src/HOL/Tools/Nitpick/nitpick.ML
author wenzelm
Sat Apr 16 16:15:37 2011 +0200 (2011-04-16 ago)
changeset 42361 23f352990944
parent 41995 03c2d29ec790
child 42415 10accf397ab6
permissions -rw-r--r--
modernized structure Proof_Context;
     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, built_in_nondefs, user_nondefs) = all_axioms_of ctxt subst
   274     val def_tables = const_def_tables ctxt subst defs
   275     val nondef_table = const_nondef_table (built_in_nondefs @ user_nondefs)
   276     val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)
   277     val psimp_table = const_psimp_table ctxt subst
   278     val choice_spec_table = const_choice_spec_table ctxt subst
   279     val user_nondefs =
   280       user_nondefs |> filter_out (is_choice_spec_axiom thy choice_spec_table)
   281     val intro_table = inductive_intro_table ctxt subst def_tables
   282     val ground_thm_table = ground_theorem_table thy
   283     val ersatz_table = ersatz_table ctxt
   284     val hol_ctxt as {wf_cache, ...} =
   285       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   286        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
   287        whacks = whacks, binary_ints = binary_ints,
   288        destroy_constrs = destroy_constrs, specialize = specialize,
   289        star_linear_preds = star_linear_preds, total_consts = total_consts,
   290        needs = needs, tac_timeout = tac_timeout, evals = evals,
   291        case_names = case_names, def_tables = def_tables,
   292        nondef_table = nondef_table, user_nondefs = user_nondefs,
   293        simp_table = simp_table, psimp_table = psimp_table,
   294        choice_spec_table = choice_spec_table, intro_table = intro_table,
   295        ground_thm_table = ground_thm_table, ersatz_table = ersatz_table,
   296        skolems = Unsynchronized.ref [], special_funs = Unsynchronized.ref [],
   297        unrolled_preds = Unsynchronized.ref [], wf_cache = Unsynchronized.ref [],
   298        constr_cache = Unsynchronized.ref []}
   299     val pseudo_frees = []
   300     val real_frees = fold Term.add_frees conj_ts []
   301     val _ = null (fold Term.add_tvars conj_ts []) orelse
   302             error "Nitpick cannot handle goals with schematic type variables."
   303     val (nondef_ts, def_ts, need_ts, got_all_mono_user_axioms,
   304          no_poly_user_axioms, binarize) =
   305       preprocess_formulas hol_ctxt assm_ts neg_t
   306     val got_all_user_axioms =
   307       got_all_mono_user_axioms andalso no_poly_user_axioms
   308 
   309     fun print_wf (x, (gfp, wf)) =
   310       pprint (Pretty.blk (0,
   311           pstrs ("The " ^ (if gfp then "co" else "") ^ "inductive predicate \"")
   312           @ Syntax.pretty_term ctxt (Const x) ::
   313           pstrs (if wf then
   314                    "\" was proved well-founded. Nitpick can compute it \
   315                    \efficiently."
   316                  else
   317                    "\" could not be proved well-founded. Nitpick might need to \
   318                    \unroll it.")))
   319     val _ = if verbose then List.app print_wf (!wf_cache) else ()
   320     val das_wort_formula = if falsify then "Negated conjecture" else "Formula"
   321     val _ =
   322       pprint_d (fn () => Pretty.chunks
   323           (pretties_for_formulas ctxt das_wort_formula [hd nondef_ts] @
   324            pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @
   325            pretties_for_formulas ctxt "Relevant nondefinitional axiom"
   326                                  (tl nondef_ts)))
   327     val _ = List.app (ignore o Term.type_of) (nondef_ts @ def_ts)
   328             handle TYPE (_, Ts, ts) =>
   329                    raise TYPE ("Nitpick.pick_them_nits_in_term", Ts, ts)
   330 
   331     val nondef_us = nondef_ts |> map (nut_from_term hol_ctxt Eq)
   332     val def_us = def_ts |> map (nut_from_term hol_ctxt DefEq)
   333     val need_us = need_ts |> map (nut_from_term hol_ctxt Eq)
   334     val (free_names, const_names) =
   335       fold add_free_and_const_names (nondef_us @ def_us @ need_us) ([], [])
   336     val (sel_names, nonsel_names) =
   337       List.partition (is_sel o nickname_of) const_names
   338     val sound_finitizes =
   339       none_true (filter_out (fn (SOME (Type (@{type_name fun}, _)), _) => true
   340                           | _ => false) finitizes)
   341     val standard = forall snd stds
   342 (*
   343     val _ =
   344       List.app (print_g o string_for_nut ctxt) (nondef_us @ def_us @ need_us)
   345 *)
   346 
   347     val unique_scope = forall (curry (op =) 1 o length o snd) cards_assigns
   348     fun monotonicity_message Ts extra =
   349       let val pretties = map (pretty_maybe_quote o pretty_for_type ctxt) Ts in
   350         Pretty.blk (0,
   351           pstrs ("The type" ^ plural_s_for_list pretties ^ " ") @
   352           pretty_serial_commas "and" pretties @
   353           pstrs (" " ^
   354           (if none_true monos then
   355              "passed the monotonicity test"
