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

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2008, 2009, 2010

 Finite model generation for HOL formulas using Kodkod.

 *)

 signature NITPICK =

 sig

   type styp = Nitpick_Util.styp

   type term_postprocessor = Nitpick_Model.term_postprocessor

   datatype mode = Auto_Try | Try | Normal

   type params =

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

      maxes_assigns: (styp option * int list) list,

      iters_assigns: (styp option * int list) list,

      bitss: int list,

      bisim_depths: int list,

      boxes: (typ option * bool option) list,

      finitizes: (typ option * bool option) list,

      monos: (typ option * bool option) list,

      stds: (typ option * bool) list,

      wfs: (styp option * bool option) list,

      sat_solver: string,

      blocking: bool,

      falsify: bool,

      debug: bool,

      verbose: bool,

      overlord: bool,

      user_axioms: bool option,

      assms: bool,

      whacks: term list,

      merge_type_vars: bool,

      binary_ints: bool option,

      destroy_constrs: bool,

      specialize: bool,

      star_linear_preds: bool,

      total_consts: bool option,

      needs: term list option,

      peephole_optim: bool,

      datatype_sym_break: int,

      kodkod_sym_break: int,

      timeout: Time.time option,

      tac_timeout: Time.time option,

      max_threads: int,

      show_datatypes: bool,

      show_skolems: bool,

      show_consts: bool,

      evals: term list,

      formats: (term option * int list) list,

      atomss: (typ option * string list) list,

      max_potential: int,

      max_genuine: int,

      check_potential: bool,

      check_genuine: bool,

      batch_size: int,

      expect: string}

   val genuineN : string

   val quasi_genuineN : string

   val potentialN : string

   val noneN : string

   val unknownN : string

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

   val unregister_frac_type : string -> theory -> theory

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

   val unregister_codatatype : typ -> theory -> theory

   val register_term_postprocessor :

     typ -> term_postprocessor -> theory -> theory

   val unregister_term_postprocessor : typ -> theory -> theory

   val pick_nits_in_term :

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

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

   val pick_nits_in_subgoal :

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

 end;

 structure Nitpick : NITPICK =

 struct

 open Nitpick_Util

 open Nitpick_HOL

 open Nitpick_Preproc

 open Nitpick_Mono

 open Nitpick_Scope

 open Nitpick_Peephole

 open Nitpick_Rep

 open Nitpick_Nut

 open Nitpick_Kodkod

 open Nitpick_Model

 structure KK = Kodkod

 datatype mode = Auto_Try | Try | Normal

 type params =

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

    maxes_assigns: (styp option * int list) list,

    iters_assigns: (styp option * int list) list,

    bitss: int list,

    bisim_depths: int list,

    boxes: (typ option * bool option) list,

    finitizes: (typ option * bool option) list,

    monos: (typ option * bool option) list,

    stds: (typ option * bool) list,

    wfs: (styp option * bool option) list,

    sat_solver: string,

    blocking: bool,

    falsify: bool,

    debug: bool,

    verbose: bool,

    overlord: bool,

    user_axioms: bool option,

    assms: bool,

    whacks: term list,

    merge_type_vars: bool,

    binary_ints: bool option,

    destroy_constrs: bool,

    specialize: bool,

    star_linear_preds: bool,

    total_consts: bool option,

    needs: term list option,

    peephole_optim: bool,

    datatype_sym_break: int,

    kodkod_sym_break: int,

    timeout: Time.time option,

    tac_timeout: Time.time option,

    max_threads: int,

    show_datatypes: bool,

    show_skolems: bool,

    show_consts: bool,

    evals: term list,

    formats: (term option * int list) list,

    atomss: (typ option * string list) list,

    max_potential: int,

    max_genuine: int,

    check_potential: bool,

    check_genuine: bool,

    batch_size: int,

    expect: string}

 val genuineN = "genuine"

 val quasi_genuineN = "quasi_genuine"

 val potentialN = "potential"

 val noneN = "none"

 val unknownN = "unknown"

