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

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2009, 2010

Model reconstruction for Nitpick.

*)

signature NITPICK_MODEL =

sig

  type styp = Nitpick_Util.styp

  type scope = Nitpick_Scope.scope

  type rep = Nitpick_Rep.rep

  type nut = Nitpick_Nut.nut

  type params =

    {show_datatypes: bool,

     show_consts: bool}

  type term_postprocessor =

    Proof.context -> string -> (typ -> term list) -> typ -> term -> term

  structure NameTable : TABLE

  val irrelevant : string

  val unknown : string

  val unrep : unit -> string

  val register_term_postprocessor :

    typ -> term_postprocessor -> theory -> theory

  val unregister_term_postprocessor : typ -> theory -> theory

  val tuple_list_for_name :

    nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list

  val dest_plain_fun : term -> bool * (term list * term list)

  val reconstruct_hol_model :

    params -> scope -> (term option * int list) list

    -> (typ option * string list) list -> styp list -> nut list -> nut list

    -> nut list -> nut NameTable.table -> Kodkod.raw_bound list

    -> Pretty.T * bool

  val prove_hol_model :

    scope -> Time.time option -> nut list -> nut list -> nut NameTable.table

    -> Kodkod.raw_bound list -> term -> bool option

end;

structure Nitpick_Model : NITPICK_MODEL =

struct

open Nitpick_Util

open Nitpick_HOL

open Nitpick_Scope

open Nitpick_Peephole

open Nitpick_Rep

open Nitpick_Nut

structure KK = Kodkod

type params =

  {show_datatypes: bool,

   show_consts: bool}

type term_postprocessor =

  Proof.context -> string -> (typ -> term list) -> typ -> term -> term

structure Data = Theory_Data(

  type T = (typ * term_postprocessor) list

  val empty = []

  val extend = I

  fun merge (x, y) = AList.merge (op =) (K true) (x, y))

fun xsym s s' () = if print_mode_active Symbol.xsymbolsN then s else s'

val irrelevant = "_"

val unknown = "?"

val unrep = xsym "\<dots>" "..."

val maybe_mixfix = xsym "_\<^sup>?" "_?"

val base_mixfix = xsym "_\<^bsub>base\<^esub>" "_.base"

val step_mixfix = xsym "_\<^bsub>step\<^esub>" "_.step"

val abs_mixfix = xsym "\<guillemotleft>_\<guillemotright>" "\"_\""

val arg_var_prefix = "x"

val cyclic_co_val_name = xsym "\<omega>" "w"

val cyclic_const_prefix = xsym "\<xi>" "X"

fun cyclic_type_name () = nitpick_prefix ^ cyclic_const_prefix ()

val opt_flag = nitpick_prefix ^ "opt"

val non_opt_flag = nitpick_prefix ^ "non_opt"

type atom_pool = ((string * int) * int list) list

fun add_wacky_syntax ctxt =

  let

    val name_of = fst o dest_Const

    val thy = ProofContext.theory_of ctxt |> Context.reject_draft

    val (maybe_t, thy) =

      Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),

                          Mixfix (maybe_mixfix (), [1000], 1000)) thy

    val (abs_t, thy) =

      Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),

                          Mixfix (abs_mixfix (), [40], 40)) thy

    val (base_t, thy) =

      Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),

                          Mixfix (base_mixfix (), [1000], 1000)) thy

    val (step_t, thy) =

      Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),

                          Mixfix (step_mixfix (), [1000], 1000)) thy

  in

    (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),

     ProofContext.transfer_syntax thy ctxt)

  end

(** Term reconstruction **)

fun nth_atom_number pool T j =

  case AList.lookup (op =) (!pool) T of

    SOME js =>

    (case find_index (curry (op =) j) js of

       ~1 => (Unsynchronized.change pool (cons (T, j :: js));

              length js + 1)

     | n => length js - n)

  | NONE => (Unsynchronized.change pool (cons (T, [j])); 1)

fun atom_suffix s =

  nat_subscript

  #> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))

     ? prefix "\<^isub>,"

fun nth_atom_name thy atomss pool prefix T j =

  let

    val ss = these (triple_lookup (type_match thy) atomss T)

    val m = nth_atom_number pool T j

  in

    if m <= length ss then

      nth ss (m - 1)

    else case T of

      Type (s, _) =>

      let val s' = shortest_name s in

        prefix ^

        (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^

        atom_suffix s m

      end

    | TFree (s, _) => prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s m

    | _ => raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])

  end

fun nth_atom thy atomss pool for_auto T j =

  if for_auto then

    Free (nth_atom_name thy atomss pool (hd (space_explode "." nitpick_prefix))

