(*  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 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,

     coalesce_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,

   coalesce_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))]

 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

 (* 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, coalesce_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 curry Pretty.blk 0 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 *)

     fun print_m f = pprint_m (curry Pretty.blk 0 o pstrs o f)

     fun print_v f = pprint_v (curry Pretty.blk 0 o pstrs o f)

     fun print_d f = pprint_d (curry Pretty.blk 0 o pstrs o f)

     (* 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

       |> coalesce_type_vars ? coalesce_type_vars_in_terms

       |> hd pairf 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 []}

     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 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

     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 _ = 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 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 nonsel_names = filter_out (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 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.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 =>

                      if scope_count (do_filter (these (!checked_problems)))

                                     scope = n then

                        Integer.add 1

                      else

                        I) (!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 out of resources"); "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 _ = scopes := all_scopes ext_ctxt sym_break cards_assigns maxes_assigns

                                  iters_assigns bisim_depths mono_Ts nonmono_Ts

     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 =

   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.get_goal |> snd |> snd |> 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;