(*  Title:      HOL/Tools/Nitpick/nitpick.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2008, 2009, 2010

Finite model generation for HOL formulas using Kodkod.

*)

signature NITPICK =

sig

  type styp = Nitpick_Util.styp

  type term_postprocessor = Nitpick_Model.term_postprocessor

  datatype mode = Auto_Try | Try | Normal

  type params =

    {cards_assigns: (typ option * int list) list,

     maxes_assigns: (styp option * int list) list,

     iters_assigns: (styp option * int list) list,

     bitss: int list,

     bisim_depths: int list,

     boxes: (typ option * bool option) list,

     finitizes: (typ option * bool option) list,

     monos: (typ option * bool option) list,

     stds: (typ option * bool) list,

     wfs: (styp option * bool option) list,

     sat_solver: string,

     blocking: bool,

     falsify: bool,

     debug: bool,

     verbose: bool,

     overlord: bool,

     user_axioms: bool option,

     assms: bool,

     whacks: term list,

     merge_type_vars: bool,

     binary_ints: bool option,

     destroy_constrs: bool,

     specialize: bool,

     star_linear_preds: bool,

     total_consts: bool option,

     needs: term list option,

     peephole_optim: bool,

     datatype_sym_break: int,

     kodkod_sym_break: int,

     timeout: Time.time option,

     tac_timeout: Time.time option,

     max_threads: int,

     show_datatypes: bool,

     show_skolems: bool,

     show_consts: bool,

     evals: term list,

     formats: (term option * int list) list,

     atomss: (typ option * string list) list,

     max_potential: int,

     max_genuine: int,

     check_potential: bool,

     check_genuine: bool,

     batch_size: int,

     expect: string}

  val genuineN : string

  val quasi_genuineN : string

  val potentialN : string

  val noneN : string

  val unknownN : string

  val register_frac_type : string -> (string * string) list -> theory -> theory

  val unregister_frac_type : string -> theory -> theory

  val register_codatatype : typ -> string -> styp list -> theory -> theory

  val unregister_codatatype : typ -> theory -> theory

  val register_term_postprocessor :

    typ -> term_postprocessor -> theory -> theory

  val unregister_term_postprocessor : typ -> theory -> theory

  val pick_nits_in_term :

    Proof.state -> params -> mode -> int -> int -> int -> (term * term) list

    -> term list -> term -> string * Proof.state

  val pick_nits_in_subgoal :

    Proof.state -> params -> mode -> int -> int -> string * Proof.state

end;

structure Nitpick : NITPICK =

struct

open Nitpick_Util

open Nitpick_HOL

open Nitpick_Preproc

open Nitpick_Mono

open Nitpick_Scope

open Nitpick_Peephole

open Nitpick_Rep

open Nitpick_Nut

open Nitpick_Kodkod

open Nitpick_Model

structure KK = Kodkod

datatype mode = Auto_Try | Try | Normal

type params =

  {cards_assigns: (typ option * int list) list,

   maxes_assigns: (styp option * int list) list,

   iters_assigns: (styp option * int list) list,

   bitss: int list,

   bisim_depths: int list,

   boxes: (typ option * bool option) list,

   finitizes: (typ option * bool option) list,

   monos: (typ option * bool option) list,

   stds: (typ option * bool) list,

   wfs: (styp option * bool option) list,

   sat_solver: string,

   blocking: bool,

   falsify: bool,

   debug: bool,

   verbose: bool,

   overlord: bool,

   user_axioms: bool option,

   assms: bool,

   whacks: term list,

   merge_type_vars: bool,

   binary_ints: bool option,

   destroy_constrs: bool,

   specialize: bool,

   star_linear_preds: bool,

   total_consts: bool option,

   needs: term list option,

   peephole_optim: bool,

   datatype_sym_break: int,

   kodkod_sym_break: int,

   timeout: Time.time option,

   tac_timeout: Time.time option,

   max_threads: int,

   show_datatypes: bool,

   show_skolems: bool,

   show_consts: bool,

   evals: term list,

   formats: (term option * int list) list,

   atomss: (typ option * string list) list,

   max_potential: int,

   max_genuine: int,

   check_potential: bool,

   check_genuine: bool,

   batch_size: int,

   expect: string}

val genuineN = "genuine"

val quasi_genuineN = "quasi_genuine"

val potentialN = "potential"

val noneN = "none"

val unknownN = "unknown"

(* TODO: eliminate these historical aliases *)

val register_frac_type = Nitpick_HOL.register_frac_type_global

val unregister_frac_type = Nitpick_HOL.unregister_frac_type_global

val register_codatatype = Nitpick_HOL.register_codatatype_global

val unregister_codatatype = Nitpick_HOL.unregister_codatatype_global

val register_term_postprocessor =

  Nitpick_Model.register_term_postprocessor_global

val unregister_term_postprocessor =

  Nitpick_Model.unregister_term_postprocessor_global

type problem_extension =

  {free_names: nut list,

   sel_names: nut list,

   nonsel_names: nut list,

   rel_table: nut NameTable.table,

   unsound: bool,

   scope: scope}

type rich_problem = KK.problem * problem_extension

fun pretties_for_formulas _ _ [] = []

  | pretties_for_formulas ctxt s ts =

    [Pretty.str (s ^ plural_s_for_list ts ^ ":"),

     Pretty.indent indent_size (Pretty.chunks

         (map2 (fn j => fn t =>

                   Pretty.block [t |> shorten_names_in_term

                                   |> Syntax.pretty_term ctxt,

                                 Pretty.str (if j = 1 then "." else ";")])