                        T j, T)

  else

    Const (nth_atom_name thy atomss pool "" T j, T)

fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =

    real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))

  | extract_real_number t = real (snd (HOLogic.dest_number t))

fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)

  | nice_term_ord tp = Real.compare (pairself extract_real_number tp)

    handle TERM ("dest_number", _) =>

           case tp of

             (t11 $ t12, t21 $ t22) =>

             (case nice_term_ord (t11, t21) of

                EQUAL => nice_term_ord (t12, t22)

              | ord => ord)

           | _ => Term_Ord.fast_term_ord tp

fun register_term_postprocessor T p = Data.map (cons (T, p))

fun unregister_term_postprocessor T = Data.map (AList.delete (op =) T)

fun tuple_list_for_name rel_table bounds name =

  the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]

fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =

    unarize_unbox_etc_term t1

  | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =

    unarize_unbox_etc_term t1

  | unarize_unbox_etc_term

        (Const (@{const_name PairBox},

                Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))

         $ t1 $ t2) =

    let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in

      Const (@{const_name Pair}, Ts ---> Type (@{type_name "*"}, Ts))

      $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2

    end

  | unarize_unbox_etc_term (Const (s, T)) =

    Const (s, uniterize_unarize_unbox_etc_type T)

  | unarize_unbox_etc_term (t1 $ t2) =

    unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2

  | unarize_unbox_etc_term (Free (s, T)) =

    Free (s, uniterize_unarize_unbox_etc_type T)

  | unarize_unbox_etc_term (Var (x, T)) =

    Var (x, uniterize_unarize_unbox_etc_type T)

  | unarize_unbox_etc_term (Bound j) = Bound j

  | unarize_unbox_etc_term (Abs (s, T, t')) =

    Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')

fun factor_out_types (T1 as Type (@{type_name "*"}, [T11, T12]))

                     (T2 as Type (@{type_name "*"}, [T21, T22])) =

    let val (n1, n2) = pairself num_factors_in_type (T11, T21) in

      if n1 = n2 then

        let

          val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22

        in

          ((Type (@{type_name "*"}, [T11, T11']), opt_T12'),

           (Type (@{type_name "*"}, [T21, T21']), opt_T22'))

        end

      else if n1 < n2 then

        case factor_out_types T1 T21 of

          (p1, (T21', NONE)) => (p1, (T21', SOME T22))

        | (p1, (T21', SOME T22')) =>

          (p1, (T21', SOME (Type (@{type_name "*"}, [T22', T22]))))

      else

        swap (factor_out_types T2 T1)

    end

  | factor_out_types (Type (@{type_name "*"}, [T11, T12])) T2 =

    ((T11, SOME T12), (T2, NONE))

  | factor_out_types T1 (Type (@{type_name "*"}, [T21, T22])) =

    ((T1, NONE), (T21, SOME T22))

  | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))

fun make_plain_fun maybe_opt T1 T2 =

  let

    fun aux T1 T2 [] =

        Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)

      | aux T1 T2 ((t1, t2) :: tps) =

        Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)

        $ aux T1 T2 tps $ t1 $ t2

  in aux T1 T2 o rev end

fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)

  | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =

    is_plain_fun t0

  | is_plain_fun _ = false

val dest_plain_fun =

  let

    fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))

      | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))

      | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =

        let val (maybe_opt, (ts1, ts2)) = aux t0 in

          (maybe_opt, (t1 :: ts1, t2 :: ts2))

        end

      | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])

  in apsnd (pairself rev) o aux end

fun break_in_two T T1 T2 t =

  let

    val ps = HOLogic.flat_tupleT_paths T

    val cut = length (HOLogic.strip_tupleT T1)

    val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)

    val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut

  in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end

fun pair_up (Type (@{type_name "*"}, [T1', T2']))

            (t1 as Const (@{const_name Pair},

                          Type (@{type_name fun},

                                [_, Type (@{type_name fun}, [_, T1])]))

             $ t11 $ t12) t2 =

    if T1 = T1' then HOLogic.mk_prod (t1, t2)

    else HOLogic.mk_prod (t11, pair_up T2' t12 t2)

  | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)

fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3

fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =

    let

      fun do_curry T1 T1a T1b T2 t =

        let

          val (maybe_opt, tsp) = dest_plain_fun t

          val tps =

            tsp |>> map (break_in_two T1 T1a T1b)