 (* TODO: eliminate these historical aliases *)

 val register_frac_type = Nitpick_HOL.register_frac_type_global

 val unregister_frac_type = Nitpick_HOL.unregister_frac_type_global

 val register_codatatype = Nitpick_HOL.register_codatatype_global

 val unregister_codatatype = Nitpick_HOL.unregister_codatatype_global

 val register_term_postprocessor =

   Nitpick_Model.register_term_postprocessor_global

 val unregister_term_postprocessor =

   Nitpick_Model.unregister_term_postprocessor_global

 type problem_extension =

   {free_names: nut list,

    sel_names: nut list,

    nonsel_names: nut list,

    rel_table: nut NameTable.table,

    unsound: bool,

    scope: scope}

 type rich_problem = KK.problem * problem_extension

 fun pretties_for_formulas _ _ [] = []

   | pretties_for_formulas ctxt s ts =

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

      Pretty.indent indent_size (Pretty.chunks

          (map2 (fn j => fn t =>

                    Pretty.block [t |> shorten_names_in_term

                                    |> Syntax.pretty_term ctxt,

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

                (length ts downto 1) ts))]

 fun install_java_message () =

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

 fun install_kodkodi_message () =

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

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

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

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

   " on a line of its own."

 val max_unsound_delay_ms = 200

 val max_unsound_delay_percent = 2

 fun unsound_delay_for_timeout NONE = max_unsound_delay_ms

   | unsound_delay_for_timeout (SOME timeout) =

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

                          Time.toMilliseconds timeout

                          * max_unsound_delay_percent div 100))

 fun passed_deadline NONE = false

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

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

 fun has_lonely_bool_var (@{const Pure.conjunction}

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

   | has_lonely_bool_var _ = false

 val syntactic_sorts =

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

   @{sort numeral}

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

     subset (op =) (S, syntactic_sorts)

   | has_tfree_syntactic_sort _ = false

 val has_syntactic_sorts = exists_type (exists_subtype has_tfree_syntactic_sort)

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

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

                            subst assm_ts orig_t =

   let

     val timer = Timer.startRealTimer ()

     val thy = Proof.theory_of state

     val ctxt = Proof.context_of state

 (* FIXME: reintroduce code before new release:

     val nitpick_thy = Thy_Info.get_theory "Nitpick"

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

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

 *)

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

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

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

          binary_ints, destroy_constrs, specialize, star_linear_preds,

          total_consts, needs, peephole_optim, datatype_sym_break,

          kodkod_sym_break, tac_timeout, max_threads, show_datatypes,

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

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

     val state_ref = Unsynchronized.ref state

     fun pprint print =

       if mode = Auto_Try then

         Unsynchronized.change state_ref o Proof.goal_message o K

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

         o Pretty.mark Isabelle_Markup.hilite

       else

         print o Pretty.string_of

     val pprint_a = pprint Output.urgent_message

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

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

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

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

 (*

     val print_g = pprint tracing o Pretty.str

 *)

     val print_n = pprint_n o K o plazy

     val print_v = pprint_v o K o plazy

     fun check_deadline () =

       if passed_deadline deadline then raise TimeLimit.TimeOut else ()

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

     val _ =

       if step = 0 then

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

       else

         pprint_n (fn () => Pretty.chunks (

             pretties_for_formulas ctxt ("Nitpicking " ^

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

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

                  else

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

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

                      o Date.fromTimeLocal o Time.now)

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

                 else orig_t

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

     val tfree_table =

       if merge_type_vars then merged_type_var_table_for_terms thy conj_ts

       else []

     val merge_tfrees = merge_type_vars_in_term thy merge_type_vars tfree_table

     val neg_t = neg_t |> merge_tfrees

     val assm_ts = assm_ts |> map merge_tfrees

     val evals = evals |> map merge_tfrees

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

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

     val original_max_potential = max_potential

     val original_max_genuine = max_genuine

     val max_bisim_depth = fold Integer.max bisim_depths ~1

     val case_names = case_const_names ctxt stds

     val defs = all_defs_of thy subst

     val nondefs = all_nondefs_of ctxt subst

     val def_tables = const_def_tables ctxt subst defs

     val nondef_table = const_nondef_table nondefs

     val simp_table = Unsynchronized.ref (const_simp_table ctxt subst)

