src/HOL/Tools/Nitpick/nitpick.ML
author blanchet
Tue Apr 19 14:04:58 2011 +0200 (2011-04-19)
changeset 42415 10accf397ab6
parent 42361 23f352990944
child 42486 01b03a124b81
permissions -rw-r--r--
use "Spec_Rules" for finding axioms -- more reliable and cleaner
     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") ^ " considered monotonic") ^
   359           ". " ^ extra))
   360       end
   361     fun is_type_fundamentally_monotonic T =
   362       (is_datatype ctxt stds T andalso not (is_quot_type ctxt T) andalso
   363        (not (is_pure_typedef ctxt T) orelse is_univ_typedef ctxt T)) orelse
   364       is_number_type ctxt T orelse is_bit_type T
   365     fun is_type_actually_monotonic T =
   366       formulas_monotonic hol_ctxt binarize T (nondef_ts, def_ts)
   367     fun is_type_kind_of_monotonic T =
   368       case triple_lookup (type_match thy) monos T of
   369         SOME (SOME false) => false
   370       | _ => is_type_actually_monotonic T
   371     fun is_type_monotonic T =
   372       unique_scope orelse
   373       case triple_lookup (type_match thy) monos T of
   374         SOME (SOME b) => b
   375       | _ => is_type_fundamentally_monotonic T orelse
   376              is_type_actually_monotonic T
   377     fun is_deep_datatype_finitizable T =
   378       triple_lookup (type_match thy) finitizes T = SOME (SOME true)
   379     fun is_shallow_datatype_finitizable (T as Type (@{type_name fun_box}, _)) =
   380         is_type_kind_of_monotonic T
   381       | is_shallow_datatype_finitizable T =
   382         case triple_lookup (type_match thy) finitizes T of
   383           SOME (SOME b) => b
   384         | _ => is_type_kind_of_monotonic T
   385     fun is_datatype_deep T =
   386       not standard orelse T = nat_T orelse is_word_type T orelse
   387       exists (curry (op =) T o domain_type o type_of) sel_names
   388     val all_Ts = ground_types_in_terms hol_ctxt binarize (nondef_ts @ def_ts)
   389                  |> sort Term_Ord.typ_ord
   390     val _ =
   391       if verbose andalso binary_ints = SOME true andalso
   392          exists (member (op =) [nat_T, int_T]) all_Ts then
   393         print_v (K "The option \"binary_ints\" will be ignored because of the \
   394                    \presence of rationals, reals, \"Suc\", \"gcd\", or \"lcm\" \
   395                    \in the problem or because of the \"non_std\" option.")
   396       else
   397         ()
   398     val _ =
   399       if not auto andalso
   400          exists (fn Type (@{type_name Datatype.node}, _) => true | _ => false)
   401                 all_Ts then
   402         print_m (K ("Warning: The problem involves directly or indirectly the \
   403                     \internal type " ^ quote @{type_name Datatype.node} ^
   404                     ". This type is very Nitpick-unfriendly, and its presence \
   405                     \usually indicates either a failure of abstraction or a \
   406                     \quirk in Nitpick."))
   407       else
   408         ()
   409     val (mono_Ts, nonmono_Ts) = List.partition is_type_monotonic all_Ts
   410     val _ =
   411       if verbose andalso not unique_scope then
   412         case filter_out is_type_fundamentally_monotonic mono_Ts of
   413           [] => ()
   414         | interesting_mono_Ts =>
   415           pprint_v (K (monotonicity_message interesting_mono_Ts
   416                           "Nitpick might be able to skip some scopes."))
   417       else
   418         ()
   419     val (deep_dataTs, shallow_dataTs) =
   420       all_Ts |> filter (is_datatype ctxt stds)
   421              |> List.partition is_datatype_deep
   422     val finitizable_dataTs =
   423       (deep_dataTs |> filter_out (is_finite_type hol_ctxt)
   424                    |> filter is_deep_datatype_finitizable) @
   425       (shallow_dataTs |> filter_out (is_finite_type hol_ctxt)
   426                       |> filter is_shallow_datatype_finitizable)
   427     val _ =
   428       if verbose andalso not (null finitizable_dataTs) then
   429         pprint_v (K (monotonicity_message finitizable_dataTs
   430                          "Nitpick can use a more precise finite encoding."))
