z) tab
    73         end)
    74     fun superfluous tcount =
    75       forall (fn tvar => the (Vartab.lookup tcount tvar) > 1)
    76     fun drop_superfluous (tvars, (_, (_, spot))) (spots, tcount) =
    77       if superfluous tcount tvars then (spots, update_count ~1 tvars tcount)
    78       else (spot :: spots, tcount)
    79     val (typing_spots, tvar_count_tab) =
    80       Var_Set_Tab.fold
    81         (fn kv as (k, _) => apfst (cons kv) #> apsnd (update_count 1 k))
    82         typing_spot_tab ([], Vartab.empty)
    83       |>> sort_distinct (rev_order o cost_ord o pairself snd)
    84   in fold drop_superfluous typing_spots ([], tvar_count_tab) |> fst end
    85 
    86 (* (4) Introduce annotations *)
    87 fun introduce_annotations ctxt spots t t' =
    88   let
    89     val thy = Proof_Context.theory_of ctxt
    90     val get_types = post_fold_term_type (K cons) []
    91     fun match_types tp =
    92       fold (Sign.typ_match thy) (op ~~ (pairself get_types tp)) Vartab.empty
    93     fun unica' b x [] = if b then [x] else []
    94       | unica' b x (y :: ys) =
    95         if x = y then unica' false x ys
    96         else unica' true y ys |> b ? cons x
    97     fun unica ord xs =
    98       case sort ord xs of x :: ys => unica' true x ys | [] => []
    99     val add_all_tfree_namesT = fold_atyps (fn TFree (x, _) => cons x | _ => I)
   100     fun erase_unica_tfrees env =
   101       let
   102         val unica =
   103           Vartab.fold (add_all_tfree_namesT o snd o snd) env []
   104           |> filter_out (Variable.is_declared ctxt)
   105           |> unica fast_string_ord
   106         val erase_unica = map_atyps
   107           (fn T as TFree (s, _) =>
   108               if Ord_List.member fast_string_ord unica s then dummyT else T
   109             | T => T)
   110       in Vartab.map (K (apsnd erase_unica)) env end
   111     val env = match_types (t', t) |> erase_unica_tfrees
   112     fun get_annot env (TFree _) = (false, (env, dummyT))
   113       | get_annot env (T as TVar (v, S)) =
   114         let val T' = Envir.subst_type env T in
   115           if T' = dummyT then (false, (env, dummyT))
   116           else (true, (Vartab.update (v, (S, dummyT)) env, T'))
   117         end
   118       | get_annot env (Type (S, Ts)) =
   119         (case fold_rev (fn T => fn (b, (env, Ts)) =>
   120                   let
   121                     val (b', (env', T)) = get_annot env T
   122                   in (b orelse b', (env', T :: Ts)) end)
   123                 Ts (false, (env, [])) of
   124            (true, (env', Ts)) => (true, (env', Type (S, Ts)))
   125          | (false, (env', _)) => (false, (env', dummyT)))
   126     fun post1 _ T (env, cp, ps as p :: ps', annots) =
   127         if p <> cp then
   128           (env, cp + 1, ps, annots)
   129         else
   130           let val (_, (env', T')) = get_annot env T in
   131             (env', cp + 1, ps', (p, T') :: annots)
   132           end
   133       | post1 _ _ accum = accum
   134     val (_, _, _, annots) = post_fold_term_type post1 (env, 0, spots, []) t'
   135     fun post2 t _ (cp, annots as (p, T) :: annots') =
   136         if p <> cp then (t, (cp + 1, annots))
   137         else (Type.constraint T t, (cp + 1, annots'))
   138       | post2 t _ x = (t, x)
   139   in post_traverse_term_type post2 (0, rev annots) t |> fst end
   140 
   141 (* (5) Annotate *)
   142 fun annotate_types ctxt t =
   143   let
   144     val t' = generalize_types ctxt t
   145     val typing_spots =
   146       t' |> typing_spot_table
   147          |> reverse_greedy
   148          |> sort int_ord
   149   in introduce_annotations ctxt typing_spots t t' end
   150 
   151 end