               (length ts downto 1) ts))]

fun install_java_message () =

  "Nitpick requires Java Development Kit 1.6/1.7 via ISABELLE_JDK_HOME setting."

fun install_kodkodi_message () =

  "Nitpick requires the external Java program Kodkodi. To install it, download \

  \the package from \"http://www21.in.tum.de/~blanchet/#software\" and add the \

  \\"kodkodi-x.y.z\" directory's full path to " ^

  Path.print (Path.expand (Path.explode "$ISABELLE_HOME_USER/etc/components")) ^

  " on a line of its own."

val max_unsound_delay_ms = 200

val max_unsound_delay_percent = 2

fun unsound_delay_for_timeout NONE = max_unsound_delay_ms

  | unsound_delay_for_timeout (SOME timeout) =

    Int.max (0, Int.min (max_unsound_delay_ms,

                         Time.toMilliseconds timeout

                         * max_unsound_delay_percent div 100))

fun passed_deadline NONE = false

  | passed_deadline (SOME time) = Time.compare (Time.now (), time) <> LESS

fun none_true assigns = forall (not_equal (SOME true) o snd) assigns

fun has_lonely_bool_var (@{const Pure.conjunction}

                         $ (@{const Trueprop} $ Free _) $ _) = true

  | has_lonely_bool_var _ = false

val syntactic_sorts =

  @{sort "{default,zero,one,plus,minus,uminus,times,inverse,abs,sgn,ord,equal}"} @

  @{sort numeral}

fun has_tfree_syntactic_sort (TFree (_, S as _ :: _)) =

    subset (op =) (S, syntactic_sorts)

  | has_tfree_syntactic_sort _ = false

val has_syntactic_sorts = exists_type (exists_subtype has_tfree_syntactic_sort)

fun plazy f = Pretty.blk (0, pstrs (f ()))

fun pick_them_nits_in_term deadline state (params : params) mode i n step

                           subst assm_ts orig_t =

  let

    val timer = Timer.startRealTimer ()

    val thy = Proof.theory_of state

    val ctxt = Proof.context_of state

(* FIXME: reintroduce code before new release:

    val nitpick_thy = Thy_Info.get_theory "Nitpick"

    val _ = Theory.subthy (nitpick_thy, thy) orelse

            error "You must import the theory \"Nitpick\" to use Nitpick"

*)

    val {cards_assigns, maxes_assigns, iters_assigns, bitss, bisim_depths,

         boxes, finitizes, monos, stds, wfs, sat_solver, falsify, debug,

         verbose, overlord, user_axioms, assms, whacks, merge_type_vars,

         binary_ints, destroy_constrs, specialize, star_linear_preds,

         total_consts, needs, peephole_optim, datatype_sym_break,

         kodkod_sym_break, tac_timeout, max_threads, show_datatypes,

         show_skolems, show_consts, evals, formats, atomss, max_potential,

         max_genuine, check_potential, check_genuine, batch_size, ...} = params

    val state_ref = Unsynchronized.ref state

    fun pprint print =

      if mode = Auto_Try then

        Unsynchronized.change state_ref o Proof.goal_message o K

        o Pretty.chunks o cons (Pretty.str "") o single

        o Pretty.mark Isabelle_Markup.hilite

      else

        print o Pretty.string_of

    val pprint_a = pprint Output.urgent_message

    fun pprint_n f = () |> mode = Normal ? pprint Output.urgent_message o f

    fun pprint_v f = () |> verbose ? pprint Output.urgent_message o f

    fun pprint_d f = () |> debug ? pprint tracing o f

    val print = pprint Output.urgent_message o curry Pretty.blk 0 o pstrs

(*

    val print_g = pprint tracing o Pretty.str

*)

    val print_n = pprint_n o K o plazy

    val print_v = pprint_v o K o plazy

    fun check_deadline () =

      if passed_deadline deadline then raise TimeLimit.TimeOut else ()

    val assm_ts = if assms orelse mode <> Normal then assm_ts else []

    val _ =

      if step = 0 then

        print_n (fn () => "Nitpicking formula...")