   431       else
   432         ()
   433     (* This detection code is an ugly hack. Fortunately, it is used only to
   434        provide a hint to the user. *)
   435     fun is_struct_induct_step (name, (Rule_Cases.Case {fixes, assumes, ...}, _)) =
   436       not (null fixes) andalso
   437       exists (String.isSuffix ".hyps" o fst) assumes andalso
   438       exists (exists (curry (op =) name o shortest_name o fst)
   439               o datatype_constrs hol_ctxt) deep_dataTs
   440     val likely_in_struct_induct_step =
   441       exists is_struct_induct_step (Proof_Context.cases_of ctxt)
   442     val _ = if standard andalso likely_in_struct_induct_step then
   443               pprint_m (fn () => Pretty.blk (0,
   444                   pstrs "Hint: To check that the induction hypothesis is \
   445                         \general enough, try this command: " @
   446                   [Pretty.mark Markup.sendback (Pretty.blk (0,
   447                        pstrs ("nitpick [non_std, show_all]")))] @ pstrs "."))
   448             else
   449               ()
   450 (*
   451     val _ = print_g "Monotonic types:"
   452     val _ = List.app (print_g o string_for_type ctxt) mono_Ts
   453     val _ = print_g "Nonmonotonic types:"
   454     val _ = List.app (print_g o string_for_type ctxt) nonmono_Ts
   455 *)
   456 
   457     val incremental = Int.max (max_potential, max_genuine) >= 2
   458     val actual_sat_solver =
   459       if sat_solver <> "smart" then
   460         if incremental andalso
   461            not (member (op =) (Kodkod_SAT.configured_sat_solvers true)
   462                        sat_solver) then
   463           (print_m (K ("An incremental SAT solver is required: \"SAT4J\" will \
   464                        \be used instead of " ^ quote sat_solver ^ "."));
   465            "SAT4J")
   466         else
   467           sat_solver
   468       else
   469         Kodkod_SAT.smart_sat_solver_name incremental
   470     val _ =
   471       if sat_solver = "smart" then
   472         print_v (fn () =>
   473             "Using SAT solver " ^ quote actual_sat_solver ^ ". The following" ^
   474             (if incremental then " incremental " else " ") ^
   475             "solvers are configured: " ^
   476             commas_quote (Kodkod_SAT.configured_sat_solvers incremental) ^ ".")
   477       else
   478         ()
   479 
   480     val too_big_scopes = Unsynchronized.ref []
   481 
   482     fun problem_for_scope unsound
   483             (scope as {card_assigns, bits, bisim_depth, datatypes, ofs, ...}) =
   484       let
   485         val _ = not (exists (fn other => scope_less_eq other scope)
   486                             (!too_big_scopes)) orelse
   487                 raise TOO_LARGE ("Nitpick.pick_them_nits_in_term.\
   488                                  \problem_for_scope", "too large scope")
   489 (*
   490         val _ = print_g "Offsets:"
   491         val _ = List.app (fn (T, j0) =>
   492                              print_g (string_for_type ctxt T ^ " = " ^
   493                                     string_of_int j0))
   494                          (Typtab.dest ofs)
   495 *)
   496         val effective_total_consts =
   497           case total_consts of
   498             SOME b => b
   499           | NONE => forall (is_exact_type datatypes true) all_Ts
   500         val main_j0 = offset_of_type ofs bool_T
   501         val (nat_card, nat_j0) = spec_of_type scope nat_T
   502         val (int_card, int_j0) = spec_of_type scope int_T
   503         val _ = (nat_j0 = main_j0 andalso int_j0 = main_j0) orelse
   504                 raise BAD ("Nitpick.pick_them_nits_in_term.problem_for_scope",
   505                            "bad offsets")
   506         val kk = kodkod_constrs peephole_optim nat_card int_card main_j0
   507         val (free_names, rep_table) =
   508           choose_reps_for_free_vars scope pseudo_frees free_names
   509                                     NameTable.empty
   510         val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table
   511         val (nonsel_names, rep_table) =
   512           choose_reps_for_consts scope effective_total_consts nonsel_names
   513                                  rep_table
   514         val (guiltiest_party, min_highest_arity) =
   515           NameTable.fold (fn (name, R) => fn (s, n) =>
   516                              let val n' = arity_of_rep R in
   517                                if n' > n then (nickname_of name, n') else (s, n)
