src/HOL/Tools/Nitpick/nitpick.ML
author blanchet
Tue May 24 00:01:33 2011 +0200 (2011-05-24 ago)
changeset 42959 ee829022381d
parent 42486 01b03a124b81
child 43020 abb5d1f907e4
permissions -rw-r--r--
use \<emdash> rather than \<midarrow>
     1 (*  Title:      HOL/Tools/Nitpick/nitpick.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2008, 2009, 2010
     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 term_postprocessor = Nitpick_Model.term_postprocessor
    12   type params =
    13     {cards_assigns: (typ option * int list) list,
    14      maxes_assigns: (styp option * int list) list,
    15      iters_assigns: (styp option * int list) list,
    16      bitss: int list,
    17      bisim_depths: int list,
    18      boxes: (typ option * bool option) list,
    19      finitizes: (typ option * bool option) list,
    20      monos: (typ option * bool option) list,
    21      stds: (typ option * bool) list,
    22      wfs: (styp option * bool option) list,
    23      sat_solver: string,
    24      blocking: bool,
    25      falsify: bool,
    26      debug: bool,
    27      verbose: bool,
    28      overlord: bool,
    29      user_axioms: bool option,
    30      assms: bool,
    31      whacks: term list,
    32      merge_type_vars: bool,
    33      binary_ints: bool option,
    34      destroy_constrs: bool,
    35      specialize: bool,
    36      star_linear_preds: bool,
    37      total_consts: bool option,
    38      needs: term list option,
    39      peephole_optim: bool,
    40      datatype_sym_break: int,
    41      kodkod_sym_break: int,
    42      timeout: Time.time option,
    43      tac_timeout: Time.time option,
    44      max_threads: int,
    45      show_datatypes: bool,
    46      show_skolems: bool,
    47      show_consts: bool,
    48      evals: term list,
    49      formats: (term option * int list) list,
    50      atomss: (typ option * string list) list,
    51      max_potential: int,
    52      max_genuine: int,
    53      check_potential: bool,
    54      check_genuine: bool,
    55      batch_size: int,
    56      expect: string}
    57 
    58   val register_frac_type : string -> (string * string) list -> theory -> theory
    59   val unregister_frac_type : string -> theory -> theory
    60   val register_codatatype : typ -> string -> styp list -> theory -> theory
    61   val unregister_codatatype : typ -> theory -> theory
    62   val register_term_postprocessor :
    63     typ -> term_postprocessor -> theory -> theory
    64   val unregister_term_postprocessor : typ -> theory -> theory
    65   val pick_nits_in_term :
    66     Proof.state -> params -> bool -> int -> int -> int -> (term * term) list
    67     -> term list -> term -> string * Proof.state
    68   val pick_nits_in_subgoal :
    69     Proof.state -> params -> bool -> int -> int -> string * Proof.state
    70 end;
    71 
    72 structure Nitpick : NITPICK =
    73 struct
    74 
    75 open Nitpick_Util
    76 open Nitpick_HOL
    77 open Nitpick_Preproc
    78 open Nitpick_Mono
    79 open Nitpick_Scope
    80 open Nitpick_Peephole
    81 open Nitpick_Rep
    82 open Nitpick_Nut
    83 open Nitpick_Kodkod
    84 open Nitpick_Model
    85 
    86 structure KK = Kodkod
    87 
    88 type params =
    89   {cards_assigns: (typ option * int list) list,
    90    maxes_assigns: (styp option * int list) list,
    91    iters_assigns: (styp option * int list) list,
    92    bitss: int list,
    93    bisim_depths: int list,
    94    boxes: (typ option * bool option) list,
    95    finitizes: (typ option * bool option) list,
    96    monos: (typ option * bool option) list,
    97    stds: (typ option * bool) list,
    98    wfs: (styp option * bool option) list,
    99    sat_solver: string,
   100    blocking: bool,
   101    falsify: bool,
   102    debug: bool,
   103    verbose: bool,
   104    overlord: bool,
   105    user_axioms: bool option,
   106    assms: bool,
   107    whacks: term list,
   108    merge_type_vars: bool,
   109    binary_ints: bool option,
   110    destroy_constrs: bool,
   111    specialize: bool,
   112    star_linear_preds: bool,
   113    total_consts: bool option,
   114    needs: term list option,
   115    peephole_optim: bool,
   116    datatype_sym_break: int,
   117    kodkod_sym_break: int,
   118    timeout: Time.time option,
   119    tac_timeout: Time.time option,
   120    max_threads: int,
   121    show_datatypes: bool,
   122    show_skolems: bool,
   123    show_consts: bool,
   124    evals: term list,
   125    formats: (term option * int list) list,
   126    atomss: (typ option * string list) list,
   127    max_potential: int,
   128    max_genuine: int,
   129    check_potential: bool,
   130    check_genuine: bool,
   131    batch_size: int,
   132    expect: string}
   133 
   134 (* TODO: eliminate these historical aliases *)
   135 val register_frac_type = Nitpick_HOL.register_frac_type_global
   136 val unregister_frac_type = Nitpick_HOL.unregister_frac_type_global
   137 val register_codatatype = Nitpick_HOL.register_codatatype_global
   138 val unregister_codatatype = Nitpick_HOL.unregister_codatatype_global
   139 val register_term_postprocessor =
   140   Nitpick_Model.register_term_postprocessor_global
   141 val unregister_term_postprocessor =
   142   Nitpick_Model.unregister_term_postprocessor_global
   143 
   144 type problem_extension =
   145   {free_names: nut list,
   146    sel_names: nut list,
   147    nonsel_names: nut list,
   148    rel_table: nut NameTable.table,
   149    unsound: bool,
   150    scope: scope}
   151 
   152 type rich_problem = KK.problem * problem_extension
   153 
   154 fun pretties_for_formulas _ _ [] = []
   155   | pretties_for_formulas ctxt s ts =
   156     [Pretty.str (s ^ plural_s_for_list ts ^ ":"),
   157      Pretty.indent indent_size (Pretty.chunks
   158          (map2 (fn j => fn t =>
   159                    Pretty.block [t |> shorten_names_in_term
   160                                    |> Syntax.pretty_term ctxt,
   161                                  Pretty.str (if j = 1 then "." else ";")])
   162                (length ts downto 1) ts))]
   163 
   164 fun install_java_message () =
   165   "Nitpick requires a Java 1.5 virtual machine called \"java\"."
