wneuper/isa: src/HOL/Tools/Nitpick/nitpick

     1 (*  Title:      HOL/Nitpick/Tools/nitpick_kodkod.ML

     2     Author:     Jasmin Blanchette, TU Muenchen

     3     Copyright   2008, 2009

     5 Kodkod problem generator part of Kodkod.

     6 *)

     8 signature NITPICK_KODKOD =

     9 sig

    10   type extended_context = Nitpick_HOL.extended_context

    11   type dtype_spec = Nitpick_Scope.dtype_spec

    12   type kodkod_constrs = Nitpick_Peephole.kodkod_constrs

    13   type nut = Nitpick_Nut.nut

    14   type nfa_transition = Kodkod.rel_expr * typ

    15   type nfa_entry = typ * nfa_transition list

    16   type nfa_table = nfa_entry list

    18   structure NameTable : TABLE

    20   val univ_card :

    21     int -> int -> int -> Kodkod.bound list -> Kodkod.formula -> int

    22   val check_arity : int -> int -> unit

    23   val kk_tuple : bool -> int -> int list -> Kodkod.tuple

    24   val tuple_set_from_atom_schema : (int * int) list -> Kodkod.tuple_set

    25   val sequential_int_bounds : int -> Kodkod.int_bound list

    26   val bounds_for_built_in_rels_in_formula :

    27     bool -> int -> int -> int -> int -> Kodkod.formula -> Kodkod.bound list

    28   val bound_for_plain_rel : Proof.context -> bool -> nut -> Kodkod.bound

    29   val bound_for_sel_rel :

    30     Proof.context -> bool -> dtype_spec list -> nut -> Kodkod.bound

    31   val merge_bounds : Kodkod.bound list -> Kodkod.bound list

    32   val declarative_axiom_for_plain_rel : kodkod_constrs -> nut -> Kodkod.formula

    33   val declarative_axioms_for_datatypes :

    34     extended_context -> int Typtab.table -> kodkod_constrs

    35     -> nut NameTable.table -> dtype_spec list -> Kodkod.formula list

    36   val kodkod_formula_from_nut :

    37     int Typtab.table -> bool -> kodkod_constrs -> nut -> Kodkod.formula

    38 end;

    40 structure Nitpick_Kodkod : NITPICK_KODKOD =

    41 struct

    43 open Nitpick_Util

    44 open Nitpick_HOL

    45 open Nitpick_Scope

    46 open Nitpick_Peephole

    47 open Nitpick_Rep

    48 open Nitpick_Nut

    50 type nfa_transition = Kodkod.rel_expr * typ

    51 type nfa_entry = typ * nfa_transition list

    52 type nfa_table = nfa_entry list

    54 structure NfaGraph = Graph(type key = typ val ord = TermOrd.typ_ord)

    56 (* int -> Kodkod.int_expr list *)

    57 fun flip_nums n = index_seq 1 n @ [0] |> map Kodkod.Num

    59 (* int -> int -> int -> Kodkod.bound list -> Kodkod.formula -> int *)

    60 fun univ_card nat_card int_card main_j0 bounds formula =

    61   let

    62     (* Kodkod.rel_expr -> int -> int *)

    63     fun rel_expr_func r k =

    64       Int.max (k, case r of

    65                     Kodkod.Atom j => j + 1

    66                   | Kodkod.AtomSeq (k', j0) => j0 + k'

    67                   | _ => 0)

    68     (* Kodkod.tuple -> int -> int *)

    69     fun tuple_func t k =

    70       case t of

    71         Kodkod.Tuple js => fold Integer.max (map (Integer.add 1) js) k

    72       | _ => k

    73     (* Kodkod.tuple_set -> int -> int *)

    74     fun tuple_set_func ts k =

    75       Int.max (k, case ts of Kodkod.TupleAtomSeq (k', j0) => j0 + k' | _ => 0)

    76     val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,

    77                   int_expr_func = K I}

    78     val tuple_F = {tuple_func = tuple_func, tuple_set_func = tuple_set_func}

    79     val card = fold (Kodkod.fold_bound expr_F tuple_F) bounds 1

    80                |> Kodkod.fold_formula expr_F formula

    81   in Int.max (main_j0 + fold Integer.max [2, nat_card, int_card] 0, card) end

    83 (* Proof.context -> bool -> string -> typ -> rep -> string *)

    84 fun bound_comment ctxt debug nick T R =

    85   short_const_name nick ^

    86   (if debug then " :: " ^ plain_string_from_yxml (Syntax.string_of_typ ctxt T)

    87    else "") ^ " : " ^ string_for_rep R

    89 (* int -> int -> unit *)

    90 fun check_arity univ_card n =

    91   if n > Kodkod.max_arity univ_card then

    92     raise LIMIT ("Nitpick_Kodkod.check_arity",

    93                  "arity " ^ string_of_int n ^ " too large for universe of \

    94                  \cardinality " ^ string_of_int univ_card)

    95   else

    96     ()

    98 (* bool -> int -> int list -> Kodkod.tuple *)

    99 fun kk_tuple debug univ_card js =

   100   if debug then

   101     Kodkod.Tuple js

   102   else

   103     Kodkod.TupleIndex (length js,

   104                        fold (fn j => fn accum => accum * univ_card + j) js 0)

   106 (* (int * int) list -> Kodkod.tuple_set *)

   107 val tuple_set_from_atom_schema =

   108   foldl1 Kodkod.TupleProduct o map Kodkod.TupleAtomSeq

   109 (* rep -> Kodkod.tuple_set *)

   110 val upper_bound_for_rep = tuple_set_from_atom_schema o atom_schema_of_rep

   112 (* int -> Kodkod.int_bound list *)

   113 fun sequential_int_bounds n =

   114   [(NONE, map (Kodkod.TupleSet o single o Kodkod.Tuple o single)

   115               (index_seq 0 n))]

   117 (* Kodkod.formula -> Kodkod.n_ary_index list *)

   118 fun built_in_rels_in_formula formula =

   119   let

   120     (* Kodkod.rel_expr -> Kodkod.n_ary_index list -> Kodkod.n_ary_index list *)

   121     fun rel_expr_func (Kodkod.Rel (n, j)) rels =

   122         (case AList.lookup (op =) (#rels initial_pool) n of

   123            SOME k => (j < k ? insert (op =) (n, j)) rels

   124          | NONE => rels)

   125       | rel_expr_func _ rels = rels

   126     val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,

   127                   int_expr_func = K I}

   128   in Kodkod.fold_formula expr_F formula [] end

   130 val max_table_size = 65536

   132 (* int -> unit *)

   133 fun check_table_size k =

   134   if k > max_table_size then

   135     raise LIMIT ("Nitpick_Kodkod.check_table_size",

   136                  "precomputed table too large (" ^ string_of_int k ^ ")")

   137   else

   138     ()

   140 (* bool -> int -> int * int -> (int -> int) -> Kodkod.tuple list *)

   141 fun tabulate_func1 debug univ_card (k, j0) f =

   142   (check_table_size k;

   143    map_filter (fn j1 => let val j2 = f j1 in

   144                           if j2 >= 0 then

   145                             SOME (kk_tuple debug univ_card [j1 + j0, j2 + j0])

   146                           else

   147                             NONE

   148                         end) (index_seq 0 k))

   149 (* bool -> int -> int * int -> int -> (int * int -> int) -> Kodkod.tuple list *)

   150 fun tabulate_op2 debug univ_card (k, j0) res_j0 f =

   151   (check_table_size (k * k);

   152    map_filter (fn j => let

   153                          val j1 = j div k

   154                          val j2 = j - j1 * k

   155                          val j3 = f (j1, j2)

   156                        in

   157                          if j3 >= 0 then

   158                            SOME (kk_tuple debug univ_card

   159                                           [j1 + j0, j2 + j0, j3 + res_j0])

   160                          else

   161                            NONE

   162                        end) (index_seq 0 (k * k)))

   163 (* bool -> int -> int * int -> int -> (int * int -> int * int)

   164    -> Kodkod.tuple list *)

   165 fun tabulate_op2_2 debug univ_card (k, j0) res_j0 f =

   166   (check_table_size (k * k);

   167    map_filter (fn j => let

   168                          val j1 = j div k

   169                          val j2 = j - j1 * k

   170                          val (j3, j4) = f (j1, j2)

   171                        in

   172                          if j3 >= 0 andalso j4 >= 0 then

   173                            SOME (kk_tuple debug univ_card

   174                                           [j1 + j0, j2 + j0, j3 + res_j0,

   175                                            j4 + res_j0])

   176                          else

   177                            NONE

   178                        end) (index_seq 0 (k * k)))

   179 (* bool -> int -> int * int -> (int * int -> int) -> Kodkod.tuple list *)

   180 fun tabulate_nat_op2 debug univ_card (k, j0) f =

   181   tabulate_op2 debug univ_card (k, j0) j0 (atom_for_nat (k, 0) o f)

   182 fun tabulate_int_op2 debug univ_card (k, j0) f =

   183   tabulate_op2 debug univ_card (k, j0) j0

   184                (atom_for_int (k, 0) o f o pairself (int_for_atom (k, 0)))

   185 (* bool -> int -> int * int -> (int * int -> int * int) -> Kodkod.tuple list *)

   186 fun tabulate_int_op2_2 debug univ_card (k, j0) f =

   187   tabulate_op2_2 debug univ_card (k, j0) j0

   188                  (pairself (atom_for_int (k, 0)) o f

   189                   o pairself (int_for_atom (k, 0)))

   191 (* int * int -> int *)

   192 fun isa_div (m, n) = m div n handle General.Div => 0

   193 fun isa_mod (m, n) = m mod n handle General.Div => m

   194 fun isa_gcd (m, 0) = m

   195   | isa_gcd (m, n) = isa_gcd (n, isa_mod (m, n))

   196 fun isa_lcm (m, n) = isa_div (m * n, isa_gcd (m, n))

   197 val isa_zgcd = isa_gcd o pairself abs

   198 (* int * int -> int * int *)

   199 fun isa_norm_frac (m, n) =

   200   if n < 0 then isa_norm_frac (~m, ~n)

   201   else if m = 0 orelse n = 0 then (0, 1)

   202   else let val p = isa_zgcd (m, n) in (isa_div (m, p), isa_div (n, p)) end

   204 (* bool -> int -> int -> int -> int -> int * int

   205    -> string * bool * Kodkod.tuple list *)

   206 fun tabulate_built_in_rel debug univ_card nat_card int_card j0 (x as (n, _)) =

   207   (check_arity univ_card n;

   208    if Kodkod.Rel x = not3_rel then

   209      ("not3", tabulate_func1 debug univ_card (2, j0) (curry (op -) 1))

   210    else if Kodkod.Rel x = suc_rel then

   211      ("suc", tabulate_func1 debug univ_card (univ_card - j0 - 1, j0)

   212                             (Integer.add 1))

   213    else if Kodkod.Rel x = nat_add_rel then

   214      ("nat_add", tabulate_nat_op2 debug univ_card (nat_card, j0) (op +))

   215    else if Kodkod.Rel x = int_add_rel then

   216      ("int_add", tabulate_int_op2 debug univ_card (int_card, j0) (op +))

   217    else if Kodkod.Rel x = nat_subtract_rel then

   218      ("nat_subtract",

   219       tabulate_op2 debug univ_card (nat_card, j0) j0 (uncurry nat_minus))

   220    else if Kodkod.Rel x = int_subtract_rel then

   221      ("int_subtract", tabulate_int_op2 debug univ_card (int_card, j0) (op -))

   222    else if Kodkod.Rel x = nat_multiply_rel then

   223      ("nat_multiply", tabulate_nat_op2 debug univ_card (nat_card, j0) (op * ))

   224    else if Kodkod.Rel x = int_multiply_rel then

   225      ("int_multiply", tabulate_int_op2 debug univ_card (int_card, j0) (op * ))

   226    else if Kodkod.Rel x = nat_divide_rel then

   227      ("nat_divide", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_div)

   228    else if Kodkod.Rel x = int_divide_rel then

   229      ("int_divide", tabulate_int_op2 debug univ_card (int_card, j0) isa_div)