     val psimp_table = const_psimp_table ctxt subst

     val choice_spec_table = const_choice_spec_table ctxt subst

     val nondefs =

       nondefs |> filter_out (is_choice_spec_axiom thy choice_spec_table)

     val intro_table = inductive_intro_table ctxt subst def_tables

     val ground_thm_table = ground_theorem_table thy

     val ersatz_table = ersatz_table ctxt

     val hol_ctxt as {wf_cache, ...} =

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

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

        whacks = whacks, binary_ints = binary_ints,

        destroy_constrs = destroy_constrs, specialize = specialize,

        star_linear_preds = star_linear_preds, total_consts = total_consts,

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

        case_names = case_names, def_tables = def_tables,

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

        psimp_table = psimp_table, choice_spec_table = choice_spec_table,

        intro_table = intro_table, ground_thm_table = ground_thm_table,

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

        special_funs = Unsynchronized.ref [],

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

        constr_cache = Unsynchronized.ref []}

     val pseudo_frees = []

     val real_frees = fold Term.add_frees conj_ts []

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

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

     val (nondef_ts, def_ts, need_ts, got_all_mono_user_axioms,

          no_poly_user_axioms, binarize) =

       preprocess_formulas hol_ctxt assm_ts neg_t

     val got_all_user_axioms =

       got_all_mono_user_axioms andalso no_poly_user_axioms

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

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

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

           @ Syntax.pretty_term ctxt (Const x) ::

           pstrs (if wf then

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

                    \efficiently."

                  else

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

                    \unroll it.")))

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

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

     val _ =

       pprint_d (fn () => Pretty.chunks

           (pretties_for_formulas ctxt das_wort_formula [hd nondef_ts] @

            pretties_for_formulas ctxt "Relevant definitional axiom" def_ts @

            pretties_for_formulas ctxt "Relevant nondefinitional axiom"

                                  (tl nondef_ts)))

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

             handle TYPE (_, Ts, ts) =>

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

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

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

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

     val (free_names, const_names) =

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

     val (sel_names, nonsel_names) =

       List.partition (is_sel o nickname_of) const_names

     val sound_finitizes = none_true finitizes

     val standard = forall snd stds

 (*

     val _ =

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

 *)

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

     fun monotonicity_message Ts extra =

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

         Pretty.blk (0,

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

           pretty_serial_commas "and" pretties @

           pstrs (" " ^

                  (if none_true monos then

                     "passed the monotonicity test"

                   else

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

                     " considered monotonic") ^

                  ". " ^ extra))

       end

     fun is_type_fundamentally_monotonic T =

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

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

       is_number_type ctxt T orelse is_bit_type T

     fun is_type_actually_monotonic T =

       formulas_monotonic hol_ctxt binarize T (nondef_ts, def_ts)

     fun is_type_kind_of_monotonic T =

       case triple_lookup (type_match thy) monos T of

         SOME (SOME false) => false

       | _ => is_type_actually_monotonic T

     fun is_type_monotonic T =

       unique_scope orelse

       case triple_lookup (type_match thy) monos T of

         SOME (SOME b) => b

       | _ => is_type_fundamentally_monotonic T orelse

              is_type_actually_monotonic T

     fun is_deep_datatype_finitizable T =

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

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

         is_type_kind_of_monotonic T

       | is_shallow_datatype_finitizable T =

         case triple_lookup (type_match thy) finitizes T of

           SOME (SOME b) => b

         | _ => is_type_kind_of_monotonic T

     fun is_datatype_deep T =

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

       is_word_type T orelse

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

     val all_Ts = ground_types_in_terms hol_ctxt binarize (nondef_ts @ def_ts)

                  |> sort Term_Ord.typ_ord

     val _ =

       if verbose andalso binary_ints = SOME true andalso

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

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

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

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

       else

         ()

     val _ =

       if mode = Normal andalso

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

                 all_Ts then

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

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

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

                     \usually indicates either a failure of abstraction or a \

                     \quirk in Nitpick."))