   166 fun install_kodkodi_message () =
   167   "Nitpick requires the external Java program Kodkodi. To install it, download \
   168   \the package from Isabelle's web page and add the \"kodkodi-x.y.z\" \
   169   \directory's full path to " ^
   170   Path.print (Path.expand (Path.appends
   171       (Path.variable "ISABELLE_HOME_USER" ::
   172        map Path.basic ["etc", "components"]))) ^ " on a line of its own."
   173 
   174 val max_unsound_delay_ms = 200
   175 val max_unsound_delay_percent = 2
   176 
   177 fun unsound_delay_for_timeout NONE = max_unsound_delay_ms
   178   | unsound_delay_for_timeout (SOME timeout) =
   179     Int.max (0, Int.min (max_unsound_delay_ms,
   180                          Time.toMilliseconds timeout
   181                          * max_unsound_delay_percent div 100))
   182 
   183 fun passed_deadline NONE = false
   184   | passed_deadline (SOME time) = Time.compare (Time.now (), time) <> LESS
   185 
   186 fun none_true assigns = forall (not_equal (SOME true) o snd) assigns
   187 
   188 fun has_lonely_bool_var (@{const Pure.conjunction}
   189                          $ (@{const Trueprop} $ Free _) $ _) = true
   190   | has_lonely_bool_var _ = false
   191 
   192 val syntactic_sorts =
   193   @{sort "{default,zero,one,plus,minus,uminus,times,inverse,abs,sgn,ord,equal}"} @
   194   @{sort number}
   195 fun has_tfree_syntactic_sort (TFree (_, S as _ :: _)) =
   196     subset (op =) (S, syntactic_sorts)
   197   | has_tfree_syntactic_sort _ = false
   198 val has_syntactic_sorts = exists_type (exists_subtype has_tfree_syntactic_sort)
   199 
   200 fun plazy f = Pretty.blk (0, pstrs (f ()))
   201 
   202 fun pick_them_nits_in_term deadline state (params : params) auto i n step
   203                            subst assm_ts orig_t =
   204   let
   205     val timer = Timer.startRealTimer ()
   206     val thy = Proof.theory_of state
   207     val ctxt = Proof.context_of state
   208 (* FIXME: reintroduce code before new release:
   209 
   210     val nitpick_thy = Thy_Info.get_theory "Nitpick"
   211     val _ = Theory.subthy (nitpick_thy, thy) orelse
   212             error "You must import the theory \"Nitpick\" to use Nitpick"
   213 *)
   214     val {cards_assigns, maxes_assigns, iters_assigns, bitss, bisim_depths,
   215          boxes, finitizes, monos, stds, wfs, sat_solver, falsify, debug,
   216          verbose, overlord, user_axioms, assms, whacks, merge_type_vars,
   217          binary_ints, destroy_constrs, specialize, star_linear_preds,
   218          total_consts, needs, peephole_optim, datatype_sym_break,
   219          kodkod_sym_break, tac_timeout, max_threads, show_datatypes,
   220          show_skolems, show_consts, evals, formats, atomss, max_potential,
   221          max_genuine, check_potential, check_genuine, batch_size, ...} = params
   222     val state_ref = Unsynchronized.ref state
   223     val pprint =
   224       if auto then
   225         Unsynchronized.change state_ref o Proof.goal_message o K
   226         o Pretty.chunks o cons (Pretty.str "") o single
   227         o Pretty.mark Markup.hilite
   228       else
   229         (fn s => (Output.urgent_message s; if debug then tracing s else ()))
   230         o Pretty.string_of
   231     fun pprint_m f = () |> not auto ? pprint o f
   232     fun pprint_v f = () |> verbose ? pprint o f
   233     fun pprint_d f = () |> debug ? pprint o f
   234     val print = pprint o curry Pretty.blk 0 o pstrs
   235 (*
   236     val print_g = pprint o Pretty.str
   237 *)
   238     val print_m = pprint_m o K o plazy
   239     val print_v = pprint_v o K o plazy
   240 
   241     fun check_deadline () =
   242       if passed_deadline deadline then raise TimeLimit.TimeOut else ()
   243 
   244     val assm_ts = if assms orelse auto then assm_ts else []
   245     val _ =
   246       if step = 0 then
   247         print_m (fn () => "Nitpicking formula...")
   248       else
   249         pprint_m (fn () => Pretty.chunks (
   250             pretties_for_formulas ctxt ("Nitpicking " ^
   251                 (if i <> 1 orelse n <> 1 then
   252                    "subgoal " ^ string_of_int i ^ " of " ^ string_of_int n
   253                  else
   254                    "goal")) [Logic.list_implies (assm_ts, orig_t)]))
   255     val _ = print_v (enclose "Timestamp: " "." o Date.fmt "%H:%M:%S"
   256                      o Date.fromTimeLocal o Time.now)
   257     val neg_t = if falsify then Logic.mk_implies (orig_t, @{prop False})
   258                 else orig_t
   259     val conj_ts = neg_t :: assm_ts @ evals @ these needs
   260     val tfree_table =
   261       if merge_type_vars then merged_type_var_table_for_terms thy conj_ts
   262       else []
   263     val merge_tfrees = merge_type_vars_in_term thy merge_type_vars tfree_table
   264     val neg_t = neg_t |> merge_tfrees
   265     val assm_ts = assm_ts |> map merge_tfrees
   266     val evals = evals |> map merge_tfrees
   267     val needs = needs |> Option.map (map merge_tfrees)
   268     val conj_ts = neg_t :: assm_ts @ evals @ these needs
   269     val original_max_potential = max_potential
   270     val original_max_genuine = max_genuine
   271     val max_bisim_depth = fold Integer.max bisim_depths ~1
   272     val case_names = case_const_names ctxt stds
   273     val defs = all_defs_of thy subst
   274     val nondefs = all_nondefs_of ctxt subst
   275     val def_tables = const_def_tables ctxt subst defs
   276     val nondef_table = const_nondef_table nondefs
   277     val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)
   278     val psimp_table = const_psimp_table ctxt subst
   279     val choice_spec_table = const_choice_spec_table ctxt subst
   280     val nondefs =
   281       nondefs |> filter_out (is_choice_spec_axiom thy choice_spec_table)
   282     val intro_table = inductive_intro_table ctxt subst def_tables
   283     val ground_thm_table = ground_theorem_table thy
   284     val ersatz_table = ersatz_table ctxt
   285     val hol_ctxt as {wf_cache, ...} =
   286       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   287        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
   288        whacks = whacks, binary_ints = binary_ints,
   289        destroy_constrs = destroy_constrs, specialize = specialize,
   290        star_linear_preds = star_linear_preds, total_consts = total_consts,
   291        needs = needs, tac_timeout = tac_timeout, evals = evals,
   292        case_names = case_names, def_tables = def_tables,
   293        nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
   294        psimp_table = psimp_table, choice_spec_table = choice_spec_table,
   295        intro_table = intro_table, ground_thm_table = ground_thm_table,
   296        ersatz_table = ersatz_table, skolems = Unsynchronized.ref [],
   297        special_funs = Unsynchronized.ref [],
   298        unrolled_preds = Unsynchronized.ref [], wf_cache = Unsynchronized.ref [],
   299        constr_cache = Unsynchronized.ref []}
   300     val pseudo_frees = []
   301     val real_frees = fold Term.add_frees conj_ts []
   302     val _ = null (fold Term.add_tvars conj_ts []) orelse
   303             error "Nitpick cannot handle goals with schematic type variables."