                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))

                |> AList.coalesce (op =)

                |> map (apsnd (make_plain_fun maybe_opt T1b T2))

        in make_plain_fun maybe_opt T1a (T1b --> T2) tps end

      and do_uncurry T1 T2 t =

        let

          val (maybe_opt, tsp) = dest_plain_fun t

          val tps =

            tsp |> op ~~

                |> maps (fn (t1, t2) =>

                            multi_pair_up T1 t1 (snd (dest_plain_fun t2)))

        in make_plain_fun maybe_opt T1 T2 tps end

      and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')

        | do_arrow T1' T2' T1 T2

                   (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =

          Const (@{const_name fun_upd},

                 (T1' --> T2') --> T1' --> T2' --> T1' --> T2')

          $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2

        | do_arrow _ _ _ _ t =

          raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])

      and do_fun T1' T2' T1 T2 t =

        case factor_out_types T1' T1 of

          ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2

        | ((_, NONE), (T1a, SOME T1b)) =>

          t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)

        | ((T1a', SOME T1b'), (_, NONE)) =>

          t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'

        | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])

      and do_term (Type (@{type_name fun}, [T1', T2']))

                  (Type (@{type_name fun}, [T1, T2])) t =

          do_fun T1' T2' T1 T2 t

        | do_term (T' as Type (@{type_name "*"}, Ts' as [T1', T2']))

                  (Type (@{type_name "*"}, [T1, T2]))

                  (Const (@{const_name Pair}, _) $ t1 $ t2) =

          Const (@{const_name Pair}, Ts' ---> T')

          $ do_term T1' T1 t1 $ do_term T2' T2 t2

        | do_term T' T t =

          if T = T' then t

          else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])

    in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end

  | typecast_fun T' _ _ _ =

    raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])

fun truth_const_sort_key @{const True} = "0"

  | truth_const_sort_key @{const False} = "2"

  | truth_const_sort_key _ = "1"

fun mk_tuple (Type (@{type_name "*"}, [T1, T2])) ts =

    HOLogic.mk_prod (mk_tuple T1 ts,

        mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))

  | mk_tuple _ (t :: _) = t

  | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])

fun varified_type_match thy (candid_T, pat_T) =

  strict_type_match thy (candid_T, Logic.varifyT_global pat_T)

fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)

                       atomss sel_names rel_table bounds card T =

  let

    val card = if card = 0 then card_of_type card_assigns T else card

    fun nth_value_of_type n =

      let

        fun term unfold =

          reconstruct_term true unfold pool wacky_names scope atomss sel_names

                           rel_table bounds T T (Atom (card, 0)) [[n]]

      in

        case term false of

          t as Const (s, _) =>

          if String.isPrefix (cyclic_const_prefix ()) s then

            HOLogic.mk_eq (t, term true)

          else

            t

        | t => t

      end

  in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end

and reconstruct_term maybe_opt unfold pool

        (wacky_names as ((maybe_name, abs_name), _))

        (scope as {hol_ctxt as {thy, ctxt, stds, ...}, binarize, card_assigns,

                   bits, datatypes, ofs, ...})

        atomss sel_names rel_table bounds =

  let

    val for_auto = (maybe_name = "")

    fun value_of_bits jss =

      let

        val j0 = offset_of_type ofs @{typ unsigned_bit}

        val js = map (Integer.add (~ j0) o the_single) jss

      in

        fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))

             js 0

      end

    val all_values =

      all_values_of_type pool wacky_names scope atomss sel_names rel_table

                         bounds 0

    fun postprocess_term (Type (@{type_name fun}, _)) = I

      | postprocess_term T =

        if null (Data.get thy) then

          I

        else case AList.lookup (varified_type_match thy) (Data.get thy) T of

          SOME postproc => postproc ctxt maybe_name all_values T

        | NONE => I

    fun postprocess_subterms Ts (t1 $ t2) =

        let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in

          postprocess_term (fastype_of1 (Ts, t)) t

        end

      | postprocess_subterms Ts (Abs (s, T, t')) =

        Abs (s, T, postprocess_subterms (T :: Ts) t')

      | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t

    fun make_set maybe_opt T1 T2 tps =

      let

        val empty_const = Const (@{const_abbrev Set.empty}, T1 --> T2)

        val insert_const = Const (@{const_name insert},

                                  T1 --> (T1 --> T2) --> T1 --> T2)

        fun aux [] =

            if maybe_opt andalso not (is_complete_type datatypes false T1) then

              insert_const $ Const (unrep (), T1) $ empty_const

            else

              empty_const

          | aux ((t1, t2) :: zs) =

            aux zs

            |> t2 <> @{const False}

               ? curry (op $)

