src/HOL/Tools/Nitpick/nitpick_kodkod.ML
author blanchet
Tue Mar 15 15:49:42 2011 +0100 (2011-03-15 ago)
changeset 41985 09b75d55008f
parent 41875 e3cd0dce9b1a
child 41995 03c2d29ec790
permissions -rw-r--r--
support non-ground "need" values
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(*  Title:      HOL/Tools/Nitpick/nitpick_kodkod.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009, 2010
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Kodkod problem generator part of Kodkod.
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*)
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signature NITPICK_KODKOD =
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sig
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  type hol_context = Nitpick_HOL.hol_context
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  type datatype_spec = Nitpick_Scope.datatype_spec
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  type kodkod_constrs = Nitpick_Peephole.kodkod_constrs
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  type nut = Nitpick_Nut.nut
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  structure NameTable : TABLE
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  val univ_card :
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    int -> int -> int -> Kodkod.bound list -> Kodkod.formula -> int
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  val check_bits : int -> Kodkod.formula -> unit
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  val check_arity : string -> int -> int -> unit
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  val kk_tuple : bool -> int -> int list -> Kodkod.tuple
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  val tuple_set_from_atom_schema : (int * int) list -> Kodkod.tuple_set
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  val sequential_int_bounds : int -> Kodkod.int_bound list
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  val pow_of_two_int_bounds : int -> int -> Kodkod.int_bound list
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  val bounds_and_axioms_for_built_in_rels_in_formulas :
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    bool -> int -> int -> int -> int -> Kodkod.formula list
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    -> Kodkod.bound list * Kodkod.formula list
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  val bound_for_plain_rel : Proof.context -> bool -> nut -> Kodkod.bound
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  val bound_for_sel_rel :
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    Proof.context -> bool -> datatype_spec list -> nut -> Kodkod.bound
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  val merge_bounds : Kodkod.bound list -> Kodkod.bound list
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  val kodkod_formula_from_nut :
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    int Typtab.table -> kodkod_constrs -> nut -> Kodkod.formula
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  val declarative_axiom_for_plain_rel : kodkod_constrs -> nut -> Kodkod.formula
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  val declarative_axioms_for_datatypes :
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    hol_context -> bool -> nut list -> int -> int -> int Typtab.table
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    -> kodkod_constrs -> nut NameTable.table -> datatype_spec list
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    -> Kodkod.formula list
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end;
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structure Nitpick_Kodkod : NITPICK_KODKOD =
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struct
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open Nitpick_Util
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open Nitpick_HOL
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open Nitpick_Scope
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open Nitpick_Peephole
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open Nitpick_Rep
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open Nitpick_Nut
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structure KK = Kodkod
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fun pull x xs = x :: filter_out (curry (op =) x) xs
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fun is_datatype_acyclic ({co = false, standard = true, deep = true, ...}
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                         : datatype_spec) = true
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  | is_datatype_acyclic _ = false
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fun flip_nums n = index_seq 1 n @ [0] |> map KK.Num
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fun univ_card nat_card int_card main_j0 bounds formula =
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  let
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    fun rel_expr_func r k =
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      Int.max (k, case r of
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                    KK.Atom j => j + 1
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                  | KK.AtomSeq (k', j0) => j0 + k'
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                  | _ => 0)
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    fun tuple_func t k =
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      case t of
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        KK.Tuple js => fold Integer.max (map (Integer.add 1) js) k
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      | _ => k
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    fun tuple_set_func ts k =
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      Int.max (k, case ts of KK.TupleAtomSeq (k', j0) => j0 + k' | _ => 0)
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    val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,
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                  int_expr_func = K I}
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    val tuple_F = {tuple_func = tuple_func, tuple_set_func = tuple_set_func}
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    val card = fold (KK.fold_bound expr_F tuple_F) bounds 1
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               |> KK.fold_formula expr_F formula
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  in Int.max (main_j0 + fold Integer.max [2, nat_card, int_card] 0, card) end
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fun check_bits bits formula =
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  let
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    fun int_expr_func (KK.Num k) () =
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        if is_twos_complement_representable bits k then
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          ()
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        else
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          raise TOO_SMALL ("Nitpick_Kodkod.check_bits",
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                           "\"bits\" value " ^ string_of_int bits ^
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                           " too small for problem")
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      | int_expr_func _ () = ()
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    val expr_F = {formula_func = K I, rel_expr_func = K I,
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                  int_expr_func = int_expr_func}
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  in KK.fold_formula expr_F formula () end
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fun check_arity guilty_party univ_card n =
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  if n > KK.max_arity univ_card then
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    raise TOO_LARGE ("Nitpick_Kodkod.check_arity",
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                     "arity " ^ string_of_int n ^
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                     (if guilty_party = "" then
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                        ""
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                      else
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                        " of Kodkod relation associated with " ^
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                        quote (original_name guilty_party)) ^
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                     " too large for universe of cardinality " ^
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                     string_of_int univ_card)
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  else
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    ()
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fun kk_tuple debug univ_card js =
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  if debug then
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    KK.Tuple js
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  else
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    KK.TupleIndex (length js,
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                   fold (fn j => fn accum => accum * univ_card + j) js 0)
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val tuple_set_from_atom_schema = foldl1 KK.TupleProduct o map KK.TupleAtomSeq
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val upper_bound_for_rep = tuple_set_from_atom_schema o atom_schema_of_rep
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val single_atom = KK.TupleSet o single o KK.Tuple o single
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fun sequential_int_bounds n = [(NONE, map single_atom (index_seq 0 n))]
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fun pow_of_two_int_bounds bits j0 =
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  let
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    fun aux 0  _ _ = []
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      | aux 1 pow_of_two j = [(SOME (~ pow_of_two), [single_atom j])]
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      | aux iter pow_of_two j =
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        (SOME pow_of_two, [single_atom j]) ::
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        aux (iter - 1) (2 * pow_of_two) (j + 1)
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  in aux (bits + 1) 1 j0 end
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fun built_in_rels_in_formulas formulas =
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  let
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    fun rel_expr_func (KK.Rel (x as (_, j))) =
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        (j < 0 andalso x <> unsigned_bit_word_sel_rel andalso
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         x <> signed_bit_word_sel_rel)
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        ? insert (op =) x
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      | rel_expr_func _ = I
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    val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,
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                  int_expr_func = K I}
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  in fold (KK.fold_formula expr_F) formulas [] end
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val max_table_size = 65536
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fun check_table_size k =
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  if k > max_table_size then
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    raise TOO_LARGE ("Nitpick_Kodkod.check_table_size",
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                     "precomputed table too large (" ^ string_of_int k ^ ")")
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  else
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    ()
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fun tabulate_func1 debug univ_card (k, j0) f =
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  (check_table_size k;
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   map_filter (fn j1 => let val j2 = f j1 in
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                          if j2 >= 0 then
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                            SOME (kk_tuple debug univ_card [j1 + j0, j2 + j0])
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                          else
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                            NONE
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                        end) (index_seq 0 k))
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fun tabulate_op2 debug univ_card (k, j0) res_j0 f =
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  (check_table_size (k * k);
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   map_filter (fn j => let
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                         val j1 = j div k
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                         val j2 = j - j1 * k
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                         val j3 = f (j1, j2)
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                       in
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                         if j3 >= 0 then
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                           SOME (kk_tuple debug univ_card
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                                          [j1 + j0, j2 + j0, j3 + res_j0])
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                         else
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                           NONE
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                       end) (index_seq 0 (k * k)))
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fun tabulate_op2_2 debug univ_card (k, j0) res_j0 f =
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  (check_table_size (k * k);
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   map_filter (fn j => let
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                         val j1 = j div k
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                         val j2 = j - j1 * k
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                         val (j3, j4) = f (j1, j2)
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                       in
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                         if j3 >= 0 andalso j4 >= 0 then
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                           SOME (kk_tuple debug univ_card
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                                          [j1 + j0, j2 + j0, j3 + res_j0,
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                                           j4 + res_j0])
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                         else
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                           NONE
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                       end) (index_seq 0 (k * k)))
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fun tabulate_nat_op2 debug univ_card (k, j0) f =
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  tabulate_op2 debug univ_card (k, j0) j0 (atom_for_nat (k, 0) o f)
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fun tabulate_int_op2 debug univ_card (k, j0) f =
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  tabulate_op2 debug univ_card (k, j0) j0
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               (atom_for_int (k, 0) o f o pairself (int_for_atom (k, 0)))