   304     val (nondef_ts, def_ts, need_ts, got_all_mono_user_axioms,
   305          no_poly_user_axioms, binarize) =
   306       preprocess_formulas hol_ctxt assm_ts neg_t
   307     val got_all_user_axioms =
   308       got_all_mono_user_axioms andalso no_poly_user_axioms
   309 
   310     fun print_wf (x, (gfp, wf)) =
   311       pprint (Pretty.blk (0,
   312           pstrs ("The " ^ (if gfp then "co" else "") ^ "inductive predicate \"")
   313           @ Syntax.pretty_term ctxt (Const x) ::
   314           pstrs (if wf then
   315                    "\" was proved well-founded. Nitpick can compute it \
   316                    \efficiently."
   317                  else
   318                    "\" could not be proved well-founded. Nitpick might need to \
   319                    \unroll it.")))
   320     val _ = if verbose then List.app print_wf (!wf_cache) else ()
   321     val das_wort_formula = if falsify then "Negated conjecture" else "Formula"
   322     val _ =
   323       pprint_d (fn () => Pretty.chunks
   324           (pretties_for_formulas ctxt das_wort_formula [hd nondef_ts] @
   325            pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @
   326            pretties_for_formulas ctxt "Relevant nondefinitional axiom"
   327                                  (tl nondef_ts)))
   328     val _ = List.app (ignore o Term.type_of) (nondef_ts @ def_ts)
   329             handle TYPE (_, Ts, ts) =>
   330                    raise TYPE ("Nitpick.pick_them_nits_in_term", Ts, ts)
   331 
   332     val nondef_us = nondef_ts |> map (nut_from_term hol_ctxt Eq)
   333     val def_us = def_ts |> map (nut_from_term hol_ctxt DefEq)
   334     val need_us = need_ts |> map (nut_from_term hol_ctxt Eq)
   335     val (free_names, const_names) =
   336       fold add_free_and_const_names (nondef_us @ def_us @ need_us) ([], [])
   337     val (sel_names, nonsel_names) =
   338       List.partition (is_sel o nickname_of) const_names
   339     val sound_finitizes =
   340       none_true (filter_out (fn (SOME (Type (@{type_name fun}, _)), _) => true
   341                           | _ => false) finitizes)
   342     val standard = forall snd stds
   343 (*
   344     val _ =
   345       List.app (print_g o string_for_nut ctxt) (nondef_us @ def_us @ need_us)
   346 *)
   347 
   348     val unique_scope = forall (curry (op =) 1 o length o snd) cards_assigns
   349     fun monotonicity_message Ts extra =
   350       let val pretties = map (pretty_maybe_quote o pretty_for_type ctxt) Ts in
   351         Pretty.blk (0,
   352           pstrs ("The type" ^ plural_s_for_list pretties ^ " ") @
   353           pretty_serial_commas "and" pretties @
   354           pstrs (" " ^
   355                  (if none_true monos then
   356                     "passed the monotonicity test"
   357                   else
   358                     (if length pretties = 1 then "is" else "are") ^
   359                     " considered monotonic") ^
   360                  ". " ^ extra))
   361       end
   362     fun is_type_fundamentally_monotonic T =
   363       (is_datatype ctxt stds T andalso not (is_quot_type ctxt T) andalso
   364        (not (is_pure_typedef ctxt T) orelse is_univ_typedef ctxt T)) orelse
   365       is_number_type ctxt T orelse is_bit_type T
   366     fun is_type_actually_monotonic T =
   367       formulas_monotonic hol_ctxt binarize T (nondef_ts, def_ts)
   368     fun is_type_kind_of_monotonic T =
   369       case triple_lookup (type_match thy) monos T of
   370         SOME (SOME false) => false
   371       | _ => is_type_actually_monotonic T
   372     fun is_type_monotonic T =
   373       unique_scope orelse
   374       case triple_lookup (type_match thy) monos T of
   375         SOME (SOME b) => b
   376       | _ => is_type_fundamentally_monotonic T orelse
   377              is_type_actually_monotonic T
   378     fun is_deep_datatype_finitizable T =
   379       triple_lookup (type_match thy) finitizes T = SOME (SOME true)
   380     fun is_shallow_datatype_finitizable (T as Type (@{type_name fun_box}, _)) =
   381         is_type_kind_of_monotonic T
   382       | is_shallow_datatype_finitizable T =
   383         case triple_lookup (type_match thy) finitizes T of
   384           SOME (SOME b) => b
   385         | _ => is_type_kind_of_monotonic T
   386     fun is_datatype_deep T =
   387       not standard orelse T = nat_T orelse is_word_type T orelse
   388       exists (curry (op =) T o domain_type o type_of) sel_names
   389     val all_Ts = ground_types_in_terms hol_ctxt binarize (nondef_ts @ def_ts)
   390                  |> sort Term_Ord.typ_ord
   391     val _ =
   392       if verbose andalso binary_ints = SOME true andalso
   393          exists (member (op =) [nat_T, int_T]) all_Ts then
   394         print_v (K "The option \"binary_ints\" will be ignored because of the \
   395                    \presence of rationals, reals, \"Suc\", \"gcd\", or \"lcm\" \
   396                    \in the problem or because of the \"non_std\" option.")