   230    else if Kodkod.Rel x = nat_modulo_rel then

   231      ("nat_modulo", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_mod)

   232    else if Kodkod.Rel x = int_modulo_rel then

   233      ("int_modulo", tabulate_int_op2 debug univ_card (int_card, j0) isa_mod)

   234    else if Kodkod.Rel x = nat_less_rel then

   235      ("nat_less", tabulate_nat_op2 debug univ_card (nat_card, j0)

   236                                    (int_for_bool o op <))

   237    else if Kodkod.Rel x = int_less_rel then

   238      ("int_less", tabulate_int_op2 debug univ_card (int_card, j0)

   239                                    (int_for_bool o op <))

   240    else if Kodkod.Rel x = gcd_rel then

   241      ("gcd", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_gcd)

   242    else if Kodkod.Rel x = lcm_rel then

   243      ("lcm", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_lcm)

   244    else if Kodkod.Rel x = norm_frac_rel then

   245      ("norm_frac", tabulate_int_op2_2 debug univ_card (int_card, j0)

   246                                       isa_norm_frac)

   247    else

   248      raise ARG ("Nitpick_Kodkod.tabulate_built_in_rel", "unknown relation"))

   250 (* bool -> int -> int -> int -> int -> int * int -> Kodkod.rel_expr

   251    -> Kodkod.bound *)

   252 fun bound_for_built_in_rel debug univ_card nat_card int_card j0 x =

   253   let

   254     val (nick, ts) = tabulate_built_in_rel debug univ_card nat_card int_card

   255                                            j0 x

   256   in ([(x, nick)], [Kodkod.TupleSet ts]) end

   258 (* bool -> int -> int -> int -> int -> Kodkod.formula -> Kodkod.bound list *)

   259 fun bounds_for_built_in_rels_in_formula debug univ_card nat_card int_card j0 =

   260   map (bound_for_built_in_rel debug univ_card nat_card int_card j0)

   261   o built_in_rels_in_formula

   263 (* Proof.context -> bool -> nut -> Kodkod.bound *)

   264 fun bound_for_plain_rel ctxt debug (u as FreeRel (x, T, R, nick)) =

   265     ([(x, bound_comment ctxt debug nick T R)],

   266      if nick = @{const_name bisim_iterator_max} then

   267        case R of

   268          Atom (k, j0) => [Kodkod.TupleSet [Kodkod.Tuple [k - 1 + j0]]]

   269        | _ => raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])

   270      else

   271        [Kodkod.TupleSet [], upper_bound_for_rep R])

   272   | bound_for_plain_rel _ _ u =

   273     raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])

   275 (* Proof.context -> bool -> dtype_spec list -> nut -> Kodkod.bound *)

   276 fun bound_for_sel_rel ctxt debug dtypes

   277         (FreeRel (x, T as Type ("fun", [T1, T2]), R as Func (Atom (_, j0), R2),

   278                   nick)) =

   279     let

   280       val constr as {delta, epsilon, exclusive, explicit_max, ...} =

   281         constr_spec dtypes (original_name nick, T1)

   282     in

   283       ([(x, bound_comment ctxt debug nick T R)],

   284        if explicit_max = 0 then

   285          [Kodkod.TupleSet []]

   286        else

   287          let val ts = Kodkod.TupleAtomSeq (epsilon - delta, delta + j0) in

   288            if R2 = Formula Neut then

   289              [ts] |> not exclusive ? cons (Kodkod.TupleSet [])

   290            else

   291              [Kodkod.TupleSet [],

   292               Kodkod.TupleProduct (ts, upper_bound_for_rep R2)]

   293          end)

   294     end

   295   | bound_for_sel_rel _ _ _ u =

   296     raise NUT ("Nitpick_Kodkod.bound_for_sel_rel", [u])

   298 (* Kodkod.bound list -> Kodkod.bound list *)

   299 fun merge_bounds bs =

   300   let

   301     (* Kodkod.bound -> int *)

   302     fun arity (zs, _) = fst (fst (hd zs))

   303     (* Kodkod.bound list -> Kodkod.bound -> Kodkod.bound list

   304        -> Kodkod.bound list *)

   305     fun add_bound ds b [] = List.revAppend (ds, [b])

   306       | add_bound ds b (c :: cs) =

   307         if arity b = arity c andalso snd b = snd c then

   308           List.revAppend (ds, (fst c @ fst b, snd c) :: cs)

   309         else

   310           add_bound (c :: ds) b cs

   311   in fold (add_bound []) bs [] end

   313 (* int -> int -> Kodkod.rel_expr list *)

   314 fun unary_var_seq j0 n = map (curry Kodkod.Var 1) (index_seq j0 n)

   316 (* int list -> Kodkod.rel_expr *)

   317 val singleton_from_combination = foldl1 Kodkod.Product o map Kodkod.Atom

   318 (* rep -> Kodkod.rel_expr list *)

   319 fun all_singletons_for_rep R =

   320   if is_lone_rep R then

   321     all_combinations_for_rep R |> map singleton_from_combination

   322   else

   323     raise REP ("Nitpick_Kodkod.all_singletons_for_rep", [R])

   325 (* Kodkod.rel_expr -> Kodkod.rel_expr list *)

   326 fun unpack_products (Kodkod.Product (r1, r2)) =

   327     unpack_products r1 @ unpack_products r2

   328   | unpack_products r = [r]

   329 fun unpack_joins (Kodkod.Join (r1, r2)) = unpack_joins r1 @ unpack_joins r2

   330   | unpack_joins r = [r]

   332 (* rep -> Kodkod.rel_expr *)

   333 val empty_rel_for_rep = empty_n_ary_rel o arity_of_rep

   334 fun full_rel_for_rep R =

   335   case atom_schema_of_rep R of

   336     [] => raise REP ("Nitpick_Kodkod.full_rel_for_rep", [R])

   337   | schema => foldl1 Kodkod.Product (map Kodkod.AtomSeq schema)

   339 (* int -> int list -> Kodkod.decl list *)

   340 fun decls_for_atom_schema j0 schema =

   341   map2 (fn j => fn x => Kodkod.DeclOne ((1, j), Kodkod.AtomSeq x))

   342        (index_seq j0 (length schema)) schema

   344 (* The type constraint below is a workaround for a Poly/ML bug. *)

   346 (* kodkod_constrs -> rep -> Kodkod.rel_expr -> Kodkod.formula *)

   347 fun d_n_ary_function ({kk_all, kk_join, kk_lone, kk_one, ...} : kodkod_constrs)

   348                      R r =

   349   let val body_R = body_rep R in

   350     if is_lone_rep body_R then

   351       let

   352         val binder_schema = atom_schema_of_reps (binder_reps R)

   353         val body_schema = atom_schema_of_rep body_R

   354         val one = is_one_rep body_R

   355         val opt_x = case r of Kodkod.Rel x => SOME x | _ => NONE

   356       in

   357         if opt_x <> NONE andalso length binder_schema = 1

   358            andalso length body_schema = 1 then

   359           (if one then Kodkod.Function else Kodkod.Functional)

   360               (the opt_x, Kodkod.AtomSeq (hd binder_schema),

   361                Kodkod.AtomSeq (hd body_schema))

   362         else

   363           let

   364             val decls = decls_for_atom_schema ~1 binder_schema

   365             val vars = unary_var_seq ~1 (length binder_schema)

   366             val kk_xone = if one then kk_one else kk_lone

   367           in kk_all decls (kk_xone (fold kk_join vars r)) end

   368       end

   369     else

   370       Kodkod.True

   371   end

   372 fun kk_n_ary_function kk R (r as Kodkod.Rel _) =

   373     if not (is_opt_rep R) then

   374       if r = suc_rel then

   375         Kodkod.False

   376       else if r = nat_add_rel then

   377         formula_for_bool (card_of_rep (body_rep R) = 1)

   378       else if r = nat_multiply_rel then

   379         formula_for_bool (card_of_rep (body_rep R) <= 2)

   380       else

   381         d_n_ary_function kk R r

   382     else if r = nat_subtract_rel then

   383       Kodkod.True

   384     else

   385       d_n_ary_function kk R r

   386   | kk_n_ary_function kk R r = d_n_ary_function kk R r

   388 (* kodkod_constrs -> Kodkod.rel_expr list -> Kodkod.formula *)

   389 fun kk_disjoint_sets _ [] = Kodkod.True

   390   | kk_disjoint_sets (kk as {kk_and, kk_no, kk_intersect, ...} : kodkod_constrs)

   391                      (r :: rs) =

   392     fold (kk_and o kk_no o kk_intersect r) rs (kk_disjoint_sets kk rs)

   394 (* int -> kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr)

   395    -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   396 fun basic_rel_let j ({kk_rel_let, ...} : kodkod_constrs) f r =

   397   if inline_rel_expr r then

   398     f r

   399   else

   400     let val x = (Kodkod.arity_of_rel_expr r, j) in

   401       kk_rel_let [Kodkod.AssignRelReg (x, r)] (f (Kodkod.RelReg x))

   402     end

   404 (* kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr) -> Kodkod.rel_expr

   405    -> Kodkod.rel_expr *)

   406 val single_rel_let = basic_rel_let 0

   407 (* kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)

   408    -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   409 fun double_rel_let kk f r1 r2 =

   410   single_rel_let kk (fn r1 => basic_rel_let 1 kk (f r1) r2) r1

   411 (* kodkod_constrs

   412    -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)

   413    -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr

   414    -> Kodkod.rel_expr *)

   415 fun triple_rel_let kk f r1 r2 r3 =

   416   double_rel_let kk (fn r1 => fn r2 => basic_rel_let 2 kk (f r1 r2) r3) r1 r2

   418 (* kodkod_constrs -> int -> Kodkod.formula -> Kodkod.rel_expr *)

   419 fun atom_from_formula ({kk_rel_if, ...} : kodkod_constrs) j0 f =

   420   kk_rel_if f (Kodkod.Atom (j0 + 1)) (Kodkod.Atom j0)

   421 (* kodkod_constrs -> rep -> Kodkod.formula -> Kodkod.rel_expr *)

   422 fun rel_expr_from_formula kk R f =

   423   case unopt_rep R of

   424     Atom (2, j0) => atom_from_formula kk j0 f

   425   | _ => raise REP ("Nitpick_Kodkod.rel_expr_from_formula", [R])

   427 (* kodkod_cotrs -> int -> int -> Kodkod.rel_expr -> Kodkod.rel_expr list *)

   428 fun unpack_vect_in_chunks ({kk_project_seq, ...} : kodkod_constrs) chunk_arity

   429                           num_chunks r =

   430   List.tabulate (num_chunks, fn j => kk_project_seq r (j * chunk_arity)

   431                                                     chunk_arity)

   433 (* kodkod_constrs -> bool -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr

   434    -> Kodkod.rel_expr *)

   435 fun kk_n_fold_join

   436         (kk as {kk_intersect, kk_product, kk_join, kk_project_seq, ...}) one R1

   437         res_R r1 r2 =

   438   case arity_of_rep R1 of

   439     1 => kk_join r1 r2

   440   | arity1 =>

   441     let

   442       val unpacked_rs1 =

   443         if inline_rel_expr r1 then unpack_vect_in_chunks kk 1 arity1 r1

   444         else unpack_products r1

   445     in

   446       if one andalso length unpacked_rs1 = arity1 then

   447         fold kk_join unpacked_rs1 r2

   448       else

   449         kk_project_seq

   450             (kk_intersect (kk_product r1 (full_rel_for_rep res_R)) r2)

   451             arity1 (arity_of_rep res_R)

   452     end

   454 (* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr list

   455    -> Kodkod.rel_expr list -> Kodkod.rel_expr *)

   456 fun kk_case_switch (kk as {kk_union, kk_product, ...}) R1 R2 r rs1 rs2 =

   457   if rs1 = rs2 then r

   458   else kk_n_fold_join kk true R1 R2 r (fold1 kk_union (map2 kk_product rs1 rs2))

   460 val lone_rep_fallback_max_card = 4096

   461 val some_j0 = 0

   463 (* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   464 fun lone_rep_fallback kk new_R old_R r =