                       (insert_const

                        $ (t1 |> t2 <> @{const True}

                                 ? curry (op $)

                                         (Const (maybe_name, T1 --> T1))))

      in

        if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})

                  tps then

          Const (unknown, T1 --> T2)

        else

          aux tps

      end

    fun make_map maybe_opt T1 T2 T2' =

      let

        val update_const = Const (@{const_name fun_upd},

                                  (T1 --> T2) --> T1 --> T2 --> T1 --> T2)

        fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)

          | aux' ((t1, t2) :: tps) =

            (case t2 of

               Const (@{const_name None}, _) => aux' tps

             | _ => update_const $ aux' tps $ t1 $ t2)

        fun aux tps =

          if maybe_opt andalso not (is_complete_type datatypes false T1) then

            update_const $ aux' tps $ Const (unrep (), T1)

            $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))

          else

            aux' tps

      in aux end

    fun polish_funs Ts t =

      (case fastype_of1 (Ts, t) of

         Type (@{type_name fun}, [T1, T2]) =>

         if is_plain_fun t then

           case T2 of

             @{typ bool} =>

             let

               val (maybe_opt, ts_pair) =

                 dest_plain_fun t ||> pairself (map (polish_funs Ts))

             in

               make_set maybe_opt T1 T2

                        (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))

             end

           | Type (@{type_name option}, [T2']) =>

             let

               val (maybe_opt, ts_pair) =

                 dest_plain_fun t ||> pairself (map (polish_funs Ts))

             in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end

           | _ => raise SAME ()

         else

           raise SAME ()

       | _ => raise SAME ())

      handle SAME () =>

             case t of

               (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)

               $ (t2 as Const (s, _)) =>

               if s = unknown then polish_funs Ts t11

               else polish_funs Ts t1 $ polish_funs Ts t2

             | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2

             | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')

             | Const (s, Type (@{type_name fun}, [T1, T2])) =>

               if s = opt_flag orelse s = non_opt_flag then

                 Abs ("x", T1,

                      Const (if is_complete_type datatypes false T1 then

                               irrelevant

                             else

                               unknown, T2))

               else

                 t

             | t => t

    fun make_fun maybe_opt T1 T2 T' ts1 ts2 =

      ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)

                 |> make_plain_fun maybe_opt T1 T2

                 |> unarize_unbox_etc_term

                 |> typecast_fun (uniterize_unarize_unbox_etc_type T')

                                 (uniterize_unarize_unbox_etc_type T1)

                                 (uniterize_unarize_unbox_etc_type T2)

    fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =

        let

          val k1 = card_of_type card_assigns T1

          val k2 = card_of_type card_assigns T2

        in

          term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))

                       [nth_combination (replicate k1 (k2, 0)) j]

          handle General.Subscript =>

                 raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",

                            signed_string_of_int j ^ " for " ^

                            string_for_rep (Vect (k1, Atom (k2, 0))))

        end

      | term_for_atom seen (Type (@{type_name "*"}, [T1, T2])) _ j k =

        let

          val k1 = card_of_type card_assigns T1

          val k2 = k div k1

        in

          list_comb (HOLogic.pair_const T1 T2,

                     map3 (fn T => term_for_atom seen T T) [T1, T2]

                          [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)

        end

      | term_for_atom seen @{typ prop} _ j k =

        HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)

      | term_for_atom _ @{typ bool} _ j _ =

        if j = 0 then @{const False} else @{const True}

      | term_for_atom _ @{typ unit} _ _ _ = @{const Unity}

      | term_for_atom seen T _ j k =

        if T = nat_T andalso is_standard_datatype thy stds nat_T then

          HOLogic.mk_number nat_T j

        else if T = int_T then

          HOLogic.mk_number int_T (int_for_atom (k, 0) j)

        else if is_fp_iterator_type T then

          HOLogic.mk_number nat_T (k - j - 1)

        else if T = @{typ bisim_iterator} then

          HOLogic.mk_number nat_T j

        else case datatype_spec datatypes T of

          NONE => nth_atom thy atomss pool for_auto T j

        | SOME {deep = false, ...} => nth_atom thy atomss pool for_auto T j

        | SOME {co, standard, constrs, ...} =>

          let

            fun tuples_for_const (s, T) =

              tuple_list_for_name rel_table bounds (ConstName (s, T, Any))

            fun cyclic_atom () =

              nth_atom thy atomss pool for_auto (Type (cyclic_type_name (), []))

                       j

            fun cyclic_var () =

              Var ((nth_atom_name thy atomss pool "" T j, 0), T)

            val discr_jsss = map (tuples_for_const o discr_for_constr o #const)