   397       else
   398         ()
   399     val _ =
   400       if not auto andalso
   401          exists (fn Type (@{type_name Datatype.node}, _) => true | _ => false)
   402                 all_Ts then
   403         print_m (K ("Warning: The problem involves directly or indirectly the \
   404                     \internal type " ^ quote @{type_name Datatype.node} ^
   405                     ". This type is very Nitpick-unfriendly, and its presence \
   406                     \usually indicates either a failure of abstraction or a \
   407                     \quirk in Nitpick."))
   408       else
   409         ()
   410     val (mono_Ts, nonmono_Ts) = List.partition is_type_monotonic all_Ts
   411     val _ =
   412       if verbose andalso not unique_scope then
   413         case filter_out is_type_fundamentally_monotonic mono_Ts of
   414           [] => ()
   415         | interesting_mono_Ts =>
   416           pprint_v (K (monotonicity_message interesting_mono_Ts
   417                           "Nitpick might be able to skip some scopes."))
   418       else
   419         ()
   420     val (deep_dataTs, shallow_dataTs) =
   421       all_Ts |> filter (is_datatype ctxt stds)
   422              |> List.partition is_datatype_deep
   423     val finitizable_dataTs =
   424       (deep_dataTs |> filter_out (is_finite_type hol_ctxt)
   425                    |> filter is_deep_datatype_finitizable) @
   426       (shallow_dataTs |> filter_out (is_finite_type hol_ctxt)
   427                       |> filter is_shallow_datatype_finitizable)
   428     val _ =
   429       if verbose andalso not (null finitizable_dataTs) then
   430         pprint_v (K (monotonicity_message finitizable_dataTs
   431                          "Nitpick can use a more precise finite encoding."))
   432       else
   433         ()
   434     (* This detection code is an ugly hack. Fortunately, it is used only to
   435        provide a hint to the user. *)
   436     fun is_struct_induct_step (name, (Rule_Cases.Case {fixes, assumes, ...}, _)) =
   437       not (null fixes) andalso
   438       exists (String.isSuffix ".hyps" o fst) assumes andalso
   439       exists (exists (curry (op =) name o shortest_name o fst)
   440               o datatype_constrs hol_ctxt) deep_dataTs
   441     val likely_in_struct_induct_step =
   442       exists is_struct_induct_step (Proof_Context.cases_of ctxt)
   443     val _ = if standard andalso likely_in_struct_induct_step then
   444               pprint_m (fn () => Pretty.blk (0,
   445                   pstrs "Hint: To check that the induction hypothesis is \
   446                         \general enough, try this command: " @
   447                   [Pretty.mark Markup.sendback (Pretty.blk (0,
   448                        pstrs ("nitpick [non_std, show_all]")))] @ pstrs "."))
   449             else
   450               ()
   451 (*
   452     val _ = print_g "Monotonic types:"
   453     val _ = List.app (print_g o string_for_type ctxt) mono_Ts
   454     val _ = print_g "Nonmonotonic types:"
   455     val _ = List.app (print_g o string_for_type ctxt) nonmono_Ts
   456 *)
   457 
   458     val incremental = Int.max (max_potential, max_genuine) >= 2
   459     val actual_sat_solver =
   460       if sat_solver <> "smart" then
   461         if incremental andalso
   462            not (member (op =) (Kodkod_SAT.configured_sat_solvers true)
   463                        sat_solver) then
   464           (print_m (K ("An incremental SAT solver is required: \"SAT4J\" will \
   465                        \be used instead of " ^ quote sat_solver ^ "."));
   466            "SAT4J")
   467         else
   468           sat_solver
   469       else
   470         Kodkod_SAT.smart_sat_solver_name incremental
   471     val _ =
   472       if sat_solver = "smart" then
   473         print_v (fn () =>
   474             "Using SAT solver " ^ quote actual_sat_solver ^ ". The following" ^
   475             (if incremental then " incremental " else " ") ^
   476             "solvers are configured: " ^
   477             commas_quote (Kodkod_SAT.configured_sat_solvers incremental) ^ ".")
   478       else
   479         ()
   480 
   481     val too_big_scopes = Unsynchronized.ref []
   482 
   483     fun problem_for_scope unsound
   484             (scope as {card_assigns, bits, bisim_depth, datatypes, ofs, ...}) =
   485       let
   486         val _ = not (exists (fn other => scope_less_eq other scope)
   487                             (!too_big_scopes)) orelse
   488                 raise TOO_LARGE ("Nitpick.pick_them_nits_in_term.\
   489                                  \problem_for_scope", "too large scope")
   490 (*
   491         val _ = print_g "Offsets:"
   492         val _ = List.app (fn (T, j0) =>
   493                              print_g (string_for_type ctxt T ^ " = " ^
   494                                     string_of_int j0))
   495                          (Typtab.dest ofs)
   496 *)
   497         val effective_total_consts =
   498           case total_consts of
   499             SOME b => b
   500           | NONE => forall (is_exact_type datatypes true) all_Ts
   501         val main_j0 = offset_of_type ofs bool_T
   502         val (nat_card, nat_j0) = spec_of_type scope nat_T
   503         val (int_card, int_j0) = spec_of_type scope int_T
   504         val _ = (nat_j0 = main_j0 andalso int_j0 = main_j0) orelse
   505                 raise BAD ("Nitpick.pick_them_nits_in_term.problem_for_scope",
   506                            "bad offsets")
   507         val kk = kodkod_constrs peephole_optim nat_card int_card main_j0
   508         val (free_names, rep_table) =
   509           choose_reps_for_free_vars scope pseudo_frees free_names
   510                                     NameTable.empty
   511         val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table
   512         val (nonsel_names, rep_table) =
   513           choose_reps_for_consts scope effective_total_consts nonsel_names
   514                                  rep_table
   515         val (guiltiest_party, min_highest_arity) =
   516           NameTable.fold (fn (name, R) => fn (s, n) =>
   517                              let val n' = arity_of_rep R in
   518                                if n' > n then (nickname_of name, n') else (s, n)
   519                              end) rep_table ("", 1)
   520         val min_univ_card =
   521           NameTable.fold (Integer.max o min_univ_card_of_rep o snd) rep_table
   522                          (univ_card nat_card int_card main_j0 [] KK.True)
   523         val _ = if debug then ()
   524                 else check_arity guiltiest_party min_univ_card min_highest_arity