   518                              end) rep_table ("", 1)
   519         val min_univ_card =
   520           NameTable.fold (Integer.max o min_univ_card_of_rep o snd) rep_table
   521                          (univ_card nat_card int_card main_j0 [] KK.True)
   522         val _ = if debug then ()
   523                 else check_arity guiltiest_party min_univ_card min_highest_arity
   524 
   525         val def_us =
   526           def_us |> map (choose_reps_in_nut scope unsound rep_table true)
   527         val nondef_us =
   528           nondef_us |> map (choose_reps_in_nut scope unsound rep_table false)
   529         val need_us =
   530           need_us |> map (choose_reps_in_nut scope unsound rep_table false)
   531 (*
   532         val _ = List.app (print_g o string_for_nut ctxt)
   533                          (free_names @ sel_names @ nonsel_names @
   534                           nondef_us @ def_us @ need_us)
   535 *)
   536         val (free_rels, pool, rel_table) =
   537           rename_free_vars free_names initial_pool NameTable.empty
   538         val (sel_rels, pool, rel_table) =
   539           rename_free_vars sel_names pool rel_table
   540         val (other_rels, pool, rel_table) =
   541           rename_free_vars nonsel_names pool rel_table
   542         val nondef_us = nondef_us |> map (rename_vars_in_nut pool rel_table)
   543         val def_us = def_us |> map (rename_vars_in_nut pool rel_table)
   544         val need_us = need_us |> map (rename_vars_in_nut pool rel_table)
   545         val nondef_fs = map (kodkod_formula_from_nut ofs kk) nondef_us
   546         val def_fs = map (kodkod_formula_from_nut ofs kk) def_us
   547         val formula = fold (fold s_and) [def_fs, nondef_fs] KK.True
   548         val comment = (if unsound then "unsound" else "sound") ^ "\n" ^
   549                       Print_Mode.setmp [] multiline_string_for_scope scope
   550         val kodkod_sat_solver =
   551           Kodkod_SAT.sat_solver_spec actual_sat_solver |> snd
   552         val bit_width = if bits = 0 then 16 else bits + 1
   553         val delay =
   554           if unsound then
   555             Option.map (fn time => Time.- (time, Time.now ())) deadline
   556             |> unsound_delay_for_timeout
   557           else
   558             0
   559         val settings = [("solver", commas_quote kodkod_sat_solver),
   560                         ("bit_width", string_of_int bit_width),
   561                         ("symmetry_breaking", string_of_int kodkod_sym_break),
   562                         ("sharing", "3"),
   563                         ("flatten", "false"),
   564                         ("delay", signed_string_of_int delay)]
   565         val plain_rels = free_rels @ other_rels
   566         val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels
   567         val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels
   568         val need_vals =
   569           map (fn dtype as {typ, ...} =>
   570                   (typ, needed_values_for_datatype need_us ofs dtype)) datatypes
   571         val sel_bounds =
   572           map (bound_for_sel_rel ctxt debug need_vals datatypes) sel_rels
   573         val dtype_axioms =
   574           declarative_axioms_for_datatypes hol_ctxt binarize need_us need_vals
   575               datatype_sym_break bits ofs kk rel_table datatypes
   576         val declarative_axioms = plain_axioms @ dtype_axioms
   577         val univ_card = Int.max (univ_card nat_card int_card main_j0
   578                                      (plain_bounds @ sel_bounds) formula,
   579                                  main_j0 |> bits > 0 ? Integer.add (bits + 1))
   580         val (built_in_bounds, built_in_axioms) =
   581           bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card
   582               nat_card int_card main_j0 (formula :: declarative_axioms)
   583         val bounds = built_in_bounds @ plain_bounds @ sel_bounds
   584                      |> not debug ? merge_bounds
   585         val axioms = built_in_axioms @ declarative_axioms
   586         val highest_arity =
   587           fold Integer.max (map (fst o fst) (maps fst bounds)) 0
   588         val formula = fold_rev s_and axioms formula
   589         val _ = if bits = 0 then () else check_bits bits formula
   590         val _ = if debug orelse formula = KK.False then ()
   591                 else check_arity "" univ_card highest_arity
   592       in
   593         SOME ({comment = comment, settings = settings, univ_card = univ_card,