   356            else
   357              (if length pretties = 1 then "is" else "are") ^ " considered monotonic") ^
   358           ". " ^ extra))
   359       end
   360     fun is_type_fundamentally_monotonic T =
   361       (is_datatype ctxt stds T andalso not (is_quot_type ctxt T) andalso
   362        (not (is_pure_typedef ctxt T) orelse is_univ_typedef ctxt T)) orelse
   363       is_number_type ctxt T orelse is_bit_type T
   364     fun is_type_actually_monotonic T =
   365       formulas_monotonic hol_ctxt binarize T (nondef_ts, def_ts)
   366     fun is_type_kind_of_monotonic T =
   367       case triple_lookup (type_match thy) monos T of
   368         SOME (SOME false) => false
   369       | _ => is_type_actually_monotonic T
   370     fun is_type_monotonic T =
   371       unique_scope orelse
   372       case triple_lookup (type_match thy) monos T of
   373         SOME (SOME b) => b
   374       | _ => is_type_fundamentally_monotonic T orelse
   375              is_type_actually_monotonic T
   376     fun is_deep_datatype_finitizable T =
   377       triple_lookup (type_match thy) finitizes T = SOME (SOME true)
   378     fun is_shallow_datatype_finitizable (T as Type (@{type_name fun_box}, _)) =
   379         is_type_kind_of_monotonic T
   380       | is_shallow_datatype_finitizable T =
   381         case triple_lookup (type_match thy) finitizes T of
   382           SOME (SOME b) => b
   383         | _ => is_type_kind_of_monotonic T
   384     fun is_datatype_deep T =
   385       not standard orelse T = nat_T orelse is_word_type T orelse
   386       exists (curry (op =) T o domain_type o type_of) sel_names
   387     val all_Ts = ground_types_in_terms hol_ctxt binarize (nondef_ts @ def_ts)
   388                  |> sort Term_Ord.typ_ord
   389     val _ =
   390       if verbose andalso binary_ints = SOME true andalso
   391          exists (member (op =) [nat_T, int_T]) all_Ts then
   392         print_v (K "The option \"binary_ints\" will be ignored because of the \
   393                    \presence of rationals, reals, \"Suc\", \"gcd\", or \"lcm\" \
   394                    \in the problem or because of the \"non_std\" option.")
   395       else
   396         ()
   397     val _ =
   398       if not auto andalso
   399          exists (fn Type (@{type_name Datatype.node}, _) => true | _ => false)
   400                 all_Ts then
   401         print_m (K ("Warning: The problem involves directly or indirectly the \
   402                     \internal type " ^ quote @{type_name Datatype.node} ^
   403                     ". This type is very Nitpick-unfriendly, and its presence \
   404                     \usually indicates either a failure of abstraction or a \
   405                     \quirk in Nitpick."))
   406       else
   407         ()
   408     val (mono_Ts, nonmono_Ts) = List.partition is_type_monotonic all_Ts
   409     val _ =
   410       if verbose andalso not unique_scope then
   411         case filter_out is_type_fundamentally_monotonic mono_Ts of
   412           [] => ()
   413         | interesting_mono_Ts =>
   414           pprint_v (K (monotonicity_message interesting_mono_Ts
   415                           "Nitpick might be able to skip some scopes."))
   416       else
   417         ()
   418     val (deep_dataTs, shallow_dataTs) =
   419       all_Ts |> filter (is_datatype ctxt stds)
   420              |> List.partition is_datatype_deep
   421     val finitizable_dataTs =
   422       (deep_dataTs |> filter_out (is_finite_type hol_ctxt)
   423                    |> filter is_deep_datatype_finitizable) @
   424       (shallow_dataTs |> filter_out (is_finite_type hol_ctxt)
   425                       |> filter is_shallow_datatype_finitizable)
   426     val _ =
   427       if verbose andalso not (null finitizable_dataTs) then
   428         pprint_v (K (monotonicity_message finitizable_dataTs
   429                          "Nitpick can use a more precise finite encoding."))
   430       else
   431         ()
   432     (* This detection code is an ugly hack. Fortunately, it is used only to
   433        provide a hint to the user. *)
   434     fun is_struct_induct_step (name, (Rule_Cases.Case {fixes, assumes, ...}, _)) =
   435       not (null fixes) andalso
   436       exists (String.isSuffix ".hyps" o fst) assumes andalso
   437       exists (exists (curry (op =) name o shortest_name o fst)
   438               o datatype_constrs hol_ctxt) deep_dataTs
   439     val likely_in_struct_induct_step =
   440       exists is_struct_induct_step (Proof_Context.cases_of ctxt)
   441     val _ = if standard andalso likely_in_struct_induct_step then
   442               pprint_m (fn () => Pretty.blk (0,
   443                   pstrs "Hint: To check that the induction hypothesis is \
   444                         \general enough, try this command: " @
   445                   [Pretty.mark Markup.sendback (Pretty.blk (0,
   446                        pstrs ("nitpick [non_std, show_all]")))] @ pstrs "."))