   525 
   526         val def_us =
   527           def_us |> map (choose_reps_in_nut scope unsound rep_table true)
   528         val nondef_us =
   529           nondef_us |> map (choose_reps_in_nut scope unsound rep_table false)
   530         val need_us =
   531           need_us |> map (choose_reps_in_nut scope unsound rep_table false)
   532 (*
   533         val _ = List.app (print_g o string_for_nut ctxt)
   534                          (free_names @ sel_names @ nonsel_names @
   535                           nondef_us @ def_us @ need_us)
   536 *)
   537         val (free_rels, pool, rel_table) =
   538           rename_free_vars free_names initial_pool NameTable.empty
   539         val (sel_rels, pool, rel_table) =
   540           rename_free_vars sel_names pool rel_table
   541         val (other_rels, pool, rel_table) =
   542           rename_free_vars nonsel_names pool rel_table
   543         val nondef_us = nondef_us |> map (rename_vars_in_nut pool rel_table)
   544         val def_us = def_us |> map (rename_vars_in_nut pool rel_table)
   545         val need_us = need_us |> map (rename_vars_in_nut pool rel_table)
   546         val nondef_fs = map (kodkod_formula_from_nut ofs kk) nondef_us
   547         val def_fs = map (kodkod_formula_from_nut ofs kk) def_us
   548         val formula = fold (fold s_and) [def_fs, nondef_fs] KK.True
   549         val comment = (if unsound then "unsound" else "sound") ^ "\n" ^
   550                       Print_Mode.setmp [] multiline_string_for_scope scope
   551         val kodkod_sat_solver =
   552           Kodkod_SAT.sat_solver_spec actual_sat_solver |> snd
   553         val bit_width = if bits = 0 then 16 else bits + 1
   554         val delay =
   555           if unsound then
   556             Option.map (fn time => Time.- (time, Time.now ())) deadline
   557             |> unsound_delay_for_timeout
   558           else
   559             0
   560         val settings = [("solver", commas_quote kodkod_sat_solver),
   561                         ("bit_width", string_of_int bit_width),
   562                         ("symmetry_breaking", string_of_int kodkod_sym_break),
   563                         ("sharing", "3"),
   564                         ("flatten", "false"),
   565                         ("delay", signed_string_of_int delay)]
   566         val plain_rels = free_rels @ other_rels
   567         val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels
   568         val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels
   569         val need_vals =
   570           map (fn dtype as {typ, ...} =>
   571                   (typ, needed_values_for_datatype need_us ofs dtype)) datatypes
   572         val sel_bounds =
   573           map (bound_for_sel_rel ctxt debug need_vals datatypes) sel_rels
   574         val dtype_axioms =
   575           declarative_axioms_for_datatypes hol_ctxt binarize need_us need_vals
   576               datatype_sym_break bits ofs kk rel_table datatypes
   577         val declarative_axioms = plain_axioms @ dtype_axioms
   578         val univ_card = Int.max (univ_card nat_card int_card main_j0
   579                                      (plain_bounds @ sel_bounds) formula,
   580                                  main_j0 |> bits > 0 ? Integer.add (bits + 1))
   581         val (built_in_bounds, built_in_axioms) =
   582           bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card
   583               nat_card int_card main_j0 (formula :: declarative_axioms)
   584         val bounds = built_in_bounds @ plain_bounds @ sel_bounds
   585                      |> not debug ? merge_bounds
   586         val axioms = built_in_axioms @ declarative_axioms
   587         val highest_arity =
   588           fold Integer.max (map (fst o fst) (maps fst bounds)) 0
   589         val formula = fold_rev s_and axioms formula
   590         val _ = if bits = 0 then () else check_bits bits formula
   591         val _ = if debug orelse formula = KK.False then ()
   592                 else check_arity "" univ_card highest_arity
   593       in
   594         SOME ({comment = comment, settings = settings, univ_card = univ_card,
   595                tuple_assigns = [], bounds = bounds,
   596                int_bounds = if bits = 0 then sequential_int_bounds univ_card
   597                             else pow_of_two_int_bounds bits main_j0,
   598                expr_assigns = [], formula = formula},
   599               {free_names = free_names, sel_names = sel_names,
   600                nonsel_names = nonsel_names, rel_table = rel_table,
   601                unsound = unsound, scope = scope})
   602       end
   603       handle TOO_LARGE (loc, msg) =>
   604              if loc = "Nitpick_Kodkod.check_arity" andalso
   605                 not (Typtab.is_empty ofs) then
   606                problem_for_scope unsound
   607                    {hol_ctxt = hol_ctxt, binarize = binarize,
   608                     card_assigns = card_assigns, bits = bits,
   609                     bisim_depth = bisim_depth, datatypes = datatypes,
   610                     ofs = Typtab.empty}
   611              else if loc = "Nitpick.pick_them_nits_in_term.\
   612                            \problem_for_scope" then
   613                NONE
   614              else
   615                (Unsynchronized.change too_big_scopes (cons scope);
   616                 print_v (fn () =>
   617                     "Limit reached: " ^ msg ^ ". Skipping " ^
   618                     (if unsound then "potential component of " else "") ^
   619                     "scope.");
   620                 NONE)
   621            | TOO_SMALL (_, msg) =>
   622              (print_v (fn () =>
   623                   "Limit reached: " ^ msg ^ ". Skipping " ^
   624                   (if unsound then "potential component of " else "") ^
   625                   "scope.");
   626               NONE)
   627 
   628     val das_wort_model =
   629       (if falsify then "counterexample" else "model")
   630       |> not standard ? prefix "nonstandard "
   631 
   632     val scopes = Unsynchronized.ref []
   633     val generated_scopes = Unsynchronized.ref []
   634     val generated_problems = Unsynchronized.ref ([] : rich_problem list)
   635     val checked_problems = Unsynchronized.ref (SOME [])
   636     val met_potential = Unsynchronized.ref 0
   637 
   638     fun update_checked_problems problems =
   639       List.app (Unsynchronized.change checked_problems o Option.map o cons
   640                 o nth problems)
   641     fun show_kodkod_warning "" = ()
   642       | show_kodkod_warning s = print_m (fn () => "Kodkod warning: " ^ s ^ ".")