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fun tabulate_int_op2_2 debug univ_card (k, j0) f =
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  tabulate_op2_2 debug univ_card (k, j0) j0
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                 (pairself (atom_for_int (k, 0)) o f
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                  o pairself (int_for_atom (k, 0)))
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fun isa_div (m, n) = m div n handle General.Div => 0
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fun isa_mod (m, n) = m mod n handle General.Div => m
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fun isa_gcd (m, 0) = m
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  | isa_gcd (m, n) = isa_gcd (n, isa_mod (m, n))
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fun isa_lcm (m, n) = isa_div (m * n, isa_gcd (m, n))
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val isa_zgcd = isa_gcd o pairself abs
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fun isa_norm_frac (m, n) =
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  if n < 0 then isa_norm_frac (~m, ~n)
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  else if m = 0 orelse n = 0 then (0, 1)
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  else let val p = isa_zgcd (m, n) in (isa_div (m, p), isa_div (n, p)) end
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fun tabulate_built_in_rel debug univ_card nat_card int_card j0
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                          (x as (n, _)) =
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  (check_arity "" univ_card n;
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   if x = not3_rel then
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     ("not3", tabulate_func1 debug univ_card (2, j0) (curry (op -) 1))
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   else if x = suc_rel then
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     ("suc", tabulate_func1 debug univ_card (univ_card - j0 - 1, j0)
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                            (Integer.add 1))
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   else if x = nat_add_rel then
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     ("nat_add", tabulate_nat_op2 debug univ_card (nat_card, j0) (op +))
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   else if x = int_add_rel then
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     ("int_add", tabulate_int_op2 debug univ_card (int_card, j0) (op +))
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   else if x = nat_subtract_rel then
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     ("nat_subtract",
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      tabulate_op2 debug univ_card (nat_card, j0) j0 (uncurry nat_minus))
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   else if x = int_subtract_rel then
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     ("int_subtract", tabulate_int_op2 debug univ_card (int_card, j0) (op -))
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   else if x = nat_multiply_rel then
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     ("nat_multiply", tabulate_nat_op2 debug univ_card (nat_card, j0) (op * ))
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   else if x = int_multiply_rel then
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     ("int_multiply", tabulate_int_op2 debug univ_card (int_card, j0) (op * ))
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   else if x = nat_divide_rel then
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     ("nat_divide", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_div)
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   else if x = int_divide_rel then
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     ("int_divide", tabulate_int_op2 debug univ_card (int_card, j0) isa_div)
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   else if x = nat_less_rel then
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     ("nat_less", tabulate_nat_op2 debug univ_card (nat_card, j0)
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                                   (int_from_bool o op <))
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   else if x = int_less_rel then
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     ("int_less", tabulate_int_op2 debug univ_card (int_card, j0)
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                                   (int_from_bool o op <))
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   else if x = gcd_rel then
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     ("gcd", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_gcd)
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   else if x = lcm_rel then
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     ("lcm", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_lcm)
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   else if x = norm_frac_rel then
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     ("norm_frac", tabulate_int_op2_2 debug univ_card (int_card, j0)
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                                      isa_norm_frac)
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   else
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     raise ARG ("Nitpick_Kodkod.tabulate_built_in_rel", "unknown relation"))
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fun bound_for_built_in_rel debug univ_card nat_card int_card main_j0
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                           (x as (n, j)) =
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  if n = 2 andalso j <= suc_rels_base then
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    let val (y as (k, j0), tabulate) = atom_seq_for_suc_rel x in
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      ([(x, "suc")],
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       if tabulate then
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         [KK.TupleSet (tabulate_func1 debug univ_card (k - 1, j0)
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                       (Integer.add 1))]
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       else
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         [KK.TupleSet [], tuple_set_from_atom_schema [y, y]])
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    end
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  else
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    let
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      val (nick, ts) = tabulate_built_in_rel debug univ_card nat_card int_card
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                                             main_j0 x
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    in ([(x, nick)], [KK.TupleSet ts]) end
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fun axiom_for_built_in_rel (x as (n, j)) =
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  if n = 2 andalso j <= suc_rels_base then
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    let val (y as (k, j0), tabulate) = atom_seq_for_suc_rel x in
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      if tabulate then
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        NONE
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      else if k < 2 then
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        SOME (KK.No (KK.Rel x))
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      else
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        SOME (KK.TotalOrdering (x, KK.AtomSeq y, KK.Atom j0, KK.Atom (j0 + 1)))
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    end
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  else
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    NONE
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fun bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card nat_card
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                                                    int_card main_j0 formulas =
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  let val rels = built_in_rels_in_formulas formulas in
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    (map (bound_for_built_in_rel debug univ_card nat_card int_card main_j0)
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         rels,
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     map_filter axiom_for_built_in_rel rels)
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  end
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fun bound_comment ctxt debug nick T R =
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  short_name nick ^
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  (if debug then " :: " ^ unyxml (Syntax.string_of_typ ctxt T) else "") ^
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  " : " ^ string_for_rep R
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fun bound_for_plain_rel ctxt debug (u as FreeRel (x, T, R, nick)) =
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    ([(x, bound_comment ctxt debug nick T R)],
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     if nick = @{const_name bisim_iterator_max} then
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       case R of
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         Atom (k, j0) => [single_atom (k - 1 + j0)]
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       | _ => raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])
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     else
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       [KK.TupleSet [], upper_bound_for_rep R])
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  | bound_for_plain_rel _ _ u =
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    raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])
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blanchet@33192
   300
fun bound_for_sel_rel ctxt debug dtypes
blanchet@35665
   301
        (FreeRel (x, T as Type (@{type_name fun}, [T1, T2]),
blanchet@35665
   302
                  R as Func (Atom (_, j0), R2), nick)) =
blanchet@33192
   303
    let
blanchet@35280
   304
      val {delta, epsilon, exclusive, explicit_max, ...} =
blanchet@33192
   305
        constr_spec dtypes (original_name nick, T1)
blanchet@33192
   306
    in
blanchet@33192
   307
      ([(x, bound_comment ctxt debug nick T R)],
blanchet@33192
   308
       if explicit_max = 0 then
blanchet@34126
   309
         [KK.TupleSet []]
blanchet@33192
   310
       else
blanchet@34126
   311
         let val ts = KK.TupleAtomSeq (epsilon - delta, delta + j0) in
blanchet@33192
   312
           if R2 = Formula Neut then
blanchet@34126
   313
             [ts] |> not exclusive ? cons (KK.TupleSet [])
blanchet@33192
   314
           else
blanchet@35072
   315
             [KK.TupleSet [],
blanchet@35178
   316
              if T1 = T2 andalso epsilon > delta andalso
blanchet@38196
   317
                 is_datatype_acyclic (the (datatype_spec dtypes T1)) then
blanchet@35072
   318
                index_seq delta (epsilon - delta)
blanchet@35072
   319
                |> map (fn j =>
blanchet@38126
   320
                           KK.TupleProduct (KK.TupleSet [KK.Tuple [j + j0]],
blanchet@35072
   321
                                            KK.TupleAtomSeq (j, j0)))
blanchet@35072
   322
                |> foldl1 KK.TupleUnion
blanchet@35072
   323
              else
blanchet@35072
   324
                KK.TupleProduct (ts, upper_bound_for_rep R2)]
blanchet@33192
   325
         end)
blanchet@33192
   326
    end
blanchet@33192
   327
  | bound_for_sel_rel _ _ _ u =
blanchet@33232
   328
    raise NUT ("Nitpick_Kodkod.bound_for_sel_rel", [u])
blanchet@33192
   329
blanchet@33192
   330
fun merge_bounds bs =
blanchet@33192
   331
  let
blanchet@33192
   332
    fun arity (zs, _) = fst (fst (hd zs))
blanchet@33192
   333
    fun add_bound ds b [] = List.revAppend (ds, [b])
blanchet@33192
   334
      | add_bound ds b (c :: cs) =
blanchet@33192
   335
        if arity b = arity c andalso snd b = snd c then
blanchet@33192
   336
          List.revAppend (ds, (fst c @ fst b, snd c) :: cs)
blanchet@33192
   337
        else
blanchet@33192
   338
          add_bound (c :: ds) b cs
blanchet@33192
   339
  in fold (add_bound []) bs [] end
blanchet@33192
   340
blanchet@34126
   341
fun unary_var_seq j0 n = map (curry KK.Var 1) (index_seq j0 n)
blanchet@33192
   342
blanchet@34126
   343
val singleton_from_combination = foldl1 KK.Product o map KK.Atom
blanchet@33192
   344
fun all_singletons_for_rep R =
blanchet@33192
   345
  if is_lone_rep R then
blanchet@33192
   346
    all_combinations_for_rep R |> map singleton_from_combination
blanchet@33192
   347
  else
blanchet@33232
   348
    raise REP ("Nitpick_Kodkod.all_singletons_for_rep", [R])
blanchet@33192
   349
blanchet@34126
   350
fun unpack_products (KK.Product (r1, r2)) =
blanchet@33192
   351
    unpack_products r1 @ unpack_products r2
blanchet@33192
   352
  | unpack_products r = [r]
blanchet@34126
   353
fun unpack_joins (KK.Join (r1, r2)) = unpack_joins r1 @ unpack_joins r2
blanchet@33192
   354
  | unpack_joins r = [r]
blanchet@33192
   355
blanchet@33192
   356
val empty_rel_for_rep = empty_n_ary_rel o arity_of_rep
blanchet@33192
   357
fun full_rel_for_rep R =
blanchet@33192
   358
  case atom_schema_of_rep R of
blanchet@33232
   359
    [] => raise REP ("Nitpick_Kodkod.full_rel_for_rep", [R])
blanchet@34126
   360
  | schema => foldl1 KK.Product (map KK.AtomSeq schema)
blanchet@33192
   361
blanchet@33192
   362
fun decls_for_atom_schema j0 schema =
blanchet@34126
   363
  map2 (fn j => fn x => KK.DeclOne ((1, j), KK.AtomSeq x))
blanchet@33192
   364
       (index_seq j0 (length schema)) schema
blanchet@33192
   365
blanchet@33192
   366
fun d_n_ary_function ({kk_all, kk_join, kk_lone, kk_one, ...} : kodkod_constrs)
blanchet@33192
   367
                     R r =
blanchet@33192
   368
  let val body_R = body_rep R in
blanchet@33192
   369
    if is_lone_rep body_R then
blanchet@33192
   370
      let
blanchet@33192
   371
        val binder_schema = atom_schema_of_reps (binder_reps R)
blanchet@33192
   372
        val body_schema = atom_schema_of_rep body_R
blanchet@33192
   373
        val one = is_one_rep body_R
blanchet@34126
   374
        val opt_x = case r of KK.Rel x => SOME x | _ => NONE
blanchet@33192
   375
      in
blanchet@34936
   376
        if opt_x <> NONE andalso length binder_schema = 1 andalso
blanchet@34936
   377
           length body_schema = 1 then
blanchet@34126
   378
          (if one then KK.Function else KK.Functional)
blanchet@34126
   379
              (the opt_x, KK.AtomSeq (hd binder_schema),
blanchet@34126
   380
               KK.AtomSeq (hd body_schema))
blanchet@33192
   381
        else
blanchet@33192
   382
          let
blanchet@33192
   383
            val decls = decls_for_atom_schema ~1 binder_schema
blanchet@33192
   384
            val vars = unary_var_seq ~1 (length binder_schema)
blanchet@33192
   385
            val kk_xone = if one then kk_one else kk_lone
blanchet@33192
   386
          in kk_all decls (kk_xone (fold kk_join vars r)) end
blanchet@33192
   387
      end
blanchet@33192
   388
    else
blanchet@34126
   389
      KK.True
blanchet@33192
   390
  end
blanchet@34126
   391
fun kk_n_ary_function kk R (r as KK.Rel x) =
blanchet@33192
   392
    if not (is_opt_rep R) then
blanchet@34124
   393
      if x = suc_rel then
blanchet@34126
   394
        KK.False
blanchet@34124
   395
      else if x = nat_add_rel then
blanchet@33192
   396
        formula_for_bool (card_of_rep (body_rep R) = 1)
blanchet@34124
   397
      else if x = nat_multiply_rel then
blanchet@33192
   398
        formula_for_bool (card_of_rep (body_rep R) <= 2)
blanchet@33192