      else

        pprint_n (fn () => Pretty.chunks (

            pretties_for_formulas ctxt ("Nitpicking " ^

                (if i <> 1 orelse n <> 1 then

                   "subgoal " ^ string_of_int i ^ " of " ^ string_of_int n

                 else

                   "goal")) [Logic.list_implies (assm_ts, orig_t)]))

    val _ = print_v (enclose "Timestamp: " "." o Date.fmt "%H:%M:%S"

                     o Date.fromTimeLocal o Time.now)

    val neg_t = if falsify then Logic.mk_implies (orig_t, @{prop False})

                else orig_t

    val conj_ts = neg_t :: assm_ts @ evals @ these needs

    val tfree_table =

      if merge_type_vars then merged_type_var_table_for_terms thy conj_ts

      else []

    val merge_tfrees = merge_type_vars_in_term thy merge_type_vars tfree_table

    val neg_t = neg_t |> merge_tfrees

    val assm_ts = assm_ts |> map merge_tfrees

    val evals = evals |> map merge_tfrees

    val needs = needs |> Option.map (map merge_tfrees)

    val conj_ts = neg_t :: assm_ts @ evals @ these needs

    val original_max_potential = max_potential

    val original_max_genuine = max_genuine

    val max_bisim_depth = fold Integer.max bisim_depths ~1

    val case_names = case_const_names ctxt stds

    val defs = all_defs_of thy subst

    val nondefs = all_nondefs_of ctxt subst

    val def_tables = const_def_tables ctxt subst defs

    val nondef_table = const_nondef_table nondefs

    val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)

    val psimp_table = const_psimp_table ctxt subst

    val choice_spec_table = const_choice_spec_table ctxt subst

    val nondefs =

      nondefs |> filter_out (is_choice_spec_axiom thy choice_spec_table)

    val intro_table = inductive_intro_table ctxt subst def_tables

    val ground_thm_table = ground_theorem_table thy

    val ersatz_table = ersatz_table ctxt

    val hol_ctxt as {wf_cache, ...} =

      {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,

       stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,

       whacks = whacks, binary_ints = binary_ints,

       destroy_constrs = destroy_constrs, specialize = specialize,

       star_linear_preds = star_linear_preds, total_consts = total_consts,

       needs = needs, tac_timeout = tac_timeout, evals = evals,

       case_names = case_names, def_tables = def_tables,

       nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,

       psimp_table = psimp_table, choice_spec_table = choice_spec_table,

       intro_table = intro_table, ground_thm_table = ground_thm_table,

       ersatz_table = ersatz_table, skolems = Unsynchronized.ref [],

       special_funs = Unsynchronized.ref [],

       unrolled_preds = Unsynchronized.ref [], wf_cache = Unsynchronized.ref [],

       constr_cache = Unsynchronized.ref []}

    val pseudo_frees = []

    val real_frees = fold Term.add_frees conj_ts []

    val _ = null (fold Term.add_tvars conj_ts []) orelse

            error "Nitpick cannot handle goals with schematic type variables."

    val (nondef_ts, def_ts, need_ts, got_all_mono_user_axioms,

         no_poly_user_axioms, binarize) =

      preprocess_formulas hol_ctxt assm_ts neg_t

    val got_all_user_axioms =

      got_all_mono_user_axioms andalso no_poly_user_axioms

    fun print_wf (x, (gfp, wf)) =

      pprint_n (fn () => Pretty.blk (0,

          pstrs ("The " ^ (if gfp then "co" else "") ^ "inductive predicate \"")

          @ Syntax.pretty_term ctxt (Const x) ::

          pstrs (if wf then

                   "\" was proved well-founded. Nitpick can compute it \

                   \efficiently."

                 else

                   "\" could not be proved well-founded. Nitpick might need to \

                   \unroll it.")))

    val _ = if verbose then List.app print_wf (!wf_cache) else ()

    val das_wort_formula = if falsify then "Negated conjecture" else "Formula"

    val _ =

      pprint_d (fn () => Pretty.chunks

          (pretties_for_formulas ctxt das_wort_formula [hd nondef_ts] @

           pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @

           pretties_for_formulas ctxt "Relevant nondefinitional axiom"

                                 (tl nondef_ts)))

    val _ = List.app (ignore o Term.type_of) (nondef_ts @ def_ts)

            handle TYPE (_, Ts, ts) =>

                   raise TYPE ("Nitpick.pick_them_nits_in_term", Ts, ts)

    val nondef_us = nondef_ts |> map (nut_from_term hol_ctxt Eq)

    val def_us = def_ts |> map (nut_from_term hol_ctxt DefEq)

    val need_us = need_ts |> map (nut_from_term hol_ctxt Eq)

    val (free_names, const_names) =

      fold add_free_and_const_names (nondef_us @ def_us @ need_us) ([], [])

    val (sel_names, nonsel_names) =

      List.partition (is_sel o nickname_of) const_names

    val sound_finitizes = none_true finitizes

    val standard = forall snd stds

(*

    val _ =

      List.app (print_g o string_for_nut ctxt) (nondef_us @ def_us @ need_us)

