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

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2008, 2009

Finite model generation for HOL formulas using Kodkod.

*)

signature NITPICK =

sig

  type styp = Nitpick_Util.styp

  type params = {

    cards_assigns: (typ option * int list) list,

    maxes_assigns: (styp option * int list) list,

    iters_assigns: (styp option * int list) list,

    bisim_depths: int list,

    boxes: (typ option * bool option) list,

    monos: (typ option * bool option) 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,

    merge_type_vars: bool,

    destroy_constrs: bool,

    specialize: bool,

    skolemize: bool,

    star_linear_preds: bool,

    uncurry: bool,

    fast_descrs: bool,

    peephole_optim: bool,

    timeout: Time.time option,

    tac_timeout: Time.time option,

    sym_break: int,

    sharing_depth: int,

    flatten_props: bool,

    max_threads: int,

    show_skolems: bool,

    show_datatypes: bool,

    show_consts: bool,

    evals: term list,

    formats: (term option * int list) list,

    max_potential: int,

    max_genuine: int,

    check_potential: bool,

    check_genuine: bool,

    batch_size: int,

    expect: 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 pick_nits_in_term :

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

  val pick_nits_in_subgoal :

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

end;

structure Nitpick : NITPICK =

struct

open Nitpick_Util

open Nitpick_HOL

open Nitpick_Mono

open Nitpick_Scope

open Nitpick_Peephole

open Nitpick_Rep

open Nitpick_Nut

open Nitpick_Kodkod

open Nitpick_Model

type params = {

  cards_assigns: (typ option * int list) list,

  maxes_assigns: (styp option * int list) list,

  iters_assigns: (styp option * int list) list,

  bisim_depths: int list,

  boxes: (typ option * bool option) list,

  monos: (typ option * bool option) 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,

  merge_type_vars: bool,

  destroy_constrs: bool,

  specialize: bool,

  skolemize: bool,

  star_linear_preds: bool,

  uncurry: bool,

  fast_descrs: bool,

  peephole_optim: bool,

  timeout: Time.time option,

  tac_timeout: Time.time option,

  sym_break: int,

  sharing_depth: int,

  flatten_props: bool,

  max_threads: int,

  show_skolems: bool,

  show_datatypes: bool,

  show_consts: bool,

  evals: term list,

  formats: (term option * int list) list,

  max_potential: int,

  max_genuine: int,

  check_potential: bool,

  check_genuine: bool,

  batch_size: int,

  expect: string}

type problem_extension = {

  free_names: nut list,

  sel_names: nut list,

  nonsel_names: nut list,

  rel_table: nut NameTable.table,

  liberal: bool,

  scope: scope,

  core: Kodkod.formula,

  defs: Kodkod.formula list}

type rich_problem = Kodkod.problem * problem_extension

(* Proof.context -> string -> term list -> Pretty.T list *)

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_const_names_in_term

                                   |> Syntax.pretty_term ctxt,

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

               (length ts downto 1) ts))]

(* unit -> string *)

fun install_kodkodi_message () =

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

  \the package from Isabelle's web page and add the \"kodkodi-x.y.z\" \

  \directory's full path to \"" ^

  Path.implode (Path.expand (Path.appends

      (Path.variable "ISABELLE_HOME_USER" ::

       map Path.basic ["etc", "components"]))) ^ "\"."

val max_liberal_delay_ms = 200

val max_liberal_delay_percent = 2

(* Time.time option -> int *)

fun liberal_delay_for_timeout NONE = max_liberal_delay_ms

  | liberal_delay_for_timeout (SOME timeout) =

    Int.max (0, Int.min (max_liberal_delay_ms,

                         Time.toMilliseconds timeout

                         * max_liberal_delay_percent div 100))

(* Time.time option -> bool *)

fun passed_deadline NONE = false

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

(* ('a * bool option) list -> bool *)

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

val weaselly_sorts =

  [@{sort default}, @{sort zero}, @{sort one}, @{sort plus}, @{sort minus},

   @{sort uminus}, @{sort times}, @{sort inverse}, @{sort abs}, @{sort sgn},

   @{sort ord}, @{sort eq}, @{sort number}]

(* theory -> typ -> bool *)

fun is_tfree_with_weaselly_sort thy (TFree (_, S)) =

    exists (curry (Sign.subsort thy) S) weaselly_sorts

  | is_tfree_with_weaselly_sort _ _ = false

(* theory term -> bool *)

val has_weaselly_sorts =

  exists_type o exists_subtype o is_tfree_with_weaselly_sort

(* (unit -> string) -> Pretty.T *)