       else

         ()

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

     val _ =

       if verbose andalso not unique_scope then

         case filter_out is_type_fundamentally_monotonic mono_Ts of

           [] => ()

         | interesting_mono_Ts =>

           pprint_v (K (monotonicity_message interesting_mono_Ts

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

       else

         ()

     val (deep_dataTs, shallow_dataTs) =

       all_Ts |> filter (is_datatype ctxt stds)

              |> List.partition is_datatype_deep

     val finitizable_dataTs =

       (deep_dataTs |> filter_out (is_finite_type hol_ctxt)

                    |> filter is_deep_datatype_finitizable) @

       (shallow_dataTs |> filter_out (is_finite_type hol_ctxt)

                       |> filter is_shallow_datatype_finitizable)

     val _ =

       if verbose andalso not (null finitizable_dataTs) then

         pprint_v (K (monotonicity_message finitizable_dataTs

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

       else

         ()

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

        provide a hint to the user. *)

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

       not (null fixes) andalso

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

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

               o datatype_constrs hol_ctxt) deep_dataTs

     val likely_in_struct_induct_step =

       exists is_struct_induct_step (Proof_Context.cases_of ctxt)

     val _ = if standard andalso likely_in_struct_induct_step then

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

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

                         \general enough, try this command: " @

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

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

             else

               ()

 (*

     val _ = print_g "Monotonic types:"

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

     val _ = print_g "Nonmonotonic types:"

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

 *)

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

     val actual_sat_solver =

       if sat_solver <> "smart" then

         if incremental andalso

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

                        sat_solver) then

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

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

            "SAT4J")

         else

           sat_solver

       else

         Kodkod_SAT.smart_sat_solver_name incremental

     val _ =

       if sat_solver = "smart" then

         print_v (fn () =>

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

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

             "solvers are configured: " ^

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

       else

         ()

     val too_big_scopes = Unsynchronized.ref []

     fun problem_for_scope unsound

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

       let

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

                             (!too_big_scopes)) orelse

                 raise TOO_LARGE ("Nitpick.pick_them_nits_in_term.\

                                  \problem_for_scope", "too large scope")

 (*

         val _ = print_g "Offsets:"

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

                              print_g (string_for_type ctxt T ^ " = " ^

                                     string_of_int j0))

                          (Typtab.dest ofs)

 *)

         val effective_total_consts =

           case total_consts of

             SOME b => b

           | NONE => forall (is_exact_type datatypes true) all_Ts

         val main_j0 = offset_of_type ofs bool_T

         val (nat_card, nat_j0) = spec_of_type scope nat_T

         val (int_card, int_j0) = spec_of_type scope int_T

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

                 raise BAD ("Nitpick.pick_them_nits_in_term.problem_for_scope",

                            "bad offsets")

         val kk = kodkod_constrs peephole_optim nat_card int_card main_j0

         val (free_names, rep_table) =

           choose_reps_for_free_vars scope pseudo_frees free_names

                                     NameTable.empty

         val (sel_names, rep_table) = choose_reps_for_all_sels scope rep_table

         val (nonsel_names, rep_table) =

           choose_reps_for_consts scope effective_total_consts nonsel_names

                                  rep_table

         val (guiltiest_party, min_highest_arity) =

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

                              let val n' = arity_of_rep R in

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

                              end) rep_table ("", 1)

         val min_univ_card =

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

                          (univ_card nat_card int_card main_j0 [] KK.True)

         val _ = if debug then ()

                 else check_arity guiltiest_party min_univ_card min_highest_arity

         val def_us =

           def_us |> map (choose_reps_in_nut scope unsound rep_table true)

         val nondef_us =

           nondef_us |> map (choose_reps_in_nut scope unsound rep_table false)

         val need_us =

           need_us |> map (choose_reps_in_nut scope unsound rep_table false)

 (*

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

                          (free_names @ sel_names @ nonsel_names @

                           nondef_us @ def_us @ need_us)