   465   if old_R = new_R then

   466     r

   467   else

   468     let val card = card_of_rep old_R in

   469       if is_lone_rep old_R andalso is_lone_rep new_R

   470          andalso card = card_of_rep new_R then

   471         if card >= lone_rep_fallback_max_card then

   472           raise LIMIT ("Nitpick_Kodkod.lone_rep_fallback",

   473                        "too high cardinality (" ^ string_of_int card ^ ")")

   474         else

   475           kk_case_switch kk old_R new_R r (all_singletons_for_rep old_R)

   476                          (all_singletons_for_rep new_R)

   477       else

   478         raise REP ("Nitpick_Kodkod.lone_rep_fallback", [old_R, new_R])

   479     end

   480 (* kodkod_constrs -> int * int -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   481 and atom_from_rel_expr kk (x as (k, j0)) old_R r =

   482   case old_R of

   483     Func (R1, R2) =>

   484     let

   485       val dom_card = card_of_rep R1

   486       val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)

   487     in

   488       atom_from_rel_expr kk x (Vect (dom_card, R2'))

   489                          (vect_from_rel_expr kk dom_card R2' old_R r)

   490     end

   491   | Opt _ => raise REP ("Nitpick_Kodkod.atom_from_rel_expr", [old_R])

   492   | _ => lone_rep_fallback kk (Atom x) old_R r

   493 (* kodkod_constrs -> rep list -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   494 and struct_from_rel_expr kk Rs old_R r =

   495   case old_R of

   496     Atom _ => lone_rep_fallback kk (Struct Rs) old_R r

   497   | Struct Rs' =>

   498     let

   499       val Rs = filter (not_equal Unit) Rs

   500       val Rs' = filter (not_equal Unit) Rs'

   501     in

   502       if Rs' = Rs then

   503         r

   504       else if map card_of_rep Rs' = map card_of_rep Rs then

   505         let

   506           val old_arities = map arity_of_rep Rs'

   507           val old_offsets = offset_list old_arities

   508           val old_rs = map2 (#kk_project_seq kk r) old_offsets old_arities

   509         in

   510           fold1 (#kk_product kk)

   511                 (map3 (rel_expr_from_rel_expr kk) Rs Rs' old_rs)

   512         end

   513       else

   514         lone_rep_fallback kk (Struct Rs) old_R r

   515     end

   516   | _ => raise REP ("Nitpick_Kodkod.struct_from_rel_expr", [old_R])

   517 (* kodkod_constrs -> int -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   518 and vect_from_rel_expr kk k R old_R r =

   519   case old_R of

   520     Atom _ => lone_rep_fallback kk (Vect (k, R)) old_R r

   521   | Vect (k', R') =>

   522     if k = k' andalso R = R' then r

   523     else lone_rep_fallback kk (Vect (k, R)) old_R r

   524   | Func (R1, Formula Neut) =>

   525     if k = card_of_rep R1 then

   526       fold1 (#kk_product kk)

   527             (map (fn arg_r =>

   528                      rel_expr_from_formula kk R (#kk_subset kk arg_r r))

   529                  (all_singletons_for_rep R1))

   530     else

   531       raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])

   532   | Func (Unit, R2) => rel_expr_from_rel_expr kk R R2 r

   533   | Func (R1, R2) =>

   534     fold1 (#kk_product kk)

   535           (map (fn arg_r =>

   536                    rel_expr_from_rel_expr kk R R2

   537                                          (kk_n_fold_join kk true R1 R2 arg_r r))

   538                (all_singletons_for_rep R1))

   539   | _ => raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])

   540 (* kodkod_constrs -> rep -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   541 and func_from_no_opt_rel_expr kk R1 R2 (Atom x) r =

   542     let

   543       val dom_card = card_of_rep R1

   544       val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)

   545     in

   546       func_from_no_opt_rel_expr kk R1 R2 (Vect (dom_card, R2'))

   547                                 (vect_from_rel_expr kk dom_card R2' (Atom x) r)

   548     end

   549   | func_from_no_opt_rel_expr kk Unit R2 old_R r =

   550     (case old_R of

   551        Vect (k, R') => rel_expr_from_rel_expr kk R2 R' r

   552      | Func (Unit, R2') => rel_expr_from_rel_expr kk R2 R2' r

   553      | Func (Atom (1, _), Formula Neut) =>

   554        (case unopt_rep R2 of

   555           Atom (2, j0) => atom_from_formula kk j0 (#kk_some kk r)

   556         | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",

   557                           [old_R, Func (Unit, R2)]))

   558      | Func (R1', R2') =>

   559        rel_expr_from_rel_expr kk R2 R2' (#kk_project_seq kk r (arity_of_rep R1')

   560                               (arity_of_rep R2'))

   561      | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",

   562                        [old_R, Func (Unit, R2)]))

   563   | func_from_no_opt_rel_expr kk R1 (Formula Neut) old_R r =

   564     (case old_R of

   565        Vect (k, Atom (2, j0)) =>

   566        let

   567          val args_rs = all_singletons_for_rep R1

   568          val vals_rs = unpack_vect_in_chunks kk 1 k r

   569          (* Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   570          fun empty_or_singleton_set_for arg_r val_r =

   571            #kk_join kk val_r (#kk_product kk (Kodkod.Atom (j0 + 1)) arg_r)

   572        in

   573          fold1 (#kk_union kk) (map2 empty_or_singleton_set_for args_rs vals_rs)

   574        end

   575      | Func (R1', Formula Neut) =>

   576        if R1 = R1' then

   577          r

   578        else

   579          let

   580            val schema = atom_schema_of_rep R1

   581            val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))

   582                     |> rel_expr_from_rel_expr kk R1' R1

   583            val kk_xeq = (if is_one_rep R1' then #kk_subset else #kk_rel_eq) kk

   584          in

   585            #kk_comprehension kk (decls_for_atom_schema ~1 schema) (kk_xeq r1 r)

   586          end

   587      | Func (Unit, (Atom (2, j0))) =>

   588        #kk_rel_if kk (#kk_rel_eq kk r (Kodkod.Atom (j0 + 1)))

   589                   (full_rel_for_rep R1) (empty_rel_for_rep R1)

   590      | Func (R1', Atom (2, j0)) =>

   591        func_from_no_opt_rel_expr kk R1 (Formula Neut)

   592            (Func (R1', Formula Neut)) (#kk_join kk r (Kodkod.Atom (j0 + 1)))

   593      | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",

   594                        [old_R, Func (R1, Formula Neut)]))

   595   | func_from_no_opt_rel_expr kk R1 R2 old_R r =

   596     case old_R of

   597       Vect (k, R) =>

   598       let

   599         val args_rs = all_singletons_for_rep R1

   600         val vals_rs = unpack_vect_in_chunks kk (arity_of_rep R) k r

   601                       |> map (rel_expr_from_rel_expr kk R2 R)

   602       in fold1 (#kk_union kk) (map2 (#kk_product kk) args_rs vals_rs) end

   603     | Func (R1', Formula Neut) =>

   604       (case R2 of

   605          Atom (x as (2, j0)) =>

   606          let val schema = atom_schema_of_rep R1 in

   607            if length schema = 1 then

   608              #kk_override kk (#kk_product kk (Kodkod.AtomSeq (hd schema))

   609                                              (Kodkod.Atom j0))

   610                              (#kk_product kk r (Kodkod.Atom (j0 + 1)))

   611            else

   612              let

   613                val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))

   614                         |> rel_expr_from_rel_expr kk R1' R1

   615                val r2 = Kodkod.Var (1, ~(length schema) - 1)

   616                val r3 = atom_from_formula kk j0 (#kk_subset kk r1 r)

   617              in

   618                #kk_comprehension kk (decls_for_atom_schema ~1 (schema @ [x]))

   619                                  (#kk_subset kk r2 r3)

   620              end

   621            end

   622          | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",

   623                            [old_R, Func (R1, R2)]))

   624     | Func (Unit, R2') =>

   625       let val j0 = some_j0 in

   626         func_from_no_opt_rel_expr kk R1 R2 (Func (Atom (1, j0), R2'))

   627                                   (#kk_product kk (Kodkod.Atom j0) r)

   628       end

   629     | Func (R1', R2') =>

   630       if R1 = R1' andalso R2 = R2' then

   631         r

   632       else

   633         let

   634           val dom_schema = atom_schema_of_rep R1

   635           val ran_schema = atom_schema_of_rep R2

   636           val dom_prod = fold1 (#kk_product kk)

   637                                (unary_var_seq ~1 (length dom_schema))

   638                          |> rel_expr_from_rel_expr kk R1' R1

   639           val ran_prod = fold1 (#kk_product kk)

   640                                (unary_var_seq (~(length dom_schema) - 1)

   641                                               (length ran_schema))

   642                          |> rel_expr_from_rel_expr kk R2' R2

   643           val app = kk_n_fold_join kk true R1' R2' dom_prod r

   644           val kk_xeq = (if is_one_rep R2' then #kk_subset else #kk_rel_eq) kk

   645         in

   646           #kk_comprehension kk (decls_for_atom_schema ~1

   647                                                       (dom_schema @ ran_schema))

   648                                (kk_xeq ran_prod app)

   649         end

   650     | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",

   651                       [old_R, Func (R1, R2)])

   652 (* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   653 and rel_expr_from_rel_expr kk new_R old_R r =

   654   let

   655     val unopt_old_R = unopt_rep old_R

   656     val unopt_new_R = unopt_rep new_R

   657   in

   658     if unopt_old_R <> old_R andalso unopt_new_R = new_R then

   659       raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr", [old_R, new_R])

   660     else if unopt_new_R = unopt_old_R then

   661       r

   662     else

   663       (case unopt_new_R of

   664          Atom x => atom_from_rel_expr kk x

   665        | Struct Rs => struct_from_rel_expr kk Rs

   666        | Vect (k, R') => vect_from_rel_expr kk k R'

   667        | Func (R1, R2) => func_from_no_opt_rel_expr kk R1 R2

   668        | _ => raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr",

   669                          [old_R, new_R]))

   670           unopt_old_R r

   671   end

   672 (* kodkod_constrs -> rep -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   673 and rel_expr_to_func kk R1 R2 = rel_expr_from_rel_expr kk (Func (R1, R2))

   675 (* kodkod_constrs -> nut -> Kodkod.formula *)

   676 fun declarative_axiom_for_plain_rel kk (FreeRel (x, _, R as Func _, nick)) =

   677     kk_n_ary_function kk (R |> nick = @{const_name List.set} ? unopt_rep)

   678                       (Kodkod.Rel x)

   679   | declarative_axiom_for_plain_rel ({kk_lone, kk_one, ...} : kodkod_constrs)

   680                                     (FreeRel (x, _, R, _)) =

   681     if is_one_rep R then kk_one (Kodkod.Rel x)

   682     else if is_lone_rep R andalso card_of_rep R > 1 then kk_lone (Kodkod.Rel x)

   683     else Kodkod.True

   684   | declarative_axiom_for_plain_rel _ u =

   685     raise NUT ("Nitpick_Kodkod.declarative_axiom_for_plain_rel", [u])

   687 (* nut NameTable.table -> styp -> Kodkod.rel_expr * rep * int *)

   688 fun const_triple rel_table (x as (s, T)) =

   689   case the_name rel_table (ConstName (s, T, Any)) of

   690     FreeRel ((n, j), _, R, _) => (Kodkod.Rel (n, j), R, n)

   691   | _ => raise TERM ("Nitpick_Kodkod.const_triple", [Const x])

   693 (* nut NameTable.table -> styp -> Kodkod.rel_expr *)

   694 fun discr_rel_expr rel_table = #1 o const_triple rel_table o discr_for_constr

   696 (* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list

   697    -> styp -> int -> nfa_transition list *)

   698 fun nfa_transitions_for_sel ext_ctxt ({kk_project, ...} : kodkod_constrs)

   699                             rel_table (dtypes : dtype_spec list) constr_x n =