   399
      else
blanchet@33192
   400
        d_n_ary_function kk R r
blanchet@34124
   401
    else if x = nat_subtract_rel then
blanchet@34126
   402
      KK.True
blanchet@33192
   403
    else
blanchet@33192
   404
      d_n_ary_function kk R r
blanchet@33192
   405
  | kk_n_ary_function kk R r = d_n_ary_function kk R r
blanchet@33192
   406
blanchet@34126
   407
fun kk_disjoint_sets _ [] = KK.True
blanchet@33192
   408
  | kk_disjoint_sets (kk as {kk_and, kk_no, kk_intersect, ...} : kodkod_constrs)
blanchet@33192
   409
                     (r :: rs) =
blanchet@33192
   410
    fold (kk_and o kk_no o kk_intersect r) rs (kk_disjoint_sets kk rs)
blanchet@33192
   411
blanchet@34124
   412
fun basic_rel_rel_let j ({kk_rel_let, ...} : kodkod_constrs) f r =
blanchet@33192
   413
  if inline_rel_expr r then
blanchet@33192
   414
    f r
blanchet@33192
   415
  else
blanchet@34126
   416
    let val x = (KK.arity_of_rel_expr r, j) in
blanchet@34126
   417
      kk_rel_let [KK.AssignRelReg (x, r)] (f (KK.RelReg x))
blanchet@33192
   418
    end
blanchet@34124
   419
val single_rel_rel_let = basic_rel_rel_let 0
blanchet@34124
   420
fun double_rel_rel_let kk f r1 r2 =
blanchet@34124
   421
  single_rel_rel_let kk (fn r1 => basic_rel_rel_let 1 kk (f r1) r2) r1
blanchet@35386
   422
fun triple_rel_rel_let kk f r1 r2 r3 =
blanchet@34124
   423
  double_rel_rel_let kk
blanchet@34124
   424
      (fn r1 => fn r2 => basic_rel_rel_let 2 kk (f r1 r2) r3) r1 r2
blanchet@33192
   425
blanchet@33192
   426
fun atom_from_formula ({kk_rel_if, ...} : kodkod_constrs) j0 f =
blanchet@34126
   427
  kk_rel_if f (KK.Atom (j0 + 1)) (KK.Atom j0)
blanchet@33192
   428
fun rel_expr_from_formula kk R f =
blanchet@33192
   429
  case unopt_rep R of
blanchet@33192
   430
    Atom (2, j0) => atom_from_formula kk j0 f
blanchet@33232
   431
  | _ => raise REP ("Nitpick_Kodkod.rel_expr_from_formula", [R])
blanchet@33192
   432
blanchet@33192
   433
fun unpack_vect_in_chunks ({kk_project_seq, ...} : kodkod_constrs) chunk_arity
blanchet@33192
   434
                          num_chunks r =
blanchet@33192
   435
  List.tabulate (num_chunks, fn j => kk_project_seq r (j * chunk_arity)
blanchet@33192
   436
                                                    chunk_arity)
blanchet@33192
   437
blanchet@33192
   438
fun kk_n_fold_join
blanchet@33192
   439
        (kk as {kk_intersect, kk_product, kk_join, kk_project_seq, ...}) one R1
blanchet@33192
   440
        res_R r1 r2 =
blanchet@33192
   441
  case arity_of_rep R1 of
blanchet@33192
   442
    1 => kk_join r1 r2
blanchet@33192
   443
  | arity1 =>
blanchet@38164
   444
    let val unpacked_rs1 = unpack_products r1 in
blanchet@33192
   445
      if one andalso length unpacked_rs1 = arity1 then
blanchet@33192
   446
        fold kk_join unpacked_rs1 r2
blanchet@38164
   447
      else if one andalso inline_rel_expr r1 then
blanchet@38164
   448
        fold kk_join (unpack_vect_in_chunks kk 1 arity1 r1) r2
blanchet@33192
   449
      else
blanchet@33192
   450
        kk_project_seq
blanchet@33192
   451
            (kk_intersect (kk_product r1 (full_rel_for_rep res_R)) r2)
blanchet@33192
   452
            arity1 (arity_of_rep res_R)
blanchet@33192
   453
    end
blanchet@33192
   454
blanchet@33192
   455
fun kk_case_switch (kk as {kk_union, kk_product, ...}) R1 R2 r rs1 rs2 =
blanchet@33192
   456
  if rs1 = rs2 then r
blanchet@33192
   457
  else kk_n_fold_join kk true R1 R2 r (fold1 kk_union (map2 kk_product rs1 rs2))
blanchet@33192
   458
blanchet@33192
   459
val lone_rep_fallback_max_card = 4096
blanchet@33192
   460
val some_j0 = 0
blanchet@33192
   461
blanchet@33192
   462
fun lone_rep_fallback kk new_R old_R r =
blanchet@33192
   463
  if old_R = new_R then
blanchet@33192
   464
    r
blanchet@33192
   465
  else
blanchet@33192
   466
    let val card = card_of_rep old_R in
blanchet@34936
   467
      if is_lone_rep old_R andalso is_lone_rep new_R andalso
blanchet@34936
   468
         card = card_of_rep new_R then
blanchet@33192
   469
        if card >= lone_rep_fallback_max_card then
blanchet@34124
   470
          raise TOO_LARGE ("Nitpick_Kodkod.lone_rep_fallback",
blanchet@34124
   471
                           "too high cardinality (" ^ string_of_int card ^ ")")
blanchet@33192
   472
        else
blanchet@33192
   473
          kk_case_switch kk old_R new_R r (all_singletons_for_rep old_R)
blanchet@33192
   474
                         (all_singletons_for_rep new_R)
blanchet@33192
   475
      else
blanchet@33232
   476
        raise REP ("Nitpick_Kodkod.lone_rep_fallback", [old_R, new_R])
blanchet@33192
   477
    end
blanchet@35280
   478
and atom_from_rel_expr kk x old_R r =
blanchet@33192
   479
  case old_R of
blanchet@33192
   480
    Func (R1, R2) =>
blanchet@33192
   481
    let
blanchet@33192
   482
      val dom_card = card_of_rep R1
blanchet@33192
   483
      val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
blanchet@33192
   484
    in
blanchet@33192
   485
      atom_from_rel_expr kk x (Vect (dom_card, R2'))
blanchet@33192
   486
                         (vect_from_rel_expr kk dom_card R2' old_R r)
blanchet@33192
   487
    end
blanchet@33232
   488
  | Opt _ => raise REP ("Nitpick_Kodkod.atom_from_rel_expr", [old_R])
blanchet@33192
   489
  | _ => lone_rep_fallback kk (Atom x) old_R r
blanchet@33192
   490
and struct_from_rel_expr kk Rs old_R r =
blanchet@33192
   491
  case old_R of
blanchet@33192
   492
    Atom _ => lone_rep_fallback kk (Struct Rs) old_R r
blanchet@33192
   493
  | Struct Rs' =>
blanchet@38190
   494
    if Rs' = Rs then
blanchet@38190
   495
      r
blanchet@38190
   496
    else if map card_of_rep Rs' = map card_of_rep Rs then
blanchet@38190
   497
      let
blanchet@38190
   498
        val old_arities = map arity_of_rep Rs'
blanchet@38190
   499
        val old_offsets = offset_list old_arities
blanchet@38190
   500
        val old_rs = map2 (#kk_project_seq kk r) old_offsets old_arities
blanchet@38190
   501
      in
blanchet@38190
   502
        fold1 (#kk_product kk)
blanchet@38190
   503
              (map3 (rel_expr_from_rel_expr kk) Rs Rs' old_rs)
blanchet@38190
   504
      end
blanchet@38190
   505
    else
blanchet@38190
   506
      lone_rep_fallback kk (Struct Rs) old_R r
blanchet@33232
   507
  | _ => raise REP ("Nitpick_Kodkod.struct_from_rel_expr", [old_R])
blanchet@33192
   508
and vect_from_rel_expr kk k R old_R r =
blanchet@33192
   509
  case old_R of
blanchet@33192
   510
    Atom _ => lone_rep_fallback kk (Vect (k, R)) old_R r
blanchet@33192
   511
  | Vect (k', R') =>
blanchet@33192
   512
    if k = k' andalso R = R' then r
blanchet@33192
   513
    else lone_rep_fallback kk (Vect (k, R)) old_R r
blanchet@33192
   514
  | Func (R1, Formula Neut) =>
blanchet@33192
   515
    if k = card_of_rep R1 then
blanchet@33192
   516
      fold1 (#kk_product kk)
blanchet@33192
   517
            (map (fn arg_r =>
blanchet@33192
   518
                     rel_expr_from_formula kk R (#kk_subset kk arg_r r))
blanchet@33192
   519
                 (all_singletons_for_rep R1))
blanchet@33192
   520
    else
blanchet@33232
   521
      raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])
blanchet@33192
   522
  | Func (R1, R2) =>
blanchet@33192
   523
    fold1 (#kk_product kk)
blanchet@33192
   524
          (map (fn arg_r =>
blanchet@33192
   525
                   rel_expr_from_rel_expr kk R R2
blanchet@33192
   526
                                         (kk_n_fold_join kk true R1 R2 arg_r r))
blanchet@33192
   527
               (all_singletons_for_rep R1))
blanchet@33232
   528
  | _ => raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])
blanchet@33192
   529
and func_from_no_opt_rel_expr kk R1 R2 (Atom x) r =
blanchet@33192
   530
    let
blanchet@33192
   531
      val dom_card = card_of_rep R1
blanchet@33192
   532
      val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
blanchet@33192
   533
    in
blanchet@33192
   534
      func_from_no_opt_rel_expr kk R1 R2 (Vect (dom_card, R2'))
blanchet@33192
   535
                                (vect_from_rel_expr kk dom_card R2' (Atom x) r)
blanchet@33192
   536
    end
blanchet@33192
   537
  | func_from_no_opt_rel_expr kk R1 (Formula Neut) old_R r =
blanchet@33192
   538
    (case old_R of
blanchet@33192
   539
       Vect (k, Atom (2, j0)) =>
blanchet@33192
   540
       let
blanchet@33192
   541
         val args_rs = all_singletons_for_rep R1
blanchet@33192
   542
         val vals_rs = unpack_vect_in_chunks kk 1 k r
blanchet@33192
   543
         fun empty_or_singleton_set_for arg_r val_r =
blanchet@34126
   544
           #kk_join kk val_r (#kk_product kk (KK.Atom (j0 + 1)) arg_r)
blanchet@33192
   545
       in
blanchet@33192
   546
         fold1 (#kk_union kk) (map2 empty_or_singleton_set_for args_rs vals_rs)
blanchet@33192
   547
       end
blanchet@33192
   548
     | Func (R1', Formula Neut) =>
blanchet@33192
   549
       if R1 = R1' then
blanchet@33192
   550
         r
blanchet@33192
   551
       else
blanchet@33192
   552
         let
blanchet@33192
   553
           val schema = atom_schema_of_rep R1
blanchet@33192
   554
           val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
blanchet@33192
   555
                    |> rel_expr_from_rel_expr kk R1' R1
blanchet@33582
   556
           val kk_xeq = (if is_one_rep R1' then #kk_subset else #kk_rel_eq) kk
blanchet@33192
   557
         in
blanchet@33582
   558
           #kk_comprehension kk (decls_for_atom_schema ~1 schema) (kk_xeq r1 r)
blanchet@33192
   559
         end
blanchet@33192
   560
     | Func (R1', Atom (2, j0)) =>
blanchet@33192
   561
       func_from_no_opt_rel_expr kk R1 (Formula Neut)
blanchet@34126
   562
           (Func (R1', Formula Neut)) (#kk_join kk r (KK.Atom (j0 + 1)))
blanchet@33232
   563
     | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
blanchet@33192
   564
                       [old_R, Func (R1, Formula Neut)]))
blanchet@33192
   565
  | func_from_no_opt_rel_expr kk R1 R2 old_R r =
blanchet@33192
   566
    case old_R of
blanchet@33192
   567
      Vect (k, R) =>
blanchet@33192
   568
      let
blanchet@33192
   569
        val args_rs = all_singletons_for_rep R1
blanchet@33192
   570
        val vals_rs = unpack_vect_in_chunks kk (arity_of_rep R) k r
blanchet@33192
   571
                      |> map (rel_expr_from_rel_expr kk R2 R)
blanchet@33192
   572
      in fold1 (#kk_union kk) (map2 (#kk_product kk) args_rs vals_rs) end
blanchet@33192
   573
    | Func (R1', Formula Neut) =>
blanchet@33192
   574
      (case R2 of
blanchet@33192
   575
         Atom (x as (2, j0)) =>
blanchet@33192
   576
         let val schema = atom_schema_of_rep R1 in
blanchet@33192
   577
           if length schema = 1 then
blanchet@34126
   578
             #kk_override kk (#kk_product kk (KK.AtomSeq (hd schema))
blanchet@34126
   579
                                             (KK.Atom j0))
blanchet@34126
   580
                             (#kk_product kk r (KK.Atom (j0 + 1)))
blanchet@33192
   581
           else
blanchet@33192
   582
             let
blanchet@33192
   583
               val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
blanchet@33192
   584
                        |> rel_expr_from_rel_expr kk R1' R1
blanchet@34126
   585
               val r2 = KK.Var (1, ~(length schema) - 1)
blanchet@33192
   586
               val r3 = atom_from_formula kk j0 (#kk_subset kk r1 r)
blanchet@33192
   587
             in
blanchet@33192
   588
               #kk_comprehension kk (decls_for_atom_schema ~1 (schema @ [x]))
blanchet@33582
   589
                                 (#kk_subset kk r2 r3)
blanchet@33192
   590
             end
blanchet@33192
   591
           end
blanchet@33232
   592
         | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
blanchet@33192
   593
                           [old_R, Func (R1, R2)]))
blanchet@33192
   594
    | Func (R1', R2') =>
blanchet@33192
   595
      if R1 = R1' andalso R2 = R2' then
blanchet@33192
   596
        r
blanchet@33192
   597
      else
blanchet@33192
   598
        let
blanchet@33192
   599
          val dom_schema = atom_schema_of_rep R1
blanchet@33192
   600
          val ran_schema = atom_schema_of_rep R2
blanchet@33192
   601
          val dom_prod = fold1 (#kk_product kk)
blanchet@33192
   602
                               (unary_var_seq ~1 (length dom_schema))
blanchet@33192
   603
                         |> rel_expr_from_rel_expr kk R1' R1
blanchet@33192
   604
          val ran_prod = fold1 (#kk_product kk)
blanchet@33192
   605
                               (unary_var_seq (~(length dom_schema) - 1)
blanchet@33192
   606
                                              (length ran_schema))
blanchet@33192
   607
                         |> rel_expr_from_rel_expr kk R2' R2
blanchet@33192
   608
          val app = kk_n_fold_join kk true R1' R2' dom_prod r
blanchet@33582
   609
          val kk_xeq = (if is_one_rep R2' then #kk_subset else #kk_rel_eq) kk
blanchet@33192
   610
        in
blanchet@33192
   611
          #kk_comprehension kk (decls_for_atom_schema ~1
blanchet@33192
   612
                                                      (dom_schema @ ran_schema))
blanchet@33582
   613
                               (kk_xeq ran_prod app)
blanchet@33192
   614
        end
blanchet@33232
   615
    | _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
blanchet@33192
   616
                      [old_R, Func (R1, R2)])
blanchet@33192
   617
and rel_expr_from_rel_expr kk new_R old_R r =
blanchet@33192
   618
  let
blanchet@33192
   619
    val unopt_old_R = unopt_rep old_R
blanchet@33192
   620
    val unopt_new_R = unopt_rep new_R
blanchet@33192
   621
  in
blanchet@33192
   622
    if unopt_old_R <> old_R andalso unopt_new_R = new_R then
blanchet@33232
   623
      raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr", [old_R, new_R])
blanchet@33192
   624
    else if unopt_new_R = unopt_old_R then
blanchet@33192
   625
      r
blanchet@33192
   626
    else
blanchet@33192
   627
      (case unopt_new_R of
blanchet@33192
   628
         Atom x => atom_from_rel_expr kk x
blanchet@33192
   629
       | Struct Rs => struct_from_rel_expr kk Rs
blanchet@33192
   630
       | Vect (k, R') => vect_from_rel_expr kk k R'
blanchet@33192
   631
       | Func (R1, R2) => func_from_no_opt_rel_expr kk R1 R2
blanchet@33232
   632
       | _ => raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr",
blanchet@33192
   633
                         [old_R, new_R]))
blanchet@33192
   634
          unopt_old_R r
blanchet@33192
   635
  end
blanchet@33192
   636
and rel_expr_to_func kk R1 R2 = rel_expr_from_rel_expr kk (Func (R1, R2))
blanchet@33192
   637
blanchet@34124
   638
fun bit_set_from_atom ({kk_join, ...} : kodkod_constrs) T r =
blanchet@34126
   639
  kk_join r (KK.Rel (if T = @{typ "unsigned_bit word"} then
blanchet@34126
   640
                       unsigned_bit_word_sel_rel
blanchet@34126
   641
                     else
blanchet@34126
   642
                       signed_bit_word_sel_rel))
blanchet@34126
   643
val int_expr_from_atom = KK.SetSum ooo bit_set_from_atom
blanchet@34124
   644
fun atom_from_int_expr (kk as {kk_rel_eq, kk_comprehension, ...}
blanchet@34124
   645
                        : kodkod_constrs) T R i =
blanchet@34124
   646
  kk_comprehension (decls_for_atom_schema ~1 (atom_schema_of_rep R))
blanchet@34126
   647
                   (kk_rel_eq (bit_set_from_atom kk T (KK.Var (1, ~1)))
blanchet@34126
   648
                              (KK.Bits i))
blanchet@34124
   649
blanchet@35280
   650
fun kodkod_formula_from_nut ofs
blanchet@33192
   651
        (kk as {kk_all, kk_exist, kk_formula_let, kk_formula_if, kk_or, kk_not,
blanchet@35072
   652
                kk_iff, kk_implies, kk_and, kk_subset, kk_rel_eq, kk_no,
blanchet@39456
   653
                kk_lone, kk_some, kk_rel_let, kk_rel_if, kk_union,
blanchet@35072
   654
                kk_difference, kk_intersect, kk_product, kk_join, kk_closure,
blanchet@35072
   655
                kk_comprehension, kk_project, kk_project_seq, kk_not3,
blanchet@35072
