src/HOL/Tools/Nitpick/nitpick.ML
author haftmann
Tue Nov 24 17:28:25 2009 +0100 (2009-11-24)
changeset 33955 fff6f11b1f09
parent 33877 e779bea3d337
child 33982 1ae222745c4a
permissions -rw-r--r--
curried take/drop
     1 (*  Title:      HOL/Nitpick/Tools/nitpick.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2008, 2009
     4 
     5 Finite model generation for HOL formulas using Kodkod.
     6 *)
     7 
     8 signature NITPICK =
     9 sig
    10   type styp = Nitpick_Util.styp
    11   type params = {
    12     cards_assigns: (typ option * int list) list,
    13     maxes_assigns: (styp option * int list) list,
    14     iters_assigns: (styp option * int list) list,
    15     bisim_depths: int list,
    16     boxes: (typ option * bool option) list,
    17     monos: (typ option * bool option) list,
    18     wfs: (styp option * bool option) list,
    19     sat_solver: string,
    20     blocking: bool,
    21     falsify: bool,
    22     debug: bool,
    23     verbose: bool,
    24     overlord: bool,
    25     user_axioms: bool option,
    26     assms: bool,
    27     merge_type_vars: bool,
    28     destroy_constrs: bool,
    29     specialize: bool,
    30     skolemize: bool,
    31     star_linear_preds: bool,
    32     uncurry: bool,
    33     fast_descrs: bool,
    34     peephole_optim: bool,
    35     timeout: Time.time option,
    36     tac_timeout: Time.time option,
    37     sym_break: int,
    38     sharing_depth: int,
    39     flatten_props: bool,
    40     max_threads: int,
    41     show_skolems: bool,
    42     show_datatypes: bool,
    43     show_consts: bool,
    44     evals: term list,
    45     formats: (term option * int list) list,
    46     max_potential: int,
    47     max_genuine: int,
    48     check_potential: bool,
    49     check_genuine: bool,
    50     batch_size: int,
    51     expect: string}
    52 
    53   val register_frac_type : string -> (string * string) list -> theory -> theory
    54   val unregister_frac_type : string -> theory -> theory
    55   val register_codatatype : typ -> string -> styp list -> theory -> theory
    56   val unregister_codatatype : typ -> theory -> theory
    57   val pick_nits_in_term :
    58     Proof.state -> params -> bool -> term list -> term -> string * Proof.state
    59   val pick_nits_in_subgoal :
    60     Proof.state -> params -> bool -> int -> string * Proof.state
    61 end;
    62 
    63 structure Nitpick : NITPICK =
    64 struct
    65 
    66 open Nitpick_Util
    67 open Nitpick_HOL
    68 open Nitpick_Mono
    69 open Nitpick_Scope
    70 open Nitpick_Peephole
    71 open Nitpick_Rep
    72 open Nitpick_Nut
    73 open Nitpick_Kodkod
    74 open Nitpick_Model
    75 
    76 type params = {
    77   cards_assigns: (typ option * int list) list,
    78   maxes_assigns: (styp option * int list) list,
    79   iters_assigns: (styp option * int list) list,
    80   bisim_depths: int list,
    81   boxes: (typ option * bool option) list,
    82   monos: (typ option * bool option) list,
    83   wfs: (styp option * bool option) list,
    84   sat_solver: string,
    85   blocking: bool,
    86   falsify: bool,
    87   debug: bool,
    88   verbose: bool,
    89   overlord: bool,
    90   user_axioms: bool option,
    91   assms: bool,
    92   merge_type_vars: bool,
    93   destroy_constrs: bool,
    94   specialize: bool,
    95   skolemize: bool,
    96   star_linear_preds: bool,
    97   uncurry: bool,
    98   fast_descrs: bool,
    99   peephole_optim: bool,
   100   timeout: Time.time option,
   101   tac_timeout: Time.time option,
   102   sym_break: int,
   103   sharing_depth: int,
   104   flatten_props: bool,
   105   max_threads: int,
   106   show_skolems: bool,
   107   show_datatypes: bool,
   108   show_consts: bool,
   109   evals: term list,
   110   formats: (term option * int list) list,
   111   max_potential: int,
   112   max_genuine: int,
   113   check_potential: bool,
   114   check_genuine: bool,
   115   batch_size: int,
   116   expect: string}
   117 
   118 type problem_extension = {
   119   free_names: nut list,
   120   sel_names: nut list,
   121   nonsel_names: nut list,
   122   rel_table: nut NameTable.table,
   123   liberal: bool,
   124   scope: scope,
   125   core: Kodkod.formula,
   126   defs: Kodkod.formula list}
   127 
   128 type rich_problem = Kodkod.problem * problem_extension
   129 
   130 (* Proof.context -> string -> term list -> Pretty.T list *)
   131 fun pretties_for_formulas _ _ [] = []
   132   | pretties_for_formulas ctxt s ts =
   133     [Pretty.str (s ^ plural_s_for_list ts ^ ":"),
   134      Pretty.indent indent_size (Pretty.chunks
   135          (map2 (fn j => fn t =>
   136                    Pretty.block [t |> shorten_const_names_in_term
   137                                    |> Syntax.pretty_term ctxt,
   138                                  Pretty.str (if j = 1 then "." else ";")])
   139                (length ts downto 1) ts))]
   140 
   141 (* unit -> string *)
   142 fun install_kodkodi_message () =
   143   "Nitpick requires the external Java program Kodkodi. To install it, download \
   144   \the package from Isabelle's web page and add the \"kodkodi-x.y.z\" \
   145   \directory's full path to \"" ^
   146   Path.implode (Path.expand (Path.appends
   147       (Path.variable "ISABELLE_HOME_USER" ::
   148        map Path.basic ["etc", "components"]))) ^ "\"."