 *)

         val (free_rels, pool, rel_table) =

           rename_free_vars free_names initial_pool NameTable.empty

         val (sel_rels, pool, rel_table) =

           rename_free_vars sel_names pool rel_table

         val (other_rels, pool, rel_table) =

           rename_free_vars nonsel_names pool rel_table

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

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

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

         val nondef_fs = map (kodkod_formula_from_nut ofs kk) nondef_us

         val def_fs = map (kodkod_formula_from_nut ofs kk) def_us

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

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

                       Print_Mode.setmp [] multiline_string_for_scope scope

         val kodkod_sat_solver =

           Kodkod_SAT.sat_solver_spec actual_sat_solver |> snd

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

         val delay =

           if unsound then

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

             |> unsound_delay_for_timeout

           else

             0

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

                         ("bit_width", string_of_int bit_width),

                         ("symmetry_breaking", string_of_int kodkod_sym_break),

                         ("sharing", "3"),

                         ("flatten", "false"),

                         ("delay", signed_string_of_int delay)]

         val plain_rels = free_rels @ other_rels

         val plain_bounds = map (bound_for_plain_rel ctxt debug) plain_rels

         val plain_axioms = map (declarative_axiom_for_plain_rel kk) plain_rels

         val need_vals =

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

                   (typ, needed_values_for_datatype need_us ofs dtype)) datatypes

         val sel_bounds =

           map (bound_for_sel_rel ctxt debug need_vals datatypes) sel_rels

         val dtype_axioms =

           declarative_axioms_for_datatypes hol_ctxt binarize need_us need_vals

               datatype_sym_break bits ofs kk rel_table datatypes

         val declarative_axioms = plain_axioms @ dtype_axioms

         val univ_card = Int.max (univ_card nat_card int_card main_j0

                                      (plain_bounds @ sel_bounds) formula,

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

         val (built_in_bounds, built_in_axioms) =

           bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card

               nat_card int_card main_j0 (formula :: declarative_axioms)

         val bounds = built_in_bounds @ plain_bounds @ sel_bounds

                      |> not debug ? merge_bounds

         val axioms = built_in_axioms @ declarative_axioms

         val highest_arity =

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

         val formula = fold_rev s_and axioms formula

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

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

                 else check_arity "" univ_card highest_arity

       in

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

                tuple_assigns = [], bounds = bounds,

                int_bounds = if bits = 0 then sequential_int_bounds univ_card

                             else pow_of_two_int_bounds bits main_j0,

                expr_assigns = [], formula = formula},

               {free_names = free_names, sel_names = sel_names,

                nonsel_names = nonsel_names, rel_table = rel_table,

                unsound = unsound, scope = scope})

       end

       handle TOO_LARGE (loc, msg) =>

              if loc = "Nitpick_Kodkod.check_arity" andalso

                 not (Typtab.is_empty ofs) then

                problem_for_scope unsound

                    {hol_ctxt = hol_ctxt, binarize = binarize,

                     card_assigns = card_assigns, bits = bits,

                     bisim_depth = bisim_depth, datatypes = datatypes,

                     ofs = Typtab.empty}

              else if loc = "Nitpick.pick_them_nits_in_term.\

                            \problem_for_scope" then

                NONE

              else

                (Unsynchronized.change too_big_scopes (cons scope);

                 print_v (fn () =>

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

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

                     "scope.");

                 NONE)

            | TOO_SMALL (_, msg) =>

              (print_v (fn () =>

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

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

                   "scope.");

               NONE)

     val das_wort_model =

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

       |> not standard ? prefix "nonstandard "

     val scopes = Unsynchronized.ref []

     val generated_scopes = Unsynchronized.ref []

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

     val checked_problems = Unsynchronized.ref (SOME [])

     val met_potential = Unsynchronized.ref 0

     fun update_checked_problems problems =

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

                 o nth problems)

     fun show_kodkod_warning "" = ()