   700   let

   701     val x as (_, T) = boxed_nth_sel_for_constr ext_ctxt constr_x n

   702     val (r, R, arity) = const_triple rel_table x

   703     val type_schema = type_schema_of_rep T R

   704   in

   705     map_filter (fn (j, T) =>

   706                    if forall (not_equal T o #typ) dtypes then NONE

   707                    else SOME (kk_project r (map Kodkod.Num [0, j]), T))

   708                (index_seq 1 (arity - 1) ~~ tl type_schema)

   709   end

   710 (* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list

   711    -> styp -> nfa_transition list *)

   712 fun nfa_transitions_for_constr ext_ctxt kk rel_table dtypes (x as (_, T)) =

   713   maps (nfa_transitions_for_sel ext_ctxt kk rel_table dtypes x)

   714        (index_seq 0 (num_sels_for_constr_type T))

   715 (* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list

   716    -> dtype_spec -> nfa_entry option *)

   717 fun nfa_entry_for_datatype _ _ _ _ ({co = true, ...} : dtype_spec) = NONE

   718   | nfa_entry_for_datatype _ _ _ _ {shallow = true, ...} = NONE

   719   | nfa_entry_for_datatype ext_ctxt kk rel_table dtypes {typ, constrs, ...} =

   720     SOME (typ, maps (nfa_transitions_for_constr ext_ctxt kk rel_table dtypes

   721                      o #const) constrs)

   723 val empty_rel = Kodkod.Product (Kodkod.None, Kodkod.None)

   725 (* nfa_table -> typ -> typ -> Kodkod.rel_expr list *)

   726 fun direct_path_rel_exprs nfa start final =

   727   case AList.lookup (op =) nfa final of

   728     SOME trans => map fst (filter (equal start o snd) trans)

   729   | NONE => []

   730 (* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> Kodkod.rel_expr *)

   731 and any_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start final =

   732     fold kk_union (direct_path_rel_exprs nfa start final)

   733          (if start = final then Kodkod.Iden else empty_rel)

   734   | any_path_rel_expr (kk as {kk_union, ...}) nfa (q :: qs) start final =

   735     kk_union (any_path_rel_expr kk nfa qs start final)

   736              (knot_path_rel_expr kk nfa qs start q final)

   737 (* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> typ

   738    -> Kodkod.rel_expr *)

   739 and knot_path_rel_expr (kk as {kk_join, kk_reflexive_closure, ...}) nfa qs start

   740                        knot final =

   741   kk_join (kk_join (any_path_rel_expr kk nfa qs knot final)

   742                    (kk_reflexive_closure (loop_path_rel_expr kk nfa qs knot)))

   743           (any_path_rel_expr kk nfa qs start knot)

   744 (* kodkod_constrs -> nfa_table -> typ list -> typ -> Kodkod.rel_expr *)

   745 and loop_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start =

   746     fold kk_union (direct_path_rel_exprs nfa start start) empty_rel

   747   | loop_path_rel_expr (kk as {kk_union, kk_closure, ...}) nfa (q :: qs) start =

   748     if start = q then

   749       kk_closure (loop_path_rel_expr kk nfa qs start)

   750     else

   751       kk_union (loop_path_rel_expr kk nfa qs start)

   752                (knot_path_rel_expr kk nfa qs start q start)

   754 (* nfa_table -> unit NfaGraph.T *)

   755 fun graph_for_nfa nfa =

   756   let

   757     (* typ -> unit NfaGraph.T -> unit NfaGraph.T *)

   758     fun new_node q = perhaps (try (NfaGraph.new_node (q, ())))

   759     (* nfa_table -> unit NfaGraph.T -> unit NfaGraph.T *)

   760     fun add_nfa [] = I

   761       | add_nfa ((_, []) :: nfa) = add_nfa nfa

   762       | add_nfa ((q, ((_, q') :: transitions)) :: nfa) =

   763         add_nfa ((q, transitions) :: nfa) o NfaGraph.add_edge (q, q') o

   764         new_node q' o new_node q

   765   in add_nfa nfa NfaGraph.empty end

   767 (* nfa_table -> nfa_table list *)

   768 fun strongly_connected_sub_nfas nfa =

   769   nfa |> graph_for_nfa |> NfaGraph.strong_conn

   770       |> map (fn keys => filter (member (op =) keys o fst) nfa)

   772 (* dtype_spec list -> kodkod_constrs -> nfa_table -> typ -> Kodkod.formula *)

   773 fun acyclicity_axiom_for_datatype dtypes kk nfa start =

   774   #kk_no kk (#kk_intersect kk

   775                  (loop_path_rel_expr kk nfa (map fst nfa) start) Kodkod.Iden)

   776 (* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list

   777    -> Kodkod.formula list *)

   778 fun acyclicity_axioms_for_datatypes ext_ctxt kk rel_table dtypes =

   779   map_filter (nfa_entry_for_datatype ext_ctxt kk rel_table dtypes) dtypes

   780   |> strongly_connected_sub_nfas

   781   |> maps (fn nfa => map (acyclicity_axiom_for_datatype dtypes kk nfa o fst)

   782                          nfa)

   784 (* extended_context -> int -> kodkod_constrs -> nut NameTable.table

   785    -> Kodkod.rel_expr -> constr_spec -> int -> Kodkod.formula *)

   786 fun sel_axiom_for_sel ext_ctxt j0

   787         (kk as {kk_all, kk_implies, kk_formula_if, kk_subset, kk_rel_eq, kk_no,

   788                 kk_join, kk_project, ...}) rel_table dom_r

   789         ({const, delta, epsilon, exclusive, explicit_max, ...} : constr_spec)

   790         n =

   791   let

   792     val x as (_, T) = boxed_nth_sel_for_constr ext_ctxt const n

   793     val (r, R, arity) = const_triple rel_table x

   794     val R2 = dest_Func R |> snd

   795     val z = (epsilon - delta, delta + j0)

   796   in

   797     if exclusive then

   798       kk_n_ary_function kk (Func (Atom z, R2)) r

   799     else

   800       let val r' = kk_join (Kodkod.Var (1, 0)) r in

   801         kk_all [Kodkod.DeclOne ((1, 0), Kodkod.AtomSeq z)]

   802                (kk_formula_if (kk_subset (Kodkod.Var (1, 0)) dom_r)

   803                               (kk_n_ary_function kk R2 r')

   804                               (kk_no r'))

   805       end

   806   end

   807 (* extended_context -> int -> kodkod_constrs -> nut NameTable.table

   808    -> constr_spec -> Kodkod.formula list *)

   809 fun sel_axioms_for_constr ext_ctxt j0 kk rel_table

   810         (constr as {const, delta, epsilon, explicit_max, ...}) =

   811   let

   812     val honors_explicit_max =

   813       explicit_max < 0 orelse epsilon - delta <= explicit_max

   814   in

   815     if explicit_max = 0 then

   816       [formula_for_bool honors_explicit_max]

   817     else

   818       let

   819         val ran_r = discr_rel_expr rel_table const

   820         val max_axiom =

   821           if honors_explicit_max then Kodkod.True

   822           else Kodkod.LE (Kodkod.Cardinality ran_r, Kodkod.Num explicit_max)

   823       in

   824         max_axiom ::

   825         map (sel_axiom_for_sel ext_ctxt j0 kk rel_table ran_r constr)

   826             (index_seq 0 (num_sels_for_constr_type (snd const)))

   827       end

   828   end

   829 (* extended_context -> int -> kodkod_constrs -> nut NameTable.table

   830    -> dtype_spec -> Kodkod.formula list *)

   831 fun sel_axioms_for_datatype ext_ctxt j0 kk rel_table

   832                             ({constrs, ...} : dtype_spec) =

   833   maps (sel_axioms_for_constr ext_ctxt j0 kk rel_table) constrs

   835 (* extended_context -> kodkod_constrs -> nut NameTable.table -> constr_spec

   836    -> Kodkod.formula list *)

   837 fun uniqueness_axiom_for_constr ext_ctxt

   838         ({kk_all, kk_implies, kk_and, kk_rel_eq, kk_lone, kk_join, ...}

   839          : kodkod_constrs) rel_table ({const, ...} : constr_spec) =

   840   let

   841     (* Kodkod.rel_expr -> Kodkod.formula *)

   842     fun conjunct_for_sel r =

   843       kk_rel_eq (kk_join (Kodkod.Var (1, 0)) r)

   844                 (kk_join (Kodkod.Var (1, 1)) r)

   845     val num_sels = num_sels_for_constr_type (snd const)

   846     val triples = map (const_triple rel_table

   847                        o boxed_nth_sel_for_constr ext_ctxt const)

   848                       (~1 upto num_sels - 1)

   849     val j0 = case triples |> hd |> #2 of

   850                Func (Atom (_, j0), _) => j0

   851              | R => raise REP ("Nitpick_Kodkod.uniqueness_axiom_for_constr",

   852                                [R])

   853     val set_r = triples |> hd |> #1

   854   in

   855     if num_sels = 0 then

   856       kk_lone set_r

   857     else

   858       kk_all (map (Kodkod.DeclOne o rpair set_r o pair 1) [0, 1])

   859              (kk_implies

   860                   (fold1 kk_and (map (conjunct_for_sel o #1) (tl triples)))

   861                   (kk_rel_eq (Kodkod.Var (1, 0)) (Kodkod.Var (1, 1))))

   862   end

   863 (* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec

   864    -> Kodkod.formula list *)

   865 fun uniqueness_axioms_for_datatype ext_ctxt kk rel_table

   866                                    ({constrs, ...} : dtype_spec) =

   867   map (uniqueness_axiom_for_constr ext_ctxt kk rel_table) constrs

   869 (* constr_spec -> int *)

   870 fun effective_constr_max ({delta, epsilon, ...} : constr_spec) = epsilon - delta

   871 (* int -> kodkod_constrs -> nut NameTable.table -> dtype_spec

   872    -> Kodkod.formula list *)

   873 fun partition_axioms_for_datatype j0 (kk as {kk_rel_eq, kk_union, ...})

   874                                   rel_table

   875                                   ({card, constrs, ...} : dtype_spec) =

   876   if forall #exclusive constrs then

   877     [Integer.sum (map effective_constr_max constrs) = card |> formula_for_bool]

   878   else

   879     let val rs = map (discr_rel_expr rel_table o #const) constrs in

   880       [kk_rel_eq (fold1 kk_union rs) (Kodkod.AtomSeq (card, j0)),

   881        kk_disjoint_sets kk rs]

   882     end

   884 (* extended_context -> int Typtab.table -> kodkod_constrs -> nut NameTable.table

   885    -> dtype_spec -> Kodkod.formula list *)

   886 fun other_axioms_for_datatype _ _ _ _ {shallow = true, ...} = []

   887   | other_axioms_for_datatype ext_ctxt ofs kk rel_table (dtype as {typ, ...}) =

   888     let val j0 = offset_of_type ofs typ in

   889       sel_axioms_for_datatype ext_ctxt j0 kk rel_table dtype @

   890       uniqueness_axioms_for_datatype ext_ctxt kk rel_table dtype @

   891       partition_axioms_for_datatype j0 kk rel_table dtype

   892     end

   894 (* extended_context -> int Typtab.table -> kodkod_constrs -> nut NameTable.table

   895    -> dtype_spec list -> Kodkod.formula list *)

   896 fun declarative_axioms_for_datatypes ext_ctxt ofs kk rel_table dtypes =

   897   acyclicity_axioms_for_datatypes ext_ctxt kk rel_table dtypes @

   898   maps (other_axioms_for_datatype ext_ctxt ofs kk rel_table) dtypes

   900 (* int Typtab.table -> bool -> kodkod_constrs -> nut -> Kodkod.formula *)

   901 fun kodkod_formula_from_nut ofs liberal

   902         (kk as {kk_all, kk_exist, kk_formula_let, kk_formula_if, kk_or, kk_not,

   903                 kk_iff, kk_implies, kk_and, kk_subset, kk_rel_eq, kk_no, kk_one,

   904                 kk_some, kk_rel_let, kk_rel_if, kk_union, kk_difference,

   905                 kk_intersect, kk_product, kk_join, kk_closure, kk_comprehension,

   906                 kk_project, kk_project_seq, kk_not3, kk_nat_less, kk_int_less,