   149 
   150 val max_liberal_delay_ms = 200
   151 val max_liberal_delay_percent = 2
   152 
   153 (* Time.time option -> int *)
   154 fun liberal_delay_for_timeout NONE = max_liberal_delay_ms
   155   | liberal_delay_for_timeout (SOME timeout) =
   156     Int.max (0, Int.min (max_liberal_delay_ms,
   157                          Time.toMilliseconds timeout
   158                          * max_liberal_delay_percent div 100))
   159 
   160 (* Time.time option -> bool *)
   161 fun passed_deadline NONE = false
   162   | passed_deadline (SOME time) = Time.compare (Time.now (), time) <> LESS
   163 
   164 (* ('a * bool option) list -> bool *)
   165 fun none_true asgns = forall (not_equal (SOME true) o snd) asgns
   166 
   167 val weaselly_sorts =
   168   [@{sort default}, @{sort zero}, @{sort one}, @{sort plus}, @{sort minus},
   169    @{sort uminus}, @{sort times}, @{sort inverse}, @{sort abs}, @{sort sgn},
   170    @{sort ord}, @{sort eq}, @{sort number}]
   171 (* theory -> typ -> bool *)
   172 fun is_tfree_with_weaselly_sort thy (TFree (_, S)) =
   173     exists (curry (Sign.subsort thy) S) weaselly_sorts
   174   | is_tfree_with_weaselly_sort _ _ = false
   175 (* theory term -> bool *)
   176 val has_weaselly_sorts =
   177   exists_type o exists_subtype o is_tfree_with_weaselly_sort
   178 
   179 (* (unit -> string) -> Pretty.T *)
   180 fun plazy f = Pretty.blk (0, pstrs (f ()))
   181 
   182 (* Time.time -> Proof.state -> params -> bool -> term -> string * Proof.state *)
   183 fun pick_them_nits_in_term deadline state (params : params) auto orig_assm_ts
   184                            orig_t =
   185   let
   186     val timer = Timer.startRealTimer ()
   187     val thy = Proof.theory_of state
   188     val ctxt = Proof.context_of state
   189     val {cards_assigns, maxes_assigns, iters_assigns, bisim_depths, boxes,
   190          monos, wfs, sat_solver, blocking, falsify, debug, verbose, overlord,
   191          user_axioms, assms, merge_type_vars, destroy_constrs, specialize,
   192          skolemize, star_linear_preds, uncurry, fast_descrs, peephole_optim,
   193          tac_timeout, sym_break, sharing_depth, flatten_props, max_threads,
   194          show_skolems, show_datatypes, show_consts, evals, formats,
   195          max_potential, max_genuine, check_potential, check_genuine, batch_size,
   196          ...} =
   197       params
   198     val state_ref = Unsynchronized.ref state
   199     (* Pretty.T -> unit *)
   200     val pprint =
   201       if auto then
   202         Unsynchronized.change state_ref o Proof.goal_message o K
   203         o Pretty.chunks o cons (Pretty.str "") o single
   204         o Pretty.mark Markup.hilite
   205       else
   206         priority o Pretty.string_of
   207     (* (unit -> Pretty.T) -> unit *)
   208     fun pprint_m f = () |> not auto ? pprint o f
   209     fun pprint_v f = () |> verbose ? pprint o f
   210     fun pprint_d f = () |> debug ? pprint o f
   211     (* string -> unit *)
   212     val print = pprint o curry Pretty.blk 0 o pstrs
   213     (* (unit -> string) -> unit *)
   214     val print_m = pprint_m o K o plazy
   215     val print_v = pprint_v o K o plazy
   216     val print_d = pprint_d o K o plazy
   217 
   218     (* unit -> unit *)
   219     fun check_deadline () =
   220       if debug andalso passed_deadline deadline then raise TimeLimit.TimeOut
   221       else ()
   222     (* unit -> 'a *)
   223     fun do_interrupted () =
   224       if passed_deadline deadline then raise TimeLimit.TimeOut
   225       else raise Interrupt
   226 
   227     val _ = print_m (K "Nitpicking...")