   656
                kk_nat_less, kk_int_less, ...}) u =
blanchet@33192
   657
  let
blanchet@33192
   658
    val main_j0 = offset_of_type ofs bool_T
blanchet@33192
   659
    val bool_j0 = main_j0
blanchet@33192
   660
    val bool_atom_R = Atom (2, main_j0)
blanchet@34126
   661
    val false_atom = KK.Atom bool_j0
blanchet@34126
   662
    val true_atom = KK.Atom (bool_j0 + 1)
blanchet@33192
   663
    fun formula_from_opt_atom polar j0 r =
blanchet@33192
   664
      case polar of
blanchet@34126
   665
        Neg => kk_not (kk_rel_eq r (KK.Atom j0))
blanchet@34126
   666
      | _ => kk_rel_eq r (KK.Atom (j0 + 1))
blanchet@33192
   667
    val formula_from_atom = formula_from_opt_atom Pos
blanchet@33192
   668
    val unpack_formulas =
blanchet@33192
   669
      map (formula_from_atom bool_j0) oo unpack_vect_in_chunks kk 1
blanchet@33192
   670
    fun kk_vect_set_bool_op connective k r1 r2 =
blanchet@33192
   671
      fold1 kk_and (map2 connective (unpack_formulas k r1)
blanchet@33192
   672
                         (unpack_formulas k r2))
blanchet@33192
   673
    fun to_f u =
blanchet@33192
   674
      case rep_of u of
blanchet@33192
   675
        Formula polar =>
blanchet@33192
   676
        (case u of
blanchet@34126
   677
           Cst (False, _, _) => KK.False
blanchet@34126
   678
         | Cst (True, _, _) => KK.True
blanchet@33854
   679
         | Op1 (Not, _, _, u1) =>
blanchet@33854
   680
           kk_not (to_f_with_polarity (flip_polarity polar) u1)
blanchet@33192
   681
         | Op1 (Finite, _, _, u1) =>
blanchet@33192
   682
           let val opt1 = is_opt_rep (rep_of u1) in
blanchet@33192
   683
             case polar of
blanchet@34936
   684
               Neut =>
blanchet@34936
   685
               if opt1 then raise NUT ("Nitpick_Kodkod.to_f (Finite)", [u])
blanchet@34936
   686
               else KK.True
blanchet@33192
   687
             | Pos => formula_for_bool (not opt1)
blanchet@34126
   688
             | Neg => KK.True
blanchet@33192
   689
           end
blanchet@34936
   690
         | Op1 (IsUnknown, _, _, u1) => kk_no (to_r u1)
blanchet@33192
   691
         | Op1 (Cast, _, _, u1) => to_f_with_polarity polar u1
blanchet@33854
   692
         | Op2 (All, _, _, u1, u2) =>
blanchet@33854
   693
           kk_all (untuple to_decl u1) (to_f_with_polarity polar u2)
blanchet@33854
   694
         | Op2 (Exist, _, _, u1, u2) =>
blanchet@33854
   695
           kk_exist (untuple to_decl u1) (to_f_with_polarity polar u2)
blanchet@33854
   696
         | Op2 (Or, _, _, u1, u2) =>
blanchet@33854
   697
           kk_or (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
blanchet@33854
   698
         | Op2 (And, _, _, u1, u2) =>
blanchet@33854
   699
           kk_and (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
blanchet@33192
   700
         | Op2 (Less, T, Formula polar, u1, u2) =>
blanchet@33192
   701
           formula_from_opt_atom polar bool_j0
blanchet@33192
   702
               (to_r (Op2 (Less, T, Opt bool_atom_R, u1, u2)))
blanchet@33192
   703
         | Op2 (Subset, _, _, u1, u2) =>
blanchet@33192
   704
           let
blanchet@33192
   705
             val dom_T = domain_type (type_of u1)
blanchet@33192
   706
             val R1 = rep_of u1
blanchet@33192
   707
             val R2 = rep_of u2
blanchet@33192
   708
             val (dom_R, ran_R) =
blanchet@33192
   709
               case min_rep R1 R2 of
blanchet@38190
   710
                 Func Rp => Rp
blanchet@33192
   711
               | R => (Atom (card_of_domain_from_rep 2 R,
blanchet@33192
   712
                             offset_of_type ofs dom_T),
blanchet@33192
   713
                       if is_opt_rep R then Opt bool_atom_R else Formula Neut)
blanchet@33192
   714
             val set_R = Func (dom_R, ran_R)
blanchet@33192
   715
           in
blanchet@33192
   716
             if not (is_opt_rep ran_R) then
blanchet@33192
   717
               to_set_bool_op kk_implies kk_subset u1 u2
blanchet@33192
   718
             else if polar = Neut then
blanchet@33232
   719
               raise NUT ("Nitpick_Kodkod.to_f (Subset)", [u])
blanchet@33192
   720
             else
blanchet@33192
   721
               let
blanchet@33886
   722
                 (* FIXME: merge with similar code below *)
blanchet@33192
   723
                 fun set_to_r widen u =
blanchet@33192
   724
                   if widen then
blanchet@33192
   725
                     kk_difference (full_rel_for_rep dom_R)
blanchet@33192
   726
                                   (kk_join (to_rep set_R u) false_atom)
blanchet@33192
   727
                   else
blanchet@33192
   728
                     kk_join (to_rep set_R u) true_atom
blanchet@33192
   729
                 val widen1 = (polar = Pos andalso is_opt_rep R1)
blanchet@33192
   730
                 val widen2 = (polar = Neg andalso is_opt_rep R2)
blanchet@33192
   731
               in kk_subset (set_to_r widen1 u1) (set_to_r widen2 u2) end
blanchet@33192
   732
           end
blanchet@33192
   733
         | Op2 (DefEq, _, _, u1, u2) =>
blanchet@33192
   734
           (case min_rep (rep_of u1) (rep_of u2) of
blanchet@38190
   735
              Formula polar =>
blanchet@33192
   736
              kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
blanchet@33192
   737
            | min_R =>
blanchet@33192
   738
              let
blanchet@33192
   739
                fun args (Op2 (Apply, _, _, u1, u2)) = u2 :: args u1
blanchet@33192
   740
                  | args (Tuple (_, _, us)) = us
blanchet@33192
   741
                  | args _ = []
blanchet@33192
   742
                val opt_arg_us = filter (is_opt_rep o rep_of) (args u1)
blanchet@33192
   743
              in
blanchet@34936
   744
                if null opt_arg_us orelse not (is_Opt min_R) orelse
blanchet@34936
   745
                   is_eval_name u1 then
blanchet@33192
   746
                  fold (kk_or o (kk_no o to_r)) opt_arg_us
blanchet@33192
   747
                       (kk_rel_eq (to_rep min_R u1) (to_rep min_R u2))
blanchet@33192
   748
                else
blanchet@34121
   749
                  kk_subset (to_rep min_R u1) (to_rep min_R u2)
blanchet@33192
   750
              end)
blanchet@35280
   751
         | Op2 (Eq, _, _, u1, u2) =>
blanchet@33192
   752
           (case min_rep (rep_of u1) (rep_of u2) of
blanchet@38190
   753
              Formula polar =>
blanchet@33192
   754
              kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
blanchet@33192
   755
            | min_R =>
blanchet@33192
   756
              if is_opt_rep min_R then
blanchet@33192
   757
                if polar = Neut then
blanchet@33192
   758
                  (* continuation of hackish optimization *)
blanchet@33192
   759
                  kk_rel_eq (to_rep min_R u1) (to_rep min_R u2)
blanchet@33192
   760
                else if is_Cst Unrep u1 then
blanchet@33192
   761
                  to_could_be_unrep (polar = Neg) u2
blanchet@33192
   762
                else if is_Cst Unrep u2 then
blanchet@33192
   763
                  to_could_be_unrep (polar = Neg) u1
blanchet@33192
   764
                else
blanchet@33192
   765
                  let
blanchet@33192
   766
                    val r1 = to_rep min_R u1
blanchet@33192
   767
                    val r2 = to_rep min_R u2
blanchet@33192
   768
                    val both_opt = forall (is_opt_rep o rep_of) [u1, u2]
blanchet@33192
   769
                  in
blanchet@33192
   770
                    (if polar = Pos then
blanchet@33192
   771
                       if not both_opt then
blanchet@33192
   772
                         kk_rel_eq r1 r2
blanchet@34936
   773
                       else if is_lone_rep min_R andalso
blanchet@34936
   774
                               arity_of_rep min_R = 1 then
blanchet@33192
   775
                         kk_some (kk_intersect r1 r2)
blanchet@33192
   776
                       else
blanchet@33192
   777
                         raise SAME ()
blanchet@33192
   778
                     else
blanchet@33192
   779
                       if is_lone_rep min_R then
blanchet@33192
   780
                         if arity_of_rep min_R = 1 then
blanchet@35072
   781
                           kk_lone (kk_union r1 r2)
blanchet@33192
   782
                         else if not both_opt then
blanchet@33192
   783
                           (r1, r2) |> is_opt_rep (rep_of u2) ? swap
blanchet@34121
   784
                                    |-> kk_subset
blanchet@33192
   785
                         else
blanchet@33192
   786
                           raise SAME ()
blanchet@33192
   787
                       else
blanchet@33192
   788
                         raise SAME ())
blanchet@33192
   789
                    handle SAME () =>
blanchet@33192
   790
                           formula_from_opt_atom polar bool_j0
blanchet@33192
   791
                               (to_guard [u1, u2] bool_atom_R
blanchet@33192
   792
                                         (rel_expr_from_formula kk bool_atom_R
blanchet@33192
   793
                                                            (kk_rel_eq r1 r2)))
blanchet@33192
   794
                  end
blanchet@33192
   795
              else
blanchet@33192
   796
                let
blanchet@33192
   797
                  val r1 = to_rep min_R u1
blanchet@33192
   798
                  val r2 = to_rep min_R u2
blanchet@33192
   799
                in
blanchet@33192
   800
                  if is_one_rep min_R then
blanchet@33192
   801
                    let
blanchet@33192
   802
                      val rs1 = unpack_products r1
blanchet@33192
   803
                      val rs2 = unpack_products r2
blanchet@33192
   804
                    in
blanchet@34936
   805
                      if length rs1 = length rs2 andalso
blanchet@34936
   806
                         map KK.arity_of_rel_expr rs1
blanchet@34936
   807
                         = map KK.arity_of_rel_expr rs2 then
blanchet@33192
   808
                        fold1 kk_and (map2 kk_subset rs1 rs2)
blanchet@33192
   809
                      else
blanchet@33192
   810
                        kk_subset r1 r2
blanchet@33192
   811
                    end
blanchet@33192
   812
                  else
blanchet@33192
   813
                    kk_rel_eq r1 r2
blanchet@33192
   814
                end)
blanchet@33192
   815
         | Op2 (Apply, T, _, u1, u2) =>
blanchet@33192
   816
           (case (polar, rep_of u1) of
blanchet@33192
   817
              (Neg, Func (R, Formula Neut)) => kk_subset (to_opt R u2) (to_r u1)
blanchet@33192
   818
            | _ =>
blanchet@33192
   819
              to_f_with_polarity polar
blanchet@33192
   820
                 (Op2 (Apply, T, Opt (Atom (2, offset_of_type ofs T)), u1, u2)))
blanchet@33192
   821
         | Op3 (Let, _, _, u1, u2, u3) =>
blanchet@33854
   822
           kk_formula_let [to_expr_assign u1 u2] (to_f_with_polarity polar u3)
blanchet@33192
   823
         | Op3 (If, _, _, u1, u2, u3) =>
blanchet@33854
   824
           kk_formula_if (to_f u1) (to_f_with_polarity polar u2)
blanchet@33854
   825
                         (to_f_with_polarity polar u3)
blanchet@34126
   826
         | FormulaReg (j, _, _) => KK.FormulaReg j
blanchet@33232
   827
         | _ => raise NUT ("Nitpick_Kodkod.to_f", [u]))
blanchet@33192
   828
      | Atom (2, j0) => formula_from_atom j0 (to_r u)
blanchet@33232
   829
      | _ => raise NUT ("Nitpick_Kodkod.to_f", [u])
blanchet@33192
   830
    and to_f_with_polarity polar u =
blanchet@33192
   831
      case rep_of u of
blanchet@33192
   832
        Formula _ => to_f u
blanchet@33192
   833
      | Atom (2, j0) => formula_from_atom j0 (to_r u)
blanchet@33192
   834
      | Opt (Atom (2, j0)) => formula_from_opt_atom polar j0 (to_r u)
blanchet@33232
   835
      | _ => raise NUT ("Nitpick_Kodkod.to_f_with_polarity", [u])
blanchet@33192
   836
    and to_r u =
blanchet@33192
   837
      case u of
blanchet@33192
   838
        Cst (False, _, Atom _) => false_atom
blanchet@33192
   839
      | Cst (True, _, Atom _) => true_atom
blanchet@35280
   840
      | Cst (Iden, _, Func (Struct [R1, R2], Formula Neut)) =>
blanchet@33192
   841
        if R1 = R2 andalso arity_of_rep R1 = 1 then
blanchet@34126
   842
          kk_intersect KK.Iden (kk_product (full_rel_for_rep R1) KK.Univ)
blanchet@33192
   843
        else
blanchet@33192
   844
          let
blanchet@33192
   845
            val schema1 = atom_schema_of_rep R1
blanchet@33192
   846
            val schema2 = atom_schema_of_rep R2
blanchet@33192
   847
            val arity1 = length schema1
blanchet@33192
   848
            val arity2 = length schema2
blanchet@33192
   849
            val r1 = fold1 kk_product (unary_var_seq 0 arity1)
blanchet@33192
   850
            val r2 = fold1 kk_product (unary_var_seq arity1 arity2)
blanchet@33192
   851
            val min_R = min_rep R1 R2
blanchet@33192
   852
          in
blanchet@33192
   853
            kk_comprehension
blanchet@33192
   854
                (decls_for_atom_schema 0 (schema1 @ schema2))
blanchet@33192
   855
                (kk_rel_eq (rel_expr_from_rel_expr kk min_R R1 r1)
blanchet@33192
   856
                           (rel_expr_from_rel_expr kk min_R R2 r2))
blanchet@33192
   857
          end
blanchet@35280
   858
      | Cst (Iden, _, Func (Atom (1, j0), Formula Neut)) => KK.Atom j0
blanchet@35665
   859
      | Cst (Iden, T as Type (@{type_name fun}, [T1, _]), R as Func (R1, _)) =>
blanchet@33192
   860
        to_rep R (Cst (Iden, T, Func (one_rep ofs T1 R1, Formula Neut)))
blanchet@34124
   861
      | Cst (Num j, T, R) =>
blanchet@34124
   862
        if is_word_type T then
blanchet@34126
   863
          atom_from_int_expr kk T R (KK.Num j)
blanchet@34124
   864
        else if T = int_T then
blanchet@34124
   865
          case atom_for_int (card_of_rep R, offset_of_type ofs int_T) j of
blanchet@34126
   866
            ~1 => if is_opt_rep R then KK.None
blanchet@33232
   867
                  else raise NUT ("Nitpick_Kodkod.to_r (Num)", [u])
blanchet@34126
   868
          | j' => KK.Atom j'
blanchet@34124
   869
        else
blanchet@34126
   870
          if j < card_of_rep R then KK.Atom (j + offset_of_type ofs T)
blanchet@34126
   871
          else if is_opt_rep R then KK.None
blanchet@34124
   872
          else raise NUT ("Nitpick_Kodkod.to_r (Num)", [u])
blanchet@33192
   873
      | Cst (Unknown, _, R) => empty_rel_for_rep R
blanchet@33192
   874
      | Cst (Unrep, _, R) => empty_rel_for_rep R
blanchet@34126
   875
      | Cst (Suc, T as @{typ "unsigned_bit word => unsigned_bit word"}, R) =>
blanchet@34126
   876
        to_bit_word_unary_op T R (curry KK.Add (KK.Num 1))
blanchet@34126
   877
      | Cst (Suc, @{typ "nat => nat"}, Func (Atom x, _)) =>
blanchet@34126
   878
        kk_intersect (KK.Rel suc_rel) (kk_product KK.Univ (KK.AtomSeq x))
blanchet@35280
   879
      | Cst (Suc, _, Func (Atom _, _)) => KK.Rel suc_rel
blanchet@35665
   880
      | Cst (Add, Type (_, [@{typ nat}, _]), _) => KK.Rel nat_add_rel
blanchet@35665
   881
      | Cst (Add, Type (_, [@{typ int}, _]), _) => KK.Rel int_add_rel
blanchet@35665
   882
      | Cst (Add, T as Type (_, [@{typ "unsigned_bit word"}, _]), R) =>
blanchet@34126
   883
        to_bit_word_binary_op T R NONE (SOME (curry KK.Add))
blanchet@35665
   884
      | Cst (Add, T as Type (_, [@{typ "signed_bit word"}, _]), R) =>
blanchet@34124
   885
        to_bit_word_binary_op T R
blanchet@34124
   886
            (SOME (fn i1 => fn i2 => fn i3 =>
blanchet@34126
   887
                 kk_implies (KK.LE (KK.Num 0, KK.BitXor (i1, i2)))
blanchet@34126
   888
                            (KK.LE (KK.Num 0, KK.BitXor (i2, i3)))))
blanchet@34126
   889
            (SOME (curry KK.Add))
blanchet@35665
   890
      | Cst (Subtract, Type (_, [@{typ nat}, _]), _) =>
blanchet@34126
   891
        KK.Rel nat_subtract_rel
blanchet@35665
   892
      | Cst (Subtract, Type (_, [@{typ int}, _]), _) =>
blanchet@34126
   893
        KK.Rel int_subtract_rel
blanchet@35665
   894