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

(* Time.time -> Proof.state -> params -> bool -> term -> string * Proof.state *)

fun pick_them_nits_in_term deadline state (params : params) auto orig_assm_ts

                           orig_t =

  let

    val timer = Timer.startRealTimer ()

    val thy = Proof.theory_of state

    val ctxt = Proof.context_of state

    val {cards_assigns, maxes_assigns, iters_assigns, bisim_depths, boxes,

         monos, wfs, sat_solver, blocking, falsify, debug, verbose, overlord,

         user_axioms, assms, merge_type_vars, destroy_constrs, specialize,

         skolemize, star_linear_preds, uncurry, fast_descrs, peephole_optim,

         tac_timeout, sym_break, sharing_depth, flatten_props, max_threads,

         show_skolems, show_datatypes, show_consts, evals, formats,

         max_potential, max_genuine, check_potential, check_genuine, batch_size,

         ...} =

      params

    val state_ref = Unsynchronized.ref state

    (* Pretty.T -> unit *)

    val pprint =

      if auto then

        Unsynchronized.change state_ref o Proof.goal_message o K

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

        o Pretty.mark Markup.hilite

      else

        priority o Pretty.string_of

    (* (unit -> Pretty.T) -> unit *)

    fun pprint_m f = () |> not auto ? pprint o f

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

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

    (* string -> unit *)

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

    (* (unit -> string) -> unit *)

    val print_m = pprint_m o K o plazy

    val print_v = pprint_v o K o plazy

    val print_d = pprint_d o K o plazy

    (* unit -> unit *)

    fun check_deadline () =

      if debug andalso passed_deadline deadline then raise TimeLimit.TimeOut

      else ()

    (* unit -> 'a *)

    fun do_interrupted () =

      if passed_deadline deadline then raise TimeLimit.TimeOut

      else raise Interrupt

    val _ = print_m (K "Nitpicking...")

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

                else orig_t

    val assms_t = if assms orelse auto then

                    Logic.mk_conjunction_list (neg_t :: orig_assm_ts)

                  else

                    neg_t

    val (assms_t, evals) =

      assms_t :: evals |> merge_type_vars ? merge_type_vars_in_terms

                       |> pairf hd tl

    val original_max_potential = max_potential

    val original_max_genuine = max_genuine

(*

    val _ = priority ("*** " ^ Syntax.string_of_term ctxt orig_t)

    val _ = List.app (fn t => priority ("*** " ^ Syntax.string_of_term ctxt t))

                     orig_assm_ts

*)

    val max_bisim_depth = fold Integer.max bisim_depths ~1

    val case_names = case_const_names thy

    val (defs, built_in_nondefs, user_nondefs) = all_axioms_of thy

    val def_table = const_def_table ctxt defs

    val nondef_table = const_nondef_table (built_in_nondefs @ user_nondefs)

    val simp_table = Unsynchronized.ref (const_simp_table ctxt)

    val psimp_table = const_psimp_table ctxt

    val intro_table = inductive_intro_table ctxt def_table

    val ground_thm_table = ground_theorem_table thy

    val ersatz_table = ersatz_table thy

    val (ext_ctxt as {skolems, special_funs, wf_cache, ...}) =

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

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

       destroy_constrs = destroy_constrs, specialize = specialize,

       skolemize = skolemize, star_linear_preds = star_linear_preds,

       uncurry = uncurry, fast_descrs = fast_descrs, tac_timeout = tac_timeout,

       evals = evals, case_names = case_names, def_table = def_table,

       nondef_table = nondef_table, user_nondefs = user_nondefs,

       simp_table = simp_table, psimp_table = psimp_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 frees = Term.add_frees assms_t []

    val _ = null (Term.add_tvars assms_t [])

            orelse raise NOT_SUPPORTED "schematic type variables"

    val (((def_ts, nondef_ts), (got_all_mono_user_axioms, no_poly_user_axioms)),

         core_t) = preprocess_term ext_ctxt assms_t

    val got_all_user_axioms =

      got_all_mono_user_axioms andalso no_poly_user_axioms

    (* styp * (bool * bool) -> unit *)

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

      pprint (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 _ =

      pprint_d (fn () =>

          Pretty.chunks

              (pretties_for_formulas ctxt "Preprocessed formula" [core_t] @

               pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @

               pretties_for_formulas ctxt "Relevant nondefinitional axiom"