                                 constrs

            val real_j = j + offset_of_type ofs T

            val constr_x as (constr_s, constr_T) =

              get_first (fn (jss, {const, ...}) =>

                            if member (op =) jss [real_j] then SOME const

                            else NONE)

                        (discr_jsss ~~ constrs) |> the

            val arg_Ts = curried_binder_types constr_T

            val sel_xs =

              map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize

                                                          constr_x)

                  (index_seq 0 (length arg_Ts))

            val sel_Rs =

              map (fn x => get_first

                               (fn ConstName (s', T', R) =>

                                   if (s', T') = x then SOME R else NONE

                                 | u => raise NUT ("Nitpick_Model.reconstruct_\

                                                   \term.term_for_atom", [u]))

                               sel_names |> the) sel_xs

            val arg_Rs = map (snd o dest_Func) sel_Rs

            val sel_jsss = map tuples_for_const sel_xs

            val arg_jsss =

              map (map_filter (fn js => if hd js = real_j then SOME (tl js)

                                        else NONE)) sel_jsss

            val uncur_arg_Ts = binder_types constr_T

            val maybe_cyclic = co orelse not standard

          in

            if maybe_cyclic andalso not (null seen) andalso

               member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then

              cyclic_var ()

            else if constr_s = @{const_name Word} then

              HOLogic.mk_number

                  (if T = @{typ "unsigned_bit word"} then nat_T else int_T)

                  (value_of_bits (the_single arg_jsss))

            else

              let

                val seen = seen |> maybe_cyclic ? cons (T, j)

                val ts =

                  if length arg_Ts = 0 then

                    []

                  else

                    map3 (fn Ts =>

                             term_for_rep (constr_s <> @{const_name FinFun})

                                          seen Ts Ts) arg_Ts arg_Rs arg_jsss

                    |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)

                    |> dest_n_tuple (length uncur_arg_Ts)

                val t =

                  if constr_s = @{const_name Abs_Frac} then

                    case ts of

                      [Const (@{const_name Pair}, _) $ t1 $ t2] =>

                      frac_from_term_pair (body_type T) t1 t2

                    | _ => raise TERM ("Nitpick_Model.reconstruct_term.\

                                       \term_for_atom (Abs_Frac)", ts)

                  else if not for_auto andalso

                          (is_abs_fun ctxt constr_x orelse

                           constr_s = @{const_name Quot}) then

                    Const (abs_name, constr_T) $ the_single ts

                  else

                    list_comb (Const constr_x, ts)

              in

                if maybe_cyclic then

                  let val var = cyclic_var () in

                    if unfold andalso not standard andalso

                       length seen = 1 andalso

                       exists_subterm

                           (fn Const (s, _) =>

                               String.isPrefix (cyclic_const_prefix ()) s

                             | t' => t' = var) t then

                      subst_atomic [(var, cyclic_atom ())] t

                    else if exists_subterm (curry (op =) var) t then

                      if co then

                        Const (@{const_name The}, (T --> bool_T) --> T)

                        $ Abs (cyclic_co_val_name (), T,

                               Const (@{const_name "op ="}, T --> T --> bool_T)

                               $ Bound 0 $ abstract_over (var, t))

                      else

                        cyclic_atom ()

                    else

                      t

                  end

                else

                  t

              end

          end

    and term_for_vect seen k R T1 T2 T' js =

      make_fun true T1 T2 T'

               (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))

               (map (term_for_rep true seen T2 T2 R o single)

                    (batch_list (arity_of_rep R) js))

    and term_for_rep _ seen T T' Unit [[]] = term_for_atom seen T T' 0 1

      | term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =

        if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k

        else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])

      | term_for_rep _ seen (Type (@{type_name "*"}, [T1, T2])) _

                     (Struct [R1, R2]) [js] =

        let

          val arity1 = arity_of_rep R1

          val (js1, js2) = chop arity1 js

        in

          list_comb (HOLogic.pair_const T1 T2,

                     map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]

                          [[js1], [js2]])

        end

      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'

                     (Vect (k, R')) [js] =

        term_for_vect seen k R' T1 T2 T' js

      | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'

                     (Func (R1, Formula Neut)) jss =

        let

          val jss1 = all_combinations_for_rep R1

          val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1

          val ts2 =

            map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))

                                       [[int_from_bool (member (op =) jss js)]])

                jss1

        in make_fun maybe_opt T1 T2 T' ts1 ts2 end

      | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'

