src/HOL/Tools/Nitpick/nitpick_kodkod.ML
author blanchet
Thu, 22 Oct 2009 14:51:47 +0200
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child 33232 f93390060bbe
permissions -rw-r--r--
added Nitpick's theory and ML files to Isabelle/HOL; the examples and the documentation are on their way.
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(*  Title:      HOL/Nitpick/Tools/nitpick_kodkod.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009
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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 extended_context = NitpickHOL.extended_context
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  type dtype_spec = NitpickScope.dtype_spec
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  type kodkod_constrs = NitpickPeephole.kodkod_constrs
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  type nut = NitpickNut.nut
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  type nfa_transition = Kodkod.rel_expr * typ
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  type nfa_entry = typ * nfa_transition list
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  type nfa_table = nfa_entry list
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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_arity : 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 bounds_for_built_in_rels_in_formula :
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    bool -> int -> int -> int -> int -> Kodkod.formula -> Kodkod.bound 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 -> dtype_spec list -> nut -> Kodkod.bound
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  val merge_bounds : Kodkod.bound list -> Kodkod.bound list
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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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    extended_context -> int Typtab.table -> kodkod_constrs
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    -> nut NameTable.table -> dtype_spec list -> Kodkod.formula list
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  val kodkod_formula_from_nut :
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    int Typtab.table -> bool -> kodkod_constrs -> nut -> Kodkod.formula
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end;
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structure NitpickKodkod : NITPICK_KODKOD =
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struct
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open NitpickUtil
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open NitpickHOL
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open NitpickScope
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open NitpickPeephole
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open NitpickRep
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open NitpickNut
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type nfa_transition = Kodkod.rel_expr * typ
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type nfa_entry = typ * nfa_transition list
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type nfa_table = nfa_entry list
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structure NfaGraph = Graph(type key = typ val ord = TermOrd.typ_ord)
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(* int -> Kodkod.int_expr list *)
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fun flip_nums n = index_seq 1 n @ [0] |> map Kodkod.Num
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(* int -> int -> int -> Kodkod.bound list -> Kodkod.formula -> int *)
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fun univ_card nat_card int_card main_j0 bounds formula =
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  let
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    (* Kodkod.rel_expr -> int -> int *)
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    fun rel_expr_func r k =
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      Int.max (k, case r of
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                    Kodkod.Atom j => j + 1
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                  | Kodkod.AtomSeq (k', j0) => j0 + k'
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                  | _ => 0)
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    (* Kodkod.tuple -> int -> int *)
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    fun tuple_func t k =
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      case t of
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        Kodkod.Tuple js => fold Integer.max (map (Integer.add 1) js) k
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      | _ => k
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    (* Kodkod.tuple_set -> int -> int *)
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    fun tuple_set_func ts k =
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      Int.max (k, case ts of Kodkod.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 (Kodkod.fold_bound expr_F tuple_F) bounds 1
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               |> Kodkod.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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(* Proof.context -> bool -> string -> typ -> rep -> string *)
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fun bound_comment ctxt debug nick T R =
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  short_const_name nick ^
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  (if debug then " :: " ^ plain_string_from_yxml (Syntax.string_of_typ ctxt T)
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   else "") ^ " : " ^ string_for_rep R
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(* int -> int -> unit *)
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fun check_arity univ_card n =
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  if n > Kodkod.max_arity univ_card then
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    raise LIMIT ("NitpickKodkod.check_arity",
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                 "arity " ^ string_of_int n ^ " too large for universe of \
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                 \cardinality " ^ string_of_int univ_card)
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  else
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    ()
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(* bool -> int -> int list -> Kodkod.tuple *)
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fun kk_tuple debug univ_card js =
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  if debug then
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    Kodkod.Tuple js
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  else
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    Kodkod.TupleIndex (length js,
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                       fold (fn j => fn accum => accum * univ_card + j) js 0)
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(* (int * int) list -> Kodkod.tuple_set *)
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val tuple_set_from_atom_schema =
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  foldl1 Kodkod.TupleProduct o map Kodkod.TupleAtomSeq
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(* rep -> Kodkod.tuple_set *)
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val upper_bound_for_rep = tuple_set_from_atom_schema o atom_schema_of_rep
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(* int -> Kodkod.int_bound list *)
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fun sequential_int_bounds n =
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  [(NONE, map (Kodkod.TupleSet o single o Kodkod.Tuple o single)
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              (index_seq 0 n))]
