(*  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 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,

     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,

     merge_type_vars: bool,

     binary_ints: bool option,

     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 -> int -> int -> int -> term list -> term

     -> string * Proof.state

   val pick_nits_in_subgoal :

     Proof.state -> params -> bool -> 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

 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,

   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,

   merge_type_vars: bool,

   binary_ints: bool option,

   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,

   unsound: bool,

   scope: scope,

   core: KK.formula,

   defs: KK.formula list}

 type rich_problem = KK.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_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_unsound_delay_ms = 200

 val max_unsound_delay_percent = 2

 (* Time.time option -> int *)

 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))

 (* 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 assigns = forall (not_equal (SOME true) o snd) assigns

 val syntactic_sorts =

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

   @{sort number}

 (* typ -> bool *)

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

     subset (op =) (S, syntactic_sorts)

   | has_tfree_syntactic_sort _ = false

 (* term -> bool *)

 val has_syntactic_sorts = exists_type (exists_subtype has_tfree_syntactic_sort)

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

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

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

    -> string * Proof.state *)

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

                            orig_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 = ThyInfo.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, monos, stds, wfs, sat_solver, blocking, falsify, debug, verbose,

          overlord, user_axioms, assms, merge_type_vars, binary_ints,

          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 _ =

       if step = 0 then

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

       else

         pprint_m (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 (orig_assm_ts, orig_t)]))

     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 stds

     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 (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,

        binary_ints = binary_ints, 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, binarize) = preprocess_term hol_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 hol_ctxt Eq core_t

     val def_us = map (nut_from_term hol_ctxt DefEq) def_ts

     val nondef_us = map (nut_from_term hol_ctxt 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 genuine_means_genuine = got_all_user_axioms andalso none_true wfs

     val standard = forall snd stds

 (*

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

                      (core_u :: def_us @ nondef_us)

 *)

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

     (* typ -> bool *)

     fun is_type_always_monotonic T =

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

        (not (is_pure_typedef thy T) orelse is_univ_typedef thy T)) orelse

       is_number_type thy T orelse is_bit_type T

     fun is_type_monotonic T =

       unique_scope orelse

       case triple_lookup (type_match thy) monos T of

         SOME (SOME b) => b

       | _ => is_type_always_monotonic T orelse

              formulas_monotonic hol_ctxt binarize T Plus def_ts nondef_ts core_t

     fun is_deep_datatype T =

       is_datatype thy stds T andalso

       (not standard 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

                                        (core_t :: def_ts @ nondef_ts)

                  |> sort TermOrd.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.")

             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_always_monotonic mono_Ts of

           [] => ()

         | interesting_mono_Ts =>

           print_v (fn () =>

                       let

                         val ss = map (quote o string_for_type ctxt)

                                      interesting_mono_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 deep_dataTs = filter is_deep_datatype all_Ts

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

        provide a hint to the user. *)

     (* string * (Rule_Cases.T * bool) -> bool *)

     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 (ProofContext.cases_of ctxt)

     val _ = if standard andalso likely_in_struct_induct_step then

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

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

                         \general enough, try this command: " @

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

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

             else

               ()

 (*

     val _ = priority "Monotonic types:"

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

     val _ = priority "Nonmonotonic types:"

     val _ = List.app (priority o string_for_type ctxt) nonmono_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 (member (op =) (Kodkod_SAT.configured_sat_solvers true)

                       sat_solver) 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 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 _ = priority "Offsets:"

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

                              priority (string_for_type ctxt T ^ " = " ^

                                        string_of_int j0))

                          (Typtab.dest ofs)

 *)

         val all_exact = forall (is_exact_type datatypes) all_Ts

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

         val repify_consts = choose_reps_for_consts scope all_exact

         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 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 [] KK.True)

         val _ = check_arity min_univ_card min_highest_arity

         val core_u = choose_reps_in_nut scope unsound rep_table false core_u

         val def_us = map (choose_reps_in_nut scope unsound rep_table true)

                          def_us

         val nondef_us = map (choose_reps_in_nut scope unsound 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

         val core_f = kodkod_formula_from_nut bits ofs kk core_u

         val def_fs = map (kodkod_formula_from_nut bits ofs kk) def_us

         val nondef_fs = map (kodkod_formula_from_nut bits ofs kk) nondef_us

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

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

                       PrintMode.setmp [] multiline_string_for_scope scope

         val kodkod_sat_solver =

           Kodkod_SAT.sat_solver_spec effective_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 (map quote kodkod_sat_solver)),