*)

    val unique_scope = forall (curry (op =) 1 o length o snd) cards_assigns

    fun monotonicity_message Ts extra =

      let val pretties = map (pretty_maybe_quote o pretty_for_type ctxt) Ts in

        Pretty.blk (0,

          pstrs ("The type" ^ plural_s_for_list pretties ^ " ") @

          pretty_serial_commas "and" pretties @

          pstrs (" " ^

                 (if none_true monos then

                    "passed the monotonicity test"

                  else

                    (if length pretties = 1 then "is" else "are") ^

                    " considered monotonic") ^

                 ". " ^ extra))

      end

    fun is_type_fundamentally_monotonic T =

      (is_datatype ctxt stds T andalso not (is_quot_type ctxt T) andalso

       (not (is_pure_typedef ctxt T) orelse is_univ_typedef ctxt T)) orelse

      is_number_type ctxt T orelse is_bit_type T

    fun is_type_actually_monotonic T =

      formulas_monotonic hol_ctxt binarize T (nondef_ts, def_ts)

    fun is_type_kind_of_monotonic T =

      case triple_lookup (type_match thy) monos T of

        SOME (SOME false) => false

      | _ => is_type_actually_monotonic T

    fun is_type_monotonic T =

      unique_scope orelse

      case triple_lookup (type_match thy) monos T of

        SOME (SOME b) => b

      | _ => is_type_fundamentally_monotonic T orelse

             is_type_actually_monotonic T

    fun is_deep_datatype_finitizable T =

      triple_lookup (type_match thy) finitizes T = SOME (SOME true)

    fun is_shallow_datatype_finitizable (T as Type (@{type_name fun_box}, _)) =

        is_type_kind_of_monotonic T

      | is_shallow_datatype_finitizable T =

        case triple_lookup (type_match thy) finitizes T of

          SOME (SOME b) => b

        | _ => is_type_kind_of_monotonic T

    fun is_datatype_deep T =

      not standard orelse T = @{typ unit} orelse T = nat_T orelse

      is_word_type T orelse

      exists (curry (op =) T o domain_type o type_of) sel_names

    val all_Ts = ground_types_in_terms hol_ctxt binarize (nondef_ts @ def_ts)

                 |> sort Term_Ord.typ_ord

    val _ =

      if verbose andalso binary_ints = SOME true andalso

         exists (member (op =) [nat_T, int_T]) all_Ts then

        print_v (K "The option \"binary_ints\" will be ignored because of the \

                   \presence of rationals, reals, \"Suc\", \"gcd\", or \"lcm\" \

                   \in the problem or because of the \"non_std\" option.")

      else

        ()

    val _ =

      if mode = Normal andalso

         exists (fn Type (@{type_name Datatype.node}, _) => true | _ => false)

                all_Ts then

        print_n (K ("Warning: The problem involves directly or indirectly the \

                    \internal type " ^ quote @{type_name Datatype.node} ^

                    ". This type is very Nitpick-unfriendly, and its presence \

                    \usually indicates either a failure of abstraction or a \

                    \quirk in Nitpick."))

      else

        ()

    val (mono_Ts, nonmono_Ts) = List.partition is_type_monotonic all_Ts

    val _ =

      if verbose andalso not unique_scope then

        case filter_out is_type_fundamentally_monotonic mono_Ts of

          [] => ()

        | interesting_mono_Ts =>

          pprint_v (K (monotonicity_message interesting_mono_Ts

                          "Nitpick might be able to skip some scopes."))

      else

        ()

    val (deep_dataTs, shallow_dataTs) =

      all_Ts |> filter (is_datatype ctxt stds)

             |> List.partition is_datatype_deep

    val finitizable_dataTs =

      (deep_dataTs |> filter_out (is_finite_type hol_ctxt)

                   |> filter is_deep_datatype_finitizable) @

      (shallow_dataTs |> filter_out (is_finite_type hol_ctxt)

                      |> filter is_shallow_datatype_finitizable)

    val _ =

      if verbose andalso not (null finitizable_dataTs) then

        pprint_v (K (monotonicity_message finitizable_dataTs

                         "Nitpick can use a more precise finite encoding."))

      else

        ()

    (* This detection code is an ugly hack. Fortunately, it is used only to

       provide a hint to the user. *)

    fun is_struct_induct_step (name, (Rule_Cases.Case {fixes, assumes, ...}, _)) =

      not (null fixes) andalso

      exists (String.isSuffix ".hyps" o fst) assumes andalso

      exists (exists (curry (op =) name o shortest_name o fst)

              o datatype_constrs hol_ctxt) deep_dataTs

    val likely_in_struct_induct_step =

      exists is_struct_induct_step (Proof_Context.cases_of ctxt)

    val _ = if standard andalso likely_in_struct_induct_step then

              pprint_n (fn () => Pretty.blk (0,

                  pstrs "Hint: To check that the induction hypothesis is \

                        \general enough, try this command: " @

                  [Pretty.mark Isabelle_Markup.sendback (Pretty.blk (0,

                       pstrs ("nitpick [non_std, show_all]")))] @ pstrs "."))

            else

              ()

(*

    val _ = print_g "Monotonic types:"

    val _ = List.app (print_g o string_for_type ctxt) mono_Ts

    val _ = print_g "Nonmonotonic types:"

    val _ = List.app (print_g o string_for_type ctxt) nonmono_Ts

*)

    val incremental = Int.max (max_potential, max_genuine) >= 2

    val actual_sat_solver =

      if sat_solver <> "smart" then

        if incremental andalso

           not (member (op =) (Kodkod_SAT.configured_sat_solvers true)

                       sat_solver) then

          (print_n (K ("An incremental SAT solver is required: \"SAT4J\" will \

                       \be used instead of " ^ quote sat_solver ^ "."));