                     (Func (R1, R2)) jss =

        let

          val arity1 = arity_of_rep R1

          val jss1 = all_combinations_for_rep R1

          val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1

          val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)

          val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []

                         o AList.lookup (op =) grouped_jss2) jss1

        in make_fun maybe_opt T1 T2 T' ts1 ts2 end

      | term_for_rep _ seen T T' (Opt R) jss =

        if null jss then Const (unknown, T)

        else term_for_rep true seen T T' R jss

      | term_for_rep _ _ T _ R jss =

        raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",

                   Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^

                   string_of_int (length jss))

  in

    postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term

    oooo term_for_rep maybe_opt []

  end

(** Constant postprocessing **)

fun dest_n_tuple_type 1 T = [T]

  | dest_n_tuple_type n (Type (_, [T1, T2])) =

    T1 :: dest_n_tuple_type (n - 1) T2

  | dest_n_tuple_type _ T =

    raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])

fun const_format thy def_table (x as (s, T)) =

  if String.isPrefix unrolled_prefix s then

    const_format thy def_table (original_name s, range_type T)

  else if String.isPrefix skolem_prefix s then

    let

      val k = unprefix skolem_prefix s

              |> strip_first_name_sep |> fst |> space_explode "@"

              |> hd |> Int.fromString |> the

    in [k, num_binder_types T - k] end

  else if original_name s <> s then

    [num_binder_types T]

  else case def_of_const thy def_table x of

    SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then

                 let val k = length (strip_abs_vars t') in

                   [k, num_binder_types T - k]

                 end

               else

                 [num_binder_types T]

  | NONE => [num_binder_types T]

fun intersect_formats _ [] = []

  | intersect_formats [] _ = []

  | intersect_formats ks1 ks2 =

    let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in

      intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))

                        (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @

      [Int.min (k1, k2)]

    end

fun lookup_format thy def_table formats t =

  case AList.lookup (fn (SOME x, SOME y) =>

                        (term_match thy) (x, y) | _ => false)

                    formats (SOME t) of

    SOME format => format

  | NONE => let val format = the (AList.lookup (op =) formats NONE) in

              case t of

                Const x => intersect_formats format

                                             (const_format thy def_table x)

              | _ => format

            end

fun format_type default_format format T =

  let

    val T = uniterize_unarize_unbox_etc_type T

    val format = format |> filter (curry (op <) 0)

  in

    if forall (curry (op =) 1) format then

      T

    else

      let

        val (binder_Ts, body_T) = strip_type T

        val batched =

          binder_Ts

          |> map (format_type default_format default_format)

          |> rev |> chunk_list_unevenly (rev format)

          |> map (HOLogic.mk_tupleT o rev)

      in List.foldl (op -->) body_T batched end

  end

fun format_term_type thy def_table formats t =

  format_type (the (AList.lookup (op =) formats NONE))

              (lookup_format thy def_table formats t) (fastype_of t)

fun repair_special_format js m format =

  m - 1 downto 0 |> chunk_list_unevenly (rev format)

                 |> map (rev o filter_out (member (op =) js))

                 |> filter_out null |> map length |> rev

fun user_friendly_const ({thy, evals, def_table, skolems, special_funs, ...}

                         : hol_context) (base_name, step_name) formats =

  let

    val default_format = the (AList.lookup (op =) formats NONE)

    fun do_const (x as (s, T)) =

      (if String.isPrefix special_prefix s then

         let

           val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')

           val (x' as (_, T'), js, ts) =

             AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)

             |> the_single

           val max_j = List.last js

           val Ts = List.take (binder_types T', max_j + 1)

           val missing_js = filter_out (member (op =) js) (0 upto max_j)

           val missing_Ts = filter_indices missing_js Ts

           fun nth_missing_var n =

             ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)

           val missing_vars = map nth_missing_var (0 upto length missing_js - 1)

           val vars = special_bounds ts @ missing_vars

           val ts' =

             map (fn j =>

                     case AList.lookup (op =) (js ~~ ts) j of

                       SOME t => do_term t

                     | NONE =>

                       Var (nth missing_vars

                                (find_index (curry (op =) j) missing_js)))

                 (0 upto max_j)

           val t = do_const x' |> fst

           val format =

             case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)