   228     val neg_t = if falsify then Logic.mk_implies (orig_t, @{prop False})
   229                 else orig_t
   230     val assms_t = if assms orelse auto then
   231                     Logic.mk_conjunction_list (neg_t :: orig_assm_ts)
   232                   else
   233                     neg_t
   234     val (assms_t, evals) =
   235       assms_t :: evals |> merge_type_vars ? merge_type_vars_in_terms
   236                        |> pairf hd tl
   237     val original_max_potential = max_potential
   238     val original_max_genuine = max_genuine
   239 (*
   240     val _ = priority ("*** " ^ Syntax.string_of_term ctxt orig_t)
   241     val _ = List.app (fn t => priority ("*** " ^ Syntax.string_of_term ctxt t))
   242                      orig_assm_ts
   243 *)
   244     val max_bisim_depth = fold Integer.max bisim_depths ~1
   245     val case_names = case_const_names thy
   246     val (defs, built_in_nondefs, user_nondefs) = all_axioms_of thy
   247     val def_table = const_def_table ctxt defs
   248     val nondef_table = const_nondef_table (built_in_nondefs @ user_nondefs)
   249     val simp_table = Unsynchronized.ref (const_simp_table ctxt)
   250     val psimp_table = const_psimp_table ctxt
   251     val intro_table = inductive_intro_table ctxt def_table
   252     val ground_thm_table = ground_theorem_table thy
   253     val ersatz_table = ersatz_table thy
   254     val (ext_ctxt as {wf_cache, ...}) =
   255       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   256        user_axioms = user_axioms, debug = debug, wfs = wfs,
   257        destroy_constrs = destroy_constrs, specialize = specialize,
   258        skolemize = skolemize, star_linear_preds = star_linear_preds,
   259        uncurry = uncurry, fast_descrs = fast_descrs, tac_timeout = tac_timeout,
   260        evals = evals, case_names = case_names, def_table = def_table,
   261        nondef_table = nondef_table, user_nondefs = user_nondefs,
   262        simp_table = simp_table, psimp_table = psimp_table,
   263        intro_table = intro_table, ground_thm_table = ground_thm_table,
   264        ersatz_table = ersatz_table, skolems = Unsynchronized.ref [],
   265        special_funs = Unsynchronized.ref [],
   266        unrolled_preds = Unsynchronized.ref [], wf_cache = Unsynchronized.ref [],
   267        constr_cache = Unsynchronized.ref []}
   268     val frees = Term.add_frees assms_t []
   269     val _ = null (Term.add_tvars assms_t [])
   270             orelse raise NOT_SUPPORTED "schematic type variables"
   271     val (((def_ts, nondef_ts), (got_all_mono_user_axioms, no_poly_user_axioms)),
   272          core_t) = preprocess_term ext_ctxt assms_t
   273     val got_all_user_axioms =
   274       got_all_mono_user_axioms andalso no_poly_user_axioms
   275 
   276     (* styp * (bool * bool) -> unit *)
   277     fun print_wf (x, (gfp, wf)) =
   278       pprint (Pretty.blk (0,
   279           pstrs ("The " ^ (if gfp then "co" else "") ^ "inductive predicate \"")
   280           @ Syntax.pretty_term ctxt (Const x) ::
   281           pstrs (if wf then
   282                    "\" was proved well-founded. Nitpick can compute it \
   283                    \efficiently."
   284                  else
   285                    "\" could not be proved well-founded. Nitpick might need to \
   286                    \unroll it.")))
   287     val _ = if verbose then List.app print_wf (!wf_cache) else ()
   288     val _ =
   289       pprint_d (fn () =>
   290           Pretty.chunks
   291               (pretties_for_formulas ctxt "Preprocessed formula" [core_t] @
   292                pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @
   293                pretties_for_formulas ctxt "Relevant nondefinitional axiom"
   294                                      nondef_ts))
   295     val _ = List.app (ignore o Term.type_of) (core_t :: def_ts @ nondef_ts)
   296             handle TYPE (_, Ts, ts) =>
   297                    raise TYPE ("Nitpick.pick_them_nits_in_term", Ts, ts)
   298 
   299     val core_u = nut_from_term ext_ctxt Eq core_t
   300     val def_us = map (nut_from_term ext_ctxt DefEq) def_ts
   301     val nondef_us = map (nut_from_term ext_ctxt Eq) nondef_ts
   302     val (free_names, const_names) =
   303       fold add_free_and_const_names (core_u :: def_us @ nondef_us) ([], [])
   304     val (sel_names, nonsel_names) =
   305       List.partition (is_sel o nickname_of) const_names
   306     val would_be_genuine = got_all_user_axioms andalso none_true wfs
   307 (*
   308     val _ = List.app (priority o string_for_nut ctxt)
   309                      (core_u :: def_us @ nondef_us)
   310 *)
   311 
   312     val unique_scope = forall (equal 1 o length o snd) cards_assigns
   313     (* typ -> bool *)
   314     fun is_free_type_monotonic T =
   315       unique_scope orelse
   316       case triple_lookup (type_match thy) monos T of
   317         SOME (SOME b) => b
   318       | _ => formulas_monotonic ext_ctxt T def_ts nondef_ts core_t
   319     fun is_datatype_monotonic T =
   320       unique_scope orelse
   321       case triple_lookup (type_match thy) monos T of
   322         SOME (SOME b) => b
   323       | _ =>
   324         not (is_pure_typedef thy T) orelse is_univ_typedef thy T
   325         orelse is_number_type thy T
   326         orelse formulas_monotonic ext_ctxt T def_ts nondef_ts core_t
   327     fun is_datatype_shallow T =
   328       not (exists (equal T o domain_type o type_of) sel_names)
   329     val Ts = ground_types_in_terms ext_ctxt (core_t :: def_ts @ nondef_ts)
   330              |> sort TermOrd.typ_ord
   331     val (all_dataTs, all_free_Ts) =
   332       List.partition (is_integer_type orf is_datatype thy) Ts
   333     val (mono_dataTs, nonmono_dataTs) =
   334       List.partition is_datatype_monotonic all_dataTs
   335     val (mono_free_Ts, nonmono_free_Ts) =
   336       List.partition is_free_type_monotonic all_free_Ts
   337 
   338     val _ =
   339       if not unique_scope andalso not (null mono_free_Ts) then
   340         print_v (fn () =>
   341                     let
   342                       val ss = map (quote o string_for_type ctxt) mono_free_Ts
   343                     in
   344                       "The type" ^ plural_s_for_list ss ^ " " ^
   345                       space_implode " " (serial_commas "and" ss) ^ " " ^
   346                       (if none_true monos then
   347                          "passed the monotonicity test"
   348                        else
   349                          (if length ss = 1 then "is" else "are") ^
   350                          " considered monotonic") ^
   351                       ". Nitpick might be able to skip some scopes."