           "SAT4J")

        else

          sat_solver

      else

        Kodkod_SAT.smart_sat_solver_name incremental

    val _ =

      if sat_solver = "smart" then

        print_v (fn () =>

            "Using SAT solver " ^ quote actual_sat_solver ^ ". The following" ^

            (if incremental then " incremental " else " ") ^

            "solvers are configured: " ^

            commas_quote (Kodkod_SAT.configured_sat_solvers incremental) ^ ".")

      else

        ()

    val too_big_scopes = Unsynchronized.ref []

    fun problem_for_scope unsound

            (scope as {card_assigns, bits, bisim_depth, datatypes, ofs, ...}) =

      let

        val _ = not (exists (fn other => scope_less_eq other scope)

                            (!too_big_scopes)) orelse

                raise TOO_LARGE ("Nitpick.pick_them_nits_in_term.\

                                 \problem_for_scope", "too large scope")

(*

        val _ = print_g "Offsets:"

        val _ = List.app (fn (T, j0) =>

                             print_g (string_for_type ctxt T ^ " = " ^

                                    string_of_int j0))

                         (Typtab.dest ofs)

*)

        val effective_total_consts =

          case total_consts of

            SOME b => b

          | NONE => forall (is_exact_type datatypes true) all_Ts

        val main_j0 = offset_of_type ofs bool_T

        val (nat_card, nat_j0) = spec_of_type scope nat_T

        val (int_card, int_j0) = spec_of_type scope int_T

        val _ = (nat_j0 = main_j0 andalso int_j0 = main_j0) orelse

                raise BAD ("Nitpick.pick_them_nits_in_term.problem_for_scope",

                           "bad offsets")

        val kk = kodkod_constrs peephole_optim nat_card int_card main_j0

        val (free_names, rep_table) =

          choose_reps_for_free_vars scope pseudo_frees free_names

                                    NameTable.empty

        val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table

        val (nonsel_names, rep_table) =

          choose_reps_for_consts scope effective_total_consts nonsel_names

                                 rep_table

        val (guiltiest_party, min_highest_arity) =

          NameTable.fold (fn (name, R) => fn (s, n) =>

                             let val n' = arity_of_rep R in

                               if n' > n then (nickname_of name, n') else (s, n)

                             end) rep_table ("", 1)

        val min_univ_card =

          NameTable.fold (Integer.max o min_univ_card_of_rep o snd) rep_table

                         (univ_card nat_card int_card main_j0 [] KK.True)

        val _ = if debug then ()

                else check_arity guiltiest_party min_univ_card min_highest_arity

        val def_us =

          def_us |> map (choose_reps_in_nut scope unsound rep_table true)

        val nondef_us =

          nondef_us |> map (choose_reps_in_nut scope unsound rep_table false)

        val need_us =

          need_us |> map (choose_reps_in_nut scope unsound rep_table false)

(*

        val _ = List.app (print_g o string_for_nut ctxt)

                         (free_names @ sel_names @ nonsel_names @

                          nondef_us @ def_us @ need_us)

*)

        val (free_rels, pool, rel_table) =

          rename_free_vars free_names initial_pool NameTable.empty

        val (sel_rels, pool, rel_table) =

          rename_free_vars sel_names pool rel_table

        val (other_rels, pool, rel_table) =

          rename_free_vars nonsel_names pool rel_table

        val nondef_us = nondef_us |> map (rename_vars_in_nut pool rel_table)

        val def_us = def_us |> map (rename_vars_in_nut pool rel_table)

        val need_us = need_us |> map (rename_vars_in_nut pool rel_table)

        val nondef_fs = map (kodkod_formula_from_nut ofs kk) nondef_us

        val def_fs = map (kodkod_formula_from_nut ofs kk) def_us

        val formula = fold (fold s_and) [def_fs, nondef_fs] KK.True

        val comment = (if unsound then "unsound" else "sound") ^ "\n" ^

                      Print_Mode.setmp [] multiline_string_for_scope scope

        val kodkod_sat_solver =

          Kodkod_SAT.sat_solver_spec actual_sat_solver |> snd

        val bit_width = if bits = 0 then 16 else bits + 1

        val delay =

          if unsound then

            Option.map (fn time => Time.- (time, Time.now ())) deadline

            |> unsound_delay_for_timeout

          else

            0

        val settings = [("solver", commas_quote kodkod_sat_solver),

                        ("bit_width", string_of_int bit_width),

                        ("symmetry_breaking", string_of_int kodkod_sym_break),

                        ("sharing", "3"),

                        ("flatten", "false"),

                        ("delay", signed_string_of_int delay)]

        val plain_rels = free_rels @ other_rels

        val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels

        val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels

        val need_vals =

          map (fn dtype as {typ, ...} =>

                  (typ, needed_values_for_datatype need_us ofs dtype)) datatypes

        val sel_bounds =

          map (bound_for_sel_rel ctxt debug need_vals datatypes) sel_rels

        val dtype_axioms =

          declarative_axioms_for_datatypes hol_ctxt binarize need_us need_vals

              datatype_sym_break bits ofs kk rel_table datatypes

        val declarative_axioms = plain_axioms @ dtype_axioms

        val univ_card = Int.max (univ_card nat_card int_card main_j0

                                     (plain_bounds @ sel_bounds) formula,

                                 main_j0 |> bits > 0 ? Integer.add (bits + 1))