                                     nondef_ts))

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

            handle TYPE (_, Ts, ts) =>

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

    val core_u = nut_from_term thy fast_descrs (!special_funs) Eq core_t

    val def_us = map (nut_from_term thy fast_descrs (!special_funs) DefEq)

                     def_ts

    val nondef_us = map (nut_from_term thy fast_descrs (!special_funs) Eq)

                        nondef_ts

    val (free_names, const_names) =

      fold add_free_and_const_names (core_u :: def_us @ nondef_us) ([], [])

    val (sel_names, nonsel_names) =

      List.partition (is_sel o nickname_of) const_names

    val would_be_genuine = got_all_user_axioms andalso none_true wfs

(*

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

                     (core_u :: def_us @ nondef_us)

*)

    val unique_scope = forall (equal 1 o length o snd) cards_assigns

    (* typ -> bool *)

    fun is_free_type_monotonic T =

      unique_scope orelse

      case triple_lookup (type_match thy) monos T of

        SOME (SOME b) => b

      | _ => formulas_monotonic ext_ctxt T def_ts nondef_ts core_t

    fun is_datatype_monotonic T =

      unique_scope orelse

      case triple_lookup (type_match thy) monos T of

        SOME (SOME b) => b

      | _ =>

        not (is_pure_typedef thy T) orelse is_univ_typedef thy T

        orelse is_number_type thy T

        orelse formulas_monotonic ext_ctxt T def_ts nondef_ts core_t

    fun is_datatype_shallow T =

      not (exists (equal T o domain_type o type_of) sel_names)

    val Ts = ground_types_in_terms ext_ctxt (core_t :: def_ts @ nondef_ts)

             |> sort TermOrd.typ_ord

    val (all_dataTs, all_free_Ts) =

      List.partition (is_integer_type orf is_datatype thy) Ts

    val (mono_dataTs, nonmono_dataTs) =

      List.partition is_datatype_monotonic all_dataTs

    val (mono_free_Ts, nonmono_free_Ts) =

      List.partition is_free_type_monotonic all_free_Ts

    val _ =

      if not unique_scope andalso not (null mono_free_Ts) then

        print_v (fn () =>

                    let

                      val ss = map (quote o string_for_type ctxt) mono_free_Ts

                    in

                      "The type" ^ plural_s_for_list ss ^ " " ^

                      space_implode " " (serial_commas "and" ss) ^ " " ^

                      (if none_true monos then

                         "passed the monotonicity test"

                       else

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

                         " considered monotonic") ^

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

                    end)

      else

        ()

    val mono_Ts = mono_dataTs @ mono_free_Ts

    val nonmono_Ts = nonmono_dataTs @ nonmono_free_Ts

    val shallow_dataTs = filter is_datatype_shallow mono_dataTs

(*

    val _ = priority "Monotonic datatypes:"

    val _ = List.app (priority o string_for_type ctxt) mono_dataTs

    val _ = priority "Nonmonotonic datatypes:"

    val _ = List.app (priority o string_for_type ctxt) nonmono_dataTs

    val _ = priority "Monotonic free types:"

    val _ = List.app (priority o string_for_type ctxt) mono_free_Ts

    val _ = priority "Nonmonotonic free types:"

    val _ = List.app (priority o string_for_type ctxt) nonmono_free_Ts

*)

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

    val effective_sat_solver =

      if sat_solver <> "smart" then

        if need_incremental andalso

           not (sat_solver mem Kodkod_SAT.configured_sat_solvers true) then

          (print_m (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 need_incremental

    val _ =

      if sat_solver = "smart" then

        print_v (fn () => "Using SAT solver " ^ quote effective_sat_solver ^

                          ". The following" ^

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

                          "solvers are configured: " ^

                          commas (map quote (Kodkod_SAT.configured_sat_solvers

                                                       need_incremental)) ^ ".")

      else

        ()

    val too_big_scopes = Unsynchronized.ref []

    (* bool -> scope -> rich_problem option *)

    fun problem_for_scope liberal

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

      let

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

                            (!too_big_scopes))

                orelse raise LIMIT ("Nitpick.pick_them_nits_in_term.\

                                    \problem_for_scope", "too big scope")

(*

        val _ = priority "Offsets:"

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

                             priority (string_for_type ctxt T ^ " = " ^

                                       string_of_int j0))

