src/HOL/Tools/Sledgehammer/sledgehammer_annotate.ML
author smolkas
Mon Feb 18 12:16:27 2013 +0100 (2013-02-18 ago)
changeset 51179 0d5f8812856f
parent 50263 0b430064296a
child 51877 71052c42edf2
permissions -rw-r--r--
split isar_step into isar_step, fix, assms; made isar_proof explicit; register fixed variables in ctxt and auto_fix terms to avoid superfluous annotations
     1 (*  Title:      HOL/Tools/Sledgehammer/sledgehammer_annotate.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Author:     Steffen Juilf Smolka, TU Muenchen
     4 
     5 Supplement term with explicit type constraints that show up as
     6 type annotations when printing the term.
     7 *)
     8 
     9 signature SLEDGEHAMMER_ANNOTATE =
    10 sig
    11   val annotate_types : Proof.context -> term -> term
    12 end
    13 
    14 structure Sledgehammer_Annotate : SLEDGEHAMMER_ANNOTATE =
    15 struct
    16 
    17 (* Util *)
    18 fun post_traverse_term_type' f _ (t as Const (_, T)) s = f t T s
    19   | post_traverse_term_type' f _ (t as Free (_, T)) s = f t T s
    20   | post_traverse_term_type' f _ (t as Var (_, T)) s = f t T s
    21   | post_traverse_term_type' f env (t as Bound i) s = f t (nth env i) s
    22   | post_traverse_term_type' f env (Abs (x, T1, b)) s =
    23     let
    24       val ((b', s'), T2) = post_traverse_term_type' f (T1 :: env) b s
    25     in f (Abs (x, T1, b')) (T1 --> T2) s' end
    26   | post_traverse_term_type' f env (u $ v) s =
    27     let
    28       val ((u', s'), Type (_, [_, T])) = post_traverse_term_type' f env u s
    29       val ((v', s''), _) = post_traverse_term_type' f env v s'
    30     in f (u' $ v') T s'' end
    31 
    32 fun post_traverse_term_type f s t =
    33   post_traverse_term_type' (fn t => fn T => fn s => (f t T s, T)) [] t s |> fst
    34 fun post_fold_term_type f s t =
    35   post_traverse_term_type (fn t => fn T => fn s => (t, f t T s)) s t |> snd
    36 
    37 (* Data structures, orders *)
    38 val cost_ord = prod_ord int_ord (prod_ord int_ord int_ord)
    39 structure Var_Set_Tab = Table(
    40   type key = indexname list
    41   val ord = list_ord Term_Ord.fast_indexname_ord)
    42 
    43 (* (1) Generalize types *)
    44 fun generalize_types ctxt t =
    45   t |> map_types (fn _ => dummyT)
    46     |> Syntax.check_term
    47          (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)
    48 
    49 (* (2) Typing-spot table *)
    50 local
    51 fun key_of_atype (TVar (z, _)) =
    52     Ord_List.insert Term_Ord.fast_indexname_ord z
    53   | key_of_atype _ = I
    54 fun key_of_type T = fold_atyps key_of_atype T []
    55 fun update_tab t T (tab, pos) =
    56   (case key_of_type T of
    57      [] => tab
    58    | key =>
    59      let val cost = (size_of_typ T, (size_of_term t, pos)) in
    60        case Var_Set_Tab.lookup tab key of
    61          NONE => Var_Set_Tab.update_new (key, cost) tab
    62        | SOME old_cost =>
    63          (case cost_ord (cost, old_cost) of
    64             LESS => Var_Set_Tab.update (key, cost) tab
    65           | _ => tab)
    66      end,
    67    pos + 1)
    68 in
    69 val typing_spot_table =
    70   post_fold_term_type update_tab (Var_Set_Tab.empty, 0) #> fst
    71 end
    72 
    73 (* (3) Reverse-greedy *)
    74 fun reverse_greedy typing_spot_tab =
    75   let
    76     fun update_count z =
    77       fold (fn tvar => fn tab =>
    78         let val c = Vartab.lookup tab tvar |> the_default 0 in
    79           Vartab.update (tvar, c + z) tab
    80         end)
    81     fun superfluous tcount =
    82       forall (fn tvar => the (Vartab.lookup tcount tvar) > 1)