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

     fun print_and_check_model genuine bounds

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

              : problem_extension) =

       let

         val (reconstructed_model, codatatypes_ok) =

           reconstruct_hol_model

               {show_datatypes = show_datatypes, show_skolems = show_skolems,

                show_consts = show_consts}

               scope formats atomss real_frees pseudo_frees free_names sel_names

               nonsel_names rel_table bounds

         val genuine_means_genuine =

           got_all_user_axioms andalso none_true wfs andalso

           sound_finitizes andalso total_consts <> SOME true andalso

           codatatypes_ok

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

       in

         (pprint_a (Pretty.chunks

              [Pretty.blk (0,

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

                           "Nitpick found a" ^

                           (if not genuine then " potentially spurious "

                            else if genuine_means_genuine then " "

                            else " quasi genuine ") ^ das_wort_model) @

                    (case pretties_for_scope scope verbose of

                       [] => []

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

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

               Pretty.indent indent_size reconstructed_model]);

          if genuine then

            (if check_genuine andalso standard then

               case prove_hol_model scope tac_timeout free_names sel_names

                                    rel_table bounds (assms_prop ()) of

                 SOME true =>

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

                        das_wort_model ^ " is really genuine.")

               | SOME false =>

                 if genuine_means_genuine then

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

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

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

                          \te@in.tum.de.")

                  else

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

                           das_wort_model ^ " is spurious.")

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

             else

               ();

             if not standard andalso likely_in_struct_induct_step then

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

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

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

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

             else

               ();

             if has_lonely_bool_var orig_t then

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

             else if has_syntactic_sorts orig_t then

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

             else

               ();

             if not genuine_means_genuine then

               if no_poly_user_axioms then

                 let

                   val options =

                     [] |> not got_all_mono_user_axioms

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

                        |> not (none_true wfs)

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

                        |> not sound_finitizes

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

                        |> total_consts = SOME true

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

                        |> not codatatypes_ok

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

                   val ss =

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

                         options

                 in

                   print ("Try again with " ^

                          space_implode " " (serial_commas "and" ss) ^

                          " to confirm that the " ^ das_wort_model ^

                          " is genuine.")

                 end

               else

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

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

                        \polymorphic axioms.")

             else

               ();

             NONE)

          else

            if not genuine then

              (Unsynchronized.inc met_potential;

               if check_potential then

                 let

                   val status = prove_hol_model scope tac_timeout free_names

                                                sel_names rel_table bounds

                                                (assms_prop ())

                 in

                   (case status of

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

                                          \above " ^ das_wort_model ^

                                          " is genuine.")

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

                                           das_wort_model ^ " is spurious.")

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

                   status

                 end

               else

                 NONE)

            else

              NONE)

         |> pair genuine_means_genuine

       end

     fun solve_any_problem (found_really_genuine, max_potential, max_genuine,

                            donno) first_time problems =

       let

         val max_potential = Int.max (0, max_potential)

         val max_genuine = Int.max (0, max_genuine)

         fun print_and_check genuine (j, bounds) =

           print_and_check_model genuine bounds (snd (nth problems j))

         val max_solutions = max_potential + max_genuine

                             |> not incremental ? Integer.min 1

       in

         if max_solutions <= 0 then

           (found_really_genuine, 0, 0, donno)

         else

           case KK.solve_any_problem debug overlord deadline max_threads

                                     max_solutions (map fst problems) of

             KK.JavaNotInstalled =>

             (print_n install_java_message;

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

           | KK.JavaTooOld =>

             (print_n install_java_message;

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

           | KK.KodkodiNotInstalled =>

             (print_n install_kodkodi_message;

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

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

             (update_checked_problems problems unsat_js; show_kodkod_warning s;

              (found_really_genuine, max_potential, max_genuine, donno))

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

             let

               val (lib_ps, con_ps) =

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

             in

               update_checked_problems problems (unsat_js @ map fst lib_ps);

               show_kodkod_warning s;

               if null con_ps then

                 let

                   val genuine_codes =

                     lib_ps |> take max_potential

                            |> map (print_and_check false)