      | Cst (Subtract, T as Type (_, [@{typ "unsigned_bit word"}, _]), R) =>
blanchet@34124
   895
        to_bit_word_binary_op T R NONE
blanchet@34124
   896
            (SOME (fn i1 => fn i2 =>
blanchet@34126
   897
                      KK.IntIf (KK.LE (i1, i2), KK.Num 0, KK.Sub (i1, i2))))
blanchet@35665
   898
      | Cst (Subtract, T as Type (_, [@{typ "signed_bit word"}, _]), R) =>
blanchet@34124
   899
        to_bit_word_binary_op T R
blanchet@34124
   900
            (SOME (fn i1 => fn i2 => fn i3 =>
blanchet@34126
   901
                 kk_implies (KK.LT (KK.BitXor (i1, i2), KK.Num 0))
blanchet@34126
   902
                            (KK.LT (KK.BitXor (i2, i3), KK.Num 0))))
blanchet@34126
   903
            (SOME (curry KK.Sub))
blanchet@35665
   904
      | Cst (Multiply, Type (_, [@{typ nat}, _]), _) =>
blanchet@34126
   905
        KK.Rel nat_multiply_rel
blanchet@35665
   906
      | Cst (Multiply, Type (_, [@{typ int}, _]), _) =>
blanchet@34126
   907
        KK.Rel int_multiply_rel
blanchet@34124
   908
      | Cst (Multiply,
blanchet@35665
   909
             T as Type (_, [Type (@{type_name word}, [bit_T]), _]), R) =>
blanchet@34124
   910
        to_bit_word_binary_op T R
blanchet@34124
   911
            (SOME (fn i1 => fn i2 => fn i3 =>
blanchet@34126
   912
                kk_or (KK.IntEq (i2, KK.Num 0))
blanchet@34126
   913
                      (KK.IntEq (KK.Div (i3, i2), i1)
blanchet@34124
   914
                       |> bit_T = @{typ signed_bit}
blanchet@34126
   915
                          ? kk_and (KK.LE (KK.Num 0,
blanchet@34126
   916
                                           foldl1 KK.BitAnd [i1, i2, i3])))))
blanchet@34126
   917
            (SOME (curry KK.Mult))
blanchet@35665
   918
      | Cst (Divide, Type (_, [@{typ nat}, _]), _) => KK.Rel nat_divide_rel
blanchet@35665
   919
      | Cst (Divide, Type (_, [@{typ int}, _]), _) => KK.Rel int_divide_rel
blanchet@35665
   920
      | Cst (Divide, T as Type (_, [@{typ "unsigned_bit word"}, _]), R) =>
blanchet@34124
   921
        to_bit_word_binary_op T R NONE
blanchet@34124
   922
            (SOME (fn i1 => fn i2 =>
blanchet@34126
   923
                      KK.IntIf (KK.IntEq (i2, KK.Num 0),
blanchet@34126
   924
                                KK.Num 0, KK.Div (i1, i2))))
blanchet@35665
   925
      | Cst (Divide, T as Type (_, [@{typ "signed_bit word"}, _]), R) =>
blanchet@34124
   926
        to_bit_word_binary_op T R
blanchet@34124
   927
            (SOME (fn i1 => fn i2 => fn i3 =>
blanchet@34126
   928
                      KK.LE (KK.Num 0, foldl1 KK.BitAnd [i1, i2, i3])))
blanchet@34124
   929
            (SOME (fn i1 => fn i2 =>
blanchet@34126
   930
                 KK.IntIf (kk_and (KK.LT (i1, KK.Num 0))
blanchet@34126
   931
                                  (KK.LT (KK.Num 0, i2)),
blanchet@34126
   932
                     KK.Sub (KK.Div (KK.Add (i1, KK.Num 1), i2), KK.Num 1),
blanchet@34126
   933
                     KK.IntIf (kk_and (KK.LT (KK.Num 0, i1))
blanchet@34126
   934
                                      (KK.LT (i2, KK.Num 0)),
blanchet@34126
   935
                         KK.Sub (KK.Div (KK.Sub (i1, KK.Num 1), i2), KK.Num 1),
blanchet@34126
   936
                         KK.IntIf (KK.IntEq (i2, KK.Num 0),
blanchet@34126
   937
                                   KK.Num 0, KK.Div (i1, i2))))))
blanchet@34126
   938
      | Cst (Gcd, _, _) => KK.Rel gcd_rel
blanchet@34126
   939
      | Cst (Lcm, _, _) => KK.Rel lcm_rel
blanchet@34126
   940
      | Cst (Fracs, _, Func (Atom (1, _), _)) => KK.None
blanchet@33192
   941
      | Cst (Fracs, _, Func (Struct _, _)) =>
blanchet@34126
   942
        kk_project_seq (KK.Rel norm_frac_rel) 2 2
blanchet@34126
   943
      | Cst (NormFrac, _, _) => KK.Rel norm_frac_rel
blanchet@35665
   944
      | Cst (NatToInt, Type (_, [@{typ nat}, _]), Func (Atom _, Atom _)) =>
blanchet@34126
   945
        KK.Iden
blanchet@35665
   946
      | Cst (NatToInt, Type (_, [@{typ nat}, _]),
blanchet@35280
   947
             Func (Atom (_, nat_j0), Opt (Atom (int_k, int_j0)))) =>
blanchet@33192
   948
        if nat_j0 = int_j0 then
blanchet@34126
   949
          kk_intersect KK.Iden
blanchet@34126
   950
              (kk_product (KK.AtomSeq (max_int_for_card int_k + 1, nat_j0))
blanchet@34126
   951
                          KK.Univ)
blanchet@33192
   952
        else
blanchet@33232
   953
          raise BAD ("Nitpick_Kodkod.to_r (NatToInt)", "\"nat_j0 <> int_j0\"")
blanchet@35665
   954
      | Cst (NatToInt, T as Type (_, [@{typ "unsigned_bit word"}, _]), R) =>
blanchet@34124
   955
        to_bit_word_unary_op T R I
blanchet@35665
   956
      | Cst (IntToNat, Type (_, [@{typ int}, _]),
blanchet@34124
   957
             Func (Atom (int_k, int_j0), nat_R)) =>
blanchet@33192
   958
        let
blanchet@33192
   959
          val abs_card = max_int_for_card int_k + 1
blanchet@33192
   960
          val (nat_k, nat_j0) = the_single (atom_schema_of_rep nat_R)
blanchet@33192
   961
          val overlap = Int.min (nat_k, abs_card)
blanchet@33192
   962
        in
blanchet@33192
   963
          if nat_j0 = int_j0 then
blanchet@34126
   964
            kk_union (kk_product (KK.AtomSeq (int_k - abs_card,
blanchet@34126
   965
                                              int_j0 + abs_card))
blanchet@34126
   966
                                 (KK.Atom nat_j0))
blanchet@34126
   967
                     (kk_intersect KK.Iden
blanchet@34126
   968
                          (kk_product (KK.AtomSeq (overlap, int_j0)) KK.Univ))
blanchet@33192
   969
          else
blanchet@33232
   970
            raise BAD ("Nitpick_Kodkod.to_r (IntToNat)", "\"nat_j0 <> int_j0\"")
blanchet@33192
   971
        end
blanchet@35665
   972
      | Cst (IntToNat, T as Type (_, [@{typ "signed_bit word"}, _]), R) =>
blanchet@34124
   973
        to_bit_word_unary_op T R
blanchet@34126
   974
            (fn i => KK.IntIf (KK.LE (i, KK.Num 0), KK.Num 0, i))
blanchet@33192
   975
      | Op1 (Not, _, R, u1) => kk_not3 (to_rep R u1)
blanchet@34126
   976
      | Op1 (Finite, _, Opt (Atom _), _) => KK.None
blanchet@33192
   977
      | Op1 (Converse, T, R, u1) =>
blanchet@33192
   978
        let
blanchet@33192
   979
          val (b_T, a_T) = HOLogic.dest_prodT (domain_type T)
blanchet@33192
   980
          val (b_R, a_R) =
blanchet@33192
   981
            case R of
blanchet@33192
   982
              Func (Struct [R1, R2], _) => (R1, R2)
blanchet@33192
   983
            | Func (R1, _) =>
blanchet@33192
   984
              if card_of_rep R1 <> 1 then
blanchet@33232
   985
                raise REP ("Nitpick_Kodkod.to_r (Converse)", [R])
blanchet@33192
   986
              else
blanchet@33192
   987
                pairself (Atom o pair 1 o offset_of_type ofs) (b_T, a_T)
blanchet@33232
   988
            | _ => raise REP ("Nitpick_Kodkod.to_r (Converse)", [R])
blanchet@33192
   989
          val body_R = body_rep R
blanchet@33192
   990
          val a_arity = arity_of_rep a_R
blanchet@33192
   991
          val b_arity = arity_of_rep b_R
blanchet@33192
   992
          val ab_arity = a_arity + b_arity
blanchet@33192
   993
          val body_arity = arity_of_rep body_R
blanchet@33192
   994
        in
blanchet@33192
   995
          kk_project (to_rep (Func (Struct [a_R, b_R], body_R)) u1)
blanchet@34126
   996
                     (map KK.Num (index_seq a_arity b_arity @
blanchet@34126
   997
                                  index_seq 0 a_arity @
blanchet@34126
   998
                                  index_seq ab_arity body_arity))
blanchet@33192
   999
          |> rel_expr_from_rel_expr kk R (Func (Struct [b_R, a_R], body_R))
blanchet@33192
  1000
        end
blanchet@33192
  1001
      | Op1 (Closure, _, R, u1) =>
blanchet@33192
  1002
        if is_opt_rep R then
blanchet@33192
  1003
          let
blanchet@33192
  1004
            val T1 = type_of u1
blanchet@33192
  1005
            val R' = rep_to_binary_rel_rep ofs T1 (unopt_rep (rep_of u1))
blanchet@33192
  1006
            val R'' = opt_rep ofs T1 R'
blanchet@33192
  1007
          in
blanchet@34124
  1008
            single_rel_rel_let kk
blanchet@33192
  1009
                (fn r =>
blanchet@33192
  1010
                    let
blanchet@33192
  1011
                      val true_r = kk_closure (kk_join r true_atom)
blanchet@33192
  1012
                      val full_r = full_rel_for_rep R'
blanchet@33192
  1013
                      val false_r = kk_difference full_r
blanchet@33192
  1014
                                        (kk_closure (kk_difference full_r
blanchet@33192
  1015
                                                        (kk_join r false_atom)))
blanchet@33192
  1016
                    in
blanchet@33192
  1017
                      rel_expr_from_rel_expr kk R R''
blanchet@33192
  1018
                          (kk_union (kk_product true_r true_atom)
blanchet@33192
  1019
                                    (kk_product false_r false_atom))
blanchet@33192
  1020
                    end) (to_rep R'' u1)
blanchet@33192
  1021
          end
blanchet@33192
  1022
        else
blanchet@33192
  1023
          let val R' = rep_to_binary_rel_rep ofs (type_of u1) (rep_of u1) in
blanchet@33192
  1024
            rel_expr_from_rel_expr kk R R' (kk_closure (to_rep R' u1))
blanchet@33192
  1025
          end
blanchet@33192
  1026
      | Op1 (SingletonSet, _, Func (R1, Opt _), Cst (Unrep, _, _)) =>
blanchet@38190
  1027
        kk_product (full_rel_for_rep R1) false_atom
blanchet@33192
  1028
      | Op1 (SingletonSet, _, R, u1) =>
blanchet@33192
  1029
        (case R of
blanchet@33192
  1030
           Func (R1, Formula Neut) => to_rep R1 u1
blanchet@35280
  1031
         | Func (R1, Opt _) =>
blanchet@34124
  1032
           single_rel_rel_let kk
blanchet@33192
  1033
               (fn r => kk_rel_if (kk_no r) (empty_rel_for_rep R)
blanchet@33192
  1034
                            (rel_expr_to_func kk R1 bool_atom_R
blanchet@33192
  1035
                                              (Func (R1, Formula Neut)) r))
blanchet@33192
  1036
               (to_opt R1 u1)
blanchet@33232
  1037
         | _ => raise NUT ("Nitpick_Kodkod.to_r (SingletonSet)", [u]))
blanchet@35671
  1038
      | Op1 (SafeThe, _, R, u1) =>
blanchet@33192
  1039
        if is_opt_rep R then
blanchet@33192
  1040
          kk_join (to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1) true_atom
blanchet@33192
  1041
        else
blanchet@33192
  1042
          to_rep (Func (R, Formula Neut)) u1
blanchet@39345
  1043
      | Op1 (First, _, R, u1) => to_nth_pair_sel 0 R u1
blanchet@39345
  1044
      | Op1 (Second, _, R, u1) => to_nth_pair_sel 1 R u1
blanchet@33192
  1045
      | Op1 (Cast, _, R, u1) =>
blanchet@33192
  1046
        ((case rep_of u1 of
blanchet@33192
  1047
            Formula _ =>
blanchet@33192
  1048
            (case unopt_rep R of
blanchet@33192
  1049
               Atom (2, j0) => atom_from_formula kk j0 (to_f u1)
blanchet@33192
  1050
             | _ => raise SAME ())
blanchet@33192
  1051
          | _ => raise SAME ())
blanchet@33192
  1052
         handle SAME () => rel_expr_from_rel_expr kk R (rep_of u1) (to_r u1))
blanchet@33192
  1053
      | Op2 (All, T, R as Opt _, u1, u2) =>
blanchet@33192
  1054
        to_r (Op1 (Not, T, R,
blanchet@33192
  1055
                   Op2 (Exist, T, R, u1, Op1 (Not, T, rep_of u2, u2))))
blanchet@35280
  1056
      | Op2 (Exist, _, Opt _, u1, u2) =>
blanchet@33192
  1057
        let val rs1 = untuple to_decl u1 in
blanchet@33192
  1058
          if not (is_opt_rep (rep_of u2)) then
blanchet@34126
  1059
            kk_rel_if (kk_exist rs1 (to_f u2)) true_atom KK.None
blanchet@33192
  1060
          else
blanchet@33192
  1061
            let val r2 = to_r u2 in
blanchet@33192
  1062
              kk_union (kk_rel_if (kk_exist rs1 (kk_rel_eq r2 true_atom))
blanchet@34126
  1063
                                  true_atom KK.None)
blanchet@33192
  1064
                       (kk_rel_if (kk_all rs1 (kk_rel_eq r2 false_atom))
blanchet@34126
  1065
                                  false_atom KK.None)
blanchet@33192
  1066
            end
blanchet@33192
  1067
        end
blanchet@33192
  1068
      | Op2 (Or, _, _, u1, u2) =>
blanchet@33192
  1069
        if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) true_atom (to_r u1)
blanchet@33192
  1070
        else kk_rel_if (to_f u1) true_atom (to_r u2)
blanchet@33192
  1071
      | Op2 (And, _, _, u1, u2) =>
blanchet@33192
  1072
        if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) (to_r u1) false_atom
blanchet@33192
  1073
        else kk_rel_if (to_f u1) (to_r u2) false_atom
blanchet@33192
  1074
      | Op2 (Less, _, _, u1, u2) =>
blanchet@34124
  1075
        (case type_of u1 of
blanchet@34124
  1076
           @{typ nat} =>
blanchet@34124
  1077
           if is_Cst Unrep u1 then to_compare_with_unrep u2 false_atom
blanchet@34124
  1078
           else if is_Cst Unrep u2 then to_compare_with_unrep u1 true_atom
blanchet@34124
  1079
           else kk_nat_less (to_integer u1) (to_integer u2)
blanchet@34124
  1080
         | @{typ int} => kk_int_less (to_integer u1) (to_integer u2)
blanchet@36127
  1081
         | _ =>
blanchet@36127
  1082
           let
blanchet@36127
  1083
             val R1 = Opt (Atom (card_of_rep (rep_of u1),
blanchet@36127
  1084
                                 offset_of_type ofs (type_of u1)))
blanchet@36127
  1085
           in
blanchet@36127
  1086
             double_rel_rel_let kk
blanchet@36127
  1087
                 (fn r1 => fn r2 =>
blanchet@36127
  1088
                     kk_rel_if
blanchet@36127
  1089
                         (fold kk_and (map_filter (fn (u, r) =>
blanchet@36127
  1090
                              if is_opt_rep (rep_of u) then SOME (kk_some r)
blanchet@36127
  1091
                              else NONE) [(u1, r1), (u2, r2)]) KK.True)
blanchet@36127
  1092
                         (atom_from_formula kk bool_j0 (KK.LT (pairself
blanchet@36127
  1093
                             (int_expr_from_atom kk (type_of u1)) (r1, r2))))
blanchet@36127
  1094
                         KK.None)
blanchet@36127
  1095
                 (to_rep R1 u1) (to_rep R1 u2)
blanchet@36127
  1096
            end)
blanchet@35280
  1097
      | Op2 (Triad, _, Opt (Atom (2, j0)), u1, u2) =>
blanchet@33192
  1098
        let
blanchet@33192
  1099
          val f1 = to_f u1
blanchet@33192
  1100
          val f2 = to_f u2
blanchet@33192
  1101
        in
blanchet@33192
  1102
          if f1 = f2 then
blanchet@33192
  1103
            atom_from_formula kk j0 f1
blanchet@33192
  1104
          else
blanchet@34126
  1105
            kk_union (kk_rel_if f1 true_atom KK.None)
blanchet@34126
  1106
                     (kk_rel_if f2 KK.None false_atom)
blanchet@33192
  1107
        end
blanchet@33192
  1108
      | Op2 (Composition, _, R, u1, u2) =>
blanchet@33192
  1109
        let
blanchet@33863
  1110
          val (a_T, b_T) = HOLogic.dest_prodT (domain_type (type_of u1))
blanchet@33863
  1111
          val (_, c_T) = HOLogic.dest_prodT (domain_type (type_of u2))
blanchet@33863
  1112
          val ab_k = card_of_domain_from_rep 2 (rep_of u1)
blanchet@33863
  1113
          val bc_k = card_of_domain_from_rep 2 (rep_of u2)
blanchet@33192
  1114
          val ac_k = card_of_domain_from_rep 2 R
blanchet@33192
  1115
          val a_k = exact_root 2 (ac_k * ab_k div bc_k)
blanchet@33192
  1116
          val b_k = exact_root 2 (ab_k * bc_k div ac_k)
blanchet@33192
  1117
          val c_k = exact_root 2 (bc_k * ac_k div ab_k)
blanchet@33192
  1118
          val a_R = Atom (a_k, offset_of_type ofs a_T)
blanchet@33192
  1119
          val b_R = Atom (b_k, offset_of_type ofs b_T)
blanchet@33192
  1120
          val c_R = Atom (c_k, offset_of_type ofs c_T)
blanchet@33192
  1121
          val body_R = body_rep R
blanchet@33192
  1122
        in
blanchet@33192
  1123
          (case body_R of
blanchet@33192
  1124
             Formula Neut =>
blanchet@33863
  1125
             kk_join (to_rep (Func (Struct [a_R, b_R], Formula Neut)) u1)
blanchet@33863
  1126