                         (Typtab.dest ofs)

*)

        val all_precise = forall (is_precise_type datatypes) Ts

        (* nut list -> rep NameTable.table -> nut list * rep NameTable.table *)

        val repify_consts = choose_reps_for_consts scope all_precise

        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 _ = forall (equal main_j0) [nat_j0, int_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 free_names NameTable.empty

        val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table

        val (nonsel_names, rep_table) = repify_consts nonsel_names rep_table

        val min_highest_arity =

          NameTable.fold (curry Int.max o arity_of_rep o snd) rep_table 1

        val min_univ_card =

          NameTable.fold (curry Int.max o min_univ_card_of_rep o snd) rep_table

                         (univ_card nat_card int_card main_j0 [] Kodkod.True)

        val _ = check_arity min_univ_card min_highest_arity

        val core_u = choose_reps_in_nut scope liberal rep_table false core_u

        val def_us = map (choose_reps_in_nut scope liberal rep_table true)

                         def_us

        val nondef_us = map (choose_reps_in_nut scope liberal rep_table false)

                            nondef_us

(*

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

                         (free_names @ sel_names @ nonsel_names @

                          core_u :: def_us @ nondef_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 core_u = rename_vars_in_nut pool rel_table core_u

        val def_us = map (rename_vars_in_nut pool rel_table) def_us

        val nondef_us = map (rename_vars_in_nut pool rel_table) nondef_us

        (* nut -> Kodkod.formula *)

        val to_f = kodkod_formula_from_nut ofs liberal kk

        val core_f = to_f core_u

        val def_fs = map to_f def_us

        val nondef_fs = map to_f nondef_us

        val formula = fold (fold s_and) [def_fs, nondef_fs] core_f

        val comment = (if liberal then "liberal" else "conservative") ^ "\n" ^

                      PrintMode.setmp [] multiline_string_for_scope scope

        val kodkod_sat_solver = Kodkod_SAT.sat_solver_spec effective_sat_solver

                                |> snd

        val delay = if liberal then

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

                                 deadline

                      |> liberal_delay_for_timeout

                    else

                      0

        val settings = [("solver", commas (map quote kodkod_sat_solver)),

                        ("skolem_depth", "-1"),

                        ("bit_width", "16"),

                        ("symmetry_breaking", signed_string_of_int sym_break),

                        ("sharing", signed_string_of_int sharing_depth),

                        ("flatten", Bool.toString flatten_props),

                        ("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 sel_bounds = map (bound_for_sel_rel ctxt debug datatypes) sel_rels

        val dtype_axioms = declarative_axioms_for_datatypes ext_ctxt ofs kk

                                                            rel_table datatypes

        val declarative_axioms = plain_axioms @ dtype_axioms

        val univ_card = univ_card nat_card int_card main_j0

                                  (plain_bounds @ sel_bounds) formula

        val built_in_bounds = bounds_for_built_in_rels_in_formula debug

                                  univ_card nat_card int_card main_j0 formula

        val bounds = built_in_bounds @ plain_bounds @ sel_bounds

                     |> not debug ? merge_bounds

        val highest_arity =

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

        val formula = fold_rev s_and declarative_axioms formula

        val _ = if formula = Kodkod.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 = sequential_int_bounds univ_card,

               expr_assigns = [], formula = formula},

              {free_names = free_names, sel_names = sel_names,

               nonsel_names = nonsel_names, rel_table = rel_table,

               liberal = liberal, scope = scope, core = core_f,

               defs = nondef_fs @ def_fs @ declarative_axioms})

      end

      handle LIMIT (loc, msg) =>

             if loc = "Nitpick_Kodkod.check_arity"

                andalso not (Typtab.is_empty ofs) then

               problem_for_scope liberal

                   {ext_ctxt = ext_ctxt, card_assigns = card_assigns,

                    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 ^

                                   ". Dropping " ^ (if liberal then "potential"

                                                    else "genuine") ^

                                   " component of scope."));

                NONE)

    (* int -> (''a * int list list) list -> ''a -> Kodkod.tuple_set *)

    fun tuple_set_for_rel univ_card =

      Kodkod.TupleSet o map (kk_tuple debug univ_card) o the

      oo AList.lookup (op =)

    val word_model = if falsify then "counterexample" else "model"

    val scopes = Unsynchronized.ref []

    val generated_scopes = Unsynchronized.ref []

    val generated_problems = Unsynchronized.ref []

    val checked_problems = Unsynchronized.ref (SOME [])

    val met_potential = Unsynchronized.ref 0

    (* rich_problem list -> int list -> unit *)

    fun update_checked_problems problems =

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

                o nth problems)