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

                   val found_really_genuine =

                     found_really_genuine orelse exists fst genuine_codes

                   val num_genuine = length genuine_codes

                   val max_genuine = max_genuine - num_genuine

                   val max_potential = max_potential

                                       - (length lib_ps - num_genuine)

                 in

                   if max_genuine <= 0 then

                     (found_really_genuine, 0, 0, donno)

                   else

                     let

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

                          pendants couldn't be satisfied and hence that most

                          probably can't be satisfied themselves. *)

                       val co_js =

                         map (fn j => j - 1) unsat_js

                         |> filter (fn j =>

                                       j >= 0 andalso

                                       scopes_equivalent

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

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

                       val bye_js = sort_distinct int_ord (map fst sat_ps @

                                                           unsat_js @ co_js)

                       val problems =

                         problems |> filter_out_indices bye_js

                                  |> max_potential <= 0

                                     ? filter_out (#unsound o snd)

                     in

                       solve_any_problem (found_really_genuine, max_potential,

                                          max_genuine, donno) false problems

                     end

                 end

               else

                 let

                   val genuine_codes =

                     con_ps |> take max_genuine

                            |> map (print_and_check true)

                   val max_genuine = max_genuine - length genuine_codes

                   val found_really_genuine =

                     found_really_genuine orelse exists fst genuine_codes

                 in

                   if max_genuine <= 0 orelse not first_time then

                     (found_really_genuine, 0, max_genuine, donno)

                   else

                     let

                       val bye_js = sort_distinct int_ord

                                                  (map fst sat_ps @ unsat_js)

                       val problems =

                         problems |> filter_out_indices bye_js

                                  |> filter_out (#unsound o snd)

                     in

                       solve_any_problem (found_really_genuine, 0, max_genuine,

                                          donno) false problems

                     end

                 end

             end

           | KK.TimedOut unsat_js =>

             (update_checked_problems problems unsat_js; raise TimeLimit.TimeOut)

           | KK.Error (s, unsat_js) =>

             (update_checked_problems problems unsat_js;

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

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

       end

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

                               donno) =

       let

         val _ =

           if null scopes then

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

           else if verbose then

             pprint_n (fn () => Pretty.chunks

                 [Pretty.blk (0,

                      pstrs ((if n > 1 then

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

                                signed_string_of_int n ^ ": "

                              else

                                "") ^

                             "Trying " ^ string_of_int (length scopes) ^

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

                  Pretty.indent indent_size

                      (Pretty.chunks (map2

                           (fn j => fn scope =>

                               Pretty.block (

                                   (case pretties_for_scope scope true of

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

                                    | pretties => pretties) @

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

                           (length scopes downto 1) scopes))])

           else

             ()

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

           (check_deadline ();

            case problem_for_scope unsound scope of

              SOME problem =>

              (problems

               |> (null problems orelse

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

                   ? cons problem, donno)

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

         val (problems, donno) =

           fold add_problem_for_scope

                (map_product pair scopes

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

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

                ([], donno)

         val _ = Unsynchronized.change generated_problems (append problems)

         val _ = Unsynchronized.change generated_scopes (append scopes)

         val _ =

           if j + 1 = n then

             let

               val (unsound_problems, sound_problems) =

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

             in

               if not (null sound_problems) andalso

                  forall (KK.is_problem_trivially_false o fst)

                         sound_problems then

                 print_n (fn () =>

                     "Warning: The conjecture " ^

                     (if falsify then "either trivially holds"

                      else "is either trivially unsatisfiable") ^

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

                     \fragment." ^

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

                                unsound_problems then

                        " Only potentially spurious " ^ das_wort_model ^

                        "s may be found."

                      else

                        ""))

               else

                 ()

             end

           else

             ()

       in

         solve_any_problem (found_really_genuine, max_potential, max_genuine,

                            donno) true (rev problems)

       end

     fun scope_count (problems : rich_problem list) scope =

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

     fun excipit did_so_and_so =

       let

         val do_filter =

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

           else I

         val total = length (!scopes)

         val unsat =

           fold (fn scope =>

                    case scope_count (do_filter (!generated_problems)) scope of

                      0 => I

                    | n =>

                      scope_count (do_filter (these (!checked_problems)))