   447             else
   448               ()
   449 (*
   450     val _ = print_g "Monotonic types:"
   451     val _ = List.app (print_g o string_for_type ctxt) mono_Ts
   452     val _ = print_g "Nonmonotonic types:"
   453     val _ = List.app (print_g o string_for_type ctxt) nonmono_Ts
   454 *)
   455 
   456     val incremental = Int.max (max_potential, max_genuine) >= 2
   457     val actual_sat_solver =
   458       if sat_solver <> "smart" then
   459         if incremental andalso
   460            not (member (op =) (Kodkod_SAT.configured_sat_solvers true)
   461                        sat_solver) then
   462           (print_m (K ("An incremental SAT solver is required: \"SAT4J\" will \
   463                        \be used instead of " ^ quote sat_solver ^ "."));
   464            "SAT4J")
   465         else
   466           sat_solver
   467       else
   468         Kodkod_SAT.smart_sat_solver_name incremental
   469     val _ =
   470       if sat_solver = "smart" then
   471         print_v (fn () =>
   472             "Using SAT solver " ^ quote actual_sat_solver ^ ". The following" ^
   473             (if incremental then " incremental " else " ") ^
   474             "solvers are configured: " ^
   475             commas_quote (Kodkod_SAT.configured_sat_solvers incremental) ^ ".")
   476       else
   477         ()
   478 
   479     val too_big_scopes = Unsynchronized.ref []
   480 
   481     fun problem_for_scope unsound
   482             (scope as {card_assigns, bits, bisim_depth, datatypes, ofs, ...}) =
   483       let
   484         val _ = not (exists (fn other => scope_less_eq other scope)
   485                             (!too_big_scopes)) orelse
   486                 raise TOO_LARGE ("Nitpick.pick_them_nits_in_term.\
   487                                  \problem_for_scope", "too large scope")
   488 (*
   489         val _ = print_g "Offsets:"
   490         val _ = List.app (fn (T, j0) =>
   491                              print_g (string_for_type ctxt T ^ " = " ^
   492                                     string_of_int j0))
   493                          (Typtab.dest ofs)
   494 *)
   495         val effective_total_consts =
   496           case total_consts of
   497             SOME b => b
   498           | NONE => forall (is_exact_type datatypes true) all_Ts
   499         val main_j0 = offset_of_type ofs bool_T
   500         val (nat_card, nat_j0) = spec_of_type scope nat_T
   501         val (int_card, int_j0) = spec_of_type scope int_T
   502         val _ = (nat_j0 = main_j0 andalso int_j0 = main_j0) orelse
   503                 raise BAD ("Nitpick.pick_them_nits_in_term.problem_for_scope",
   504                            "bad offsets")
   505         val kk = kodkod_constrs peephole_optim nat_card int_card main_j0
   506         val (free_names, rep_table) =
   507           choose_reps_for_free_vars scope pseudo_frees free_names
   508                                     NameTable.empty
   509         val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table
   510         val (nonsel_names, rep_table) =
   511           choose_reps_for_consts scope effective_total_consts nonsel_names
   512                                  rep_table
   513         val (guiltiest_party, min_highest_arity) =
   514           NameTable.fold (fn (name, R) => fn (s, n) =>
   515                              let val n' = arity_of_rep R in
   516                                if n' > n then (nickname_of name, n') else (s, n)
   517                              end) rep_table ("", 1)
   518         val min_univ_card =
   519           NameTable.fold (Integer.max o min_univ_card_of_rep o snd) rep_table
   520                          (univ_card nat_card int_card main_j0 [] KK.True)
   521         val _ = if debug then ()
   522                 else check_arity guiltiest_party min_univ_card min_highest_arity
   523 
   524         val def_us =
   525           def_us |> map (choose_reps_in_nut scope unsound rep_table true)
   526         val nondef_us =
   527           nondef_us |> map (choose_reps_in_nut scope unsound rep_table false)
   528         val need_us =
   529           need_us |> map (choose_reps_in_nut scope unsound rep_table false)
   530 (*
   531         val _ = List.app (print_g o string_for_nut ctxt)
   532                          (free_names @ sel_names @ nonsel_names @
   533                           nondef_us @ def_us @ need_us)
   534 *)
   535         val (free_rels, pool, rel_table) =
   536           rename_free_vars free_names initial_pool NameTable.empty
   537         val (sel_rels, pool, rel_table) =
   538           rename_free_vars sel_names pool rel_table
   539         val (other_rels, pool, rel_table) =
   540           rename_free_vars nonsel_names pool rel_table
   541         val nondef_us = nondef_us |> map (rename_vars_in_nut pool rel_table)
   542         val def_us = def_us |> map (rename_vars_in_nut pool rel_table)
   543         val need_us = need_us |> map (rename_vars_in_nut pool rel_table)
   544         val nondef_fs = map (kodkod_formula_from_nut ofs kk) nondef_us
   545         val def_fs = map (kodkod_formula_from_nut ofs kk) def_us
   546         val formula = fold (fold s_and) [def_fs, nondef_fs] KK.True