   352                     end)
   353       else
   354         ()
   355     val mono_Ts = mono_dataTs @ mono_free_Ts
   356     val nonmono_Ts = nonmono_dataTs @ nonmono_free_Ts
   357     val shallow_dataTs = filter is_datatype_shallow mono_dataTs
   358 (*
   359     val _ = priority "Monotonic datatypes:"
   360     val _ = List.app (priority o string_for_type ctxt) mono_dataTs
   361     val _ = priority "Nonmonotonic datatypes:"
   362     val _ = List.app (priority o string_for_type ctxt) nonmono_dataTs
   363     val _ = priority "Monotonic free types:"
   364     val _ = List.app (priority o string_for_type ctxt) mono_free_Ts
   365     val _ = priority "Nonmonotonic free types:"
   366     val _ = List.app (priority o string_for_type ctxt) nonmono_free_Ts
   367 *)
   368 
   369     val need_incremental = Int.max (max_potential, max_genuine) >= 2
   370     val effective_sat_solver =
   371       if sat_solver <> "smart" then
   372         if need_incremental andalso
   373            not (sat_solver mem Kodkod_SAT.configured_sat_solvers true) then
   374           (print_m (K ("An incremental SAT solver is required: \"SAT4J\" will \
   375                        \be used instead of " ^ quote sat_solver ^ "."));
   376            "SAT4J")
   377         else
   378           sat_solver
   379       else
   380         Kodkod_SAT.smart_sat_solver_name need_incremental
   381     val _ =
   382       if sat_solver = "smart" then
   383         print_v (fn () => "Using SAT solver " ^ quote effective_sat_solver ^
   384                           ". The following" ^
   385                           (if need_incremental then " incremental " else " ") ^
   386                           "solvers are configured: " ^
   387                           commas (map quote (Kodkod_SAT.configured_sat_solvers
   388                                                        need_incremental)) ^ ".")
   389       else
   390         ()
   391 
   392     val too_big_scopes = Unsynchronized.ref []
   393 
   394     (* bool -> scope -> rich_problem option *)
   395     fun problem_for_scope liberal
   396             (scope as {card_assigns, bisim_depth, datatypes, ofs, ...}) =
   397       let
   398         val _ = not (exists (fn other => scope_less_eq other scope)
   399                             (!too_big_scopes))
   400                 orelse raise LIMIT ("Nitpick.pick_them_nits_in_term.\
   401                                     \problem_for_scope", "too big scope")
   402 (*
   403         val _ = priority "Offsets:"
   404         val _ = List.app (fn (T, j0) =>
   405                              priority (string_for_type ctxt T ^ " = " ^
   406                                        string_of_int j0))
   407                          (Typtab.dest ofs)
   408 *)
   409         val all_precise = forall (is_precise_type datatypes) Ts
   410         (* nut list -> rep NameTable.table -> nut list * rep NameTable.table *)
   411         val repify_consts = choose_reps_for_consts scope all_precise
   412         val main_j0 = offset_of_type ofs bool_T
   413         val (nat_card, nat_j0) = spec_of_type scope nat_T
   414         val (int_card, int_j0) = spec_of_type scope int_T
   415         val _ = forall (equal main_j0) [nat_j0, int_j0]
   416                 orelse raise BAD ("Nitpick.pick_them_nits_in_term.\
   417                                   \problem_for_scope", "bad offsets")
   418         val kk = kodkod_constrs peephole_optim nat_card int_card main_j0
   419         val (free_names, rep_table) =
   420           choose_reps_for_free_vars scope free_names NameTable.empty
   421         val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table
   422         val (nonsel_names, rep_table) = repify_consts nonsel_names rep_table
   423         val min_highest_arity =
   424           NameTable.fold (curry Int.max o arity_of_rep o snd) rep_table 1
   425         val min_univ_card =
   426           NameTable.fold (curry Int.max o min_univ_card_of_rep o snd) rep_table
   427                          (univ_card nat_card int_card main_j0 [] Kodkod.True)
   428         val _ = check_arity min_univ_card min_highest_arity
   429 
   430         val core_u = choose_reps_in_nut scope liberal rep_table false core_u
   431         val def_us = map (choose_reps_in_nut scope liberal rep_table true)
   432                          def_us
   433         val nondef_us = map (choose_reps_in_nut scope liberal rep_table false)
   434                             nondef_us
   435 (*
   436         val _ = List.app (priority o string_for_nut ctxt)
   437                          (free_names @ sel_names @ nonsel_names @
   438                           core_u :: def_us @ nondef_us)
   439 *)
   440         val (free_rels, pool, rel_table) =
   441           rename_free_vars free_names initial_pool NameTable.empty
   442         val (sel_rels, pool, rel_table) =
   443           rename_free_vars sel_names pool rel_table