   643 
   644     fun print_and_check_model genuine bounds
   645             ({free_names, sel_names, nonsel_names, rel_table, scope, ...}
   646              : problem_extension) =
   647       let
   648         val (reconstructed_model, codatatypes_ok) =
   649           reconstruct_hol_model
   650               {show_datatypes = show_datatypes, show_skolems = show_skolems,
   651                show_consts = show_consts}
   652               scope formats atomss real_frees pseudo_frees free_names sel_names
   653               nonsel_names rel_table bounds
   654         val genuine_means_genuine =
   655           got_all_user_axioms andalso none_true wfs andalso
   656           sound_finitizes andalso total_consts <> SOME true andalso
   657           codatatypes_ok
   658         fun assms_prop () = Logic.mk_conjunction_list (neg_t :: assm_ts)
   659       in
   660         (pprint (Pretty.chunks
   661              [Pretty.blk (0,
   662                   (pstrs ((if auto then "Auto " else "") ^ "Nitpick found a" ^
   663                           (if not genuine then " potentially spurious "
   664                            else if genuine_means_genuine then " "
   665                            else " quasi genuine ") ^ das_wort_model) @
   666                    (case pretties_for_scope scope verbose of
   667                       [] => []
   668                     | pretties => pstrs " for " @ pretties) @
   669                    [Pretty.str ":\n"])),
   670               Pretty.indent indent_size reconstructed_model]);
   671          if genuine then
   672            (if check_genuine andalso standard then
   673               case prove_hol_model scope tac_timeout free_names sel_names
   674                                    rel_table bounds (assms_prop ()) of
   675                 SOME true =>
   676                 print ("Confirmation by \"auto\": The above " ^
   677                        das_wort_model ^ " is really genuine.")
   678               | SOME false =>
   679                 if genuine_means_genuine then
   680                   error ("A supposedly genuine " ^ das_wort_model ^ " was \
   681                          \shown to be spurious by \"auto\".\nThis should never \
   682                          \happen.\nPlease send a bug report to blanchet\
   683                          \te@in.tum.de.")
   684                  else
   685                    print ("Refutation by \"auto\": The above " ^
   686                           das_wort_model ^ " is spurious.")
   687                | NONE => print "No confirmation by \"auto\"."
   688             else
   689               ();
   690             if not standard andalso likely_in_struct_induct_step then
   691               print "The existence of a nonstandard model suggests that the \
   692                     \induction hypothesis is not general enough or may even be \
   693                     \wrong. See the Nitpick manual's \"Inductive Properties\" \
   694                     \section for details (\"isabelle doc nitpick\")."
   695             else
   696               ();
   697             if has_lonely_bool_var orig_t then
   698               print "Hint: Maybe you forgot a colon after the lemma's name?"
   699             else if has_syntactic_sorts orig_t then
   700               print "Hint: Maybe you forgot a type constraint?"
   701             else
   702               ();
   703             if not genuine_means_genuine then
   704               if no_poly_user_axioms then
   705                 let
   706                   val options =
   707                     [] |> not got_all_mono_user_axioms
   708                           ? cons ("user_axioms", "\"true\"")
   709                        |> not (none_true wfs)
   710                           ? cons ("wf", "\"smart\" or \"false\"")
   711                        |> not sound_finitizes
   712                           ? cons ("finitize", "\"smart\" or \"false\"")
   713                        |> total_consts = SOME true
   714                           ? cons ("total_consts", "\"smart\" or \"false\"")
   715                        |> not codatatypes_ok
   716                           ? cons ("bisim_depth", "a nonnegative value")
   717                   val ss =
   718                     map (fn (name, value) => quote name ^ " set to " ^ value)
   719                         options
   720                 in
   721                   print ("Try again with " ^
   722                          space_implode " " (serial_commas "and" ss) ^
   723                          " to confirm that the " ^ das_wort_model ^
   724                          " is genuine.")
   725                 end
   726               else
   727                 print ("Nitpick is unable to guarantee the authenticity of \
   728                        \the " ^ das_wort_model ^ " in the presence of \
   729                        \polymorphic axioms.")
   730             else
   731               ();
   732             NONE)
   733          else
   734            if not genuine then
   735              (Unsynchronized.inc met_potential;
   736               if check_potential then
   737                 let
   738                   val status = prove_hol_model scope tac_timeout free_names
   739                                                sel_names rel_table bounds
   740                                                (assms_prop ())
   741                 in
   742                   (case status of
   743                      SOME true => print ("Confirmation by \"auto\": The \
   744                                          \above " ^ das_wort_model ^
   745                                          " is genuine.")
   746                    | SOME false => print ("Refutation by \"auto\": The above " ^
   747                                           das_wort_model ^ " is spurious.")