   907                 ...}) u =

   908   let

   909     val main_j0 = offset_of_type ofs bool_T

   910     val bool_j0 = main_j0

   911     val bool_atom_R = Atom (2, main_j0)

   912     val false_atom = Kodkod.Atom bool_j0

   913     val true_atom = Kodkod.Atom (bool_j0 + 1)

   915     (* polarity -> int -> Kodkod.rel_expr -> Kodkod.formula *)

   916     fun formula_from_opt_atom polar j0 r =

   917       case polar of

   918         Neg => kk_not (kk_rel_eq r (Kodkod.Atom j0))

   919       | _ => kk_rel_eq r (Kodkod.Atom (j0 + 1))

   920     (* int -> Kodkod.rel_expr -> Kodkod.formula *)

   921     val formula_from_atom = formula_from_opt_atom Pos

   923     (* Kodkod.formula -> Kodkod.formula -> Kodkod.formula *)

   924     fun kk_notimplies f1 f2 = kk_and f1 (kk_not f2)

   925     (* Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   926     val kk_or3 =

   927       double_rel_let kk

   928           (fn r1 => fn r2 =>

   929               kk_rel_if (kk_subset true_atom (kk_union r1 r2)) true_atom

   930                         (kk_intersect r1 r2))

   931     val kk_and3 =

   932       double_rel_let kk

   933           (fn r1 => fn r2 =>

   934               kk_rel_if (kk_subset false_atom (kk_union r1 r2)) false_atom

   935                         (kk_intersect r1 r2))

   936     fun kk_notimplies3 r1 r2 = kk_and3 r1 (kk_not3 r2)

   938     (* int -> Kodkod.rel_expr -> Kodkod.formula list *)

   939     val unpack_formulas =

   940       map (formula_from_atom bool_j0) oo unpack_vect_in_chunks kk 1

   941     (* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula) -> int

   942        -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)

   943     fun kk_vect_set_op connective k r1 r2 =

   944       fold1 kk_product (map2 (atom_from_formula kk bool_j0 oo connective)

   945                              (unpack_formulas k r1) (unpack_formulas k r2))

   946     (* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula) -> int

   947        -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula *)

   948     fun kk_vect_set_bool_op connective k r1 r2 =

   949       fold1 kk_and (map2 connective (unpack_formulas k r1)

   950                          (unpack_formulas k r2))

   952     (* nut -> Kodkod.formula *)

   953     fun to_f u =

   954       case rep_of u of

   955         Formula polar =>

   956         (case u of

   957            Cst (False, _, _) => Kodkod.False

   958          | Cst (True, _, _) => Kodkod.True

   959          | Op1 (Not, _, _, u1) =>

   960            kk_not (to_f_with_polarity (flip_polarity polar) u1)

   961          | Op1 (Finite, _, _, u1) =>

   962            let val opt1 = is_opt_rep (rep_of u1) in

   963              case polar of

   964                Neut => if opt1 then

   965                          raise NUT ("Nitpick_Kodkod.to_f (Finite)", [u])

   966                        else

   967                          Kodkod.True

   968              | Pos => formula_for_bool (not opt1)

   969              | Neg => Kodkod.True

   970            end

   971          | Op1 (Cast, _, _, u1) => to_f_with_polarity polar u1

   972          | Op2 (All, _, _, u1, u2) =>

   973            kk_all (untuple to_decl u1) (to_f_with_polarity polar u2)

   974          | Op2 (Exist, _, _, u1, u2) =>

   975            kk_exist (untuple to_decl u1) (to_f_with_polarity polar u2)

   976          | Op2 (Or, _, _, u1, u2) =>

   977            kk_or (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)

   978          | Op2 (And, _, _, u1, u2) =>

   979            kk_and (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)

   980          | Op2 (Less, T, Formula polar, u1, u2) =>

   981            formula_from_opt_atom polar bool_j0

   982                (to_r (Op2 (Less, T, Opt bool_atom_R, u1, u2)))

   983          | Op2 (Subset, _, _, u1, u2) =>

   984            let

   985              val dom_T = domain_type (type_of u1)

   986              val R1 = rep_of u1

   987              val R2 = rep_of u2

   988              val (dom_R, ran_R) =

   989                case min_rep R1 R2 of

   990                  Func (Unit, R') =>

   991                  (Atom (1, offset_of_type ofs dom_T), R')

   992                | Func Rp => Rp

   993                | R => (Atom (card_of_domain_from_rep 2 R,

   994                              offset_of_type ofs dom_T),

   995                        if is_opt_rep R then Opt bool_atom_R else Formula Neut)

   996              val set_R = Func (dom_R, ran_R)

   997            in

   998              if not (is_opt_rep ran_R) then

   999                to_set_bool_op kk_implies kk_subset u1 u2

  1000              else if polar = Neut then

  1001                raise NUT ("Nitpick_Kodkod.to_f (Subset)", [u])

  1002              else

  1003                let

  1004                  (* FIXME: merge with similar code below *)

  1005                  (* bool -> nut -> Kodkod.rel_expr *)

  1006                  fun set_to_r widen u =

  1007                    if widen then

  1008                      kk_difference (full_rel_for_rep dom_R)

  1009                                    (kk_join (to_rep set_R u) false_atom)

  1010                    else

  1011                      kk_join (to_rep set_R u) true_atom

  1012                  val widen1 = (polar = Pos andalso is_opt_rep R1)

  1013                  val widen2 = (polar = Neg andalso is_opt_rep R2)

  1014                in kk_subset (set_to_r widen1 u1) (set_to_r widen2 u2) end

  1015            end

  1016          | Op2 (DefEq, _, _, u1, u2) =>

  1017            (case min_rep (rep_of u1) (rep_of u2) of

  1018               Unit => Kodkod.True

  1019             | Formula polar =>

  1020               kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)

  1021             | min_R =>

  1022               let

  1023                 (* nut -> nut list *)

  1024                 fun args (Op2 (Apply, _, _, u1, u2)) = u2 :: args u1

  1025                   | args (Tuple (_, _, us)) = us

  1026                   | args _ = []

  1027                 val opt_arg_us = filter (is_opt_rep o rep_of) (args u1)

  1028               in

  1029                 if null opt_arg_us orelse not (is_Opt min_R)

  1030                    orelse is_eval_name u1 then

  1031                   fold (kk_or o (kk_no o to_r)) opt_arg_us

  1032                        (kk_rel_eq (to_rep min_R u1) (to_rep min_R u2))

  1033                 else

  1034                   kk_no (kk_difference (to_rep min_R u1) (to_rep min_R u2))

  1035               end)

  1036          | Op2 (Eq, T, R, u1, u2) =>

  1037            (case min_rep (rep_of u1) (rep_of u2) of

  1038               Unit => Kodkod.True

  1039             | Formula polar =>

  1040               kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)

  1041             | min_R =>

  1042               if is_opt_rep min_R then

  1043                 if polar = Neut then

  1044                   (* continuation of hackish optimization *)

  1045                   kk_rel_eq (to_rep min_R u1) (to_rep min_R u2)

  1046                 else if is_Cst Unrep u1 then

  1047                   to_could_be_unrep (polar = Neg) u2

  1048                 else if is_Cst Unrep u2 then

  1049                   to_could_be_unrep (polar = Neg) u1

  1050                 else

  1051                   let

  1052                     val r1 = to_rep min_R u1

  1053                     val r2 = to_rep min_R u2

  1054                     val both_opt = forall (is_opt_rep o rep_of) [u1, u2]

  1055                   in

  1056                     (if polar = Pos then

  1057                        if not both_opt then

  1058                          kk_rel_eq r1 r2

  1059                        else if is_lone_rep min_R

  1060                                andalso arity_of_rep min_R = 1 then

  1061                          kk_some (kk_intersect r1 r2)

  1062                        else

  1063                          raise SAME ()

  1064                      else

  1065                        if is_lone_rep min_R then

  1066                          if arity_of_rep min_R = 1 then

  1067                            kk_subset (kk_product r1 r2) Kodkod.Iden

  1068                          else if not both_opt then

  1069                            (r1, r2) |> is_opt_rep (rep_of u2) ? swap

  1070                                     |> uncurry kk_difference |> kk_no

  1071                          else

  1072                            raise SAME ()

  1073                        else

  1074                          raise SAME ())

  1075                     handle SAME () =>

  1076                            formula_from_opt_atom polar bool_j0

  1077                                (to_guard [u1, u2] bool_atom_R

  1078                                          (rel_expr_from_formula kk bool_atom_R

  1079                                                             (kk_rel_eq r1 r2)))

  1080                   end

  1081               else

  1082                 let

  1083                   val r1 = to_rep min_R u1

  1084                   val r2 = to_rep min_R u2

  1085                 in

  1086                   if is_one_rep min_R then

  1087                     let

  1088                       val rs1 = unpack_products r1

  1089                       val rs2 = unpack_products r2

  1090                     in

  1091                       if length rs1 = length rs2

  1092                          andalso map Kodkod.arity_of_rel_expr rs1

  1093                                  = map Kodkod.arity_of_rel_expr rs2 then

  1094                         fold1 kk_and (map2 kk_subset rs1 rs2)

  1095                       else

  1096                         kk_subset r1 r2

  1097                     end

  1098                   else

  1099                     kk_rel_eq r1 r2

  1100                 end)

  1101          | Op2 (The, T, _, u1, u2) =>

  1102            to_f_with_polarity polar

  1103                               (Op2 (The, T, Opt (Atom (2, bool_j0)), u1, u2))

  1104          | Op2 (Eps, T, _, u1, u2) =>

  1105            to_f_with_polarity polar

  1106                               (Op2 (Eps, T, Opt (Atom (2, bool_j0)), u1, u2))

  1107          | Op2 (Apply, T, _, u1, u2) =>

  1108            (case (polar, rep_of u1) of

  1109               (Neg, Func (R, Formula Neut)) => kk_subset (to_opt R u2) (to_r u1)

  1110             | _ =>

  1111               to_f_with_polarity polar

  1112                  (Op2 (Apply, T, Opt (Atom (2, offset_of_type ofs T)), u1, u2)))

  1113          | Op3 (Let, _, _, u1, u2, u3) =>

  1114            kk_formula_let [to_expr_assign u1 u2] (to_f_with_polarity polar u3)

  1115          | Op3 (If, _, _, u1, u2, u3) =>

  1116            kk_formula_if (to_f u1) (to_f_with_polarity polar u2)

  1117                          (to_f_with_polarity polar u3)

  1118          | FormulaReg (j, _, _) => Kodkod.FormulaReg j

  1119          | _ => raise NUT ("Nitpick_Kodkod.to_f", [u]))

  1120       | Atom (2, j0) => formula_from_atom j0 (to_r u)

  1121       | _ => raise NUT ("Nitpick_Kodkod.to_f", [u])

  1122     (* polarity -> nut -> Kodkod.formula *)

  1123     and to_f_with_polarity polar u =

  1124       case rep_of u of

  1125         Formula _ => to_f u

  1126       | Atom (2, j0) => formula_from_atom j0 (to_r u)

  1127       | Opt (Atom (2, j0)) => formula_from_opt_atom polar j0 (to_r u)

  1128       | _ => raise NUT ("Nitpick_Kodkod.to_f_with_polarity", [u])

  1129     (* nut -> Kodkod.rel_expr *)

  1130     and to_r u =

  1131       case u of

  1132         Cst (False, _, Atom _) => false_atom

  1133       | Cst (True, _, Atom _) => true_atom

  1134       | Cst (Iden, T, Func (Struct [R1, R2], Formula Neut)) =>

  1135         if R1 = R2 andalso arity_of_rep R1 = 1 then

  1136           kk_intersect Kodkod.Iden (kk_product (full_rel_for_rep R1)

  1137                                                Kodkod.Univ)

  1138         else

  1139           let

  1140             val schema1 = atom_schema_of_rep R1

  1141             val schema2 = atom_schema_of_rep R2

  1142             val arity1 = length schema1

  1143             val arity2 = length schema2

  1144             val r1 = fold1 kk_product (unary_var_seq 0 arity1)

  1145             val r2 = fold1 kk_product (unary_var_seq arity1 arity2)