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(* Kodkod.formula -> Kodkod.n_ary_index list *)
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fun built_in_rels_in_formula formula =
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  let
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    (* Kodkod.rel_expr -> Kodkod.n_ary_index list -> Kodkod.n_ary_index list *)
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    fun rel_expr_func (Kodkod.Rel (n, j)) rels =
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        (case AList.lookup (op =) (#rels initial_pool) n of
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           SOME k => (j < k ? insert (op =) (n, j)) rels
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         | NONE => rels)
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      | rel_expr_func _ rels = rels
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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 Kodkod.fold_formula expr_F formula [] end
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val max_table_size = 65536
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(* int -> unit *)
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fun check_table_size k =
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  if k > max_table_size then
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    raise LIMIT ("NitpickKodkod.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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(* bool -> int -> int * int -> (int -> int) -> Kodkod.tuple list *)
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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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(* bool -> int -> int * int -> int -> (int * int -> int) -> Kodkod.tuple list *)
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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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(* bool -> int -> int * int -> int -> (int * int -> int * int)
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   -> Kodkod.tuple list *)
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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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(* bool -> int -> int * int -> (int * int -> int) -> Kodkod.tuple list *)
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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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(* bool -> int -> int * int -> (int * int -> int * int) -> Kodkod.tuple list *)
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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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(* int * int -> int *)
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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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(* int * int -> int * int *)
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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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   203
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(* bool -> int -> int -> int -> int -> int * int
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   -> string * bool * Kodkod.tuple list *)
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   206
fun tabulate_built_in_rel debug univ_card nat_card int_card j0 (x as (n, _)) =
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   207
  (check_arity univ_card n;
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   if Kodkod.Rel 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 Kodkod.Rel 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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   213
   else if Kodkod.Rel 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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   215
   else if Kodkod.Rel 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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   217
   else if Kodkod.Rel x = nat_subtract_rel then
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   218
     ("nat_subtract",
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   219
      tabulate_op2 debug univ_card (nat_card, j0) j0 (op nat_minus))
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   220
   else if Kodkod.Rel x = int_subtract_rel then
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parents:
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   221
     ("int_subtract", tabulate_int_op2 debug univ_card (int_card, j0) (op -))
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   222
   else if Kodkod.Rel x = nat_multiply_rel then
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parents:
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   223
     ("nat_multiply", tabulate_nat_op2 debug univ_card (nat_card, j0) (op * ))
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   224
   else if Kodkod.Rel 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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   226
   else if Kodkod.Rel 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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   228
   else if Kodkod.Rel x = int_divide_rel then
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   229
     ("int_divide", tabulate_int_op2 debug univ_card (int_card, j0) isa_div)
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   230
   else if Kodkod.Rel x = nat_modulo_rel then
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     ("nat_modulo", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_mod)
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   232
   else if Kodkod.Rel x = int_modulo_rel then
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parents:
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   233
     ("int_modulo", tabulate_int_op2 debug univ_card (int_card, j0) isa_mod)
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   234
   else if Kodkod.Rel x = nat_less_rel then
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parents:
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     ("nat_less", tabulate_nat_op2 debug univ_card (nat_card, j0)
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   236
                                   (int_for_bool o op <))
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   237
   else if Kodkod.Rel x = int_less_rel then
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parents:
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   238
     ("int_less", tabulate_int_op2 debug univ_card (int_card, j0)
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   239
                                   (int_for_bool o op <))
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   240
   else if Kodkod.Rel x = gcd_rel then
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parents:
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     ("gcd", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_gcd)
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   242
   else if Kodkod.Rel x = lcm_rel then
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     ("lcm", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_lcm)
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   244
   else if Kodkod.Rel 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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   246
                                      isa_norm_frac)
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   247
   else
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     raise ARG ("NitpickKodkod.tabulate_built_in_rel", "unknown relation"))
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   249
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(* bool -> int -> int -> int -> int -> int * int -> Kodkod.rel_expr