    (* bool -> Kodkod.raw_bound list -> problem_extension -> bool option *)

    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_skolems = show_skolems,

                                 show_datatypes = show_datatypes,

                                 show_consts = show_consts}

              scope formats frees free_names sel_names nonsel_names rel_table

              bounds

        val would_be_genuine = would_be_genuine andalso codatatypes_ok

      in

        pprint (Pretty.chunks

            [Pretty.blk (0,

                 (pstrs ("Nitpick found a" ^

                         (if not genuine then " potential "

                          else if would_be_genuine then " "

                          else " likely genuine ") ^ word_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 then

             (case prove_hol_model scope tac_timeout free_names sel_names

                                   rel_table bounds assms_t of

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

                                    word_model ^ " is really genuine.")

              | SOME false =>

                if would_be_genuine then

                  error ("A supposedly genuine " ^ word_model ^ " was shown to\

                         \be spurious by \"auto\".\nThis should never happen.\n\

                         \Please send a bug report to blanchet\

                         \te@in.tum.de.")

                else

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

                         " is spurious.")

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

           else

             ();

           if has_weaselly_sorts thy orig_t then

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

           else

             ();

           if not would_be_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 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 " ^ word_model ^ " is genuine.")

               end

             else

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

                      \the " ^ word_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_t

               in

                 (case status of

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

                                        word_model ^ " is genuine.")

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

                                         word_model ^ " is spurious.")

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

                 status

               end

             else

               NONE)

          else

            NONE

      end

    (* int -> int -> int -> bool -> rich_problem list -> int * int * int *)

    fun solve_any_problem 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)

        (* bool -> int * Kodkod.raw_bound list -> bool option *)

        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 need_incremental ? curry Int.min 1

      in

        if max_solutions <= 0 then

          (0, 0, donno)

        else

          case Kodkod.solve_any_problem overlord deadline max_threads

                                        max_solutions (map fst problems) of

            Kodkod.NotInstalled =>

            (print_m install_kodkodi_message;

             (max_potential, max_genuine, donno + 1))

          | Kodkod.Normal ([], unsat_js) =>

            (update_checked_problems problems unsat_js;

             (max_potential, max_genuine, donno))

          | Kodkod.Normal (sat_ps, unsat_js) =>

            let

              val (lib_ps, con_ps) =

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

            in

              update_checked_problems problems (unsat_js @ map fst lib_ps);

              if null con_ps then

                let

                  val num_genuine = Library.take (max_potential, lib_ps)

                                    |> map (print_and_check false)

                                    |> filter (equal (SOME true)) |> length

                  val max_genuine = max_genuine - num_genuine

                  val max_potential = max_potential

                                      - (length lib_ps - num_genuine)

                in

                  if max_genuine <= 0 then

                    (0, 0, donno)

                  else

                    let

                      (* "co_js" is the list of conservative problems whose

                         liberal 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 (#liberal o snd)

                    in

                      solve_any_problem max_potential max_genuine donno false

                                        problems

                    end

                end

              else

                let

                  val _ = Library.take (max_genuine, con_ps)

                          |> List.app (ignore o print_and_check true)

                  val max_genuine = max_genuine - length con_ps

                in

                  if max_genuine <= 0 orelse not first_time then

                    (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 (#liberal o snd)

                    in solve_any_problem 0 max_genuine donno false problems end

                end

            end

          | Kodkod.TimedOut unsat_js =>

            (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)

          | Kodkod.Interrupted NONE =>

            (checked_problems := NONE; do_interrupted ())

          | Kodkod.Interrupted (SOME unsat_js) =>

            (update_checked_problems problems unsat_js; do_interrupted ())

          | Kodkod.Error (s, unsat_js) =>

            (update_checked_problems problems unsat_js;

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

             (max_potential, max_genuine, donno + 1))

      end

    (* int -> int -> scope list -> int * int * int -> int * int * int *)

    fun run_batch j n scopes (max_potential, max_genuine, donno) =

      let

        val _ =

          if null scopes then

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

          else if verbose then

            pprint (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

            ()

        (* scope * bool -> rich_problem list * bool

           -> rich_problem list * bool *)

        fun add_problem_for_scope (scope as {datatypes, ...}, liberal)