  1146             val min_R = min_rep R1 R2

  1147           in

  1148             kk_comprehension

  1149                 (decls_for_atom_schema 0 (schema1 @ schema2))

  1150                 (kk_rel_eq (rel_expr_from_rel_expr kk min_R R1 r1)

  1151                            (rel_expr_from_rel_expr kk min_R R2 r2))

  1152           end

  1153       | Cst (Iden, T, Func (Atom (1, j0), Formula Neut)) => Kodkod.Atom j0

  1154       | Cst (Iden, T as Type ("fun", [T1, _]), R as Func (R1, _)) =>

  1155         to_rep R (Cst (Iden, T, Func (one_rep ofs T1 R1, Formula Neut)))

  1156       | Cst (Num j, @{typ int}, R) =>

  1157          (case atom_for_int (card_of_rep R, offset_of_type ofs int_T) j of

  1158             ~1 => if is_opt_rep R then Kodkod.None

  1159                   else raise NUT ("Nitpick_Kodkod.to_r (Num)", [u])

  1160           | j' => Kodkod.Atom j')

  1161       | Cst (Num j, T, R) =>

  1162         if j < card_of_rep R then Kodkod.Atom (j + offset_of_type ofs T)

  1163         else if is_opt_rep R then Kodkod.None

  1164         else raise NUT ("Nitpick_Kodkod.to_r", [u])

  1165       | Cst (Unknown, _, R) => empty_rel_for_rep R

  1166       | Cst (Unrep, _, R) => empty_rel_for_rep R

  1167       | Cst (Suc, T, Func (Atom x, _)) =>

  1168         if domain_type T <> nat_T then suc_rel

  1169         else kk_intersect suc_rel (kk_product Kodkod.Univ (Kodkod.AtomSeq x))

  1170       | Cst (Add, Type ("fun", [@{typ nat}, _]), _) => nat_add_rel

  1171       | Cst (Add, Type ("fun", [@{typ int}, _]), _) => int_add_rel

  1172       | Cst (Subtract, Type ("fun", [@{typ nat}, _]), _) => nat_subtract_rel

  1173       | Cst (Subtract, Type ("fun", [@{typ int}, _]), _) => int_subtract_rel

  1174       | Cst (Multiply, Type ("fun", [@{typ nat}, _]), _) => nat_multiply_rel

  1175       | Cst (Multiply, Type ("fun", [@{typ int}, _]), _) => int_multiply_rel

  1176       | Cst (Divide, Type ("fun", [@{typ nat}, _]), _) => nat_divide_rel

  1177       | Cst (Divide, Type ("fun", [@{typ int}, _]), _) => int_divide_rel

  1178       | Cst (Modulo, Type ("fun", [@{typ nat}, _]), _) => nat_modulo_rel

  1179       | Cst (Modulo, Type ("fun", [@{typ int}, _]), _) => int_modulo_rel

  1180       | Cst (Gcd, _, _) => gcd_rel

  1181       | Cst (Lcm, _, _) => lcm_rel

  1182       | Cst (Fracs, _, Func (Atom (1, _), _)) => Kodkod.None

  1183       | Cst (Fracs, _, Func (Struct _, _)) =>

  1184         kk_project_seq norm_frac_rel 2 2

  1185       | Cst (NormFrac, _, _) => norm_frac_rel

  1186       | Cst (NatToInt, _, Func (Atom _, Atom _)) => Kodkod.Iden

  1187       | Cst (NatToInt, _,

  1188              Func (Atom (nat_k, nat_j0), Opt (Atom (int_k, int_j0)))) =>

  1189         if nat_j0 = int_j0 then

  1190           kk_intersect Kodkod.Iden

  1191               (kk_product (Kodkod.AtomSeq (max_int_for_card int_k + 1, nat_j0))

  1192                           Kodkod.Univ)

  1193         else

  1194           raise BAD ("Nitpick_Kodkod.to_r (NatToInt)", "\"nat_j0 <> int_j0\"")

  1195       | Cst (IntToNat, _, Func (Atom (int_k, int_j0), nat_R)) =>

  1196         let

  1197           val abs_card = max_int_for_card int_k + 1

  1198           val (nat_k, nat_j0) = the_single (atom_schema_of_rep nat_R)

  1199           val overlap = Int.min (nat_k, abs_card)

  1200         in

  1201           if nat_j0 = int_j0 then

  1202             kk_union (kk_product (Kodkod.AtomSeq (int_k - abs_card,

  1203                                                   int_j0 + abs_card))

  1204                                  (Kodkod.Atom nat_j0))

  1205                      (kk_intersect Kodkod.Iden

  1206                           (kk_product (Kodkod.AtomSeq (overlap, int_j0))

  1207                                       Kodkod.Univ))

  1208           else

  1209             raise BAD ("Nitpick_Kodkod.to_r (IntToNat)", "\"nat_j0 <> int_j0\"")

  1210         end

  1211       | Op1 (Not, _, R, u1) => kk_not3 (to_rep R u1)

  1212       | Op1 (Finite, _, Opt (Atom _), _) => Kodkod.None

  1213       | Op1 (Converse, T, R, u1) =>

  1214         let

  1215           val (b_T, a_T) = HOLogic.dest_prodT (domain_type T)

  1216           val (b_R, a_R) =

  1217             case R of

  1218               Func (Struct [R1, R2], _) => (R1, R2)

  1219             | Func (R1, _) =>

  1220               if card_of_rep R1 <> 1 then

  1221                 raise REP ("Nitpick_Kodkod.to_r (Converse)", [R])

  1222               else

  1223                 pairself (Atom o pair 1 o offset_of_type ofs) (b_T, a_T)

  1224             | _ => raise REP ("Nitpick_Kodkod.to_r (Converse)", [R])

  1225           val body_R = body_rep R

  1226           val a_arity = arity_of_rep a_R

  1227           val b_arity = arity_of_rep b_R

  1228           val ab_arity = a_arity + b_arity

  1229           val body_arity = arity_of_rep body_R

  1230         in

  1231           kk_project (to_rep (Func (Struct [a_R, b_R], body_R)) u1)

  1232                      (map Kodkod.Num (index_seq a_arity b_arity @

  1233                                       index_seq 0 a_arity @

  1234                                       index_seq ab_arity body_arity))

  1235           |> rel_expr_from_rel_expr kk R (Func (Struct [b_R, a_R], body_R))

  1236         end

  1237       | Op1 (Closure, _, R, u1) =>

  1238         if is_opt_rep R then

  1239           let

  1240             val T1 = type_of u1

  1241             val R' = rep_to_binary_rel_rep ofs T1 (unopt_rep (rep_of u1))

  1242             val R'' = opt_rep ofs T1 R'

  1243           in

  1244             single_rel_let kk

  1245                 (fn r =>

  1246                     let

  1247                       val true_r = kk_closure (kk_join r true_atom)

  1248                       val full_r = full_rel_for_rep R'

  1249                       val false_r = kk_difference full_r

  1250                                         (kk_closure (kk_difference full_r

  1251                                                         (kk_join r false_atom)))

  1252                     in

  1253                       rel_expr_from_rel_expr kk R R''

  1254                           (kk_union (kk_product true_r true_atom)

  1255                                     (kk_product false_r false_atom))

  1256                     end) (to_rep R'' u1)

  1257           end

  1258         else

  1259           let val R' = rep_to_binary_rel_rep ofs (type_of u1) (rep_of u1) in

  1260             rel_expr_from_rel_expr kk R R' (kk_closure (to_rep R' u1))

  1261           end

  1262       | Op1 (SingletonSet, _, Func (R1, Opt _), Cst (Unrep, _, _)) =>

  1263         (if R1 = Unit then I else kk_product (full_rel_for_rep R1)) false_atom

  1264       | Op1 (SingletonSet, _, R, u1) =>

  1265         (case R of

  1266            Func (R1, Formula Neut) => to_rep R1 u1

  1267          | Func (Unit, Opt R) => to_guard [u1] R true_atom

  1268          | Func (R1, R2 as Opt _) =>

  1269            single_rel_let kk

  1270                (fn r => kk_rel_if (kk_no r) (empty_rel_for_rep R)

  1271                             (rel_expr_to_func kk R1 bool_atom_R

  1272                                               (Func (R1, Formula Neut)) r))

  1273                (to_opt R1 u1)

  1274          | _ => raise NUT ("Nitpick_Kodkod.to_r (SingletonSet)", [u]))

  1275       | Op1 (Tha, T, R, u1) =>

  1276         if is_opt_rep R then

  1277           kk_join (to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1) true_atom

  1278         else

  1279           to_rep (Func (R, Formula Neut)) u1

  1280       | Op1 (First, T, R, u1) => to_nth_pair_sel 0 T R u1

  1281       | Op1 (Second, T, R, u1) => to_nth_pair_sel 1 T R u1

  1282       | Op1 (Cast, _, R, u1) =>

  1283         ((case rep_of u1 of

  1284             Formula _ =>

  1285             (case unopt_rep R of

  1286                Atom (2, j0) => atom_from_formula kk j0 (to_f u1)

  1287              | _ => raise SAME ())

  1288           | _ => raise SAME ())

  1289          handle SAME () => rel_expr_from_rel_expr kk R (rep_of u1) (to_r u1))

  1290       | Op2 (All, T, R as Opt _, u1, u2) =>

  1291         to_r (Op1 (Not, T, R,

  1292                    Op2 (Exist, T, R, u1, Op1 (Not, T, rep_of u2, u2))))

  1293       | Op2 (Exist, T, Opt _, u1, u2) =>

  1294         let val rs1 = untuple to_decl u1 in

  1295           if not (is_opt_rep (rep_of u2)) then

  1296             kk_rel_if (kk_exist rs1 (to_f u2)) true_atom Kodkod.None

  1297           else

  1298             let val r2 = to_r u2 in

  1299               kk_union (kk_rel_if (kk_exist rs1 (kk_rel_eq r2 true_atom))

  1300                                   true_atom Kodkod.None)

  1301                        (kk_rel_if (kk_all rs1 (kk_rel_eq r2 false_atom))

  1302                                   false_atom Kodkod.None)

  1303             end

  1304         end

  1305       | Op2 (Or, _, _, u1, u2) =>

  1306         if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) true_atom (to_r u1)

  1307         else kk_rel_if (to_f u1) true_atom (to_r u2)

  1308       | Op2 (And, _, _, u1, u2) =>

  1309         if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) (to_r u1) false_atom

  1310         else kk_rel_if (to_f u1) (to_r u2) false_atom

  1311       | Op2 (Less, _, _, u1, u2) =>

  1312         if type_of u1 = nat_T then

  1313           if is_Cst Unrep u1 then to_compare_with_unrep u2 false_atom

  1314           else if is_Cst Unrep u2 then to_compare_with_unrep u1 true_atom

  1315           else kk_nat_less (to_integer u1) (to_integer u2)

  1316         else

  1317           kk_int_less (to_integer u1) (to_integer u2)

  1318       | Op2 (The, T, R, u1, u2) =>

  1319         if is_opt_rep R then

  1320           let val r1 = to_opt (Func (unopt_rep R, bool_atom_R)) u1 in

  1321             kk_rel_if (kk_one (kk_join r1 true_atom)) (kk_join r1 true_atom)

  1322                       (kk_rel_if (kk_or (kk_some (kk_join r1 true_atom))

  1323                                         (kk_subset (full_rel_for_rep R)

  1324                                                    (kk_join r1 false_atom)))

  1325                                  (to_rep R u2) (empty_rel_for_rep R))

  1326           end

  1327         else

  1328           let val r1 = to_rep (Func (R, Formula Neut)) u1 in

  1329             kk_rel_if (kk_one r1) r1 (to_rep R u2)

  1330           end

  1331       | Op2 (Eps, T, R, u1, u2) =>

  1332         if is_opt_rep (rep_of u1) then

  1333           let

  1334             val r1 = to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1

  1335             val r2 = to_rep R u2

  1336           in

  1337             kk_union (kk_rel_if (kk_one (kk_join r1 true_atom))

  1338                                 (kk_join r1 true_atom) (empty_rel_for_rep R))