   444         val (other_rels, pool, rel_table) =
   445           rename_free_vars nonsel_names pool rel_table
   446         val core_u = rename_vars_in_nut pool rel_table core_u
   447         val def_us = map (rename_vars_in_nut pool rel_table) def_us
   448         val nondef_us = map (rename_vars_in_nut pool rel_table) nondef_us
   449         (* nut -> Kodkod.formula *)
   450         val to_f = kodkod_formula_from_nut ofs liberal kk
   451         val core_f = to_f core_u
   452         val def_fs = map to_f def_us
   453         val nondef_fs = map to_f nondef_us
   454         val formula = fold (fold s_and) [def_fs, nondef_fs] core_f
   455         val comment = (if liberal then "liberal" else "conservative") ^ "\n" ^
   456                       PrintMode.setmp [] multiline_string_for_scope scope
   457         val kodkod_sat_solver = Kodkod_SAT.sat_solver_spec effective_sat_solver
   458                                 |> snd
   459         val delay = if liberal then
   460                       Option.map (fn time => Time.- (time, Time.now ()))
   461                                  deadline
   462                       |> liberal_delay_for_timeout
   463                     else
   464                       0
   465         val settings = [("solver", commas (map quote kodkod_sat_solver)),
   466                         ("skolem_depth", "-1"),
   467                         ("bit_width", "16"),
   468                         ("symmetry_breaking", signed_string_of_int sym_break),
   469                         ("sharing", signed_string_of_int sharing_depth),
   470                         ("flatten", Bool.toString flatten_props),
   471                         ("delay", signed_string_of_int delay)]
   472         val plain_rels = free_rels @ other_rels
   473         val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels
   474         val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels
   475         val sel_bounds = map (bound_for_sel_rel ctxt debug datatypes) sel_rels
   476         val dtype_axioms = declarative_axioms_for_datatypes ext_ctxt ofs kk
   477                                                             rel_table datatypes
   478         val declarative_axioms = plain_axioms @ dtype_axioms
   479         val univ_card = univ_card nat_card int_card main_j0
   480                                   (plain_bounds @ sel_bounds) formula
   481         val built_in_bounds = bounds_for_built_in_rels_in_formula debug
   482                                   univ_card nat_card int_card main_j0 formula
   483         val bounds = built_in_bounds @ plain_bounds @ sel_bounds
   484                      |> not debug ? merge_bounds
   485         val highest_arity =
   486           fold Integer.max (map (fst o fst) (maps fst bounds)) 0
   487         val formula = fold_rev s_and declarative_axioms formula
   488         val _ = if formula = Kodkod.False then ()
   489                 else check_arity univ_card highest_arity
   490       in
   491         SOME ({comment = comment, settings = settings, univ_card = univ_card,
   492                tuple_assigns = [], bounds = bounds,
   493                int_bounds = sequential_int_bounds univ_card,
   494                expr_assigns = [], formula = formula},
   495               {free_names = free_names, sel_names = sel_names,
   496                nonsel_names = nonsel_names, rel_table = rel_table,
   497                liberal = liberal, scope = scope, core = core_f,
   498                defs = nondef_fs @ def_fs @ declarative_axioms})
   499       end
   500       handle LIMIT (loc, msg) =>
   501              if loc = "Nitpick_Kodkod.check_arity"
   502                 andalso not (Typtab.is_empty ofs) then
   503                problem_for_scope liberal
   504                    {ext_ctxt = ext_ctxt, card_assigns = card_assigns,
   505                     bisim_depth = bisim_depth, datatypes = datatypes,
   506                     ofs = Typtab.empty}
   507              else if loc = "Nitpick.pick_them_nits_in_term.\
   508                            \problem_for_scope" then
   509                NONE
   510              else
   511                (Unsynchronized.change too_big_scopes (cons scope);
   512                 print_v (fn () => ("Limit reached: " ^ msg ^
   513                                    ". Dropping " ^ (if liberal then "potential"
   514                                                     else "genuine") ^
   515                                    " component of scope."));
   516                 NONE)
   517 
   518     (* int -> (''a * int list list) list -> ''a -> Kodkod.tuple_set *)
   519     fun tuple_set_for_rel univ_card =
   520       Kodkod.TupleSet o map (kk_tuple debug univ_card) o the
   521       oo AList.lookup (op =)
   522 
   523     val word_model = if falsify then "counterexample" else "model"
   524 
   525     val scopes = Unsynchronized.ref []
   526     val generated_scopes = Unsynchronized.ref []