   594                tuple_assigns = [], bounds = bounds,
   595                int_bounds = if bits = 0 then sequential_int_bounds univ_card
   596                             else pow_of_two_int_bounds bits main_j0,
   597                expr_assigns = [], formula = formula},
   598               {free_names = free_names, sel_names = sel_names,
   599                nonsel_names = nonsel_names, rel_table = rel_table,
   600                unsound = unsound, scope = scope})
   601       end
   602       handle TOO_LARGE (loc, msg) =>
   603              if loc = "Nitpick_Kodkod.check_arity" andalso
   604                 not (Typtab.is_empty ofs) then
   605                problem_for_scope unsound
   606                    {hol_ctxt = hol_ctxt, binarize = binarize,
   607                     card_assigns = card_assigns, bits = bits,
   608                     bisim_depth = bisim_depth, datatypes = datatypes,
   609                     ofs = Typtab.empty}
   610              else if loc = "Nitpick.pick_them_nits_in_term.\
   611                            \problem_for_scope" then
   612                NONE
   613              else
   614                (Unsynchronized.change too_big_scopes (cons scope);
   615                 print_v (fn () =>
   616                     "Limit reached: " ^ msg ^ ". Skipping " ^
   617                     (if unsound then "potential component of " else "") ^
   618                     "scope.");
   619                 NONE)
   620            | TOO_SMALL (_, msg) =>
   621              (print_v (fn () =>
   622                   "Limit reached: " ^ msg ^ ". Skipping " ^
   623                   (if unsound then "potential component of " else "") ^
   624                   "scope.");
   625               NONE)
   626 
   627     val das_wort_model =
   628       (if falsify then "counterexample" else "model")
   629       |> not standard ? prefix "nonstandard "
   630 
   631     val scopes = Unsynchronized.ref []
   632     val generated_scopes = Unsynchronized.ref []
   633     val generated_problems = Unsynchronized.ref ([] : rich_problem list)
   634     val checked_problems = Unsynchronized.ref (SOME [])
   635     val met_potential = Unsynchronized.ref 0
   636 
   637     fun update_checked_problems problems =
   638       List.app (Unsynchronized.change checked_problems o Option.map o cons
   639                 o nth problems)
   640     fun show_kodkod_warning "" = ()
   641       | show_kodkod_warning s = print_m (fn () => "Kodkod warning: " ^ s ^ ".")
   642 
   643     fun print_and_check_model genuine bounds
   644             ({free_names, sel_names, nonsel_names, rel_table, scope, ...}
   645              : problem_extension) =
   646       let
   647         val (reconstructed_model, codatatypes_ok) =
   648           reconstruct_hol_model
   649               {show_datatypes = show_datatypes, show_skolems = show_skolems,
   650                show_consts = show_consts}
   651               scope formats atomss real_frees pseudo_frees free_names sel_names
   652               nonsel_names rel_table bounds
   653         val genuine_means_genuine =
   654           got_all_user_axioms andalso none_true wfs andalso
   655           sound_finitizes andalso total_consts <> SOME true andalso
   656           codatatypes_ok
   657         fun assms_prop () = Logic.mk_conjunction_list (neg_t :: assm_ts)
   658       in
   659         (pprint (Pretty.chunks
   660              [Pretty.blk (0,
   661                   (pstrs ((if auto then "Auto " else "") ^ "Nitpick found a" ^
   662                           (if not genuine then " potentially spurious "
   663                            else if genuine_means_genuine then " "
   664                            else " quasi genuine ") ^ das_wort_model) @
   665                    (case pretties_for_scope scope verbose of
   666                       [] => []
   667                     | pretties => pstrs " for " @ pretties) @
   668                    [Pretty.str ":\n"])),
   669               Pretty.indent indent_size reconstructed_model]);
   670          if genuine then
   671            (if check_genuine andalso standard then
   672               case prove_hol_model scope tac_timeout free_names sel_names
   673                                    rel_table bounds (assms_prop ()) of
   674                 SOME true =>
   675                 print ("Confirmation by \"auto\": The above " ^
   676                        das_wort_model ^ " is really genuine.")