    83     fun drop_superfluous (tvars, (_, (_, spot))) (spots, tcount) =
    84       if superfluous tcount tvars then (spots, update_count ~1 tvars tcount)
    85       else (spot :: spots, tcount)
    86     val (typing_spots, tvar_count_tab) =
    87       Var_Set_Tab.fold
    88         (fn kv as (k, _) => apfst (cons kv) #> apsnd (update_count 1 k))
    89         typing_spot_tab ([], Vartab.empty)
    90       |>> sort_distinct (rev_order o cost_ord o pairself snd)
    91   in fold drop_superfluous typing_spots ([], tvar_count_tab) |> fst end
    92 
    93 (* (4) Introduce annotations *)
    94 fun introduce_annotations ctxt spots t t' =
    95   let
    96     val thy = Proof_Context.theory_of ctxt
    97     val get_types = post_fold_term_type (K cons) []
    98     fun match_types tp =
    99       fold (Sign.typ_match thy) (op ~~ (pairself get_types tp)) Vartab.empty
   100     fun unica' b x [] = if b then [x] else []
   101       | unica' b x (y :: ys) =
   102         if x = y then unica' false x ys
   103         else unica' true y ys |> b ? cons x
   104     fun unica ord xs =
   105       case sort ord xs of x :: ys => unica' true x ys | [] => []
   106     val add_all_tfree_namesT = fold_atyps (fn TFree (x, _) => cons x | _ => I)
   107     fun erase_unica_tfrees env =
   108       let
   109         val unica =
   110           Vartab.fold (add_all_tfree_namesT o snd o snd) env []
   111           |> filter_out (Variable.is_declared ctxt)
   112           |> unica fast_string_ord
   113         val erase_unica = map_atyps
   114           (fn T as TFree (s, _) =>
   115               if Ord_List.member fast_string_ord unica s then dummyT else T
   116             | T => T)
   117       in Vartab.map (K (apsnd erase_unica)) env end
   118     val env = match_types (t', t) |> erase_unica_tfrees
   119     fun get_annot env (TFree _) = (false, (env, dummyT))
   120       | get_annot env (T as TVar (v, S)) =
   121         let val T' = Envir.subst_type env T in
   122           if T' = dummyT then (false, (env, dummyT))
   123           else (true, (Vartab.update (v, (S, dummyT)) env, T'))
   124         end
   125       | get_annot env (Type (S, Ts)) =
   126         (case fold_rev (fn T => fn (b, (env, Ts)) =>
   127                   let
   128                     val (b', (env', T)) = get_annot env T
   129                   in (b orelse b', (env', T :: Ts)) end)
   130                 Ts (false, (env, [])) of
   131            (true, (env', Ts)) => (true, (env', Type (S, Ts)))
   132          | (false, (env', _)) => (false, (env', dummyT)))
   133     fun post1 _ T (env, cp, ps as p :: ps', annots) =
   134         if p <> cp then
   135           (env, cp + 1, ps, annots)
   136         else
   137           let val (_, (env', T')) = get_annot env T in
   138             (env', cp + 1, ps', (p, T') :: annots)
   139           end
   140       | post1 _ _ accum = accum
   141     val (_, _, _, annots) = post_fold_term_type post1 (env, 0, spots, []) t'
   142     fun post2 t _ (cp, annots as (p, T) :: annots') =
   143         if p <> cp then (t, (cp + 1, annots))
   144         else (Type.constraint T t, (cp + 1, annots'))
   145       | post2 t _ x = (t, x)
   146   in post_traverse_term_type post2 (0, rev annots) t |> fst end
   147 
   148 (* (5) Annotate *)
   149 fun annotate_types ctxt t =
   150   let
   151     val t' = generalize_types ctxt t
   152     val typing_spots =
   153       t' |> typing_spot_table
   154          |> reverse_greedy
   155          |> sort int_ord
   156   in introduce_annotations ctxt typing_spots t t' end
   157 
   158 end