                     (to_rep (Func (Struct [b_R, c_R], Formula Neut)) u2)
blanchet@33192
  1127
           | Opt (Atom (2, _)) =>
blanchet@33192
  1128
             let
blanchet@33886
  1129
               (* FIXME: merge with similar code above *)
blanchet@33886
  1130
               fun must R1 R2 u =
blanchet@33886
  1131
                 kk_join (to_rep (Func (Struct [R1, R2], body_R)) u) true_atom
blanchet@33886
  1132
               fun may R1 R2 u =
blanchet@33886
  1133
                 kk_difference
blanchet@33886
  1134
                     (full_rel_for_rep (Struct [R1, R2]))
blanchet@33886
  1135
                     (kk_join (to_rep (Func (Struct [R1, R2], body_R)) u)
blanchet@33886
  1136
                              false_atom)
blanchet@33886
  1137
             in
blanchet@33886
  1138
               kk_union
blanchet@33886
  1139
                   (kk_product (kk_join (must a_R b_R u1) (must b_R c_R u2))
blanchet@33886
  1140
                               true_atom)
blanchet@33886
  1141
                   (kk_product (kk_difference
blanchet@33886
  1142
                                   (full_rel_for_rep (Struct [a_R, c_R]))
blanchet@33886
  1143
                                   (kk_join (may a_R b_R u1) (may b_R c_R u2)))
blanchet@33886
  1144
                               false_atom)
blanchet@33886
  1145
             end
blanchet@33232
  1146
           | _ => raise NUT ("Nitpick_Kodkod.to_r (Composition)", [u]))
blanchet@33192
  1147
          |> rel_expr_from_rel_expr kk R (Func (Struct [a_R, c_R], body_R))
blanchet@33192
  1148
        end
blanchet@33192
  1149
      | Op2 (Apply, @{typ nat}, _,
blanchet@33192
  1150
             Op2 (Apply, _, _, Cst (Subtract, _, _), u1), u2) =>
blanchet@33192
  1151
        if is_Cst Unrep u2 andalso not (is_opt_rep (rep_of u1)) then
blanchet@34126
  1152
          KK.Atom (offset_of_type ofs nat_T)
blanchet@33192
  1153
        else
blanchet@34126
  1154
          fold kk_join (map to_integer [u1, u2]) (KK.Rel nat_subtract_rel)
blanchet@35312
  1155
      | Op2 (Apply, _, R, u1, u2) => to_apply R u1 u2
blanchet@35280
  1156
      | Op2 (Lambda, _, R as Opt (Atom (1, j0)), u1, u2) =>
blanchet@34126
  1157
        to_guard [u1, u2] R (KK.Atom j0)
blanchet@35280
  1158
      | Op2 (Lambda, _, Func (_, Formula Neut), u1, u2) =>
blanchet@33192
  1159
        kk_comprehension (untuple to_decl u1) (to_f u2)
blanchet@35280
  1160
      | Op2 (Lambda, _, Func (_, R2), u1, u2) =>
blanchet@33192
  1161
        let
blanchet@33192
  1162
          val dom_decls = untuple to_decl u1
blanchet@33192
  1163
          val ran_schema = atom_schema_of_rep R2
blanchet@33192
  1164
          val ran_decls = decls_for_atom_schema ~1 ran_schema
blanchet@33192
  1165
          val ran_vars = unary_var_seq ~1 (length ran_decls)
blanchet@33192
  1166
        in
blanchet@33192
  1167
          kk_comprehension (dom_decls @ ran_decls)
blanchet@33192
  1168
                           (kk_subset (fold1 kk_product ran_vars)
blanchet@33192
  1169
                                      (to_rep R2 u2))
blanchet@33192
  1170
        end
blanchet@33192
  1171
      | Op3 (Let, _, R, u1, u2, u3) =>
blanchet@33192
  1172
        kk_rel_let [to_expr_assign u1 u2] (to_rep R u3)
blanchet@33192
  1173
      | Op3 (If, _, R, u1, u2, u3) =>
blanchet@33192
  1174
        if is_opt_rep (rep_of u1) then
blanchet@35386
  1175
          triple_rel_rel_let kk
blanchet@33192
  1176
              (fn r1 => fn r2 => fn r3 =>
blanchet@33192
  1177
                  let val empty_r = empty_rel_for_rep R in
blanchet@33192
  1178
                    fold1 kk_union
blanchet@33192
  1179
                          [kk_rel_if (kk_rel_eq r1 true_atom) r2 empty_r,
blanchet@33192
  1180
                           kk_rel_if (kk_rel_eq r1 false_atom) r3 empty_r,
blanchet@33192
  1181
                           kk_rel_if (kk_rel_eq r2 r3)
blanchet@33192
  1182
                                (if inline_rel_expr r2 then r2 else r3) empty_r]
blanchet@33192
  1183
                  end)
blanchet@33192
  1184
              (to_r u1) (to_rep R u2) (to_rep R u3)
blanchet@33192
  1185
        else
blanchet@33192
  1186
          kk_rel_if (to_f u1) (to_rep R u2) (to_rep R u3)
blanchet@33192
  1187
      | Tuple (_, R, us) =>
blanchet@33192
  1188
        (case unopt_rep R of
blanchet@33192
  1189
           Struct Rs => to_product Rs us
blanchet@33192
  1190
         | Vect (k, R) => to_product (replicate k R) us
blanchet@33192
  1191
         | Atom (1, j0) =>
blanchet@38190
  1192
           kk_rel_if (kk_some (fold1 kk_product (map to_r us)))
blanchet@38190
  1193
                     (KK.Atom j0) KK.None
blanchet@33232
  1194
         | _ => raise NUT ("Nitpick_Kodkod.to_r (Tuple)", [u]))
blanchet@33192
  1195
      | Construct ([u'], _, _, []) => to_r u'
blanchet@35280
  1196
      | Construct (discr_u :: sel_us, _, _, arg_us) =>
blanchet@33192
  1197
        let
blanchet@33192
  1198
          val set_rs =
blanchet@33192
  1199
            map2 (fn sel_u => fn arg_u =>
blanchet@33192
  1200
                     let
blanchet@33192
  1201
                       val (R1, R2) = dest_Func (rep_of sel_u)
blanchet@33192
  1202
                       val sel_r = to_r sel_u
blanchet@33192
  1203
                       val arg_r = to_opt R2 arg_u
blanchet@33192
  1204
                     in
blanchet@33192
  1205
                       if is_one_rep R2 then
blanchet@33192
  1206
                         kk_n_fold_join kk true R2 R1 arg_r
blanchet@33192
  1207
                              (kk_project sel_r (flip_nums (arity_of_rep R2)))
blanchet@33192
  1208
                       else
blanchet@34288
  1209
                         kk_comprehension [KK.DeclOne ((1, ~1), to_r discr_u)]
blanchet@34126
  1210
                             (kk_rel_eq (kk_join (KK.Var (1, ~1)) sel_r) arg_r)
blanchet@35695
  1211
                         |> is_opt_rep (rep_of arg_u) ? to_guard [arg_u] R1
blanchet@33192
  1212
                     end) sel_us arg_us
blanchet@33192
  1213
        in fold1 kk_intersect set_rs end
blanchet@34126
  1214
      | BoundRel (x, _, _, _) => KK.Var x
blanchet@34126
  1215
      | FreeRel (x, _, _, _) => KK.Rel x
blanchet@34126
  1216
      | RelReg (j, _, R) => KK.RelReg (arity_of_rep R, j)
blanchet@33232
  1217
      | u => raise NUT ("Nitpick_Kodkod.to_r", [u])
blanchet@33192
  1218
    and to_decl (BoundRel (x, _, R, _)) =
blanchet@34126
  1219
        KK.DeclOne (x, KK.AtomSeq (the_single (atom_schema_of_rep R)))
blanchet@33232
  1220
      | to_decl u = raise NUT ("Nitpick_Kodkod.to_decl", [u])
blanchet@35280
  1221
    and to_expr_assign (FormulaReg (j, _, _)) u =
blanchet@34126
  1222
        KK.AssignFormulaReg (j, to_f u)
blanchet@33192
  1223
      | to_expr_assign (RelReg (j, _, R)) u =
blanchet@34126
  1224
        KK.AssignRelReg ((arity_of_rep R, j), to_r u)
blanchet@33232
  1225
      | to_expr_assign u1 _ = raise NUT ("Nitpick_Kodkod.to_expr_assign", [u1])
blanchet@39345
  1226
    and to_atom (x as (_, j0)) u =
blanchet@33192
  1227
      case rep_of u of
blanchet@33192
  1228
        Formula _ => atom_from_formula kk j0 (to_f u)
blanchet@33192
  1229
      | R => atom_from_rel_expr kk x R (to_r u)
blanchet@38190
  1230
    and to_struct Rs u = struct_from_rel_expr kk Rs (rep_of u) (to_r u)
blanchet@38190
  1231
    and to_vect k R u = vect_from_rel_expr kk k R (rep_of u) (to_r u)
blanchet@38190
  1232
    and to_func R1 R2 u = rel_expr_to_func kk R1 R2 (rep_of u) (to_r u)
blanchet@33192
  1233
    and to_opt R u =
blanchet@33192
  1234
      let val old_R = rep_of u in
blanchet@33192
  1235
        if is_opt_rep old_R then
blanchet@33192
  1236
          rel_expr_from_rel_expr kk (Opt R) old_R (to_r u)
blanchet@33192
  1237
        else
blanchet@33192
  1238
          to_rep R u
blanchet@33192
  1239
      end
blanchet@33192
  1240
    and to_rep (Atom x) u = to_atom x u
blanchet@33192
  1241
      | to_rep (Struct Rs) u = to_struct Rs u
blanchet@33192
  1242
      | to_rep (Vect (k, R)) u = to_vect k R u
blanchet@33192
  1243
      | to_rep (Func (R1, R2)) u = to_func R1 R2 u
blanchet@33192
  1244
      | to_rep (Opt R) u = to_opt R u
blanchet@33232
  1245
      | to_rep R _ = raise REP ("Nitpick_Kodkod.to_rep", [R])
blanchet@33192
  1246
    and to_integer u = to_opt (one_rep ofs (type_of u) (rep_of u)) u
blanchet@33192
  1247
    and to_guard guard_us R r =
blanchet@33192
  1248
      let
blanchet@33192
  1249
        val unpacked_rs = unpack_joins r
blanchet@33192
  1250
        val plain_guard_rs =
blanchet@33192
  1251
          map to_r (filter (is_Opt o rep_of) guard_us)
blanchet@33192
  1252
          |> filter_out (member (op =) unpacked_rs)
blanchet@33192
  1253
        val func_guard_us =
blanchet@33192
  1254
          filter ((is_Func andf is_opt_rep) o rep_of) guard_us
blanchet@33192
  1255
        val func_guard_rs = map to_r func_guard_us
blanchet@33192
  1256
        val guard_fs =
blanchet@33192
  1257
          map kk_no plain_guard_rs @
blanchet@33192
  1258
          map2 (kk_not oo kk_n_ary_function kk)
blanchet@33192
  1259
               (map (unopt_rep o rep_of) func_guard_us) func_guard_rs
blanchet@33192
  1260
      in
blanchet@35695
  1261
        if null guard_fs then r
blanchet@35695
  1262
        else kk_rel_if (fold1 kk_or guard_fs) (empty_rel_for_rep R) r
blanchet@33192
  1263
      end
blanchet@33192
  1264
    and to_project new_R old_R r j0 =
blanchet@33192
  1265
      rel_expr_from_rel_expr kk new_R old_R
blanchet@33192
  1266
                             (kk_project_seq r j0 (arity_of_rep old_R))
blanchet@38190
  1267
    and to_product Rs us = fold1 kk_product (map (uncurry to_opt) (Rs ~~ us))
blanchet@39345
  1268
    and to_nth_pair_sel n res_R u =
blanchet@33192
  1269
      case u of
blanchet@33192
  1270
        Tuple (_, _, us) => to_rep res_R (nth us n)
blanchet@33192
  1271
      | _ => let
blanchet@33192
  1272
               val R = rep_of u
blanchet@33192
  1273
               val (a_T, b_T) = HOLogic.dest_prodT (type_of u)
blanchet@33192
  1274
               val Rs =
blanchet@33192
  1275
                 case unopt_rep R of
blanchet@33192
  1276
                   Struct (Rs as [_, _]) => Rs
blanchet@33192
  1277
                 | _ =>
blanchet@33192
  1278
                   let
blanchet@33192
  1279
                     val res_card = card_of_rep res_R
blanchet@33192
  1280
                     val other_card = card_of_rep R div res_card
blanchet@33192
  1281
                     val (a_card, b_card) = (res_card, other_card)
blanchet@33192
  1282
                                            |> n = 1 ? swap
blanchet@33192
  1283
                   in
blanchet@33192
  1284
                     [Atom (a_card, offset_of_type ofs a_T),
blanchet@33192
  1285
                      Atom (b_card, offset_of_type ofs b_T)]
blanchet@33192
  1286
                   end
blanchet@33192
  1287
               val nth_R = nth Rs n
blanchet@33192
  1288
               val j0 = if n = 0 then 0 else arity_of_rep (hd Rs)
blanchet@38190
  1289
             in to_project res_R nth_R (to_rep (Opt (Struct Rs)) u) j0 end
blanchet@33192
  1290
    and to_set_bool_op connective set_oper u1 u2 =
blanchet@33192
  1291
      let
blanchet@33192
  1292
        val min_R = min_rep (rep_of u1) (rep_of u2)
blanchet@33192
  1293
        val r1 = to_rep min_R u1
blanchet@33192
  1294
        val r2 = to_rep min_R u2
blanchet@33192
  1295
      in
blanchet@33192
  1296
        case min_R of
blanchet@33192
  1297
          Vect (k, Atom _) => kk_vect_set_bool_op connective k r1 r2
blanchet@35280
  1298
        | Func (_, Formula Neut) => set_oper r1 r2
blanchet@35280
  1299
        | Func (_, Atom _) => set_oper (kk_join r1 true_atom)
blanchet@35280
  1300
                                       (kk_join r2 true_atom)
blanchet@33232
  1301
        | _ => raise REP ("Nitpick_Kodkod.to_set_bool_op", [min_R])
blanchet@33192
  1302
      end
blanchet@34124
  1303
    and to_bit_word_unary_op T R oper =
blanchet@34124
  1304
      let
blanchet@34124
  1305
        val Ts = strip_type T ||> single |> op @
blanchet@34126
  1306
        fun int_arg j = int_expr_from_atom kk (nth Ts j) (KK.Var (1, j))
blanchet@34124
  1307
      in
blanchet@34124
  1308
        kk_comprehension (decls_for_atom_schema 0 (atom_schema_of_rep R))
blanchet@34126
  1309
            (KK.FormulaLet
blanchet@34126
  1310
                 (map (fn j => KK.AssignIntReg (j, int_arg j)) (0 upto 1),
blanchet@34126
  1311
                  KK.IntEq (KK.IntReg 1, oper (KK.IntReg 0))))
blanchet@34124
  1312
      end
blanchet@34124
  1313
    and to_bit_word_binary_op T R opt_guard opt_oper =
blanchet@34124
  1314
      let
blanchet@34124
  1315
        val Ts = strip_type T ||> single |> op @
blanchet@34126
  1316
        fun int_arg j = int_expr_from_atom kk (nth Ts j) (KK.Var (1, j))
blanchet@34124
  1317
      in
blanchet@34124
  1318
        kk_comprehension (decls_for_atom_schema 0 (atom_schema_of_rep R))
blanchet@34126
  1319
            (KK.FormulaLet
blanchet@34126
  1320
                 (map (fn j => KK.AssignIntReg (j, int_arg j)) (0 upto 2),
blanchet@34124
  1321
                  fold1 kk_and
blanchet@34124
  1322
                        ((case opt_guard of
blanchet@34124
  1323
                            NONE => []
blanchet@34124
  1324
                          | SOME guard =>
blanchet@34126
  1325
                            [guard (KK.IntReg 0) (KK.IntReg 1) (KK.IntReg 2)]) @
blanchet@34124
  1326
                         (case opt_oper of
blanchet@34124
  1327
                            NONE => []
blanchet@34124
  1328
                          | SOME oper =>
blanchet@34126
  1329
                            [KK.IntEq (KK.IntReg 2,
blanchet@34126
  1330
                                       oper (KK.IntReg 0) (KK.IntReg 1))]))))
blanchet@34124
  1331
      end
blanchet@39345
  1332
    and to_apply (R as Formula _) _ _ =
blanchet@36127
  1333
        raise REP ("Nitpick_Kodkod.to_apply", [R])
blanchet@36127
  1334
      | to_apply res_R func_u arg_u =
blanchet@36127
  1335
        case unopt_rep (rep_of func_u) of
blanchet@38190
  1336
          Atom (1, j0) =>
blanchet@33192
  1337
          to_guard [arg_u] res_R
blanchet@36127
  1338
                   (rel_expr_from_rel_expr kk res_R (Atom (1, j0)) (to_r func_u))
blanchet@36127
  1339
        | Atom (k, _) =>
blanchet@36127
  1340
          let
blanchet@36127
  1341
            val dom_card = card_of_rep (rep_of arg_u)
blanchet@36127
  1342
            val ran_R = Atom (exact_root dom_card k,
blanchet@36127
  1343
                              offset_of_type ofs (range_type (type_of func_u)))
blanchet@36127
  1344
          in
blanchet@36127
  1345
            to_apply_vect dom_card ran_R res_R (to_vect dom_card ran_R func_u)
blanchet@36127
  1346
                          arg_u
blanchet@36127
  1347
          end
blanchet@36127
  1348
        | Vect (1, R') =>
blanchet@36127
  1349
          to_guard [arg_u] res_R
blanchet@36127
  1350
                   (rel_expr_from_rel_expr kk res_R R' (to_r func_u))
blanchet@36127
  1351
        | Vect (k, R') => to_apply_vect k R' res_R (to_r func_u) arg_u
blanchet@36127
  1352
        | Func (R, Formula Neut) =>
blanchet@36127
  1353
          to_guard [arg_u] res_R (rel_expr_from_formula kk res_R
blanchet@36127
  1354
                                      (kk_subset (to_opt R arg_u) (to_r func_u)))
blanchet@36127
  1355
        | Func (R1, R2) =>
blanchet@36127
  1356
          rel_expr_from_rel_expr kk res_R R2
blanchet@36127
  1357
              (kk_n_fold_join kk true R1 R2 (to_opt R1 arg_u) (to_r func_u))
blanchet@36127
  1358
          |> body_rep R2 = Formula Neut ? to_guard [arg_u] res_R
blanchet@36127
  1359
        | _ => raise NUT ("Nitpick_Kodkod.to_apply", [func_u])
blanchet@33192
  1360
    and to_apply_vect k R' res_R func_r arg_u =
blanchet@33192
  1361
      let
blanchet@33192
  1362
        val arg_R = one_rep ofs (type_of arg_u) (unopt_rep (rep_of arg_u))
blanchet@33192
  1363
        val vect_r = vect_from_rel_expr kk k res_R (Vect (k, R')) func_r