   547         val comment = (if unsound then "unsound" else "sound") ^ "\n" ^
   548                       Print_Mode.setmp [] multiline_string_for_scope scope
   549         val kodkod_sat_solver =
   550           Kodkod_SAT.sat_solver_spec actual_sat_solver |> snd
   551         val bit_width = if bits = 0 then 16 else bits + 1
   552         val delay =
   553           if unsound then
   554             Option.map (fn time => Time.- (time, Time.now ())) deadline
   555             |> unsound_delay_for_timeout
   556           else
   557             0
   558         val settings = [("solver", commas_quote kodkod_sat_solver),
   559                         ("bit_width", string_of_int bit_width),
   560                         ("symmetry_breaking", string_of_int kodkod_sym_break),
   561                         ("sharing", "3"),
   562                         ("flatten", "false"),
   563                         ("delay", signed_string_of_int delay)]
   564         val plain_rels = free_rels @ other_rels
   565         val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels
   566         val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels
   567         val need_vals =
   568           map (fn dtype as {typ, ...} =>
   569                   (typ, needed_values_for_datatype need_us ofs dtype)) datatypes
   570         val sel_bounds =
   571           map (bound_for_sel_rel ctxt debug need_vals datatypes) sel_rels
   572         val dtype_axioms =
   573           declarative_axioms_for_datatypes hol_ctxt binarize need_us need_vals
   574               datatype_sym_break bits ofs kk rel_table datatypes
   575         val declarative_axioms = plain_axioms @ dtype_axioms
   576         val univ_card = Int.max (univ_card nat_card int_card main_j0
   577                                      (plain_bounds @ sel_bounds) formula,
   578                                  main_j0 |> bits > 0 ? Integer.add (bits + 1))
   579         val (built_in_bounds, built_in_axioms) =
   580           bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card
   581               nat_card int_card main_j0 (formula :: declarative_axioms)
   582         val bounds = built_in_bounds @ plain_bounds @ sel_bounds
   583                      |> not debug ? merge_bounds
   584         val axioms = built_in_axioms @ declarative_axioms
   585         val highest_arity =
   586           fold Integer.max (map (fst o fst) (maps fst bounds)) 0
   587         val formula = fold_rev s_and axioms formula
   588         val _ = if bits = 0 then () else check_bits bits formula
   589         val _ = if debug orelse formula = KK.False then ()
   590                 else check_arity "" univ_card highest_arity
   591       in
   592         SOME ({comment = comment, settings = settings, univ_card = univ_card,
   593                tuple_assigns = [], bounds = bounds,
   594                int_bounds = if bits = 0 then sequential_int_bounds univ_card
   595                             else pow_of_two_int_bounds bits main_j0,
   596                expr_assigns = [], formula = formula},
   597               {free_names = free_names, sel_names = sel_names,
   598                nonsel_names = nonsel_names, rel_table = rel_table,
   599                unsound = unsound, scope = scope})
   600       end
   601       handle TOO_LARGE (loc, msg) =>
   602              if loc = "Nitpick_Kodkod.check_arity" andalso
   603                 not (Typtab.is_empty ofs) then
   604                problem_for_scope unsound
   605                    {hol_ctxt = hol_ctxt, binarize = binarize,
   606                     card_assigns = card_assigns, bits = bits,
   607                     bisim_depth = bisim_depth, datatypes = datatypes,
   608                     ofs = Typtab.empty}
   609              else if loc = "Nitpick.pick_them_nits_in_term.\
   610                            \problem_for_scope" then
   611                NONE
   612              else
   613                (Unsynchronized.change too_big_scopes (cons scope);
   614                 print_v (fn () =>
   615                     "Limit reached: " ^ msg ^ ". Skipping " ^
   616                     (if unsound then "potential component of " else "") ^
   617                     "scope.");
   618                 NONE)
   619            | TOO_SMALL (_, msg) =>
   620              (print_v (fn () =>
   621                   "Limit reached: " ^ msg ^ ". Skipping " ^
   622                   (if unsound then "potential component of " else "") ^
   623                   "scope.");
   624               NONE)
   625 
   626     val das_wort_model =
   627       (if falsify then "counterexample" else "model")
   628       |> not standard ? prefix "nonstandard "
   629 
   630     val scopes = Unsynchronized.ref []
   631     val generated_scopes = Unsynchronized.ref []
   632     val generated_problems = Unsynchronized.ref ([] : rich_problem list)
   633     val checked_problems = Unsynchronized.ref (SOME [])
   634     val met_potential = Unsynchronized.ref 0
   635 
   636     fun update_checked_problems problems =
   637       List.app (Unsynchronized.change checked_problems o Option.map o cons
   638                 o nth problems)
   639     fun show_kodkod_warning "" = ()
   640       | show_kodkod_warning s = print_m (fn () => "Kodkod warning: " ^ s ^ ".")