        val (built_in_bounds, built_in_axioms) =

          bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card

              nat_card int_card main_j0 (formula :: declarative_axioms)

        val bounds = built_in_bounds @ plain_bounds @ sel_bounds

                     |> not debug ? merge_bounds

        val axioms = built_in_axioms @ declarative_axioms

        val highest_arity =

          fold Integer.max (map (fst o fst) (maps fst bounds)) 0

        val formula = fold_rev s_and axioms formula

        val _ = if bits = 0 then () else check_bits bits formula

        val _ = if debug orelse formula = KK.False then ()

                else check_arity "" univ_card highest_arity

      in

        SOME ({comment = comment, settings = settings, univ_card = univ_card,

               tuple_assigns = [], bounds = bounds,

               int_bounds = if bits = 0 then sequential_int_bounds univ_card

                            else pow_of_two_int_bounds bits main_j0,

               expr_assigns = [], formula = formula},

              {free_names = free_names, sel_names = sel_names,

               nonsel_names = nonsel_names, rel_table = rel_table,

               unsound = unsound, scope = scope})

      end

      handle TOO_LARGE (loc, msg) =>

             if loc = "Nitpick_Kodkod.check_arity" andalso

                not (Typtab.is_empty ofs) then

               problem_for_scope unsound

                   {hol_ctxt = hol_ctxt, binarize = binarize,

                    card_assigns = card_assigns, bits = bits,

                    bisim_depth = bisim_depth, datatypes = datatypes,

                    ofs = Typtab.empty}

             else if loc = "Nitpick.pick_them_nits_in_term.\

                           \problem_for_scope" then

               NONE

             else

               (Unsynchronized.change too_big_scopes (cons scope);

                print_v (fn () =>

                    "Limit reached: " ^ msg ^ ". Skipping " ^

                    (if unsound then "potential component of " else "") ^

                    "scope.");

                NONE)

           | TOO_SMALL (_, msg) =>

             (print_v (fn () =>

                  "Limit reached: " ^ msg ^ ". Skipping " ^

                  (if unsound then "potential component of " else "") ^

                  "scope.");

              NONE)

    val das_wort_model =

      (if falsify then "counterexample" else "model")

      |> not standard ? prefix "nonstandard "

    val scopes = Unsynchronized.ref []

    val generated_scopes = Unsynchronized.ref []

    val generated_problems = Unsynchronized.ref ([] : rich_problem list)

    val checked_problems = Unsynchronized.ref (SOME [])

    val met_potential = Unsynchronized.ref 0

    fun update_checked_problems problems =

      List.app (Unsynchronized.change checked_problems o Option.map o cons

                o nth problems)

    fun show_kodkod_warning "" = ()

      | show_kodkod_warning s = print_n (fn () => "Kodkod warning: " ^ s ^ ".")

    fun print_and_check_model genuine bounds

            ({free_names, sel_names, nonsel_names, rel_table, scope, ...}

             : problem_extension) =

      let

        val (reconstructed_model, codatatypes_ok) =

          reconstruct_hol_model

              {show_datatypes = show_datatypes, show_skolems = show_skolems,

               show_consts = show_consts}

              scope formats atomss real_frees pseudo_frees free_names sel_names

              nonsel_names rel_table bounds

        val genuine_means_genuine =

          got_all_user_axioms andalso none_true wfs andalso

          sound_finitizes andalso total_consts <> SOME true andalso

          codatatypes_ok

        fun assms_prop () = Logic.mk_conjunction_list (neg_t :: assm_ts)

      in

        (pprint_a (Pretty.chunks

             [Pretty.blk (0,

                  (pstrs ((if mode = Auto_Try then "Auto " else "") ^

                          "Nitpick found a" ^

                          (if not genuine then " potentially spurious "

                           else if genuine_means_genuine then " "

                           else " quasi genuine ") ^ das_wort_model) @

                   (case pretties_for_scope scope verbose of

                      [] => []

                    | pretties => pstrs " for " @ pretties) @

                   [Pretty.str ":\n"])),

              Pretty.indent indent_size reconstructed_model]);

         if genuine then

           (if check_genuine andalso standard then

              case prove_hol_model scope tac_timeout free_names sel_names

                                   rel_table bounds (assms_prop ()) of

                SOME true =>

                print ("Confirmation by \"auto\": The above " ^

                       das_wort_model ^ " is really genuine.")

              | SOME false =>

                if genuine_means_genuine then

                  error ("A supposedly genuine " ^ das_wort_model ^ " was \

                         \shown to be spurious by \"auto\".\nThis should never \

                         \happen.\nPlease send a bug report to blanchet\

                         \te@in.tum.de.")

                 else

                   print ("Refutation by \"auto\": The above " ^

                          das_wort_model ^ " is spurious.")

               | NONE => print "No confirmation by \"auto\"."

            else

              ();

            if not standard andalso likely_in_struct_induct_step then

              print "The existence of a nonstandard model suggests that the \

                    \induction hypothesis is not general enough or may even be \

                    \wrong. See the Nitpick manual's \"Inductive Properties\" \

                    \section for details (\"isabelle doc nitpick\")."