   677               | SOME false =>
   678                 if genuine_means_genuine then
   679                   error ("A supposedly genuine " ^ das_wort_model ^ " was \
   680                          \shown to be spurious by \"auto\".\nThis should never \
   681                          \happen.\nPlease send a bug report to blanchet\
   682                          \te@in.tum.de.")
   683                  else
   684                    print ("Refutation by \"auto\": The above " ^
   685                           das_wort_model ^ " is spurious.")
   686                | NONE => print "No confirmation by \"auto\"."
   687             else
   688               ();
   689             if not standard andalso likely_in_struct_induct_step then
   690               print "The existence of a nonstandard model suggests that the \
   691                     \induction hypothesis is not general enough or may even be \
   692                     \wrong. See the Nitpick manual's \"Inductive Properties\" \
   693                     \section for details (\"isabelle doc nitpick\")."
   694             else
   695               ();
   696             if has_lonely_bool_var orig_t then
   697               print "Hint: Maybe you forgot a colon after the lemma's name?"
   698             else if has_syntactic_sorts orig_t then
   699               print "Hint: Maybe you forgot a type constraint?"
   700             else
   701               ();
   702             if not genuine_means_genuine then
   703               if no_poly_user_axioms then
   704                 let
   705                   val options =
   706                     [] |> not got_all_mono_user_axioms
   707                           ? cons ("user_axioms", "\"true\"")
   708                        |> not (none_true wfs)
   709                           ? cons ("wf", "\"smart\" or \"false\"")
   710                        |> not sound_finitizes
   711                           ? cons ("finitize", "\"smart\" or \"false\"")
   712                        |> total_consts = SOME true
   713                           ? cons ("total_consts", "\"smart\" or \"false\"")
   714                        |> not codatatypes_ok
   715                           ? cons ("bisim_depth", "a nonnegative value")
   716                   val ss =
   717                     map (fn (name, value) => quote name ^ " set to " ^ value)
   718                         options
   719                 in
   720                   print ("Try again with " ^
   721                          space_implode " " (serial_commas "and" ss) ^
   722                          " to confirm that the " ^ das_wort_model ^
   723                          " is genuine.")
   724                 end
   725               else
   726                 print ("Nitpick is unable to guarantee the authenticity of \
   727                        \the " ^ das_wort_model ^ " in the presence of \
   728                        \polymorphic axioms.")
   729             else
   730               ();
   731             NONE)
   732          else
   733            if not genuine then
   734              (Unsynchronized.inc met_potential;
   735               if check_potential then
   736                 let
   737                   val status = prove_hol_model scope tac_timeout free_names
   738                                                sel_names rel_table bounds
   739                                                (assms_prop ())
   740                 in
   741                   (case status of
   742                      SOME true => print ("Confirmation by \"auto\": The \
   743                                          \above " ^ das_wort_model ^
   744                                          " is genuine.")
   745                    | SOME false => print ("Refutation by \"auto\": The above " ^
   746                                           das_wort_model ^ " is spurious.")