   527     val generated_problems = Unsynchronized.ref []
   528     val checked_problems = Unsynchronized.ref (SOME [])
   529     val met_potential = Unsynchronized.ref 0
   530 
   531     (* rich_problem list -> int list -> unit *)
   532     fun update_checked_problems problems =
   533       List.app (Unsynchronized.change checked_problems o Option.map o cons
   534                 o nth problems)
   535 
   536     (* bool -> Kodkod.raw_bound list -> problem_extension -> bool option *)
   537     fun print_and_check_model genuine bounds
   538             ({free_names, sel_names, nonsel_names, rel_table, scope, ...}
   539              : problem_extension) =
   540       let
   541         val (reconstructed_model, codatatypes_ok) =
   542           reconstruct_hol_model {show_skolems = show_skolems,
   543                                  show_datatypes = show_datatypes,
   544                                  show_consts = show_consts}
   545               scope formats frees free_names sel_names nonsel_names rel_table
   546               bounds
   547         val would_be_genuine = would_be_genuine andalso codatatypes_ok
   548       in
   549         pprint (Pretty.chunks
   550             [Pretty.blk (0,
   551                  (pstrs ("Nitpick found a" ^
   552                          (if not genuine then " potential "
   553                           else if would_be_genuine then " "
   554                           else " likely genuine ") ^ word_model) @
   555                   (case pretties_for_scope scope verbose of
   556                      [] => []
   557                    | pretties => pstrs " for " @ pretties) @
   558                   [Pretty.str ":\n"])),
   559              Pretty.indent indent_size reconstructed_model]);
   560         if genuine then
   561           (if check_genuine then
   562              (case prove_hol_model scope tac_timeout free_names sel_names
   563                                    rel_table bounds assms_t of
   564                 SOME true => print ("Confirmation by \"auto\": The above " ^
   565                                     word_model ^ " is really genuine.")
   566               | SOME false =>
   567                 if would_be_genuine then
   568                   error ("A supposedly genuine " ^ word_model ^ " was shown to\
   569                          \be spurious by \"auto\".\nThis should never happen.\n\
   570                          \Please send a bug report to blanchet\
   571                          \te@in.tum.de.")
   572                 else
   573                   print ("Refutation by \"auto\": The above " ^ word_model ^
   574                          " is spurious.")
   575               | NONE => print "No confirmation by \"auto\".")
   576            else
   577              ();
   578            if has_weaselly_sorts thy orig_t then
   579              print "Hint: Maybe you forgot a type constraint?"
   580            else
   581              ();
   582            if not would_be_genuine then
   583              if no_poly_user_axioms then
   584                let
   585                  val options =
   586                    [] |> not got_all_mono_user_axioms
   587                          ? cons ("user_axioms", "\"true\"")
   588                       |> not (none_true wfs)
   589                          ? cons ("wf", "\"smart\" or \"false\"")
   590                       |> not codatatypes_ok
   591                          ? cons ("bisim_depth", "a nonnegative value")
   592                  val ss =
   593                    map (fn (name, value) => quote name ^ " set to " ^ value)
   594                        options
   595                in
   596                  print ("Try again with " ^
   597                         space_implode " " (serial_commas "and" ss) ^
   598                         " to confirm that the " ^ word_model ^ " is genuine.")
   599                end
   600              else
   601                print ("Nitpick is unable to guarantee the authenticity of \
   602                       \the " ^ word_model ^ " in the presence of polymorphic \
   603                       \axioms.")
   604            else
   605              ();
   606            NONE)
   607         else
   608           if not genuine then
   609             (Unsynchronized.inc met_potential;
   610              if check_potential then
   611                let
   612                  val status = prove_hol_model scope tac_timeout free_names
   613                                               sel_names rel_table bounds assms_t
   614                in
   615                  (case status of
   616                     SOME true => print ("Confirmation by \"auto\": The above " ^
   617                                         word_model ^ " is genuine.")
   618                   | SOME false => print ("Refutation by \"auto\": The above " ^
   619                                          word_model ^ " is spurious.")