                         ("skolem_depth", "-1"),

                         ("bit_width", string_of_int bit_width),

                         ("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 hol_ctxt binarize 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 = 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 bits = 0 then () else check_bits bits formula

         val _ = if 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 univ_card,

                expr_assigns = [], formula = formula},

               {free_names = free_names, sel_names = sel_names,

                nonsel_names = nonsel_names, rel_table = rel_table,

                unsound = unsound, scope = scope, core = core_f,

                defs = nondef_fs @ def_fs @ declarative_axioms})

       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"

                                                     else "genuine") ^

                                    " component of scope."));

                 NONE)

            | TOO_SMALL (loc, msg) =>

              (print_v (fn () => ("Limit reached: " ^ msg ^

                                  ". Skipping " ^ (if unsound then "potential"

                                                   else "genuine") ^

                                  " component of scope."));

               NONE)

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

     fun tuple_set_for_rel univ_card =

       KK.TupleSet o map (kk_tuple debug univ_card) o the oo AList.lookup (op =)

     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

     (* 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 -> KK.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 genuine_means_genuine = genuine_means_genuine andalso codatatypes_ok

       in

         pprint (Pretty.chunks

             [Pretty.blk (0,

                  (pstrs ("Nitpick found a" ^

                          (if not genuine then " potential "

                           else if genuine_means_genuine then " "

                           else " likely 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_t 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 perhaps even \

                    \wrong. See the \"Inductive Properties\" section of the \

                    \Nitpick manual for details (\"isabelle doc nitpick\")."

            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 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_t

                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

       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 * KK.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 KK.solve_any_problem overlord deadline max_threads max_solutions

                                     (map fst problems) of

             KK.NotInstalled =>

             (print_m install_kodkodi_message;

              (max_potential, max_genuine, donno + 1))

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

             (update_checked_problems problems unsat_js;

              (max_potential, max_genuine, donno))

           | KK.Normal (sat_ps, unsat_js) =>

             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);

               if null con_ps then

                 let

                   val num_genuine = take max_potential lib_ps

                                     |> map (print_and_check false)

                                     |> filter (curry (op =) (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 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 max_potential max_genuine donno false

                                         problems

                     end

                 end

               else

                 let

                   val _ = 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 (#unsound o snd)

                     in solve_any_problem 0 max_genuine donno false problems end

                 end

             end

           | KK.TimedOut unsat_js =>

             (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)

           | KK.Interrupted NONE => (checked_problems := NONE; do_interrupted ())

           | KK.Interrupted (SOME unsat_js) =>

             (update_checked_problems problems unsat_js; do_interrupted ())

           | KK.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, ...}, 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_m (fn () =>

                     "Warning: The conjecture either trivially holds for the \

                     \given scopes or (more likely) lies outside Nitpick's \

                     \supported fragment." ^

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

                                unsound_problems then

                        " Only potential counterexamples may be found."

                      else

                        ""))

               else

                 ()

             end

           else

             ()

       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 (#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

            " 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 -> KK.outcome *)

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

         if donno > 0 andalso max_genuine > 0 then

           (print_m (fn () => excipit "ran out of some resource"); "unknown")

         else if max_genuine = original_max_genuine then

           if max_potential = original_max_potential then

             (print_m (fn () =>

                  "Nitpick found no " ^ das_wort_model ^ "." ^

                  (if not standard andalso likely_in_struct_induct_step then

                     " This suggests that the induction hypothesis might be \

                     \general enough to prove this subgoal."

                   else

                     "")); "none")

           else

             (print_m (fn () =>

                  "Nitpick could not find a" ^

                  (if max_genuine = 1 then " better " ^ das_wort_model ^ "."

                   else "ny better " ^ das_wort_model ^ "s.")); "potential")

         else

           if genuine_means_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 hol_ctxt binarize sym_break cards_assigns maxes_assigns

                  iters_assigns bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs

     val _ = if skipped > 0 then

               print_m (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

     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 -> int -> int -> int -> term

    -> string * Proof.state *)

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

                       step 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 i n step

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

 fun pick_nits_in_subgoal state params auto i step =

   let

     val ctxt = Proof.context_of state

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

   in

     case Logic.count_prems t of

       0 => (priority "No subgoal!"; ("none", state))

     | n =>

       let

         val assms = map term_of (Assumption.all_assms_of ctxt)

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

       in

         pick_nits_in_term state params auto i n step assms

                           (subst_bounds (frees, t))

       end

   end

 end;