                                  scope = n

                      ? Integer.add 1) (!generated_scopes) 0

       in

         "Nitpick " ^ did_so_and_so ^

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

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

            ^ plural_s total

          else

            "") ^ "."

       end

     val (skipped, the_scopes) =

       all_scopes hol_ctxt binarize cards_assigns maxes_assigns iters_assigns

                  bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs

                  finitizable_dataTs

     val _ = if skipped > 0 then

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

                                 string_of_int skipped ^ " scope" ^

                                 plural_s skipped ^

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

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

             else

               ()

     val _ = scopes := the_scopes

     fun run_batches _ _ []

                     (found_really_genuine, max_potential, max_genuine, donno) =

         if donno > 0 andalso max_genuine > 0 then

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

         else if max_genuine = original_max_genuine then

           if max_potential = original_max_potential then

             (print_n (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

                     "")); if skipped > 0 then unknownN else noneN)

           else

             (print_n (fn () =>

                  excipit ("could not find a" ^

                           (if max_genuine = 1 then

                              " better " ^ das_wort_model ^ "."

                            else

                              "ny better " ^ das_wort_model ^ "s.") ^

                           " It checked"));

              potentialN)

         else if found_really_genuine then

           genuineN

         else

           quasi_genuineN

       | 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 batches = batch_list batch_size (!scopes)

     val outcome_code =

       run_batches 0 (length batches) batches

                   (false, max_potential, max_genuine, 0)

       handle TimeLimit.TimeOut =>

              (print_n (fn () => excipit "ran out of time after checking");

               if !met_potential > 0 then potentialN else unknownN)

     val _ = print_v (fn () =>

                 "Total time: " ^ string_from_time (Timer.checkRealTimer timer) ^

                 ".")

   in (outcome_code, !state_ref) end

 (* Give the inner timeout a chance. *)

 val timeout_bonus = seconds 1.0

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

                       step subst assm_ts orig_t =

   let val print_n = if mode = Normal then Output.urgent_message else K () in

     if getenv "KODKODI" = "" then

       (* The "expect" argument is deliberately ignored if Kodkodi is missing so

          that the "Nitpick_Examples" can be processed on any machine. *)

       (print_n (Pretty.string_of (plazy install_kodkodi_message));

        ("no_kodkodi", state))

     else

       let

         val unknown_outcome = (unknownN, state)

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

         val outcome as (outcome_code, _) =

           time_limit (if debug orelse is_none timeout then NONE

                       else SOME (Time.+ (the timeout, timeout_bonus)))

               (pick_them_nits_in_term deadline state params mode i n step subst

                                       assm_ts) orig_t

           handle TOO_LARGE (_, details) =>

                  (print_n ("Limit reached: " ^ details ^ "."); unknown_outcome)

                | TOO_SMALL (_, details) =>

                  (print_n ("Limit reached: " ^ details ^ "."); unknown_outcome)

                | Kodkod.SYNTAX (_, details) =>

                  (print_n ("Malformed Kodkodi output: " ^ details ^ ".");

                   unknown_outcome)

                | TimeLimit.TimeOut =>

                  (print_n "Nitpick ran out of time."; unknown_outcome)

       in

         if expect = "" orelse outcome_code = expect then outcome

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

       end

   end

 fun is_fixed_equation ctxt

                       (Const (@{const_name "=="}, _) $ Free (s, _) $ Const _) =

     Variable.is_fixed ctxt s

   | is_fixed_equation _ _ = false

 fun extract_fixed_frees ctxt (assms, t) =

   let

     val (subst, other_assms) =

       List.partition (is_fixed_equation ctxt) assms

       |>> map Logic.dest_equals

   in (subst, other_assms, subst_atomic subst t) end

 fun pick_nits_in_subgoal state params mode 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 => (Output.urgent_message "No subgoal!"; (noneN, state))

     | n =>

       let

         val t = Logic.goal_params t i |> fst

         val assms = map term_of (Assumption.all_assms_of ctxt)

         val (subst, assms, t) = extract_fixed_frees ctxt (assms, t)

       in pick_nits_in_term state params mode i n step subst assms t end

   end

 end;