   620                   | NONE => print "No confirmation by \"auto\".");
   621                  status
   622                end
   623              else
   624                NONE)
   625           else
   626             NONE
   627       end
   628     (* int -> int -> int -> bool -> rich_problem list -> int * int * int *)
   629     fun solve_any_problem max_potential max_genuine donno first_time problems =
   630       let
   631         val max_potential = Int.max (0, max_potential)
   632         val max_genuine = Int.max (0, max_genuine)
   633         (* bool -> int * Kodkod.raw_bound list -> bool option *)
   634         fun print_and_check genuine (j, bounds) =
   635           print_and_check_model genuine bounds (snd (nth problems j))
   636         val max_solutions = max_potential + max_genuine
   637                             |> not need_incremental ? curry Int.min 1
   638       in
   639         if max_solutions <= 0 then
   640           (0, 0, donno)
   641         else
   642           case Kodkod.solve_any_problem overlord deadline max_threads
   643                                         max_solutions (map fst problems) of
   644             Kodkod.NotInstalled =>
   645             (print_m install_kodkodi_message;
   646              (max_potential, max_genuine, donno + 1))
   647           | Kodkod.Normal ([], unsat_js) =>
   648             (update_checked_problems problems unsat_js;
   649              (max_potential, max_genuine, donno))
   650           | Kodkod.Normal (sat_ps, unsat_js) =>
   651             let
   652               val (lib_ps, con_ps) =
   653                 List.partition (#liberal o snd o nth problems o fst) sat_ps
   654             in
   655               update_checked_problems problems (unsat_js @ map fst lib_ps);
   656               if null con_ps then
   657                 let
   658                   val num_genuine = take max_potential lib_ps
   659                                     |> map (print_and_check false)
   660                                     |> filter (equal (SOME true)) |> length
   661                   val max_genuine = max_genuine - num_genuine
   662                   val max_potential = max_potential
   663                                       - (length lib_ps - num_genuine)
   664                 in
   665                   if max_genuine <= 0 then
   666                     (0, 0, donno)
   667                   else
   668                     let
   669                       (* "co_js" is the list of conservative problems whose
   670                          liberal pendants couldn't be satisfied and hence that
   671                          most probably can't be satisfied themselves. *)
   672                       val co_js =
   673                         map (fn j => j - 1) unsat_js
   674                         |> filter (fn j =>
   675                                       j >= 0 andalso
   676                                       scopes_equivalent
   677                                           (#scope (snd (nth problems j)))
   678                                           (#scope (snd (nth problems (j + 1)))))
   679                       val bye_js = sort_distinct int_ord (map fst sat_ps @
   680                                                           unsat_js @ co_js)
   681                       val problems =
   682                         problems |> filter_out_indices bye_js
   683                                  |> max_potential <= 0
   684                                     ? filter_out (#liberal o snd)
   685                     in
   686                       solve_any_problem max_potential max_genuine donno false
   687                                         problems
   688                     end
   689                 end
   690               else
   691                 let
   692                   val _ = take max_genuine con_ps
   693                           |> List.app (ignore o print_and_check true)
   694                   val max_genuine = max_genuine - length con_ps
   695                 in
   696                   if max_genuine <= 0 orelse not first_time then
   697                     (0, max_genuine, donno)
   698                   else
   699                     let
   700                       val bye_js = sort_distinct int_ord
   701                                                  (map fst sat_ps @ unsat_js)
   702                       val problems =
   703                         problems |> filter_out_indices bye_js
   704                                  |> filter_out (#liberal o snd)
   705                     in solve_any_problem 0 max_genuine donno false problems end
   706                 end
   707             end
   708           | Kodkod.TimedOut unsat_js =>
   709             (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)
   710           | Kodkod.Interrupted NONE =>
   711             (checked_problems := NONE; do_interrupted ())
   712           | Kodkod.Interrupted (SOME unsat_js) =>
   713             (update_checked_problems problems unsat_js; do_interrupted ())
   714           | Kodkod.Error (s, unsat_js) =>
   715             (update_checked_problems problems unsat_js;
   716              print_v (K ("Kodkod error: " ^ s ^ "."));
   717              (max_potential, max_genuine, donno + 1))
   718       end
   719 
   720     (* int -> int -> scope list -> int * int * int -> int * int * int *)
   721     fun run_batch j n scopes (max_potential, max_genuine, donno) =
   722       let
   723         val _ =
   724           if null scopes then
   725             print_m (K "The scope specification is inconsistent.")
   726           else if verbose then
   727             pprint (Pretty.chunks
   728                 [Pretty.blk (0,
   729                      pstrs ((if n > 1 then
   730                                "Batch " ^ string_of_int (j + 1) ^ " of " ^
   731                                signed_string_of_int n ^ ": "
   732                              else
   733                                "") ^
   734                             "Trying " ^ string_of_int (length scopes) ^
   735                             " scope" ^ plural_s_for_list scopes ^ ":")),
   736                  Pretty.indent indent_size
   737                      (Pretty.chunks (map2
   738                           (fn j => fn scope =>
   739                               Pretty.block (
   740                                   (case pretties_for_scope scope true of
   741                                      [] => [Pretty.str "Empty"]
   742                                    | pretties => pretties) @
   743                                   [Pretty.str (if j = 1 then "." else ";")]))
   744                           (length scopes downto 1) scopes))])
   745           else
   746             ()
   747         (* scope * bool -> rich_problem list * bool
   748            -> rich_problem list * bool *)
   749         fun add_problem_for_scope (scope as {datatypes, ...}, liberal)
   750                                   (problems, donno) =
   751           (check_deadline ();
   752            case problem_for_scope liberal scope of
   753              SOME problem =>
   754              (problems
   755               |> (null problems orelse
   756                   not (Kodkod.problems_equivalent (fst problem)
   757                                                   (fst (hd problems))))
   758                   ? cons problem, donno)
   759            | NONE => (problems, donno + 1))
   760         val (problems, donno) =
   761           fold add_problem_for_scope
   762                (map_product pair scopes
   763                     ((if max_genuine > 0 then [false] else []) @
   764                      (if max_potential > 0 then [true] else [])))
   765                ([], donno)
   766         val _ = Unsynchronized.change generated_problems (append problems)
   767         val _ = Unsynchronized.change generated_scopes (append scopes)
   768       in
   769         solve_any_problem max_potential max_genuine donno true (rev problems)
   770       end
   771 
   772     (* rich_problem list -> scope -> int *)
   773     fun scope_count (problems : rich_problem list) scope =
   774       length (filter (scopes_equivalent scope o #scope o snd) problems)
   775     (* string -> string *)
   776     fun excipit did_so_and_so =
   777       let
   778         (* rich_problem list -> rich_problem list *)
   779         val do_filter =
   780           if !met_potential = max_potential then filter_out (#liberal o snd)
   781           else I
   782         val total = length (!scopes)
   783         val unsat =
   784           fold (fn scope =>
   785                    case scope_count (do_filter (!generated_problems)) scope of
   786                      0 => I
   787                    | n =>
   788                      scope_count (do_filter (these (!checked_problems)))
   789                                  scope = n
   790                      ? Integer.add 1) (!generated_scopes) 0
   791       in
   792         "Nitpick " ^ did_so_and_so ^
   793         (if is_some (!checked_problems) andalso total > 0 then
   794            " after checking " ^
   795            string_of_int (Int.min (total - 1, unsat)) ^ " of " ^
   796            string_of_int total ^ " scope" ^ plural_s total
   797          else
   798            "") ^ "."