  1339                      (kk_rel_if (kk_or (kk_subset r2 (kk_join r1 true_atom))

  1340                                        (kk_subset (full_rel_for_rep R)

  1341                                                   (kk_join r1 false_atom)))

  1342                                 r2 (empty_rel_for_rep R))

  1343           end

  1344         else

  1345           let

  1346             val r1 = to_rep (Func (unopt_rep R, Formula Neut)) u1

  1347             val r2 = to_rep R u2

  1348           in

  1349             kk_union (kk_rel_if (kk_one r1) r1 (empty_rel_for_rep R))

  1350                      (kk_rel_if (kk_or (kk_no r1) (kk_subset r2 r1))

  1351                                 r2 (empty_rel_for_rep R))

  1352           end

  1353       | Op2 (Triad, T, Opt (Atom (2, j0)), u1, u2) =>

  1354         let

  1355           val f1 = to_f u1

  1356           val f2 = to_f u2

  1357         in

  1358           if f1 = f2 then

  1359             atom_from_formula kk j0 f1

  1360           else

  1361             kk_union (kk_rel_if f1 true_atom Kodkod.None)

  1362                      (kk_rel_if f2 Kodkod.None false_atom)

  1363         end

  1364       | Op2 (Union, _, R, u1, u2) =>

  1365         to_set_op kk_or kk_or3 kk_union kk_union kk_intersect false R u1 u2

  1366       | Op2 (SetDifference, _, R, u1, u2) =>

  1367         to_set_op kk_notimplies kk_notimplies3 kk_difference kk_intersect

  1368                   kk_union true R u1 u2

  1369       | Op2 (Intersect, _, R, u1, u2) =>

  1370         to_set_op kk_and kk_and3 kk_intersect kk_intersect kk_union false R

  1371                   u1 u2

  1372       | Op2 (Composition, _, R, u1, u2) =>

  1373         let

  1374           val (a_T, b_T) = HOLogic.dest_prodT (domain_type (type_of u1))

  1375           val (_, c_T) = HOLogic.dest_prodT (domain_type (type_of u2))

  1376           val ab_k = card_of_domain_from_rep 2 (rep_of u1)

  1377           val bc_k = card_of_domain_from_rep 2 (rep_of u2)

  1378           val ac_k = card_of_domain_from_rep 2 R

  1379           val a_k = exact_root 2 (ac_k * ab_k div bc_k)

  1380           val b_k = exact_root 2 (ab_k * bc_k div ac_k)

  1381           val c_k = exact_root 2 (bc_k * ac_k div ab_k)

  1382           val a_R = Atom (a_k, offset_of_type ofs a_T)

  1383           val b_R = Atom (b_k, offset_of_type ofs b_T)

  1384           val c_R = Atom (c_k, offset_of_type ofs c_T)

  1385           val body_R = body_rep R

  1386         in

  1387           (case body_R of

  1388              Formula Neut =>

  1389              kk_join (to_rep (Func (Struct [a_R, b_R], Formula Neut)) u1)

  1390                      (to_rep (Func (Struct [b_R, c_R], Formula Neut)) u2)

  1391            | Opt (Atom (2, _)) =>

  1392              let

  1393                (* FIXME: merge with similar code above *)

  1394                (* rep -> rep -> nut -> Kodkod.rel_expr *)

  1395                fun must R1 R2 u =

  1396                  kk_join (to_rep (Func (Struct [R1, R2], body_R)) u) true_atom

  1397                fun may R1 R2 u =

  1398                  kk_difference

  1399                      (full_rel_for_rep (Struct [R1, R2]))

  1400                      (kk_join (to_rep (Func (Struct [R1, R2], body_R)) u)

  1401                               false_atom)

  1402              in

  1403                kk_union

  1404                    (kk_product (kk_join (must a_R b_R u1) (must b_R c_R u2))

  1405                                true_atom)

  1406                    (kk_product (kk_difference

  1407                                    (full_rel_for_rep (Struct [a_R, c_R]))

  1408                                    (kk_join (may a_R b_R u1) (may b_R c_R u2)))

  1409                                false_atom)

  1410              end

  1411            | _ => raise NUT ("Nitpick_Kodkod.to_r (Composition)", [u]))

  1412           |> rel_expr_from_rel_expr kk R (Func (Struct [a_R, c_R], body_R))

  1413         end

  1414       | Op2 (Product, T, R, u1, u2) =>

  1415         let

  1416           val (a_T, b_T) = HOLogic.dest_prodT (domain_type T)

  1417           val a_k = card_of_domain_from_rep 2 (rep_of u1)

  1418           val b_k = card_of_domain_from_rep 2 (rep_of u2)

  1419           val a_R = Atom (a_k, offset_of_type ofs a_T)

  1420           val b_R = Atom (b_k, offset_of_type ofs b_T)

  1421           val body_R = body_rep R

  1422         in

  1423           (case body_R of

  1424              Formula Neut =>

  1425              kk_product (to_rep (Func (a_R, Formula Neut)) u1)

  1426                         (to_rep (Func (b_R, Formula Neut)) u2)

  1427            | Opt (Atom (2, _)) =>

  1428              let

  1429                (* Kodkod.rel_expr -> rep -> nut -> Kodkod.rel_expr *)

  1430                fun do_nut r R u = kk_join (to_rep (Func (R, body_R)) u) r

  1431                (* Kodkod.rel_expr -> Kodkod.rel_expr *)

  1432                fun do_term r =

  1433                  kk_product (kk_product (do_nut r a_R u1) (do_nut r b_R u2)) r

  1434              in kk_union (do_term true_atom) (do_term false_atom) end

  1435            | _ => raise NUT ("Nitpick_Kodkod.to_r (Product)", [u]))

  1436           |> rel_expr_from_rel_expr kk R (Func (Struct [a_R, b_R], body_R))

  1437         end

  1438       | Op2 (Image, T, R, u1, u2) =>

  1439         (case (rep_of u1, rep_of u2) of

  1440            (Func (R11, R12), Func (R21, Formula Neut)) =>

  1441            if R21 = R11 andalso is_lone_rep R12 then

  1442              let

  1443                (* Kodkod.rel_expr -> Kodkod.rel_expr *)

  1444                fun big_join r = kk_n_fold_join kk false R21 R12 r (to_r u1)

  1445                val core_r = big_join (to_r u2)

  1446                val core_R = Func (R12, Formula Neut)

  1447              in

  1448                if is_opt_rep R12 then

  1449                  let

  1450                    val schema = atom_schema_of_rep R21

  1451                    val decls = decls_for_atom_schema ~1 schema

  1452                    val vars = unary_var_seq ~1 (length decls)

  1453                    val f = kk_some (big_join (fold1 kk_product vars))

  1454                  in

  1455                    kk_rel_if (kk_all decls f)

  1456                              (rel_expr_from_rel_expr kk R core_R core_r)

  1457                              (rel_expr_from_rel_expr kk R (opt_rep ofs T core_R)

  1458                                               (kk_product core_r true_atom))

  1459                  end

  1460                else

  1461                  rel_expr_from_rel_expr kk R core_R core_r

  1462              end

  1463            else

  1464              raise NUT ("Nitpick_Kodkod.to_r (Image)", [u1, u2])

  1465          | _ => raise NUT ("Nitpick_Kodkod.to_r (Image)", [u1, u2]))

  1466       | Op2 (Apply, @{typ nat}, _,

  1467              Op2 (Apply, _, _, Cst (Subtract, _, _), u1), u2) =>

  1468         if is_Cst Unrep u2 andalso not (is_opt_rep (rep_of u1)) then

  1469           Kodkod.Atom (offset_of_type ofs nat_T)

  1470         else

  1471           fold kk_join [to_integer u1, to_integer u2] nat_subtract_rel

  1472       | Op2 (Apply, _, R, u1, u2) =>

  1473         if is_Cst Unrep u2 andalso is_set_type (type_of u1)

  1474            andalso is_FreeName u1 then

  1475           false_atom

  1476         else

  1477           to_apply R u1 u2

  1478       | Op2 (Lambda, T, R as Opt (Atom (1, j0)), u1, u2) =>

  1479         to_guard [u1, u2] R (Kodkod.Atom j0)

  1480       | Op2 (Lambda, T, Func (_, Formula Neut), u1, u2) =>

  1481         kk_comprehension (untuple to_decl u1) (to_f u2)

  1482       | Op2 (Lambda, T, Func (_, R2), u1, u2) =>

  1483         let

  1484           val dom_decls = untuple to_decl u1

  1485           val ran_schema = atom_schema_of_rep R2

  1486           val ran_decls = decls_for_atom_schema ~1 ran_schema

  1487           val ran_vars = unary_var_seq ~1 (length ran_decls)

  1488         in

  1489           kk_comprehension (dom_decls @ ran_decls)

  1490                            (kk_subset (fold1 kk_product ran_vars)

  1491                                       (to_rep R2 u2))

  1492         end

  1493       | Op3 (Let, _, R, u1, u2, u3) =>

  1494         kk_rel_let [to_expr_assign u1 u2] (to_rep R u3)

  1495       | Op3 (If, _, R, u1, u2, u3) =>

  1496         if is_opt_rep (rep_of u1) then

  1497           triple_rel_let kk

  1498               (fn r1 => fn r2 => fn r3 =>

  1499                   let val empty_r = empty_rel_for_rep R in

  1500                     fold1 kk_union

  1501                           [kk_rel_if (kk_rel_eq r1 true_atom) r2 empty_r,

  1502                            kk_rel_if (kk_rel_eq r1 false_atom) r3 empty_r,

  1503                            kk_rel_if (kk_rel_eq r2 r3)

  1504                                 (if inline_rel_expr r2 then r2 else r3) empty_r]

  1505                   end)

  1506               (to_r u1) (to_rep R u2) (to_rep R u3)

  1507         else

  1508           kk_rel_if (to_f u1) (to_rep R u2) (to_rep R u3)

  1509       | Tuple (_, R, us) =>

  1510         (case unopt_rep R of

  1511            Struct Rs => to_product Rs us

  1512          | Vect (k, R) => to_product (replicate k R) us

  1513          | Atom (1, j0) =>

  1514            (case filter (not_equal Unit o rep_of) us of

  1515               [] => Kodkod.Atom j0

  1516             | us' =>

  1517               kk_rel_if (kk_some (fold1 kk_product (map to_r us')))

  1518                         (Kodkod.Atom j0) Kodkod.None)

  1519          | _ => raise NUT ("Nitpick_Kodkod.to_r (Tuple)", [u]))

  1520       | Construct ([u'], _, _, []) => to_r u'

  1521       | Construct (_ :: sel_us, T, R, arg_us) =>

  1522         let

  1523           val set_rs =

  1524             map2 (fn sel_u => fn arg_u =>

  1525                      let

  1526                        val (R1, R2) = dest_Func (rep_of sel_u)

  1527                        val sel_r = to_r sel_u

  1528                        val arg_r = to_opt R2 arg_u

  1529                      in

  1530                        if is_one_rep R2 then

  1531                          kk_n_fold_join kk true R2 R1 arg_r

  1532                               (kk_project sel_r (flip_nums (arity_of_rep R2)))

  1533                        else

  1534                          kk_comprehension

  1535                              (decls_for_atom_schema ~1 (atom_schema_of_rep R1))

  1536                              (kk_rel_eq (kk_join (Kodkod.Var (1, ~1)) sel_r)

  1537                                         arg_r)

  1538                      end) sel_us arg_us

  1539         in fold1 kk_intersect set_rs end

  1540       | BoundRel (x, _, _, _) => Kodkod.Var x

  1541       | FreeRel (x, _, _, _) => Kodkod.Rel x

  1542       | RelReg (j, _, R) => Kodkod.RelReg (arity_of_rep R, j)

  1543       | u => raise NUT ("Nitpick_Kodkod.to_r", [u])

  1544     (* nut -> Kodkod.decl *)

  1545     and to_decl (BoundRel (x, _, R, _)) =

  1546         Kodkod.DeclOne (x, Kodkod.AtomSeq (the_single (atom_schema_of_rep R)))

  1547       | to_decl u = raise NUT ("Nitpick_Kodkod.to_decl", [u])