   747                    | NONE => print "No confirmation by \"auto\".");
   748                   status
   749                 end
   750               else
   751                 NONE)
   752            else
   753              NONE)
   754         |> pair genuine_means_genuine
   755       end
   756     fun solve_any_problem (found_really_genuine, max_potential, max_genuine,
   757                            donno) first_time problems =
   758       let
   759         val max_potential = Int.max (0, max_potential)
   760         val max_genuine = Int.max (0, max_genuine)
   761         fun print_and_check genuine (j, bounds) =
   762           print_and_check_model genuine bounds (snd (nth problems j))
   763         val max_solutions = max_potential + max_genuine
   764                             |> not incremental ? Integer.min 1
   765       in
   766         if max_solutions <= 0 then
   767           (found_really_genuine, 0, 0, donno)
   768         else
   769           case KK.solve_any_problem debug overlord deadline max_threads
   770                                     max_solutions (map fst problems) of
   771             KK.JavaNotInstalled =>
   772             (print_m install_java_message;
   773              (found_really_genuine, max_potential, max_genuine, donno + 1))
   774           | KK.JavaTooOld =>
   775             (print_m install_java_message;
   776              (found_really_genuine, max_potential, max_genuine, donno + 1))
   777           | KK.KodkodiNotInstalled =>
   778             (print_m install_kodkodi_message;
   779              (found_really_genuine, max_potential, max_genuine, donno + 1))
   780           | KK.Normal ([], unsat_js, s) =>
   781             (update_checked_problems problems unsat_js; show_kodkod_warning s;
   782              (found_really_genuine, max_potential, max_genuine, donno))
   783           | KK.Normal (sat_ps, unsat_js, s) =>
   784             let
   785               val (lib_ps, con_ps) =
   786                 List.partition (#unsound o snd o nth problems o fst) sat_ps
   787             in
   788               update_checked_problems problems (unsat_js @ map fst lib_ps);
   789               show_kodkod_warning s;
   790               if null con_ps then
   791                 let
   792                   val genuine_codes =
   793                     lib_ps |> take max_potential
   794                            |> map (print_and_check false)
   795                            |> filter (curry (op =) (SOME true) o snd)
   796                   val found_really_genuine =
   797                     found_really_genuine orelse exists fst genuine_codes
   798                   val num_genuine = length genuine_codes
   799                   val max_genuine = max_genuine - num_genuine
   800                   val max_potential = max_potential
   801                                       - (length lib_ps - num_genuine)
   802                 in
   803                   if max_genuine <= 0 then
   804                     (found_really_genuine, 0, 0, donno)
   805                   else
   806                     let
   807                       (* "co_js" is the list of sound problems whose unsound
   808                          pendants couldn't be satisfied and hence that most
   809                          probably can't be satisfied themselves. *)
   810                       val co_js =
   811                         map (fn j => j - 1) unsat_js
   812                         |> filter (fn j =>
   813                                       j >= 0 andalso
   814                                       scopes_equivalent
   815                                           (#scope (snd (nth problems j)),
   816                                            #scope (snd (nth problems (j + 1)))))
   817                       val bye_js = sort_distinct int_ord (map fst sat_ps @
   818                                                           unsat_js @ co_js)
   819                       val problems =
   820                         problems |> filter_out_indices bye_js
   821                                  |> max_potential <= 0
   822                                     ? filter_out (#unsound o snd)
   823                     in
   824                       solve_any_problem (found_really_genuine, max_potential,
   825                                          max_genuine, donno) false problems
   826                     end
   827                 end
   828               else
   829                 let
   830                   val genuine_codes =
   831                     con_ps |> take max_genuine
   832                            |> map (print_and_check true)
   833                   val max_genuine = max_genuine - length genuine_codes
   834                   val found_really_genuine =
   835                     found_really_genuine orelse exists fst genuine_codes
   836                 in
   837                   if max_genuine <= 0 orelse not first_time then
   838                     (found_really_genuine, 0, max_genuine, donno)
   839                   else
   840                     let
   841                       val bye_js = sort_distinct int_ord
   842                                                  (map fst sat_ps @ unsat_js)
   843                       val problems =
   844                         problems |> filter_out_indices bye_js
   845                                  |> filter_out (#unsound o snd)
   846                     in
   847                       solve_any_problem (found_really_genuine, 0, max_genuine,
   848                                          donno) false problems
   849                     end
   850                 end
   851             end
   852           | KK.TimedOut unsat_js =>
   853             (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)
   854           | KK.Error (s, unsat_js) =>
   855             (update_checked_problems problems unsat_js;
   856              print_v (K ("Kodkod error: " ^ s ^ "."));
   857              (found_really_genuine, max_potential, max_genuine, donno + 1))
   858       end
   859 
   860     fun run_batch j n scopes (found_really_genuine, max_potential, max_genuine,
   861                               donno) =
   862       let
   863         val _ =
   864           if null scopes then
   865             print_m (K "The scope specification is inconsistent.")