   641 
   642     fun print_and_check_model genuine bounds
   643             ({free_names, sel_names, nonsel_names, rel_table, scope, ...}
   644              : problem_extension) =
   645       let
   646         val (reconstructed_model, codatatypes_ok) =
   647           reconstruct_hol_model
   648               {show_datatypes = show_datatypes, show_skolems = show_skolems,
   649                show_consts = show_consts}
   650               scope formats atomss real_frees pseudo_frees free_names sel_names
   651               nonsel_names rel_table bounds
   652         val genuine_means_genuine =
   653           got_all_user_axioms andalso none_true wfs andalso
   654           sound_finitizes andalso total_consts <> SOME true andalso
   655           codatatypes_ok
   656         fun assms_prop () = Logic.mk_conjunction_list (neg_t :: assm_ts)
   657       in
   658         (pprint (Pretty.chunks
   659              [Pretty.blk (0,
   660                   (pstrs ((if auto then "Auto " else "") ^ "Nitpick found a" ^
   661                           (if not genuine then " potentially spurious "
   662                            else if genuine_means_genuine then " "
   663                            else " quasi genuine ") ^ das_wort_model) @
   664                    (case pretties_for_scope scope verbose of
   665                       [] => []
   666                     | pretties => pstrs " for " @ pretties) @
   667                    [Pretty.str ":\n"])),
   668               Pretty.indent indent_size reconstructed_model]);
   669          if genuine then
   670            (if check_genuine andalso standard then
   671               case prove_hol_model scope tac_timeout free_names sel_names
   672                                    rel_table bounds (assms_prop ()) of
   673                 SOME true =>
   674                 print ("Confirmation by \"auto\": The above " ^
   675                        das_wort_model ^ " is really genuine.")
   676               | SOME false =>
   677                 if genuine_means_genuine then
   678                   error ("A supposedly genuine " ^ das_wort_model ^ " was \
   679                          \shown to be spurious by \"auto\".\nThis should never \
   680                          \happen.\nPlease send a bug report to blanchet\
   681                          \te@in.tum.de.")
   682                  else
   683                    print ("Refutation by \"auto\": The above " ^
   684                           das_wort_model ^ " is spurious.")
   685                | NONE => print "No confirmation by \"auto\"."
   686             else
   687               ();
   688             if not standard andalso likely_in_struct_induct_step then
   689               print "The existence of a nonstandard model suggests that the \
   690                     \induction hypothesis is not general enough or may even be \
   691                     \wrong. See the Nitpick manual's \"Inductive Properties\" \
   692                     \section for details (\"isabelle doc nitpick\")."
   693             else
   694               ();
   695             if has_lonely_bool_var orig_t then
   696               print "Hint: Maybe you forgot a colon after the lemma's name?"
   697             else if has_syntactic_sorts orig_t then
   698               print "Hint: Maybe you forgot a type constraint?"
   699             else
   700               ();
   701             if not genuine_means_genuine then
   702               if no_poly_user_axioms then
   703                 let
   704                   val options =
   705                     [] |> not got_all_mono_user_axioms
   706                           ? cons ("user_axioms", "\"true\"")
   707                        |> not (none_true wfs)
   708                           ? cons ("wf", "\"smart\" or \"false\"")
   709                        |> not sound_finitizes
   710                           ? cons ("finitize", "\"smart\" or \"false\"")
   711                        |> total_consts = SOME true
   712                           ? cons ("total_consts", "\"smart\" or \"false\"")
   713                        |> not codatatypes_ok
   714                           ? cons ("bisim_depth", "a nonnegative value")
   715                   val ss =
   716                     map (fn (name, value) => quote name ^ " set to " ^ value)
   717                         options
   718                 in
   719                   print ("Try again with " ^
   720                          space_implode " " (serial_commas "and" ss) ^
   721                          " to confirm that the " ^ das_wort_model ^
   722                          " is genuine.")
   723                 end
   724               else
   725                 print ("Nitpick is unable to guarantee the authenticity of \
   726                        \the " ^ das_wort_model ^ " in the presence of \
   727                        \polymorphic axioms.")
   728             else
   729               ();
   730             NONE)
   731          else
   732            if not genuine then
   733              (Unsynchronized.inc met_potential;
   734               if check_potential then
   735                 let
   736                   val status = prove_hol_model scope tac_timeout free_names
   737                                                sel_names rel_table bounds
   738                                                (assms_prop ())
   739                 in
   740                   (case status of
   741                      SOME true => print ("Confirmation by \"auto\": The \
   742                                          \above " ^ das_wort_model ^
   743                                          " is genuine.")