            else

              ();

            if has_lonely_bool_var orig_t then

              print "Hint: Maybe you forgot a colon after the lemma's name?"

            else if has_syntactic_sorts orig_t then

              print "Hint: Maybe you forgot a type constraint?"

            else

              ();

            if not genuine_means_genuine then

              if no_poly_user_axioms then

                let

                  val options =

                    [] |> not got_all_mono_user_axioms

                          ? cons ("user_axioms", "\"true\"")

                       |> not (none_true wfs)

                          ? cons ("wf", "\"smart\" or \"false\"")

                       |> not sound_finitizes

                          ? cons ("finitize", "\"smart\" or \"false\"")

                       |> total_consts = SOME true

                          ? cons ("total_consts", "\"smart\" or \"false\"")

                       |> not codatatypes_ok

                          ? cons ("bisim_depth", "a nonnegative value")

                  val ss =

                    map (fn (name, value) => quote name ^ " set to " ^ value)

                        options

                in

                  print ("Try again with " ^

                         space_implode " " (serial_commas "and" ss) ^

                         " to confirm that the " ^ das_wort_model ^

                         " is genuine.")

                end

              else

                print ("Nitpick is unable to guarantee the authenticity of \

                       \the " ^ das_wort_model ^ " in the presence of \

                       \polymorphic axioms.")

            else

              ();

            NONE)

         else

           if not genuine then

             (Unsynchronized.inc met_potential;

              if check_potential then

                let

                  val status = prove_hol_model scope tac_timeout free_names

                                               sel_names rel_table bounds

                                               (assms_prop ())

                in

                  (case status of

                     SOME true => print ("Confirmation by \"auto\": The \

                                         \above " ^ das_wort_model ^

                                         " is genuine.")

                   | SOME false => print ("Refutation by \"auto\": The above " ^

                                          das_wort_model ^ " is spurious.")

                   | NONE => print "No confirmation by \"auto\".");

                  status

                end

              else

                NONE)

           else

             NONE)

        |> pair genuine_means_genuine

      end

    fun solve_any_problem (found_really_genuine, max_potential, max_genuine,

                           donno) first_time problems =

      let

        val max_potential = Int.max (0, max_potential)

        val max_genuine = Int.max (0, max_genuine)

        fun print_and_check genuine (j, bounds) =

          print_and_check_model genuine bounds (snd (nth problems j))

        val max_solutions = max_potential + max_genuine

                            |> not incremental ? Integer.min 1

      in

        if max_solutions <= 0 then

          (found_really_genuine, 0, 0, donno)

        else

          case KK.solve_any_problem debug overlord deadline max_threads

                                    max_solutions (map fst problems) of

            KK.JavaNotInstalled =>

            (print_n install_java_message;

             (found_really_genuine, max_potential, max_genuine, donno + 1))

          | KK.JavaTooOld =>

            (print_n install_java_message;

             (found_really_genuine, max_potential, max_genuine, donno + 1))

          | KK.KodkodiNotInstalled =>

            (print_n install_kodkodi_message;

             (found_really_genuine, max_potential, max_genuine, donno + 1))

          | KK.Normal ([], unsat_js, s) =>

            (update_checked_problems problems unsat_js; show_kodkod_warning s;

             (found_really_genuine, max_potential, max_genuine, donno))

          | KK.Normal (sat_ps, unsat_js, s) =>

            let

              val (lib_ps, con_ps) =

                List.partition (#unsound o snd o nth problems o fst) sat_ps

            in

              update_checked_problems problems (unsat_js @ map fst lib_ps);

              show_kodkod_warning s;

              if null con_ps then

                let

                  val genuine_codes =

                    lib_ps |> take max_potential

                           |> map (print_and_check false)

                           |> filter (curry (op =) (SOME true) o snd)

                  val found_really_genuine =

                    found_really_genuine orelse exists fst genuine_codes

                  val num_genuine = length genuine_codes

                  val max_genuine = max_genuine - num_genuine

                  val max_potential = max_potential

                                      - (length lib_ps - num_genuine)

                in

                  if max_genuine <= 0 then

                    (found_really_genuine, 0, 0, donno)

                  else

                    let

                      (* "co_js" is the list of sound problems whose unsound

                         pendants couldn't be satisfied and hence that most

                         probably can't be satisfied themselves. *)

                      val co_js =

                        map (fn j => j - 1) unsat_js

                        |> filter (fn j =>

                                      j >= 0 andalso

                                      scopes_equivalent

                                          (#scope (snd (nth problems j)),

                                           #scope (snd (nth problems (j + 1)))))

                      val bye_js = sort_distinct int_ord (map fst sat_ps @

                                                          unsat_js @ co_js)

                      val problems =

                        problems |> filter_out_indices bye_js

                                 |> max_potential <= 0

                                    ? filter_out (#unsound o snd)

                    in

                      solve_any_problem (found_really_genuine, max_potential,

                                         max_genuine, donno) false problems

                    end

                end

              else

                let

                  val genuine_codes =

                    con_ps |> take max_genuine

                           |> map (print_and_check true)