   866           else if verbose then
   867             pprint (Pretty.chunks
   868                 [Pretty.blk (0,
   869                      pstrs ((if n > 1 then
   870                                "Batch " ^ string_of_int (j + 1) ^ " of " ^
   871                                signed_string_of_int n ^ ": "
   872                              else
   873                                "") ^
   874                             "Trying " ^ string_of_int (length scopes) ^
   875                             " scope" ^ plural_s_for_list scopes ^ ":")),
   876                  Pretty.indent indent_size
   877                      (Pretty.chunks (map2
   878                           (fn j => fn scope =>
   879                               Pretty.block (
   880                                   (case pretties_for_scope scope true of
   881                                      [] => [Pretty.str "Empty"]
   882                                    | pretties => pretties) @
   883                                   [Pretty.str (if j = 1 then "." else ";")]))
   884                           (length scopes downto 1) scopes))])
   885           else
   886             ()
   887         fun add_problem_for_scope (scope, unsound) (problems, donno) =
   888           (check_deadline ();
   889            case problem_for_scope unsound scope of
   890              SOME problem =>
   891              (problems
   892               |> (null problems orelse
   893                   not (KK.problems_equivalent (fst problem, fst (hd problems))))
   894                   ? cons problem, donno)
   895            | NONE => (problems, donno + 1))
   896         val (problems, donno) =
   897           fold add_problem_for_scope
   898                (map_product pair scopes
   899                     ((if max_genuine > 0 then [false] else []) @
   900                      (if max_potential > 0 then [true] else [])))
   901                ([], donno)
   902         val _ = Unsynchronized.change generated_problems (append problems)
   903         val _ = Unsynchronized.change generated_scopes (append scopes)
   904         val _ =
   905           if j + 1 = n then
   906             let
   907               val (unsound_problems, sound_problems) =
   908                 List.partition (#unsound o snd) (!generated_problems)
   909             in
   910               if not (null sound_problems) andalso
   911                  forall (KK.is_problem_trivially_false o fst)
   912                         sound_problems then
   913                 print_m (fn () =>
   914                     "Warning: The conjecture either trivially holds for the \
   915                     \given scopes or lies outside Nitpick's supported \
   916                     \fragment." ^
   917                     (if exists (not o KK.is_problem_trivially_false o fst)
   918                                unsound_problems then
   919                        " Only potentially spurious " ^ das_wort_model ^
   920                        "s may be found."
   921                      else
   922                        ""))
   923               else
   924                 ()
   925             end
   926           else
   927             ()
   928       in
   929         solve_any_problem (found_really_genuine, max_potential, max_genuine,
   930                            donno) true (rev problems)
   931       end
   932 
   933     fun scope_count (problems : rich_problem list) scope =
   934       length (filter (curry scopes_equivalent scope o #scope o snd) problems)
   935     fun excipit did_so_and_so =
   936       let
   937         val do_filter =
   938           if !met_potential = max_potential then filter_out (#unsound o snd)
   939           else I
   940         val total = length (!scopes)
   941         val unsat =
   942           fold (fn scope =>
   943                    case scope_count (do_filter (!generated_problems)) scope of
   944                      0 => I
   945                    | n =>
   946                      scope_count (do_filter (these (!checked_problems)))
   947                                  scope = n
   948                      ? Integer.add 1) (!generated_scopes) 0
   949       in
   950         "Nitpick " ^ did_so_and_so ^
   951         (if is_some (!checked_problems) andalso total > 0 then
   952            " " ^ string_of_int unsat ^ " of " ^ string_of_int total ^ " scope"
   953            ^ plural_s total
   954          else
   955            "") ^ "."
   956       end
   957 
   958     val (skipped, the_scopes) =
   959       all_scopes hol_ctxt binarize cards_assigns maxes_assigns iters_assigns
   960                  bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs
   961                  finitizable_dataTs
   962     val _ = if skipped > 0 then
   963               print_m (fn () => "Too many scopes. Skipping " ^
   964                                 string_of_int skipped ^ " scope" ^
   965                                 plural_s skipped ^
   966                                 ". (Consider using \"mono\" or \
   967                                 \\"merge_type_vars\" to prevent this.)")