   744                    | SOME false => print ("Refutation by \"auto\": The above " ^
   745                                           das_wort_model ^ " is spurious.")
   746                    | NONE => print "No confirmation by \"auto\".");
   747                   status
   748                 end
   749               else
   750                 NONE)
   751            else
   752              NONE)
   753         |> pair genuine_means_genuine
   754       end
   755     fun solve_any_problem (found_really_genuine, max_potential, max_genuine,
   756                            donno) first_time problems =
   757       let
   758         val max_potential = Int.max (0, max_potential)
   759         val max_genuine = Int.max (0, max_genuine)
   760         fun print_and_check genuine (j, bounds) =
   761           print_and_check_model genuine bounds (snd (nth problems j))
   762         val max_solutions = max_potential + max_genuine
   763                             |> not incremental ? Integer.min 1
   764       in
   765         if max_solutions <= 0 then
   766           (found_really_genuine, 0, 0, donno)
   767         else
   768           case KK.solve_any_problem debug overlord deadline max_threads
   769                                     max_solutions (map fst problems) of
   770             KK.JavaNotInstalled =>
   771             (print_m install_java_message;
   772              (found_really_genuine, max_potential, max_genuine, donno + 1))
   773           | KK.JavaTooOld =>
   774             (print_m install_java_message;
   775              (found_really_genuine, max_potential, max_genuine, donno + 1))
   776           | KK.KodkodiNotInstalled =>
   777             (print_m install_kodkodi_message;
   778              (found_really_genuine, max_potential, max_genuine, donno + 1))
   779           | KK.Normal ([], unsat_js, s) =>
   780             (update_checked_problems problems unsat_js; show_kodkod_warning s;
   781              (found_really_genuine, max_potential, max_genuine, donno))
   782           | KK.Normal (sat_ps, unsat_js, s) =>
   783             let
   784               val (lib_ps, con_ps) =
   785                 List.partition (#unsound o snd o nth problems o fst) sat_ps
   786             in
   787               update_checked_problems problems (unsat_js @ map fst lib_ps);
   788               show_kodkod_warning s;
   789               if null con_ps then
   790                 let
   791                   val genuine_codes =
   792                     lib_ps |> take max_potential
   793                            |> map (print_and_check false)
   794                            |> filter (curry (op =) (SOME true) o snd)
   795                   val found_really_genuine =
   796                     found_really_genuine orelse exists fst genuine_codes
   797                   val num_genuine = length genuine_codes
   798                   val max_genuine = max_genuine - num_genuine
   799                   val max_potential = max_potential
   800                                       - (length lib_ps - num_genuine)
   801                 in
   802                   if max_genuine <= 0 then
   803                     (found_really_genuine, 0, 0, donno)
   804                   else
   805                     let
   806                       (* "co_js" is the list of sound problems whose unsound
   807                          pendants couldn't be satisfied and hence that most
   808                          probably can't be satisfied themselves. *)
   809                       val co_js =
   810                         map (fn j => j - 1) unsat_js
   811                         |> filter (fn j =>
   812                                       j >= 0 andalso
   813                                       scopes_equivalent
   814                                           (#scope (snd (nth problems j)),
   815                                            #scope (snd (nth problems (j + 1)))))
   816                       val bye_js = sort_distinct int_ord (map fst sat_ps @
   817                                                           unsat_js @ co_js)
   818                       val problems =
   819                         problems |> filter_out_indices bye_js
   820                                  |> max_potential <= 0
   821                                     ? filter_out (#unsound o snd)
   822                     in
   823                       solve_any_problem (found_really_genuine, max_potential,
   824                                          max_genuine, donno) false problems
   825                     end
   826                 end
   827               else
   828                 let
   829                   val genuine_codes =
   830                     con_ps |> take max_genuine
   831                            |> map (print_and_check true)
   832                   val max_genuine = max_genuine - length genuine_codes
   833                   val found_really_genuine =
   834                     found_really_genuine orelse exists fst genuine_codes
   835                 in
   836                   if max_genuine <= 0 orelse not first_time then
   837                     (found_really_genuine, 0, max_genuine, donno)
   838                   else
   839                     let
   840                       val bye_js = sort_distinct int_ord
   841                                                  (map fst sat_ps @ unsat_js)
   842                       val problems =
   843                         problems |> filter_out_indices bye_js
   844                                  |> filter_out (#unsound o snd)
   845                     in
   846                       solve_any_problem (found_really_genuine, 0, max_genuine,
   847                                          donno) false problems
   848                     end
   849                 end
   850             end
   851           | KK.TimedOut unsat_js =>
   852             (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)
   853           | KK.Error (s, unsat_js) =>
   854             (update_checked_problems problems unsat_js;
   855              print_v (K ("Kodkod error: " ^ s ^ "."));
   856              (found_really_genuine, max_potential, max_genuine, donno + 1))
   857       end
   858 
   859     fun run_batch j n scopes (found_really_genuine, max_potential, max_genuine,
   860                               donno) =
   861       let
   862         val _ =
   863           if null scopes then
   864             print_m (K "The scope specification is inconsistent.")