  1548     (* nut -> Kodkod.expr_assign *)

  1549     and to_expr_assign (FormulaReg (j, _, R)) u =

  1550         Kodkod.AssignFormulaReg (j, to_f u)

  1551       | to_expr_assign (RelReg (j, _, R)) u =

  1552         Kodkod.AssignRelReg ((arity_of_rep R, j), to_r u)

  1553       | to_expr_assign u1 _ = raise NUT ("Nitpick_Kodkod.to_expr_assign", [u1])

  1554     (* int * int -> nut -> Kodkod.rel_expr *)

  1555     and to_atom (x as (k, j0)) u =

  1556       case rep_of u of

  1557         Formula _ => atom_from_formula kk j0 (to_f u)

  1558       | Unit => if k = 1 then Kodkod.Atom j0

  1559                 else raise NUT ("Nitpick_Kodkod.to_atom", [u])

  1560       | R => atom_from_rel_expr kk x R (to_r u)

  1561     (* rep list -> nut -> Kodkod.rel_expr *)

  1562     and to_struct Rs u =

  1563       case rep_of u of

  1564         Unit => full_rel_for_rep (Struct Rs)

  1565       | R' => struct_from_rel_expr kk Rs R' (to_r u)

  1566     (* int -> rep -> nut -> Kodkod.rel_expr *)

  1567     and to_vect k R u =

  1568       case rep_of u of

  1569         Unit => full_rel_for_rep (Vect (k, R))

  1570       | R' => vect_from_rel_expr kk k R R' (to_r u)

  1571     (* rep -> rep -> nut -> Kodkod.rel_expr *)

  1572     and to_func R1 R2 u =

  1573       case rep_of u of

  1574         Unit => full_rel_for_rep (Func (R1, R2))

  1575       | R' => rel_expr_to_func kk R1 R2 R' (to_r u)

  1576     (* rep -> nut -> Kodkod.rel_expr *)

  1577     and to_opt R u =

  1578       let val old_R = rep_of u in

  1579         if is_opt_rep old_R then

  1580           rel_expr_from_rel_expr kk (Opt R) old_R (to_r u)

  1581         else

  1582           to_rep R u

  1583       end

  1584     (* rep -> nut -> Kodkod.rel_expr *)

  1585     and to_rep (Atom x) u = to_atom x u

  1586       | to_rep (Struct Rs) u = to_struct Rs u

  1587       | to_rep (Vect (k, R)) u = to_vect k R u

  1588       | to_rep (Func (R1, R2)) u = to_func R1 R2 u

  1589       | to_rep (Opt R) u = to_opt R u

  1590       | to_rep R _ = raise REP ("Nitpick_Kodkod.to_rep", [R])

  1591     (* nut -> Kodkod.rel_expr *)

  1592     and to_integer u = to_opt (one_rep ofs (type_of u) (rep_of u)) u

  1593     (* nut list -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)

  1594     and to_guard guard_us R r =

  1595       let

  1596         val unpacked_rs = unpack_joins r

  1597         val plain_guard_rs =

  1598           map to_r (filter (is_Opt o rep_of) guard_us)

  1599           |> filter_out (member (op =) unpacked_rs)

  1600         val func_guard_us =

  1601           filter ((is_Func andf is_opt_rep) o rep_of) guard_us

  1602         val func_guard_rs = map to_r func_guard_us

  1603         val guard_fs =

  1604           map kk_no plain_guard_rs @

  1605           map2 (kk_not oo kk_n_ary_function kk)

  1606                (map (unopt_rep o rep_of) func_guard_us) func_guard_rs

  1607       in

  1608         if null guard_fs then

  1609           r

  1610         else

  1611           kk_rel_if (fold1 kk_or guard_fs) (empty_rel_for_rep R) r

  1612       end

  1613     (* rep -> rep -> Kodkod.rel_expr -> int -> Kodkod.rel_expr *)

  1614     and to_project new_R old_R r j0 =

  1615       rel_expr_from_rel_expr kk new_R old_R

  1616                              (kk_project_seq r j0 (arity_of_rep old_R))

  1617     (* rep list -> nut list -> Kodkod.rel_expr *)

  1618     and to_product Rs us =

  1619       case map (uncurry to_opt) (filter (not_equal Unit o fst) (Rs ~~ us)) of

  1620         [] => raise REP ("Nitpick_Kodkod.to_product", Rs)

  1621       | rs => fold1 kk_product rs

  1622     (* int -> typ -> rep -> nut -> Kodkod.rel_expr *)

  1623     and to_nth_pair_sel n res_T res_R u =

  1624       case u of

  1625         Tuple (_, _, us) => to_rep res_R (nth us n)

  1626       | _ => let

  1627                val R = rep_of u

  1628                val (a_T, b_T) = HOLogic.dest_prodT (type_of u)

  1629                val Rs =

  1630                  case unopt_rep R of

  1631                    Struct (Rs as [_, _]) => Rs

  1632                  | _ =>

  1633                    let

  1634                      val res_card = card_of_rep res_R

  1635                      val other_card = card_of_rep R div res_card

  1636                      val (a_card, b_card) = (res_card, other_card)

  1637                                             |> n = 1 ? swap

  1638                    in

  1639                      [Atom (a_card, offset_of_type ofs a_T),

  1640                       Atom (b_card, offset_of_type ofs b_T)]

  1641                    end

  1642                val nth_R = nth Rs n

  1643                val j0 = if n = 0 then 0 else arity_of_rep (hd Rs)

  1644              in

  1645                case arity_of_rep nth_R of

  1646                  0 => to_guard [u] res_R

  1647                                (to_rep res_R (Cst (Unity, res_T, Unit)))

  1648                | arity => to_project res_R nth_R (to_rep (Opt (Struct Rs)) u) j0

  1649              end

  1650     (* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula)

  1651        -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula) -> nut -> nut

  1652        -> Kodkod.formula *)

  1653     and to_set_bool_op connective set_oper u1 u2 =

  1654       let

  1655         val min_R = min_rep (rep_of u1) (rep_of u2)

  1656         val r1 = to_rep min_R u1

  1657         val r2 = to_rep min_R u2

  1658       in

  1659         case min_R of

  1660           Vect (k, Atom _) => kk_vect_set_bool_op connective k r1 r2

  1661         | Func (R1, Formula Neut) => set_oper r1 r2

  1662         | Func (Unit, Atom (2, j0)) =>

  1663           connective (formula_from_atom j0 r1) (formula_from_atom j0 r2)

  1664         | Func (R1, Atom _) => set_oper (kk_join r1 true_atom)

  1665                                         (kk_join r2 true_atom)

  1666         | _ => raise REP ("Nitpick_Kodkod.to_set_bool_op", [min_R])

  1667       end

  1668     (* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula)

  1669        -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)

  1670        -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula)

  1671        -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula)

  1672        -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula) -> bool -> rep

  1673        -> nut -> nut -> Kodkod.rel_expr *)

  1674     and to_set_op connective connective3 set_oper true_set_oper false_set_oper

  1675                   neg_second R u1 u2 =

  1676       let

  1677         val min_R = min_rep (rep_of u1) (rep_of u2)

  1678         val r1 = to_rep min_R u1

  1679         val r2 = to_rep min_R u2

  1680         val unopt_R = unopt_rep R

  1681       in

  1682         rel_expr_from_rel_expr kk unopt_R (unopt_rep min_R)

  1683             (case min_R of

  1684                Opt (Vect (k, Atom _)) => kk_vect_set_op connective k r1 r2

  1685              | Vect (k, Atom _) => kk_vect_set_op connective k r1 r2

  1686              | Func (_, Formula Neut) => set_oper r1 r2

  1687              | Func (Unit, _) => connective3 r1 r2

  1688              | Func (R1, _) =>

  1689                double_rel_let kk

  1690                    (fn r1 => fn r2 =>

  1691                        kk_union

  1692                            (kk_product

  1693                                 (true_set_oper (kk_join r1 true_atom)

  1694                                      (kk_join r2 (atom_for_bool bool_j0

  1695                                                              (not neg_second))))

  1696                                 true_atom)

  1697                            (kk_product

  1698                                 (false_set_oper (kk_join r1 false_atom)

  1699                                      (kk_join r2 (atom_for_bool bool_j0

  1700                                                                 neg_second)))

  1701                                 false_atom))

  1702                    r1 r2

  1703              | _ => raise REP ("Nitpick_Kodkod.to_set_op", [min_R]))

  1704       end

  1705     (* rep -> rep -> Kodkod.rel_expr -> nut -> Kodkod.rel_expr *)

  1706     and to_apply res_R func_u arg_u =

  1707       case unopt_rep (rep_of func_u) of

  1708         Unit =>

  1709         let val j0 = offset_of_type ofs (type_of func_u) in

  1710           to_guard [arg_u] res_R

  1711                    (rel_expr_from_rel_expr kk res_R (Atom (1, j0))

  1712                                            (Kodkod.Atom j0))

  1713         end

  1714       | Atom (1, j0) =>

  1715         to_guard [arg_u] res_R

  1716                  (rel_expr_from_rel_expr kk res_R (Atom (1, j0)) (to_r func_u))

  1717       | Atom (k, j0) =>

  1718         let

  1719           val dom_card = card_of_rep (rep_of arg_u)

  1720           val ran_R = Atom (exact_root dom_card k,

  1721                             offset_of_type ofs (range_type (type_of func_u)))

  1722         in

  1723           to_apply_vect dom_card ran_R res_R (to_vect dom_card ran_R func_u)

  1724                         arg_u

  1725         end

  1726       | Vect (1, R') =>

  1727         to_guard [arg_u] res_R

  1728                  (rel_expr_from_rel_expr kk res_R R' (to_r func_u))

  1729       | Vect (k, R') => to_apply_vect k R' res_R (to_r func_u) arg_u

  1730       | Func (R, Formula Neut) =>

  1731         to_guard [arg_u] res_R (rel_expr_from_formula kk res_R

  1732                                     (kk_subset (to_opt R arg_u) (to_r func_u)))

  1733       | Func (Unit, R2) =>

  1734         to_guard [arg_u] res_R

  1735                  (rel_expr_from_rel_expr kk res_R R2 (to_r func_u))

  1736       | Func (R1, R2) =>

  1737         rel_expr_from_rel_expr kk res_R R2

  1738             (kk_n_fold_join kk true R1 R2 (to_opt R1 arg_u) (to_r func_u))

  1739         |> body_rep R2 = Formula Neut ? to_guard [arg_u] res_R

  1740       | _ => raise NUT ("Nitpick_Kodkod.to_apply", [func_u])

  1741     (* int -> rep -> rep -> Kodkod.rel_expr -> nut *)

  1742     and to_apply_vect k R' res_R func_r arg_u =

  1743       let

  1744         val arg_R = one_rep ofs (type_of arg_u) (unopt_rep (rep_of arg_u))

  1745         val vect_r = vect_from_rel_expr kk k res_R (Vect (k, R')) func_r

  1746         val vect_rs = unpack_vect_in_chunks kk (arity_of_rep res_R) k vect_r

  1747       in

  1748         kk_case_switch kk arg_R res_R (to_opt arg_R arg_u)

  1749                        (all_singletons_for_rep arg_R) vect_rs

  1750       end

  1751     (* bool -> nut -> Kodkod.formula *)

  1752     and to_could_be_unrep neg u =

  1753       if neg andalso is_opt_rep (rep_of u) then kk_no (to_r u)

  1754       else Kodkod.False

  1755     (* nut -> Kodkod.rel_expr -> Kodkod.rel_expr *)

  1756     and to_compare_with_unrep u r =

  1757       if is_opt_rep (rep_of u) then

  1758         kk_rel_if (kk_some (to_r u)) r (empty_rel_for_rep (rep_of u))

  1759       else

  1760         r

  1761   in to_f_with_polarity Pos u end

  1763 end;

author	blanchet
	Tue, 24 Nov 2009 18:36:18 +0100
changeset 33892	3937da7e13ea
parent 33886	cde73f8dbe4e
child 33982	1ae222745c4a
permissions	-rw-r--r--