                                 | _ => false) formats (SOME t) of

               SOME format =>

               repair_special_format js (num_binder_types T') format

             | NONE =>

               const_format thy def_table x'

               |> repair_special_format js (num_binder_types T')

               |> intersect_formats default_format

         in

           (list_comb (t, ts') |> fold_rev abs_var vars,

            format_type default_format format T)

         end

       else if String.isPrefix uncurry_prefix s then

         let

           val (ss, s') = unprefix uncurry_prefix s

                          |> strip_first_name_sep |>> space_explode "@"

         in

           if String.isPrefix step_prefix s' then

             do_const (s', T)

           else

             let

               val k = the (Int.fromString (hd ss))

               val j = the (Int.fromString (List.last ss))

               val (before_Ts, (tuple_T, rest_T)) =

                 strip_n_binders j T ||> (strip_n_binders 1 #>> hd)

               val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T

             in do_const (s', T') end

         end

       else if String.isPrefix unrolled_prefix s then

         let val t = Const (original_name s, range_type T) in

           (lambda (Free (iter_var_prefix, nat_T)) t,

            format_type default_format

                        (lookup_format thy def_table formats t) T)

         end

       else if String.isPrefix base_prefix s then

         (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),

          format_type default_format default_format T)

       else if String.isPrefix step_prefix s then

         (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),

          format_type default_format default_format T)

       else if String.isPrefix quot_normal_prefix s then

         let val t = Const (nitpick_prefix ^ "normalize quotient type", T) in

           (t, format_term_type thy def_table formats t)

         end

       else if String.isPrefix skolem_prefix s then

         let

           val ss = the (AList.lookup (op =) (!skolems) s)

           val (Ts, Ts') = chop (length ss) (binder_types T)

           val frees = map Free (ss ~~ Ts)

           val s' = original_name s

         in

           (fold lambda frees (Const (s', Ts' ---> T)),

            format_type default_format

                        (lookup_format thy def_table formats (Const x)) T)

         end

       else if String.isPrefix eval_prefix s then

         let

           val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))

         in (t, format_term_type thy def_table formats t) end

       else if s = @{const_name undefined_fast_The} then

         (Const (nitpick_prefix ^ "The fallback", T),

          format_type default_format

                      (lookup_format thy def_table formats

                           (Const (@{const_name The}, (T --> bool_T) --> T))) T)

       else if s = @{const_name undefined_fast_Eps} then

         (Const (nitpick_prefix ^ "Eps fallback", T),

          format_type default_format

                      (lookup_format thy def_table formats

                           (Const (@{const_name Eps}, (T --> bool_T) --> T))) T)

       else

         let val t = Const (original_name s, T) in

           (t, format_term_type thy def_table formats t)

         end)

      |>> map_types uniterize_unarize_unbox_etc_type

      |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name

  in do_const end

fun assign_operator_for_const (s, T) =

  if String.isPrefix ubfp_prefix s then

    if is_fun_type T then xsym "\<subseteq>" "<=" ()

    else xsym "\<le>" "<=" ()

  else if String.isPrefix lbfp_prefix s then

    if is_fun_type T then xsym "\<supseteq>" ">=" ()

    else xsym "\<ge>" ">=" ()

  else if original_name s <> s then

    assign_operator_for_const (strip_first_name_sep s |> snd, T)

  else

    "="

(** Model reconstruction **)

fun unfold_outer_the_binders (t as Const (@{const_name The}, _)

                                   $ Abs (s, T, Const (@{const_name "op ="}, _)

                                                $ Bound 0 $ t')) =

    betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders

  | unfold_outer_the_binders t = t

fun bisimilar_values _ 0 _ = true

  | bisimilar_values coTs max_depth (t1, t2) =

    let val T = fastype_of t1 in

      if exists_subtype (member (op =) coTs) T then

        let

          val ((head1, args1), (head2, args2)) =

            pairself (strip_comb o unfold_outer_the_binders) (t1, t2)

          val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)

        in

          head1 = head2 andalso

          forall (bisimilar_values coTs max_depth) (args1 ~~ args2)

        end

      else

        t1 = t2

    end

fun reconstruct_hol_model {show_datatypes, show_consts}

        ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,

                      debug, binary_ints, destroy_constrs, specialize,

                      star_linear_preds, fast_descrs, tac_timeout, evals,

                      case_names, def_table, nondef_table, user_nondefs,

                      simp_table, psimp_table, choice_spec_table, intro_table,

                      ground_thm_table, ersatz_table, skolems, special_funs,

                      unrolled_preds, wf_cache, constr_cache},

         binarize, card_assigns, bits, bisim_depth, datatypes, ofs} : scope)

        formats atomss all_frees free_names sel_names nonsel_names rel_table

        bounds =

  let

    val pool = Unsynchronized.ref []

    val (wacky_names as (_, base_step_names), ctxt) =

      add_wacky_syntax ctxt

    val hol_ctxt =

      {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, star_linear_preds = star_linear_preds,