   865           else if verbose then
   866             pprint (Pretty.chunks
   867                 [Pretty.blk (0,
   868                      pstrs ((if n > 1 then
   869                                "Batch " ^ string_of_int (j + 1) ^ " of " ^
   870                                signed_string_of_int n ^ ": "
   871                              else
   872                                "") ^
   873                             "Trying " ^ string_of_int (length scopes) ^
   874                             " scope" ^ plural_s_for_list scopes ^ ":")),
   875                  Pretty.indent indent_size
   876                      (Pretty.chunks (map2
   877                           (fn j => fn scope =>
   878                               Pretty.block (
   879                                   (case pretties_for_scope scope true of
   880                                      [] => [Pretty.str "Empty"]
   881                                    | pretties => pretties) @
   882                                   [Pretty.str (if j = 1 then "." else ";")]))
   883                           (length scopes downto 1) scopes))])
   884           else
   885             ()
   886         fun add_problem_for_scope (scope, unsound) (problems, donno) =
   887           (check_deadline ();
   888            case problem_for_scope unsound scope of
   889              SOME problem =>
   890              (problems
   891               |> (null problems orelse
   892                   not (KK.problems_equivalent (fst problem, fst (hd problems))))
   893                   ? cons problem, donno)
   894            | NONE => (problems, donno + 1))
   895         val (problems, donno) =
   896           fold add_problem_for_scope
   897                (map_product pair scopes
   898                     ((if max_genuine > 0 then [false] else []) @
   899                      (if max_potential > 0 then [true] else [])))
   900                ([], donno)
   901         val _ = Unsynchronized.change generated_problems (append problems)
   902         val _ = Unsynchronized.change generated_scopes (append scopes)
   903         val _ =
   904           if j + 1 = n then
   905             let
   906               val (unsound_problems, sound_problems) =
   907                 List.partition (#unsound o snd) (!generated_problems)
   908             in
   909               if not (null sound_problems) andalso
   910                  forall (KK.is_problem_trivially_false o fst)
   911                         sound_problems then
   912                 print_m (fn () =>
   913                     "Warning: The conjecture either trivially holds for the \
   914                     \given scopes or lies outside Nitpick's supported \
   915                     \fragment." ^
   916                     (if exists (not o KK.is_problem_trivially_false o fst)
   917                                unsound_problems then
   918                        " Only potentially spurious " ^ das_wort_model ^
   919                        "s may be found."
   920                      else
   921                        ""))
   922               else
   923                 ()
   924             end
   925           else
   926             ()
   927       in
   928         solve_any_problem (found_really_genuine, max_potential, max_genuine,
   929                            donno) true (rev problems)
   930       end
   931 
   932     fun scope_count (problems : rich_problem list) scope =
   933       length (filter (curry scopes_equivalent scope o #scope o snd) problems)
   934     fun excipit did_so_and_so =
   935       let
   936         val do_filter =
   937           if !met_potential = max_potential then filter_out (#unsound o snd)
   938           else I
   939         val total = length (!scopes)
   940         val unsat =
   941           fold (fn scope =>
   942                    case scope_count (do_filter (!generated_problems)) scope of
   943                      0 => I
   944                    | n =>
   945                      scope_count (do_filter (these (!checked_problems)))
   946                                  scope = n
   947                      ? Integer.add 1) (!generated_scopes) 0
   948       in
   949         "Nitpick " ^ did_so_and_so ^
   950         (if is_some (!checked_problems) andalso total > 0 then
   951            " " ^ string_of_int unsat ^ " of " ^ string_of_int total ^ " scope"
   952            ^ plural_s total
   953          else
   954            "") ^ "."
   955       end
   956 
   957     val (skipped, the_scopes) =
   958       all_scopes hol_ctxt binarize cards_assigns maxes_assigns iters_assigns
   959                  bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs
   960                  finitizable_dataTs
   961     val _ = if skipped > 0 then
   962               print_m (fn () => "Too many scopes. Skipping " ^
   963                                 string_of_int skipped ^ " scope" ^
   964                                 plural_s skipped ^
   965                                 ". (Consider using \"mono\" or \
   966                                 \\"merge_type_vars\" to prevent this.)")