blanchet@33192
  1364
        val vect_rs = unpack_vect_in_chunks kk (arity_of_rep res_R) k vect_r
blanchet@33192
  1365
      in
blanchet@33192
  1366
        kk_case_switch kk arg_R res_R (to_opt arg_R arg_u)
blanchet@33192
  1367
                       (all_singletons_for_rep arg_R) vect_rs
blanchet@33192
  1368
      end
blanchet@33192
  1369
    and to_could_be_unrep neg u =
blanchet@34126
  1370
      if neg andalso is_opt_rep (rep_of u) then kk_no (to_r u) else KK.False
blanchet@33192
  1371
    and to_compare_with_unrep u r =
blanchet@33892
  1372
      if is_opt_rep (rep_of u) then
blanchet@33892
  1373
        kk_rel_if (kk_some (to_r u)) r (empty_rel_for_rep (rep_of u))
blanchet@33892
  1374
      else
blanchet@33892
  1375
        r
blanchet@33192
  1376
  in to_f_with_polarity Pos u end
blanchet@33192
  1377
blanchet@41802
  1378
fun declarative_axiom_for_plain_rel kk (FreeRel (x, _, R as Func _, nick)) =
blanchet@41802
  1379
    kk_n_ary_function kk (R |> nick = @{const_name List.set} ? unopt_rep)
blanchet@41802
  1380
                      (KK.Rel x)
blanchet@41802
  1381
  | declarative_axiom_for_plain_rel ({kk_lone, kk_one, ...} : kodkod_constrs)
blanchet@41802
  1382
                                    (FreeRel (x, _, R, _)) =
blanchet@41802
  1383
    if is_one_rep R then kk_one (KK.Rel x)
blanchet@41802
  1384
    else if is_lone_rep R andalso card_of_rep R > 1 then kk_lone (KK.Rel x)
blanchet@41802
  1385
    else KK.True
blanchet@41802
  1386
  | declarative_axiom_for_plain_rel _ u =
blanchet@41802
  1387
    raise NUT ("Nitpick_Kodkod.declarative_axiom_for_plain_rel", [u])
blanchet@41802
  1388
blanchet@41802
  1389
fun const_triple rel_table (x as (s, T)) =
blanchet@41802
  1390
  case the_name rel_table (ConstName (s, T, Any)) of
blanchet@41802
  1391
    FreeRel ((n, j), _, R, _) => (KK.Rel (n, j), R, n)
blanchet@41802
  1392
  | _ => raise TERM ("Nitpick_Kodkod.const_triple", [Const x])
blanchet@41802
  1393
blanchet@41802
  1394
fun discr_rel_expr rel_table = #1 o const_triple rel_table o discr_for_constr
blanchet@41802
  1395
blanchet@41802
  1396
fun nfa_transitions_for_sel hol_ctxt binarize
blanchet@41802
  1397
                            ({kk_project, ...} : kodkod_constrs) rel_table
blanchet@41802
  1398
                            (dtypes : datatype_spec list) constr_x n =
blanchet@41802
  1399
  let
blanchet@41802
  1400
    val x as (_, T) =
blanchet@41802
  1401
      binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize constr_x n
blanchet@41802
  1402
    val (r, R, arity) = const_triple rel_table x
blanchet@41802
  1403
    val type_schema = type_schema_of_rep T R
blanchet@41802
  1404
  in
blanchet@41802
  1405
    map_filter (fn (j, T) =>
blanchet@41802
  1406
                   if forall (not_equal T o #typ) dtypes then NONE
blanchet@41802
  1407
                   else SOME ((x, kk_project r (map KK.Num [0, j])), T))
blanchet@41802
  1408
               (index_seq 1 (arity - 1) ~~ tl type_schema)
blanchet@41802
  1409
  end
blanchet@41802
  1410
fun nfa_transitions_for_constr hol_ctxt binarize kk rel_table dtypes
blanchet@41802
  1411
                               (x as (_, T)) =
blanchet@41802
  1412
  maps (nfa_transitions_for_sel hol_ctxt binarize kk rel_table dtypes x)
blanchet@41802
  1413
       (index_seq 0 (num_sels_for_constr_type T))
blanchet@41802
  1414
fun nfa_entry_for_datatype _ _ _ _ _ ({co = true, ...} : datatype_spec) = NONE
blanchet@41802
  1415
  | nfa_entry_for_datatype _ _ _ _ _ {standard = false, ...} = NONE
blanchet@41802
  1416
  | nfa_entry_for_datatype _ _ _ _ _ {deep = false, ...} = NONE
blanchet@41802
  1417
  | nfa_entry_for_datatype hol_ctxt binarize kk rel_table dtypes
blanchet@41802
  1418
                           {typ, constrs, ...} =
blanchet@41802
  1419
    SOME (typ, maps (nfa_transitions_for_constr hol_ctxt binarize kk rel_table
blanchet@41802
  1420
                                                dtypes o #const) constrs)
blanchet@41802
  1421
blanchet@41802
  1422
val empty_rel = KK.Product (KK.None, KK.None)
blanchet@41802
  1423
blanchet@41802
  1424
fun direct_path_rel_exprs nfa start_T final_T =
blanchet@41802
  1425
  case AList.lookup (op =) nfa final_T of
blanchet@41802
  1426
    SOME trans => map (snd o fst) (filter (curry (op =) start_T o snd) trans)
blanchet@41802
  1427
  | NONE => []
blanchet@41802
  1428
and any_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start_T
blanchet@41802
  1429
                      final_T =
blanchet@41802
  1430
    fold kk_union (direct_path_rel_exprs nfa start_T final_T)
blanchet@41802
  1431
         (if start_T = final_T then KK.Iden else empty_rel)
blanchet@41802
  1432
  | any_path_rel_expr (kk as {kk_union, ...}) nfa (T :: Ts) start_T final_T =
blanchet@41802
  1433
    kk_union (any_path_rel_expr kk nfa Ts start_T final_T)
blanchet@41802
  1434
             (knot_path_rel_expr kk nfa Ts start_T T final_T)
blanchet@41802
  1435
and knot_path_rel_expr (kk as {kk_join, kk_reflexive_closure, ...}) nfa Ts
blanchet@41802
  1436
                       start_T knot_T final_T =
blanchet@41802
  1437
  kk_join (kk_join (any_path_rel_expr kk nfa Ts knot_T final_T)
blanchet@41802
  1438
                   (kk_reflexive_closure (loop_path_rel_expr kk nfa Ts knot_T)))
blanchet@41802
  1439
          (any_path_rel_expr kk nfa Ts start_T knot_T)
blanchet@41802
  1440
and loop_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start_T =
blanchet@41802
  1441
    fold kk_union (direct_path_rel_exprs nfa start_T start_T) empty_rel
blanchet@41802
  1442
  | loop_path_rel_expr (kk as {kk_union, kk_closure, ...}) nfa (T :: Ts)
blanchet@41802
  1443
                       start_T =
blanchet@41802
  1444
    if start_T = T then
blanchet@41802
  1445
      kk_closure (loop_path_rel_expr kk nfa Ts start_T)
blanchet@41802
  1446
    else
blanchet@41802
  1447
      kk_union (loop_path_rel_expr kk nfa Ts start_T)
blanchet@41802
  1448
               (knot_path_rel_expr kk nfa Ts start_T T start_T)
blanchet@41802
  1449
blanchet@41802
  1450
fun add_nfa_to_graph [] = I
blanchet@41802
  1451
  | add_nfa_to_graph ((_, []) :: nfa) = add_nfa_to_graph nfa
blanchet@41802
  1452
  | add_nfa_to_graph ((T, ((_, T') :: transitions)) :: nfa) =
blanchet@41802
  1453
    add_nfa_to_graph ((T, transitions) :: nfa) o Typ_Graph.add_edge (T, T') o
blanchet@41802
  1454
    Typ_Graph.default_node (T', ()) o Typ_Graph.default_node (T, ())
blanchet@41802
  1455
blanchet@41802
  1456
fun strongly_connected_sub_nfas nfa =
blanchet@41802
  1457
  add_nfa_to_graph nfa Typ_Graph.empty
blanchet@41802
  1458
  |> Typ_Graph.strong_conn
blanchet@41802
  1459
  |> map (fn keys => filter (member (op =) keys o fst) nfa)
blanchet@41802
  1460
blanchet@41802
  1461
fun acyclicity_axiom_for_datatype (kk as {kk_no, kk_intersect, ...}) nfa
blanchet@41802
  1462
                                  start_T =
blanchet@41802
  1463
  kk_no (kk_intersect
blanchet@41802
  1464
             (loop_path_rel_expr kk nfa (pull start_T (map fst nfa)) start_T)
blanchet@41802
  1465
             KK.Iden)
blanchet@41802
  1466
(* Cycle breaking in the bounds takes care of singly recursive datatypes, hence
blanchet@41802
  1467
   the first equation. *)
blanchet@41802
  1468
fun acyclicity_axioms_for_datatypes _ [_] = []
blanchet@41802
  1469
  | acyclicity_axioms_for_datatypes kk nfas =
blanchet@41802
  1470
    maps (fn nfa => map (acyclicity_axiom_for_datatype kk nfa o fst) nfa) nfas
blanchet@41802
  1471
blanchet@41802
  1472
fun atom_equation_for_nut ofs kk (u, j) =
blanchet@41802
  1473
  let val dummy_u = RelReg (0, type_of u, rep_of u) in
blanchet@41802
  1474
    case Op2 (DefEq, bool_T, Formula Pos, dummy_u, u)
blanchet@41802
  1475
         |> kodkod_formula_from_nut ofs kk of
blanchet@41802
  1476
      KK.RelEq (KK.RelReg _, r) => KK.RelEq (KK.Atom j, r)
blanchet@41802
  1477
    | _ => raise BAD ("Nitpick_Kodkod.atom_equation_for_nut",
blanchet@41802
  1478
                      "malformed Kodkod formula")
blanchet@41802
  1479
  end
blanchet@41802
  1480
blanchet@41875
  1481
fun needed_value_axioms_for_datatype [] _ _ _ = []
blanchet@41875
  1482
  | needed_value_axioms_for_datatype need_us ofs kk
blanchet@41802
  1483
        ({typ, card, constrs, ...} : datatype_spec) =
blanchet@41802
  1484
    let
blanchet@41802
  1485
      fun aux (u as Construct (FreeRel (_, _, _, s) :: _, T, _, us)) =
blanchet@41802
  1486
          fold aux us
blanchet@41802
  1487
          #> (fn NONE => NONE
blanchet@41802
  1488
               | accum as SOME (loose, fixed) =>
blanchet@41802
  1489
                 if T = typ then
blanchet@41802
  1490
                   case AList.lookup (op =) fixed u of
blanchet@41802
  1491
                     SOME _ => accum
blanchet@41802
  1492
                   | NONE =>
blanchet@41802
  1493
                     let
blanchet@41802
  1494
                       val constr_s = constr_name_for_sel_like s
blanchet@41802
  1495
                       val {delta, epsilon, ...} =
blanchet@41802
  1496
                         constrs
blanchet@41802
  1497
                         |> List.find (fn {const, ...} => fst const = constr_s)
blanchet@41802
  1498
                         |> the
blanchet@41802
  1499
                       val j0 = offset_of_type ofs T
blanchet@41802
  1500
                     in
blanchet@41802
  1501
                       case find_first (fn j => j >= delta andalso
blanchet@41802
  1502
                                        j < delta + epsilon) loose of
blanchet@41802
  1503
                         SOME j =>
blanchet@41802
  1504
                         SOME (remove (op =) j loose, (u, j0 + j) :: fixed)
blanchet@41802
  1505
                       | NONE => NONE
blanchet@41802
  1506
                     end
blanchet@41802
  1507
                 else
blanchet@41802
  1508
                   accum)
blanchet@41985
  1509
        | aux _ = I
blanchet@41802
  1510
    in
blanchet@41875
  1511
      case SOME (index_seq 0 card, []) |> fold aux need_us of
blanchet@41802
  1512
        SOME (_, fixed) => fixed |> map (atom_equation_for_nut ofs kk)
blanchet@41802
  1513
      | NONE => [KK.False]
blanchet@41802
  1514
    end
blanchet@41802
  1515
blanchet@41802
  1516
fun all_ge ({kk_join, kk_reflexive_closure, ...} : kodkod_constrs) z r =
blanchet@41802
  1517
  kk_join r (kk_reflexive_closure (KK.Rel (suc_rel_for_atom_seq z)))
blanchet@41802
  1518
fun gt ({kk_subset, kk_join, kk_closure, ...} : kodkod_constrs) z r1 r2 =
blanchet@41802
  1519
  kk_subset r1 (kk_join r2 (kk_closure (KK.Rel (suc_rel_for_atom_seq z))))
blanchet@41802
  1520
blanchet@41802
  1521
fun constr_quadruple ({const = (s, T), delta, epsilon, ...} : constr_spec) =
blanchet@41802
  1522
  (delta, (epsilon, (num_binder_types T, s)))
blanchet@41802
  1523
val constr_ord =
blanchet@41802
  1524
  prod_ord int_ord (prod_ord int_ord (prod_ord int_ord string_ord))
blanchet@41802
  1525
  o pairself constr_quadruple
blanchet@41802
  1526
blanchet@41802
  1527
fun datatype_ord (({card = card1, self_rec = self_rec1, constrs = constr1, ...},
blanchet@41802
  1528
                   {card = card2, self_rec = self_rec2, constrs = constr2, ...})
blanchet@41802
  1529
                  : datatype_spec * datatype_spec) =
blanchet@41802
  1530
  prod_ord int_ord (prod_ord bool_ord int_ord)
blanchet@41802
  1531
           ((card1, (self_rec1, length constr1)),
blanchet@41802
  1532
            (card2, (self_rec2, length constr2)))
blanchet@41802
  1533
blanchet@41802
  1534
(* We must absolutely tabulate "suc" for all datatypes whose selector bounds
blanchet@41802
  1535
   break cycles; otherwise, we may end up with two incompatible symmetry
blanchet@41802
  1536
   breaking orders, leading to spurious models. *)
blanchet@41802
  1537
fun should_tabulate_suc_for_type dtypes T =
blanchet@41802
  1538
  is_asymmetric_nondatatype T orelse
blanchet@41802
  1539
  case datatype_spec dtypes T of
blanchet@41802
  1540
    SOME {self_rec, ...} => self_rec
blanchet@41802
  1541
  | NONE => false
blanchet@41802
  1542
blanchet@41802
  1543
fun lex_order_rel_expr (kk as {kk_implies, kk_and, kk_subset, kk_join, ...})
blanchet@41802
  1544
                       dtypes sel_quadruples =
blanchet@41802
  1545
  case sel_quadruples of
blanchet@41802
  1546
    [] => KK.True
blanchet@41802
  1547
  | ((r, Func (Atom _, Atom x), 2), (_, Type (_, [_, T]))) :: sel_quadruples' =>
blanchet@41802
  1548
    let val z = (x, should_tabulate_suc_for_type dtypes T) in
blanchet@41802
  1549
      if null sel_quadruples' then
blanchet@41802
  1550
        gt kk z (kk_join (KK.Var (1, 1)) r) (kk_join (KK.Var (1, 0)) r)
blanchet@41802
  1551
      else
blanchet@41802
  1552
        kk_and (kk_subset (kk_join (KK.Var (1, 1)) r)
blanchet@41802
  1553
                          (all_ge kk z (kk_join (KK.Var (1, 0)) r)))
blanchet@41802
  1554
               (kk_implies (kk_subset (kk_join (KK.Var (1, 1)) r)
blanchet@41802
  1555
                                      (kk_join (KK.Var (1, 0)) r))
blanchet@41802
  1556
                           (lex_order_rel_expr kk dtypes sel_quadruples'))
blanchet@41802
  1557
    end
blanchet@41802
  1558
    (* Skip constructors components that aren't atoms, since we cannot compare
blanchet@41802
  1559
       these easily. *)
blanchet@41802
  1560
  | _ :: sel_quadruples' => lex_order_rel_expr kk dtypes sel_quadruples'
blanchet@41802
  1561
blanchet@41802
  1562
fun is_nil_like_constr_type dtypes T =
blanchet@41802
  1563
  case datatype_spec dtypes T of
blanchet@41802
  1564
    SOME {constrs, ...} =>
blanchet@41802
  1565
    (case filter_out (is_self_recursive_constr_type o snd o #const) constrs of
blanchet@41802
  1566
       [{const = (_, T'), ...}] => T = T'
blanchet@41802
  1567
     | _ => false)
blanchet@41802
  1568
  | NONE => false
blanchet@41802
  1569
blanchet@41802
  1570
fun sym_break_axioms_for_constr_pair hol_ctxt binarize
blanchet@41802
  1571
       (kk as {kk_all, kk_or, kk_implies, kk_and, kk_some, kk_intersect,
blanchet@41802
  1572
               kk_join, ...}) rel_table nfas dtypes
blanchet@41802
  1573
       (constr_ord,
blanchet@41802
  1574
        ({const = const1 as (_, T1), delta = delta1, epsilon = epsilon1, ...},
blanchet@41802
  1575
         {const = const2 as (_, _), delta = delta2, epsilon = epsilon2, ...})
blanchet@41802
  1576
        : constr_spec * constr_spec) =
blanchet@41802
  1577
  let
blanchet@41802
  1578
    val dataT = body_type T1
blanchet@41802
  1579
    val nfa = nfas |> find_first (exists (curry (op =) dataT o fst)) |> these
blanchet@41802
  1580
    val rec_Ts = nfa |> map fst
blanchet@41802
  1581
    fun rec_and_nonrec_sels (x as (_, T)) =
blanchet@41802
  1582
      index_seq 0 (num_sels_for_constr_type T)
blanchet@41802
  1583
      |> map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize x)
blanchet@41802
  1584
      |> List.partition (member (op =) rec_Ts o range_type o snd)
blanchet@41802
  1585
    val sel_xs1 = rec_and_nonrec_sels const1 |> op @
blanchet@41802
  1586
  in
blanchet@41802
  1587
    if constr_ord = EQUAL andalso null sel_xs1 then
blanchet@41802
  1588
      []
blanchet@41802
  1589
    else
blanchet@41802
  1590
      let
blanchet@41802
  1591
        val z =
blanchet@41802
  1592
          (case #2 (const_triple rel_table (discr_for_constr const1)) of
blanchet@41802
  1593
             Func (Atom x, Formula _) => x
blanchet@41802
  1594
           | R => raise REP ("Nitpick_Kodkod.sym_break_axioms_for_constr_pair",
blanchet@41802
  1595
                             [R]), should_tabulate_suc_for_type dtypes dataT)
blanchet@41802
  1596
        val (rec_sel_xs2, nonrec_sel_xs2) = rec_and_nonrec_sels const2
blanchet@41802
  1597
        val sel_xs2 = rec_sel_xs2 @ nonrec_sel_xs2
blanchet@41802
  1598
        fun sel_quadruples2 () = sel_xs2 |> map (`(const_triple rel_table))
blanchet@41802
  1599
        (* If the two constructors are the same, we drop the first selector
blanchet@41802
  1600
           because that one is always checked by the lexicographic order.