   748                    | NONE => print "No confirmation by \"auto\".");
   749                   status
   750                 end
   751               else
   752                 NONE)
   753            else
   754              NONE)
   755         |> pair genuine_means_genuine
   756       end
   757     fun solve_any_problem (found_really_genuine, max_potential, max_genuine,
   758                            donno) first_time problems =
   759       let
   760         val max_potential = Int.max (0, max_potential)
   761         val max_genuine = Int.max (0, max_genuine)
   762         fun print_and_check genuine (j, bounds) =
   763           print_and_check_model genuine bounds (snd (nth problems j))
   764         val max_solutions = max_potential + max_genuine
   765                             |> not incremental ? Integer.min 1
   766       in
   767         if max_solutions <= 0 then
   768           (found_really_genuine, 0, 0, donno)
   769         else
   770           case KK.solve_any_problem debug overlord deadline max_threads
   771                                     max_solutions (map fst problems) of
   772             KK.JavaNotInstalled =>
   773             (print_m install_java_message;
   774              (found_really_genuine, max_potential, max_genuine, donno + 1))
   775           | KK.JavaTooOld =>
   776             (print_m install_java_message;
   777              (found_really_genuine, max_potential, max_genuine, donno + 1))
   778           | KK.KodkodiNotInstalled =>
   779             (print_m install_kodkodi_message;
   780              (found_really_genuine, max_potential, max_genuine, donno + 1))
   781           | KK.Normal ([], unsat_js, s) =>
   782             (update_checked_problems problems unsat_js; show_kodkod_warning s;
   783              (found_really_genuine, max_potential, max_genuine, donno))
   784           | KK.Normal (sat_ps, unsat_js, s) =>
   785             let
   786               val (lib_ps, con_ps) =
   787                 List.partition (#unsound o snd o nth problems o fst) sat_ps
   788             in
   789               update_checked_problems problems (unsat_js @ map fst lib_ps);
   790               show_kodkod_warning s;
   791               if null con_ps then
   792                 let
   793                   val genuine_codes =
   794                     lib_ps |> take max_potential
   795                            |> map (print_and_check false)
   796                            |> filter (curry (op =) (SOME true) o snd)
   797                   val found_really_genuine =
   798                     found_really_genuine orelse exists fst genuine_codes
   799                   val num_genuine = length genuine_codes
   800                   val max_genuine = max_genuine - num_genuine
   801                   val max_potential = max_potential
   802                                       - (length lib_ps - num_genuine)
   803                 in
   804                   if max_genuine <= 0 then
   805                     (found_really_genuine, 0, 0, donno)
   806                   else
   807                     let
   808                       (* "co_js" is the list of sound problems whose unsound
   809                          pendants couldn't be satisfied and hence that most
   810                          probably can't be satisfied themselves. *)
   811                       val co_js =
   812                         map (fn j => j - 1) unsat_js
   813                         |> filter (fn j =>
   814                                       j >= 0 andalso
   815                                       scopes_equivalent
   816                                           (#scope (snd (nth problems j)),
   817                                            #scope (snd (nth problems (j + 1)))))
   818                       val bye_js = sort_distinct int_ord (map fst sat_ps @
   819                                                           unsat_js @ co_js)
   820                       val problems =
   821                         problems |> filter_out_indices bye_js
   822                                  |> max_potential <= 0
   823                                     ? filter_out (#unsound o snd)
   824                     in
   825                       solve_any_problem (found_really_genuine, max_potential,
   826                                          max_genuine, donno) false problems
   827                     end
   828                 end
   829               else
   830                 let
   831                   val genuine_codes =
   832                     con_ps |> take max_genuine
   833                            |> map (print_and_check true)
   834                   val max_genuine = max_genuine - length genuine_codes
   835                   val found_really_genuine =
   836                     found_really_genuine orelse exists fst genuine_codes
   837                 in
   838                   if max_genuine <= 0 orelse not first_time then
   839                     (found_really_genuine, 0, max_genuine, donno)
   840                   else
   841                     let
   842                       val bye_js = sort_distinct int_ord
   843                                                  (map fst sat_ps @ unsat_js)
   844                       val problems =
   845                         problems |> filter_out_indices bye_js
   846                                  |> filter_out (#unsound o snd)
   847                     in
   848                       solve_any_problem (found_really_genuine, 0, max_genuine,
   849                                          donno) false problems
   850                     end
   851                 end
   852             end
   853           | KK.TimedOut unsat_js =>
   854             (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)
   855           | KK.Error (s, unsat_js) =>
   856             (update_checked_problems problems unsat_js;
   857              print_v (K ("Kodkod error: " ^ s ^ "."));
   858              (found_really_genuine, max_potential, max_genuine, donno + 1))
   859       end
   860 
   861     fun run_batch j n scopes (found_really_genuine, max_potential, max_genuine,
   862                               donno) =
   863       let
   864         val _ =
   865           if null scopes then
   866             print_m (K "The scope specification is inconsistent.")
   867           else if verbose then
   868             pprint (Pretty.chunks
   869                 [Pretty.blk (0,
   870                      pstrs ((if n > 1 then
   871                                "Batch " ^ string_of_int (j + 1) ^ " of " ^
   872                                signed_string_of_int n ^ ": "
   873                              else
   874                                "") ^
   875                             "Trying " ^ string_of_int (length scopes) ^
   876                             " scope" ^ plural_s_for_list scopes ^ ":")),
   877                  Pretty.indent indent_size
   878                      (Pretty.chunks (map2
   879                           (fn j => fn scope =>
   880                               Pretty.block (
   881                                   (case pretties_for_scope scope true of
   882                                      [] => [Pretty.str "Empty"]
   883                                    | pretties => pretties) @
   884                                   [Pretty.str (if j = 1 then "." else ";")]))
   885                           (length scopes downto 1) scopes))])
   886           else
   887             ()
   888         fun add_problem_for_scope (scope, unsound) (problems, donno) =
   889           (check_deadline ();
   890            case problem_for_scope unsound scope of
   891              SOME problem =>
   892              (problems
   893               |> (null problems orelse
   894                   not (KK.problems_equivalent (fst problem, fst (hd problems))))
   895                   ? cons problem, donno)
   896            | NONE => (problems, donno + 1))
   897         val (problems, donno) =
   898           fold add_problem_for_scope
   899                (map_product pair scopes
   900                     ((if max_genuine > 0 then [false] else []) @
   901                      (if max_potential > 0 then [true] else [])))
   902                ([], donno)
   903         val _ = Unsynchronized.change generated_problems (append problems)
   904         val _ = Unsynchronized.change generated_scopes (append scopes)
   905         val _ =
   906           if j + 1 = n then
   907             let
   908               val (unsound_problems, sound_problems) =
   909                 List.partition (#unsound o snd) (!generated_problems)
   910             in
   911               if not (null sound_problems) andalso
   912                  forall (KK.is_problem_trivially_false o fst)
   913                         sound_problems then
   914                 print_m (fn () =>
   915                     "Warning: The conjecture either trivially holds for the \
   916                     \given scopes or lies outside Nitpick's supported \
   917                     \fragment." ^
   918                     (if exists (not o KK.is_problem_trivially_false o fst)
   919                                unsound_problems then
   920                        " Only potentially spurious " ^ das_wort_model ^
   921                        "s may be found."