   967             else
   968               ()
   969     val _ = scopes := the_scopes
   970 
   971     fun run_batches _ _ []
   972                     (found_really_genuine, max_potential, max_genuine, donno) =
   973         if donno > 0 andalso max_genuine > 0 then
   974           (print_m (fn () => excipit "checked"); "unknown")
   975         else if max_genuine = original_max_genuine then
   976           if max_potential = original_max_potential then
   977             (print_m (fn () =>
   978                  "Nitpick found no " ^ das_wort_model ^ "." ^
   979                  (if not standard andalso likely_in_struct_induct_step then
   980                     " This suggests that the induction hypothesis might be \
   981                     \general enough to prove this subgoal."
   982                   else
   983                     "")); if skipped > 0 then "unknown" else "none")
   984           else
   985             (print_m (fn () =>
   986                  excipit ("could not find a" ^
   987                           (if max_genuine = 1 then
   988                              " better " ^ das_wort_model ^ "."
   989                            else
   990                              "ny better " ^ das_wort_model ^ "s.") ^
   991                           " It checked"));
   992              "potential")
   993         else if found_really_genuine then
   994           "genuine"
   995         else
   996           "quasi_genuine"
   997       | run_batches j n (batch :: batches) z =
   998         let val (z as (_, _, max_genuine, _)) = run_batch j n batch z in
   999           run_batches (j + 1) n (if max_genuine > 0 then batches else []) z
  1000         end
  1001 
  1002     val batches = batch_list batch_size (!scopes)
  1003     val outcome_code =
  1004       run_batches 0 (length batches) batches
  1005                   (false, max_potential, max_genuine, 0)
  1006       handle TimeLimit.TimeOut =>
  1007              (print_m (fn () => excipit "ran out of time after checking");
  1008               if !met_potential > 0 then "potential" else "unknown")
  1009     val _ = print_v (fn () =>
  1010                 "Total time: " ^ string_from_time (Timer.checkRealTimer timer) ^
  1011                 ".")
  1012   in (outcome_code, !state_ref) end
  1013 
  1014 (* Give the inner timeout a chance. *)
  1015 val timeout_bonus = seconds 1.0
  1016 
  1017 fun pick_nits_in_term state (params as {debug, timeout, expect, ...}) auto i n
  1018                       step subst assm_ts orig_t =
  1019   let val print_m = if auto then K () else Output.urgent_message in
  1020     if getenv "KODKODI" = "" then
  1021       (* The "expect" argument is deliberately ignored if Kodkodi is missing so
  1022          that the "Nitpick_Examples" can be processed on any machine. *)
  1023       (print_m (Pretty.string_of (plazy install_kodkodi_message));
  1024        ("no_kodkodi", state))
  1025     else
  1026       let
  1027         val unknown_outcome = ("unknown", state)
  1028         val deadline = Option.map (curry Time.+ (Time.now ())) timeout
  1029         val outcome as (outcome_code, _) =
  1030           time_limit (if debug orelse is_none timeout then NONE
  1031                       else SOME (Time.+ (the timeout, timeout_bonus)))
  1032               (pick_them_nits_in_term deadline state params auto i n step subst
  1033                                       assm_ts) orig_t
  1034           handle TOO_LARGE (_, details) =>
  1035                  (print_m ("Limit reached: " ^ details ^ "."); unknown_outcome)
  1036                | TOO_SMALL (_, details) =>
  1037                  (print_m ("Limit reached: " ^ details ^ "."); unknown_outcome)
  1038                | Kodkod.SYNTAX (_, details) =>
  1039                  (print_m ("Malformed Kodkodi output: " ^ details ^ ".");
  1040                   unknown_outcome)
  1041                | TimeLimit.TimeOut =>
  1042                  (print_m "Nitpick ran out of time."; unknown_outcome)
  1043       in
  1044         if expect = "" orelse outcome_code = expect then outcome
  1045         else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")
  1046       end
  1047   end
  1048 
  1049 fun is_fixed_equation fixes
  1050                       (Const (@{const_name "=="}, _) $ Free (s, _) $ Const _) =
  1051     member (op =) fixes s
  1052   | is_fixed_equation _ _ = false
  1053 fun extract_fixed_frees ctxt (assms, t) =
  1054   let
  1055     val fixes = Variable.fixes_of ctxt |> map snd
  1056     val (subst, other_assms) =
  1057       List.partition (is_fixed_equation fixes) assms
  1058       |>> map Logic.dest_equals
  1059   in (subst, other_assms, subst_atomic subst t) end
  1060 
  1061 fun pick_nits_in_subgoal state params auto i step =
  1062   let
  1063     val ctxt = Proof.context_of state
  1064     val t = state |> Proof.raw_goal |> #goal |> prop_of
  1065   in
  1066     case Logic.count_prems t of
  1067       0 => (Output.urgent_message "No subgoal!"; ("none", state))
  1068     | n =>
  1069       let
  1070         val t = Logic.goal_params t i |> fst
  1071         val assms = map term_of (Assumption.all_assms_of ctxt)
  1072         val (subst, assms, t) = extract_fixed_frees ctxt (assms, t)
  1073       in pick_nits_in_term state params auto i n step subst assms t end
  1074   end
  1075 
  1076 end;