                  val max_genuine = max_genuine - length genuine_codes

                  val found_really_genuine =

                    found_really_genuine orelse exists fst genuine_codes

                in

                  if max_genuine <= 0 orelse not first_time then

                    (found_really_genuine, 0, max_genuine, donno)

                  else

                    let

                      val bye_js = sort_distinct int_ord

                                                 (map fst sat_ps @ unsat_js)

                      val problems =

                        problems |> filter_out_indices bye_js

                                 |> filter_out (#unsound o snd)

                    in

                      solve_any_problem (found_really_genuine, 0, max_genuine,

                                         donno) false problems

                    end

                end

            end

          | KK.TimedOut unsat_js =>

            (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)

          | KK.Error (s, unsat_js) =>

            (update_checked_problems problems unsat_js;

             print_v (K ("Kodkod error: " ^ s ^ "."));

             (found_really_genuine, max_potential, max_genuine, donno + 1))

      end

    fun run_batch j n scopes (found_really_genuine, max_potential, max_genuine,

                              donno) =

      let

        val _ =

          if null scopes then

            print_n (K "The scope specification is inconsistent.")

          else if verbose then

            pprint_n (fn () => Pretty.chunks

                [Pretty.blk (0,

                     pstrs ((if n > 1 then

                               "Batch " ^ string_of_int (j + 1) ^ " of " ^

                               signed_string_of_int n ^ ": "

                             else

                               "") ^

                            "Trying " ^ string_of_int (length scopes) ^

                            " scope" ^ plural_s_for_list scopes ^ ":")),

                 Pretty.indent indent_size

                     (Pretty.chunks (map2

                          (fn j => fn scope =>

                              Pretty.block (

                                  (case pretties_for_scope scope true of

                                     [] => [Pretty.str "Empty"]

                                   | pretties => pretties) @

                                  [Pretty.str (if j = 1 then "." else ";")]))

                          (length scopes downto 1) scopes))])

          else

            ()

        fun add_problem_for_scope (scope, unsound) (problems, donno) =

          (check_deadline ();

           case problem_for_scope unsound scope of

             SOME problem =>

             (problems

              |> (null problems orelse

                  not (KK.problems_equivalent (fst problem, fst (hd problems))))

                  ? cons problem, donno)

           | NONE => (problems, donno + 1))

        val (problems, donno) =

          fold add_problem_for_scope

               (map_product pair scopes

                    ((if max_genuine > 0 then [false] else []) @

                     (if max_potential > 0 then [true] else [])))

               ([], donno)

        val _ = Unsynchronized.change generated_problems (append problems)

        val _ = Unsynchronized.change generated_scopes (append scopes)

        val _ =

          if j + 1 = n then

            let

              val (unsound_problems, sound_problems) =

                List.partition (#unsound o snd) (!generated_problems)

            in

              if not (null sound_problems) andalso

                 forall (KK.is_problem_trivially_false o fst)

                        sound_problems then

                print_n (fn () =>

                    "Warning: The conjecture " ^

                    (if falsify then "either trivially holds"

                     else "is either trivially unsatisfiable") ^

                    " for the given scopes or lies outside Nitpick's supported \

                    \fragment." ^

                    (if exists (not o KK.is_problem_trivially_false o fst)

                               unsound_problems then

                       " Only potentially spurious " ^ das_wort_model ^

                       "s may be found."

                     else

                       ""))

              else

                ()

            end

          else

            ()

      in

        solve_any_problem (found_really_genuine, max_potential, max_genuine,

                           donno) true (rev problems)

      end

    fun scope_count (problems : rich_problem list) scope =

      length (filter (curry scopes_equivalent scope o #scope o snd) problems)

    fun excipit did_so_and_so =

      let

        val do_filter =

          if !met_potential = max_potential then filter_out (#unsound o snd)

          else I

        val total = length (!scopes)

        val unsat =

          fold (fn scope =>

                   case scope_count (do_filter (!generated_problems)) scope of

                     0 => I

                   | n =>

                     scope_count (do_filter (these (!checked_problems)))

                                 scope = n

                     ? Integer.add 1) (!generated_scopes) 0

      in

        "Nitpick " ^ did_so_and_so ^

        (if is_some (!checked_problems) andalso total > 0 then

           " " ^ string_of_int unsat ^ " of " ^ string_of_int total ^ " scope"

           ^ plural_s total

         else

           "") ^ "."

      end

    val (skipped, the_scopes) =

      all_scopes hol_ctxt binarize cards_assigns maxes_assigns iters_assigns

                 bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs

                 finitizable_dataTs

    val _ = if skipped > 0 then

              print_n (fn () => "Too many scopes. Skipping " ^

                                string_of_int skipped ^ " scope" ^

                                plural_s skipped ^

                                ". (Consider using \"mono\" or \

                                \\"merge_type_vars\" to prevent this.)")

            else

              ()

    val _ = scopes := the_scopes

    fun run_batches _ _ []

                    (found_really_genuine, max_potential, max_genuine, donno) =

        if donno > 0 andalso max_genuine > 0 then

          (print_n (fn () => excipit "checked"); unknownN)