   922                      else
   923                        ""))
   924               else
   925                 ()
   926             end
   927           else
   928             ()
   929       in
   930         solve_any_problem (found_really_genuine, max_potential, max_genuine,
   931                            donno) true (rev problems)
   932       end
   933 
   934     fun scope_count (problems : rich_problem list) scope =
   935       length (filter (curry scopes_equivalent scope o #scope o snd) problems)
   936     fun excipit did_so_and_so =
   937       let
   938         val do_filter =
   939           if !met_potential = max_potential then filter_out (#unsound o snd)
   940           else I
   941         val total = length (!scopes)
   942         val unsat =
   943           fold (fn scope =>
   944                    case scope_count (do_filter (!generated_problems)) scope of
   945                      0 => I
   946                    | n =>
   947                      scope_count (do_filter (these (!checked_problems)))
   948                                  scope = n
   949                      ? Integer.add 1) (!generated_scopes) 0
   950       in
   951         "Nitpick " ^ did_so_and_so ^
   952         (if is_some (!checked_problems) andalso total > 0 then
   953            " " ^ string_of_int unsat ^ " of " ^ string_of_int total ^ " scope"
   954            ^ plural_s total
   955          else
   956            "") ^ "."
   957       end
   958 
   959     val (skipped, the_scopes) =
   960       all_scopes hol_ctxt binarize cards_assigns maxes_assigns iters_assigns
   961                  bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs
   962                  finitizable_dataTs
   963     val _ = if skipped > 0 then
   964               print_m (fn () => "Too many scopes. Skipping " ^
   965                                 string_of_int skipped ^ " scope" ^
   966                                 plural_s skipped ^
   967                                 ". (Consider using \"mono\" or \
   968                                 \\"merge_type_vars\" to prevent this.)")
   969             else
   970               ()
   971     val _ = scopes := the_scopes
   972 
   973     fun run_batches _ _ []
   974                     (found_really_genuine, max_potential, max_genuine, donno) =
   975         if donno > 0 andalso max_genuine > 0 then
   976           (print_m (fn () => excipit "checked"); "unknown")
   977         else if max_genuine = original_max_genuine then
   978           if max_potential = original_max_potential then
   979             (print_m (fn () =>
   980                  "Nitpick found no " ^ das_wort_model ^ "." ^
   981                  (if not standard andalso likely_in_struct_induct_step then
   982                     " This suggests that the induction hypothesis might be \
   983                     \general enough to prove this subgoal."
   984                   else
   985                     "")); if skipped > 0 then "unknown" else "none")
   986           else
   987             (print_m (fn () =>
   988                  excipit ("could not find a" ^
   989                           (if max_genuine = 1 then
   990                              " better " ^ das_wort_model ^ "."
   991                            else
   992                              "ny better " ^ das_wort_model ^ "s.") ^
   993                           " It checked"));
   994              "potential")
   995         else if found_really_genuine then
   996           "genuine"
   997         else
   998           "quasi_genuine"
   999       | run_batches j n (batch :: batches) z =
  1000         let val (z as (_, _, max_genuine, _)) = run_batch j n batch z in
  1001           run_batches (j + 1) n (if max_genuine > 0 then batches else []) z
  1002         end
  1003 
  1004     val batches = batch_list batch_size (!scopes)
  1005     val outcome_code =
  1006       run_batches 0 (length batches) batches
  1007                   (false, max_potential, max_genuine, 0)
  1008       handle TimeLimit.TimeOut =>
  1009              (print_m (fn () => excipit "ran out of time after checking");
  1010               if !met_potential > 0 then "potential" else "unknown")
  1011     val _ = print_v (fn () =>
  1012                 "Total time: " ^ string_from_time (Timer.checkRealTimer timer) ^
  1013                 ".")
  1014   in (outcome_code, !state_ref) end
  1015 
  1016 (* Give the inner timeout a chance. *)
  1017 val timeout_bonus = seconds 1.0
  1018 
  1019 fun pick_nits_in_term state (params as {debug, timeout, expect, ...}) auto i n
  1020                       step subst assm_ts orig_t =
  1021   let val print_m = if auto then K () else Output.urgent_message in
  1022     if getenv "KODKODI" = "" then
  1023       (* The "expect" argument is deliberately ignored if Kodkodi is missing so
  1024          that the "Nitpick_Examples" can be processed on any machine. *)
  1025       (print_m (Pretty.string_of (plazy install_kodkodi_message));
  1026        ("no_kodkodi", state))
  1027     else
  1028       let
  1029         val unknown_outcome = ("unknown", state)
  1030         val deadline = Option.map (curry Time.+ (Time.now ())) timeout
  1031         val outcome as (outcome_code, _) =
  1032           time_limit (if debug orelse is_none timeout then NONE
  1033                       else SOME (Time.+ (the timeout, timeout_bonus)))
  1034               (pick_them_nits_in_term deadline state params auto i n step subst
  1035                                       assm_ts) orig_t
  1036           handle TOO_LARGE (_, details) =>
  1037                  (print_m ("Limit reached: " ^ details ^ "."); unknown_outcome)
  1038                | TOO_SMALL (_, details) =>
  1039                  (print_m ("Limit reached: " ^ details ^ "."); unknown_outcome)
  1040                | Kodkod.SYNTAX (_, details) =>
  1041                  (print_m ("Malformed Kodkodi output: " ^ details ^ ".");
  1042                   unknown_outcome)
  1043                | TimeLimit.TimeOut =>
  1044                  (print_m "Nitpick ran out of time."; unknown_outcome)
  1045       in
  1046         if expect = "" orelse outcome_code = expect then outcome
  1047         else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")
  1048       end
  1049   end
  1050 
  1051 fun is_fixed_equation ctxt
  1052                       (Const (@{const_name "=="}, _) $ Free (s, _) $ Const _) =
  1053     Variable.is_fixed ctxt s
  1054   | is_fixed_equation _ _ = false
  1055 fun extract_fixed_frees ctxt (assms, t) =
  1056   let
  1057     val (subst, other_assms) =
  1058       List.partition (is_fixed_equation ctxt) assms
  1059       |>> map Logic.dest_equals
  1060   in (subst, other_assms, subst_atomic subst t) end
  1061 
  1062 fun pick_nits_in_subgoal state params auto i step =
  1063   let
  1064     val ctxt = Proof.context_of state
  1065     val t = state |> Proof.raw_goal |> #goal |> prop_of
  1066   in
  1067     case Logic.count_prems t of
  1068       0 => (Output.urgent_message "No subgoal!"; ("none", state))
  1069     | n =>
  1070       let
  1071         val t = Logic.goal_params t i |> fst
  1072         val assms = map term_of (Assumption.all_assms_of ctxt)
  1073         val (subst, assms, t) = extract_fixed_frees ctxt (assms, t)
  1074       in pick_nits_in_term state params auto i n step subst assms t end
  1075   end
  1076 
  1077 end;