       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,

       choice_spec_table = choice_spec_table, intro_table = intro_table,

       ground_thm_table = ground_thm_table, ersatz_table = ersatz_table,

       skolems = skolems, special_funs = special_funs,

       unrolled_preds = unrolled_preds, wf_cache = wf_cache,

       constr_cache = constr_cache}

    val scope =

      {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,

       bits = bits, bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}

    fun term_for_rep maybe_opt unfold =

      reconstruct_term maybe_opt unfold pool wacky_names scope atomss

                       sel_names rel_table bounds

    fun nth_value_of_type card T n =

      let

        fun aux unfold = term_for_rep true unfold T T (Atom (card, 0)) [[n]]

      in

        case aux false of

          t as Const (s, _) =>

          if String.isPrefix (cyclic_const_prefix ()) s then

            HOLogic.mk_eq (t, aux true)

          else

            t

        | t => t

      end

    val all_values =

      all_values_of_type pool wacky_names scope atomss sel_names rel_table

                         bounds

    fun is_codatatype_wellformed (cos : dtype_spec list)

                                 ({typ, card, ...} : dtype_spec) =

      let

        val ts = all_values card typ

        val max_depth = Integer.sum (map #card cos)

      in

        forall (not o bisimilar_values (map #typ cos) max_depth)

               (all_distinct_unordered_pairs_of ts)

      end

    fun pretty_for_assign name =

      let

        val (oper, (t1, T'), T) =

          case name of

            FreeName (s, T, _) =>

            let val t = Free (s, uniterize_unarize_unbox_etc_type T) in

              ("=", (t, format_term_type thy def_table formats t), T)

            end

          | ConstName (s, T, _) =>

            (assign_operator_for_const (s, T),

             user_friendly_const hol_ctxt base_step_names formats (s, T), T)

          | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\

                            \pretty_for_assign", [name])

        val t2 = if rep_of name = Any then

                   Const (@{const_name undefined}, T')

                 else

                   tuple_list_for_name rel_table bounds name

                   |> term_for_rep (not (is_fully_representable_set name)) false

                                   T T' (rep_of name)

      in

        Pretty.block (Pretty.breaks

            [setmp_show_all_types (Syntax.pretty_term ctxt) t1,

             Pretty.str oper, Syntax.pretty_term ctxt t2])

      end

    fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =

      Pretty.block (Pretty.breaks

          (Syntax.pretty_typ ctxt (uniterize_unarize_unbox_etc_type typ) ::

           (case typ of

              Type (@{type_name fin_fun}, _) => [Pretty.str "[finite]"]

            | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]

            | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]

            | _ => []) @

           [Pretty.str "=",

            Pretty.enum "," "{" "}"

                (map (Syntax.pretty_term ctxt) (all_values card typ) @

                 (if fun_from_pair complete false then []

                  else [Pretty.str (unrep ())]))]))

    fun integer_datatype T =

      [{typ = T, card = card_of_type card_assigns T, co = false,

        standard = true, complete = (false, false), concrete = (true, true),

        deep = true, constrs = []}]

      handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []

    val (codatatypes, datatypes) =

      datatypes |> filter #deep |> List.partition #co

                ||> append (integer_datatype int_T

                            |> is_standard_datatype thy stds nat_T

                               ? append (integer_datatype nat_T))

    val block_of_datatypes =

      if show_datatypes andalso not (null datatypes) then

        [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")

                         (map pretty_for_datatype datatypes)]

      else

        []

    val block_of_codatatypes =

      if show_datatypes andalso not (null codatatypes) then

        [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")

                         (map pretty_for_datatype codatatypes)]

      else

        []

    fun block_of_names show title names =

      if show andalso not (null names) then

        Pretty.str (title ^ plural_s_for_list names ^ ":")

        :: map (Pretty.indent indent_size o pretty_for_assign)

               (sort_wrt (original_name o nickname_of) names)

      else

        []

    val (skolem_names, nonskolem_nonsel_names) =

      List.partition is_skolem_name nonsel_names

    val (eval_names, noneval_nonskolem_nonsel_names) =

      List.partition (String.isPrefix eval_prefix o nickname_of)

                     nonskolem_nonsel_names

      ||> filter_out (member (op =) [@{const_name bisim},

                                     @{const_name bisim_iterator_max}]

                      o nickname_of)

    val free_names =

      map (fn x as (s, T) =>

              case filter (curry (op =) x

                       o pairf nickname_of

                               (uniterize_unarize_unbox_etc_type o type_of))

                       free_names of