   968             else
   969               ()
   970     val _ = scopes := the_scopes
   971 
   972     fun run_batches _ _ []
   973                     (found_really_genuine, max_potential, max_genuine, donno) =
   974         if donno > 0 andalso max_genuine > 0 then
   975           (print_m (fn () => excipit "checked"); "unknown")
   976         else if max_genuine = original_max_genuine then
   977           if max_potential = original_max_potential then
   978             (print_m (fn () =>
   979                  "Nitpick found no " ^ das_wort_model ^ "." ^
   980                  (if not standard andalso likely_in_struct_induct_step then
   981                     " This suggests that the induction hypothesis might be \
   982                     \general enough to prove this subgoal."
   983                   else
   984                     "")); if skipped > 0 then "unknown" else "none")
   985           else
   986             (print_m (fn () =>
   987                  excipit ("could not find a" ^
   988                           (if max_genuine = 1 then
   989                              " better " ^ das_wort_model ^ "."
   990                            else
   991                              "ny better " ^ das_wort_model ^ "s.") ^
   992                           " It checked"));
   993              "potential")
   994         else if found_really_genuine then
   995           "genuine"
   996         else
   997           "quasi_genuine"
   998       | run_batches j n (batch :: batches) z =
   999         let val (z as (_, _, max_genuine, _)) = run_batch j n batch z in
  1000           run_batches (j + 1) n (if max_genuine > 0 then batches else []) z
  1001         end
  1002 
  1003     val batches = batch_list batch_size (!scopes)
  1004     val outcome_code =
  1005       run_batches 0 (length batches) batches
  1006                   (false, max_potential, max_genuine, 0)
  1007       handle TimeLimit.TimeOut =>
  1008              (print_m (fn () => excipit "ran out of time after checking");
  1009               if !met_potential > 0 then "potential" else "unknown")
  1010     val _ = print_v (fn () =>
  1011                 "Total time: " ^ string_from_time (Timer.checkRealTimer timer) ^
  1012                 ".")
  1013   in (outcome_code, !state_ref) end
  1014 
  1015 (* Give the inner timeout a chance. *)
  1016 val timeout_bonus = seconds 1.0
  1017 
  1018 fun pick_nits_in_term state (params as {debug, timeout, expect, ...}) auto i n
  1019                       step subst assm_ts orig_t =
  1020   let val print_m = if auto then K () else Output.urgent_message in
  1021     if getenv "KODKODI" = "" then
  1022       (* The "expect" argument is deliberately ignored if Kodkodi is missing so
  1023          that the "Nitpick_Examples" can be processed on any machine. *)
  1024       (print_m (Pretty.string_of (plazy install_kodkodi_message));
  1025        ("no_kodkodi", state))
  1026     else
  1027       let
  1028         val unknown_outcome = ("unknown", state)
  1029         val deadline = Option.map (curry Time.+ (Time.now ())) timeout
  1030         val outcome as (outcome_code, _) =
  1031           time_limit (if debug orelse is_none timeout then NONE
  1032                       else SOME (Time.+ (the timeout, timeout_bonus)))
  1033               (pick_them_nits_in_term deadline state params auto i n step subst
  1034                                       assm_ts) orig_t
  1035           handle TOO_LARGE (_, details) =>
  1036                  (print_m ("Limit reached: " ^ details ^ "."); unknown_outcome)
  1037                | TOO_SMALL (_, details) =>
  1038                  (print_m ("Limit reached: " ^ details ^ "."); unknown_outcome)
  1039                | Kodkod.SYNTAX (_, details) =>
  1040                  (print_m ("Malformed Kodkodi output: " ^ details ^ ".");
  1041                   unknown_outcome)
  1042                | TimeLimit.TimeOut =>
  1043                  (print_m "Nitpick ran out of time."; unknown_outcome)
  1044       in
  1045         if expect = "" orelse outcome_code = expect then outcome
  1046         else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")
  1047       end
  1048   end
  1049 
  1050 fun is_fixed_equation fixes
  1051                       (Const (@{const_name "=="}, _) $ Free (s, _) $ Const _) =
  1052     member (op =) fixes s
  1053   | is_fixed_equation _ _ = false
  1054 fun extract_fixed_frees ctxt (assms, t) =
  1055   let
  1056     val fixes = Variable.fixes_of ctxt |> map snd
  1057     val (subst, other_assms) =
  1058       List.partition (is_fixed_equation fixes) 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;