   799       end
   800 
   801     (* int -> int -> scope list -> int * int * int -> Kodkod.outcome *)
   802     fun run_batches _ _ [] (max_potential, max_genuine, donno) =
   803         if donno > 0 andalso max_genuine > 0 then
   804           (print_m (fn () => excipit "ran into difficulties"); "unknown")
   805         else if max_genuine = original_max_genuine then
   806           if max_potential = original_max_potential then
   807             (print_m (K ("Nitpick found no " ^ word_model ^ ".")); "none")
   808           else
   809             (print_m (K ("Nitpick could not find " ^
   810                          (if max_genuine = 1 then "a better " ^ word_model ^ "."
   811                           else "any better " ^ word_model ^ "s.")));
   812              "potential")
   813         else
   814           if would_be_genuine then "genuine" else "likely_genuine"
   815       | run_batches j n (batch :: batches) z =
   816         let val (z as (_, max_genuine, _)) = run_batch j n batch z in
   817           run_batches (j + 1) n (if max_genuine > 0 then batches else []) z
   818         end
   819 
   820     val (skipped, the_scopes) =
   821       all_scopes ext_ctxt sym_break cards_assigns maxes_assigns iters_assigns
   822                  bisim_depths mono_Ts nonmono_Ts shallow_dataTs
   823     val _ = if skipped > 0 then
   824               print_m (fn () => "Too many scopes. Dropping " ^
   825                                 string_of_int skipped ^ " scope" ^
   826                                 plural_s skipped ^
   827                                 ". (Consider using \"mono\" or \
   828                                 \\"merge_type_vars\" to prevent this.)")
   829             else
   830               ()
   831     val _ = scopes := the_scopes
   832 
   833     val batches = batch_list batch_size (!scopes)
   834     val outcome_code =
   835       (run_batches 0 (length batches) batches (max_potential, max_genuine, 0)
   836        handle Exn.Interrupt => do_interrupted ())
   837       handle TimeLimit.TimeOut =>
   838              (print_m (fn () => excipit "ran out of time");
   839               if !met_potential > 0 then "potential" else "unknown")
   840            | Exn.Interrupt => if auto orelse debug then raise Interrupt
   841                               else error (excipit "was interrupted")
   842     val _ = print_v (fn () => "Total time: " ^
   843                               signed_string_of_int (Time.toMilliseconds
   844                                     (Timer.checkRealTimer timer)) ^ " ms.")
   845   in (outcome_code, !state_ref) end
   846   handle Exn.Interrupt =>
   847          if auto orelse #debug params then
   848            raise Interrupt
   849          else
   850            if passed_deadline deadline then
   851              (priority "Nitpick ran out of time."; ("unknown", state))
   852            else
   853              error "Nitpick was interrupted."
   854 
   855 (* Proof.state -> params -> bool -> term -> string * Proof.state *)
   856 fun pick_nits_in_term state (params as {debug, timeout, expect, ...})
   857                       auto orig_assm_ts orig_t =
   858   if getenv "KODKODI" = "" then
   859     (if auto then ()
   860      else warning (Pretty.string_of (plazy install_kodkodi_message));
   861      ("unknown", state))
   862   else
   863     let
   864       val deadline = Option.map (curry Time.+ (Time.now ())) timeout
   865       val outcome as (outcome_code, _) =
   866         time_limit (if debug then NONE else timeout)
   867             (pick_them_nits_in_term deadline state params auto orig_assm_ts)
   868             orig_t
   869     in
   870       if expect = "" orelse outcome_code = expect then outcome
   871       else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")
   872     end
   873 
   874 (* Proof.state -> params -> thm -> int -> string * Proof.state *)
   875 fun pick_nits_in_subgoal state params auto subgoal =
   876   let
   877     val ctxt = Proof.context_of state
   878     val t = state |> Proof.raw_goal |> #goal |> prop_of
   879   in
   880     if Logic.count_prems t = 0 then
   881       (priority "No subgoal!"; ("none", state))
   882     else
   883       let
   884         val assms = map term_of (Assumption.all_assms_of ctxt)
   885         val (t, frees) = Logic.goal_params t subgoal
   886       in pick_nits_in_term state params auto assms (subst_bounds (frees, t)) end
   887   end
   888 
   889 end;