                                  (problems, donno) =

          (check_deadline ();

           case problem_for_scope liberal scope of

             SOME problem =>

             (problems

              |> (null problems orelse

                  not (Kodkod.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)

      in

        solve_any_problem max_potential max_genuine donno true (rev problems)

      end

    (* rich_problem list -> scope -> int *)

    fun scope_count (problems : rich_problem list) scope =

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

    (* string -> string *)

    fun excipit did_so_and_so =

      let

        (* rich_problem list -> rich_problem list *)

        val do_filter =

          if !met_potential = max_potential then filter_out (#liberal 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

           " after checking " ^

           string_of_int (Int.min (total - 1, unsat)) ^ " of " ^

           string_of_int total ^ " scope" ^ plural_s total

         else

           "") ^ "."

      end

    (* int -> int -> scope list -> int * int * int -> Kodkod.outcome *)

    fun run_batches _ _ [] (max_potential, max_genuine, donno) =

        if donno > 0 andalso max_genuine > 0 then

          (print_m (fn () => excipit "ran into difficulties"); "unknown")

        else if max_genuine = original_max_genuine then

          if max_potential = original_max_potential then

            (print_m (K ("Nitpick found no " ^ word_model ^ ".")); "none")

          else

            (print_m (K ("Nitpick could not find " ^

                         (if max_genuine = 1 then "a better " ^ word_model ^ "."

                          else "any better " ^ word_model ^ "s.")));

             "potential")

        else

          if would_be_genuine then "genuine" else "likely_genuine"

      | run_batches j n (batch :: batches) z =

        let val (z as (_, max_genuine, _)) = run_batch j n batch z in

          run_batches (j + 1) n (if max_genuine > 0 then batches else []) z

        end

    val (skipped, the_scopes) =

      all_scopes ext_ctxt sym_break cards_assigns maxes_assigns iters_assigns

                 bisim_depths mono_Ts nonmono_Ts shallow_dataTs

    val _ = if skipped > 0 then

              print_m (fn () => "Too many scopes. Dropping " ^

                                string_of_int skipped ^ " scope" ^

                                plural_s skipped ^

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

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

            else

              ()

    val _ = scopes := the_scopes

    val batches = batch_list batch_size (!scopes)

    val outcome_code =

      (run_batches 0 (length batches) batches (max_potential, max_genuine, 0)

       handle Exn.Interrupt => do_interrupted ())

      handle TimeLimit.TimeOut =>

             (print_m (fn () => excipit "ran out of time");

              if !met_potential > 0 then "potential" else "unknown")

           | Exn.Interrupt => if auto orelse debug then raise Interrupt

                              else error (excipit "was interrupted")

    val _ = print_v (fn () => "Total time: " ^

                              signed_string_of_int (Time.toMilliseconds

                                    (Timer.checkRealTimer timer)) ^ " ms.")

  in (outcome_code, !state_ref) end

  handle Exn.Interrupt =>

         if auto orelse #debug params then

           raise Interrupt

         else

           if passed_deadline deadline then

             (priority "Nitpick ran out of time."; ("unknown", state))

           else

             error "Nitpick was interrupted."

(* Proof.state -> params -> bool -> term -> string * Proof.state *)

fun pick_nits_in_term state (params as {debug, timeout, expect, ...})

                      auto orig_assm_ts orig_t =

  if getenv "KODKODI" = "" then

    (if auto then ()

     else warning (Pretty.string_of (plazy install_kodkodi_message));

     ("unknown", state))

  else

    let

      val deadline = Option.map (curry Time.+ (Time.now ())) timeout

      val outcome as (outcome_code, _) =

        time_limit (if debug then NONE else timeout)

            (pick_them_nits_in_term deadline state params auto orig_assm_ts)

            orig_t

    in

      if expect = "" orelse outcome_code = expect then outcome

      else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")

    end

(* Proof.state -> params -> thm -> int -> string * Proof.state *)

fun pick_nits_in_subgoal state params auto subgoal =

  let

    val ctxt = Proof.context_of state

    val t = state |> Proof.raw_goal |> #goal |> prop_of

  in

    if Logic.count_prems t = 0 then

      (priority "No subgoal!"; ("none", state))

    else

      let

        val assms = map term_of (Assumption.all_assms_of ctxt)

        val (t, frees) = Logic.goal_params t subgoal

      in pick_nits_in_term state params auto assms (subst_bounds (frees, t)) end

  end

end;