blanchet@41802
  1601
           We sometimes also filter out direct subterms, because those are
blanchet@41802
  1602
           already handled by the acyclicity breaking in the bound
blanchet@41802
  1603
           declarations. *)
blanchet@41802
  1604
        fun filter_out_sels no_direct sel_xs =
blanchet@41802
  1605
          apsnd (filter_out
blanchet@41802
  1606
                     (fn ((x, _), T) =>
blanchet@41802
  1607
                         (constr_ord = EQUAL andalso x = hd sel_xs) orelse
blanchet@41802
  1608
                         (T = dataT andalso
blanchet@41802
  1609
                          (no_direct orelse not (member (op =) sel_xs x)))))
blanchet@41802
  1610
        fun subterms_r no_direct sel_xs j =
blanchet@41802
  1611
          loop_path_rel_expr kk (map (filter_out_sels no_direct sel_xs) nfa)
blanchet@41802
  1612
                           (filter_out (curry (op =) dataT) (map fst nfa)) dataT
blanchet@41802
  1613
          |> kk_join (KK.Var (1, j))
blanchet@41802
  1614
      in
blanchet@41802
  1615
        [kk_all [KK.DeclOne ((1, 0), discr_rel_expr rel_table const1),
blanchet@41802
  1616
                 KK.DeclOne ((1, 1), discr_rel_expr rel_table const2)]
blanchet@41802
  1617
             (kk_implies
blanchet@41802
  1618
                 (if delta2 >= epsilon1 then KK.True
blanchet@41802
  1619
                  else if delta1 >= epsilon2 - 1 then KK.False
blanchet@41802
  1620
                  else gt kk z (KK.Var (1, 1)) (KK.Var (1, 0)))
blanchet@41802
  1621
                 (kk_or
blanchet@41802
  1622
                      (if is_nil_like_constr_type dtypes T1 then
blanchet@41802
  1623
                         KK.True
blanchet@41802
  1624
                       else
blanchet@41802
  1625
                         kk_some (kk_intersect (subterms_r false sel_xs2 1)
blanchet@41802
  1626
                                               (all_ge kk z (KK.Var (1, 0)))))
blanchet@41802
  1627
                      (case constr_ord of
blanchet@41802
  1628
                         EQUAL =>
blanchet@41802
  1629
                         kk_and
blanchet@41802
  1630
                             (lex_order_rel_expr kk dtypes (sel_quadruples2 ()))
blanchet@41802
  1631
                             (kk_all [KK.DeclOne ((1, 2),
blanchet@41802
  1632
                                                  subterms_r true sel_xs1 0)]
blanchet@41802
  1633
                                     (gt kk z (KK.Var (1, 1)) (KK.Var (1, 2))))
blanchet@41802
  1634
                       | LESS =>
blanchet@41802
  1635
                         kk_all [KK.DeclOne ((1, 2),
blanchet@41802
  1636
                                 subterms_r false sel_xs1 0)]
blanchet@41802
  1637
                                (gt kk z (KK.Var (1, 1)) (KK.Var (1, 2)))
blanchet@41802
  1638
                       | GREATER => KK.False)))]
blanchet@41802
  1639
      end
blanchet@41802
  1640
  end
blanchet@41802
  1641
blanchet@41802
  1642
fun sym_break_axioms_for_datatype hol_ctxt binarize kk rel_table nfas dtypes
blanchet@41802
  1643
                                  ({constrs, ...} : datatype_spec) =
blanchet@41802
  1644
  let
blanchet@41802
  1645
    val constrs = sort constr_ord constrs
blanchet@41802
  1646
    val constr_pairs = all_distinct_unordered_pairs_of constrs
blanchet@41802
  1647
  in
blanchet@41802
  1648
    map (pair EQUAL) (constrs ~~ constrs) @
blanchet@41802
  1649
    map (pair LESS) constr_pairs @
blanchet@41802
  1650
    map (pair GREATER) (map swap constr_pairs)
blanchet@41802
  1651
    |> maps (sym_break_axioms_for_constr_pair hol_ctxt binarize kk rel_table
blanchet@41802
  1652
                                              nfas dtypes)
blanchet@41802
  1653
  end
blanchet@41802
  1654
blanchet@41875
  1655
fun is_datatype_in_needed_value T (Construct (_, T', _, us)) =
blanchet@41875
  1656
    T = T' orelse exists (is_datatype_in_needed_value T) us
blanchet@41875
  1657
  | is_datatype_in_needed_value _ _ = false
blanchet@41802
  1658
blanchet@41802
  1659
val min_sym_break_card = 7
blanchet@41802
  1660
blanchet@41875
  1661
fun sym_break_axioms_for_datatypes hol_ctxt binarize need_us datatype_sym_break
blanchet@41875
  1662
                                   kk rel_table nfas dtypes =
blanchet@41802
  1663
  if datatype_sym_break = 0 then
blanchet@41802
  1664
    []
blanchet@41802
  1665
  else
blanchet@41803
  1666
    dtypes |> filter is_datatype_acyclic
blanchet@41803
  1667
           |> filter (fn {constrs = [_], ...} => false
blanchet@41803
  1668
                       | {card, constrs, ...} =>
blanchet@41803
  1669
                         card >= min_sym_break_card andalso
blanchet@41803
  1670
                         forall (forall (not o is_higher_order_type)
blanchet@41803
  1671
                                 o binder_types o snd o #const) constrs)
blanchet@41803
  1672
           |> filter_out
blanchet@41803
  1673
                  (fn {typ, ...} =>
blanchet@41875
  1674
                      exists (is_datatype_in_needed_value typ) need_us)
blanchet@41803
  1675
           |> (fn dtypes' =>
blanchet@41803
  1676
                  dtypes' |> length dtypes' > datatype_sym_break
blanchet@41803
  1677
                             ? (sort (datatype_ord o swap)
blanchet@41803
  1678
                                #> take datatype_sym_break))
blanchet@41803
  1679
           |> maps (sym_break_axioms_for_datatype hol_ctxt binarize kk rel_table
blanchet@41803
  1680
                                                  nfas dtypes)
blanchet@41803
  1681
blanchet@41802
  1682
blanchet@41802
  1683
fun sel_axiom_for_sel hol_ctxt binarize j0
blanchet@41802
  1684
        (kk as {kk_all, kk_formula_if, kk_subset, kk_no, kk_join, ...})
blanchet@41802
  1685
        rel_table dom_r ({const, delta, epsilon, exclusive, ...} : constr_spec)
blanchet@41802
  1686
        n =
blanchet@41802
  1687
  let
blanchet@41802
  1688
    val x = binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize const n
blanchet@41802
  1689
    val (r, R, _) = const_triple rel_table x
blanchet@41802
  1690
    val R2 = dest_Func R |> snd
blanchet@41802
  1691
    val z = (epsilon - delta, delta + j0)
blanchet@41802
  1692
  in
blanchet@41802
  1693
    if exclusive then
blanchet@41802
  1694
      kk_n_ary_function kk (Func (Atom z, R2)) r
blanchet@41802
  1695
    else
blanchet@41802
  1696
      let val r' = kk_join (KK.Var (1, 0)) r in
blanchet@41802
  1697
        kk_all [KK.DeclOne ((1, 0), KK.AtomSeq z)]
blanchet@41802
  1698
               (kk_formula_if (kk_subset (KK.Var (1, 0)) dom_r)
blanchet@41802
  1699
                              (kk_n_ary_function kk R2 r') (kk_no r'))
blanchet@41802
  1700
      end
blanchet@41802
  1701
  end
blanchet@41802
  1702
fun sel_axioms_for_constr hol_ctxt binarize bits j0 kk rel_table
blanchet@41802
  1703
        (constr as {const, delta, epsilon, explicit_max, ...}) =
blanchet@41802
  1704
  let
blanchet@41802
  1705
    val honors_explicit_max =
blanchet@41802
  1706
      explicit_max < 0 orelse epsilon - delta <= explicit_max
blanchet@41802
  1707
  in
blanchet@41802
  1708
    if explicit_max = 0 then
blanchet@41802
  1709
      [formula_for_bool honors_explicit_max]
blanchet@41802
  1710
    else
blanchet@41802
  1711
      let
blanchet@41802
  1712
        val dom_r = discr_rel_expr rel_table const
blanchet@41802
  1713
        val max_axiom =
blanchet@41802
  1714
          if honors_explicit_max then
blanchet@41802
  1715
            KK.True
blanchet@41802
  1716
          else if bits = 0 orelse
blanchet@41802
  1717
               is_twos_complement_representable bits (epsilon - delta) then
blanchet@41802
  1718
            KK.LE (KK.Cardinality dom_r, KK.Num explicit_max)
blanchet@41802
  1719
          else
blanchet@41802
  1720
            raise TOO_SMALL ("Nitpick_Kodkod.sel_axioms_for_constr",
blanchet@41802
  1721
                             "\"bits\" value " ^ string_of_int bits ^
blanchet@41802
  1722
                             " too small for \"max\"")
blanchet@41802
  1723
      in
blanchet@41802
  1724
        max_axiom ::
blanchet@41802
  1725
        map (sel_axiom_for_sel hol_ctxt binarize j0 kk rel_table dom_r constr)
blanchet@41802
  1726
            (index_seq 0 (num_sels_for_constr_type (snd const)))
blanchet@41802
  1727
      end
blanchet@41802
  1728
  end
blanchet@41802
  1729
fun sel_axioms_for_datatype hol_ctxt binarize bits j0 kk rel_table
blanchet@41802
  1730
                            ({constrs, ...} : datatype_spec) =
blanchet@41802
  1731
  maps (sel_axioms_for_constr hol_ctxt binarize bits j0 kk rel_table) constrs
blanchet@41802
  1732
blanchet@41802
  1733
fun uniqueness_axiom_for_constr hol_ctxt binarize
blanchet@41802
  1734
        ({kk_all, kk_implies, kk_and, kk_rel_eq, kk_lone, kk_join, ...}
blanchet@41802
  1735
         : kodkod_constrs) rel_table ({const, ...} : constr_spec) =
blanchet@41802
  1736
  let
blanchet@41802
  1737
    fun conjunct_for_sel r =
blanchet@41802
  1738
      kk_rel_eq (kk_join (KK.Var (1, 0)) r) (kk_join (KK.Var (1, 1)) r)
blanchet@41802
  1739
    val num_sels = num_sels_for_constr_type (snd const)
blanchet@41802
  1740
    val triples =
blanchet@41802
  1741
      map (const_triple rel_table
blanchet@41802
  1742
           o binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize const)
blanchet@41802
  1743
          (~1 upto num_sels - 1)
blanchet@41802
  1744
    val set_r = triples |> hd |> #1
blanchet@41802
  1745
  in
blanchet@41802
  1746
    if num_sels = 0 then
blanchet@41802
  1747
      kk_lone set_r
blanchet@41802
  1748
    else
blanchet@41802
  1749
      kk_all (map (KK.DeclOne o rpair set_r o pair 1) [0, 1])
blanchet@41802
  1750
             (kk_implies
blanchet@41802
  1751
                  (fold1 kk_and (map (conjunct_for_sel o #1) (tl triples)))
blanchet@41802
  1752
                  (kk_rel_eq (KK.Var (1, 0)) (KK.Var (1, 1))))
blanchet@41802
  1753
  end
blanchet@41802
  1754
fun uniqueness_axioms_for_datatype hol_ctxt binarize kk rel_table
blanchet@41802
  1755
                                   ({constrs, ...} : datatype_spec) =
blanchet@41802
  1756
  map (uniqueness_axiom_for_constr hol_ctxt binarize kk rel_table) constrs
blanchet@41802
  1757
blanchet@41802
  1758
fun effective_constr_max ({delta, epsilon, ...} : constr_spec) = epsilon - delta
blanchet@41802
  1759
fun partition_axioms_for_datatype j0 (kk as {kk_rel_eq, kk_union, ...})
blanchet@41802
  1760
                                  rel_table
blanchet@41802
  1761
                                  ({card, constrs, ...} : datatype_spec) =
blanchet@41802
  1762
  if forall #exclusive constrs then
blanchet@41802
  1763
    [Integer.sum (map effective_constr_max constrs) = card |> formula_for_bool]
blanchet@41802
  1764
  else
blanchet@41802
  1765
    let val rs = map (discr_rel_expr rel_table o #const) constrs in
blanchet@41802
  1766
      [kk_rel_eq (fold1 kk_union rs) (KK.AtomSeq (card, j0)),
blanchet@41802
  1767
       kk_disjoint_sets kk rs]
blanchet@41802
  1768
    end
blanchet@41802
  1769
blanchet@41802
  1770
fun other_axioms_for_datatype _ _ _ _ _ _ {deep = false, ...} = []
blanchet@41802
  1771
  | other_axioms_for_datatype hol_ctxt binarize bits ofs kk rel_table
blanchet@41802
  1772
                              (dtype as {typ, ...}) =
blanchet@41802
  1773
    let val j0 = offset_of_type ofs typ in
blanchet@41802
  1774
      sel_axioms_for_datatype hol_ctxt binarize bits j0 kk rel_table dtype @
blanchet@41802
  1775
      uniqueness_axioms_for_datatype hol_ctxt binarize kk rel_table dtype @
blanchet@41802
  1776
      partition_axioms_for_datatype j0 kk rel_table dtype
blanchet@41802
  1777
    end
blanchet@41802
  1778
blanchet@41875
  1779
fun declarative_axioms_for_datatypes hol_ctxt binarize need_us
blanchet@41802
  1780
        datatype_sym_break bits ofs kk rel_table dtypes =
blanchet@41802
  1781
  let
blanchet@41802
  1782
    val nfas =
blanchet@41802
  1783
      dtypes |> map_filter (nfa_entry_for_datatype hol_ctxt binarize kk
blanchet@41802
  1784
                                                   rel_table dtypes)
blanchet@41802
  1785
             |> strongly_connected_sub_nfas
blanchet@41802
  1786
  in
blanchet@41802
  1787
    acyclicity_axioms_for_datatypes kk nfas @
blanchet@41875
  1788
    maps (needed_value_axioms_for_datatype need_us ofs kk) dtypes @
blanchet@41875
  1789
    sym_break_axioms_for_datatypes hol_ctxt binarize need_us datatype_sym_break
blanchet@41875
  1790
                                   kk rel_table nfas dtypes @
blanchet@41802
  1791
    maps (other_axioms_for_datatype hol_ctxt binarize bits ofs kk rel_table)
blanchet@41802
  1792
         dtypes
blanchet@41802
  1793
  end
blanchet@41802
  1794
blanchet@33192
  1795
end;