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   251
   -> Kodkod.bound *)
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   252
fun bound_for_built_in_rel debug univ_card nat_card int_card j0 x =
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   253
  let
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   254
    val (nick, ts) = tabulate_built_in_rel debug univ_card nat_card int_card
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   255
                                           j0 x
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   256
  in ([(x, nick)], [Kodkod.TupleSet ts]) end
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   257
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(* bool -> int -> int -> int -> int -> Kodkod.formula -> Kodkod.bound list *)
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   259
fun bounds_for_built_in_rels_in_formula debug univ_card nat_card int_card j0 =
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  map (bound_for_built_in_rel debug univ_card nat_card int_card j0)
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   261
  o built_in_rels_in_formula
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   262
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parents:
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   263
(* Proof.context -> bool -> nut -> Kodkod.bound *)
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parents:
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   264
fun bound_for_plain_rel ctxt debug (u as FreeRel (x, T, R, nick)) =
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   265
    ([(x, bound_comment ctxt debug nick T R)],
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   266
     if nick = @{const_name bisim_iterator_max} then
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   267
       case R of
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   268
         Atom (k, j0) => [Kodkod.TupleSet [Kodkod.Tuple [k - 1 + j0]]]
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       | _ => raise NUT ("NitpickKodkod.bound_for_plain_rel", [u])
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   270
     else
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       [Kodkod.TupleSet [], upper_bound_for_rep R])
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  | bound_for_plain_rel _ _ u =
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   273
    raise NUT ("NitpickKodkod.bound_for_plain_rel", [u])
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   274
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   275
(* Proof.context -> bool -> dtype_spec list -> nut -> Kodkod.bound *)
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   276
fun bound_for_sel_rel ctxt debug dtypes
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        (FreeRel (x, T as Type ("fun", [T1, T2]), R as Func (Atom (_, j0), R2),
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   278
                  nick)) =
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   279
    let
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   280
      val constr as {delta, epsilon, exclusive, explicit_max, ...} =
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   281
        constr_spec dtypes (original_name nick, T1)
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   282
    in
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   283
      ([(x, bound_comment ctxt debug nick T R)],
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   284
       if explicit_max = 0 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   285
         [Kodkod.TupleSet []]
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   286
       else
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   287
         let val ts = Kodkod.TupleAtomSeq (epsilon - delta, delta + j0) in
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   288
           if R2 = Formula Neut then
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   289
             [ts] |> not exclusive ? cons (Kodkod.TupleSet [])
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   290
           else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   291
             [Kodkod.TupleSet [],
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   292
              Kodkod.TupleProduct (ts, upper_bound_for_rep R2)]
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   293
         end)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   294
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   295
  | bound_for_sel_rel _ _ _ u =
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   296
    raise NUT ("NitpickKodkod.bound_for_sel_rel", [u])
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   297
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   298
(* Kodkod.bound list -> Kodkod.bound list *)
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   299
fun merge_bounds bs =
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   300
  let
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   301
    (* Kodkod.bound -> int *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   302
    fun arity (zs, _) = fst (fst (hd zs))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   303
    (* Kodkod.bound list -> Kodkod.bound -> Kodkod.bound list
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   304
       -> Kodkod.bound list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   305
    fun add_bound ds b [] = List.revAppend (ds, [b])
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   306
      | add_bound ds b (c :: cs) =
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   307
        if arity b = arity c andalso snd b = snd c then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   308
          List.revAppend (ds, (fst c @ fst b, snd c) :: cs)
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   309
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   310
          add_bound (c :: ds) b cs
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   311
  in fold (add_bound []) bs [] end
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   312
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   313
(* int -> int -> Kodkod.rel_expr list *)
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   314
fun unary_var_seq j0 n = map (curry Kodkod.Var 1) (index_seq j0 n)
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   315
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   316
(* int list -> Kodkod.rel_expr *)
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   317
val singleton_from_combination = foldl1 Kodkod.Product o map Kodkod.Atom
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   318
(* rep -> Kodkod.rel_expr list *)
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   319
fun all_singletons_for_rep R =
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   320
  if is_lone_rep R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   321
    all_combinations_for_rep R |> map singleton_from_combination
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parents:
diff changeset
   322
  else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   323
    raise REP ("NitpickKodkod.all_singletons_for_rep", [R])
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diff changeset
   324
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   325
(* Kodkod.rel_expr -> Kodkod.rel_expr list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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diff changeset
   326
fun unpack_products (Kodkod.Product (r1, r2)) =
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parents:
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   327
    unpack_products r1 @ unpack_products r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   328
  | unpack_products r = [r]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   329
fun unpack_joins (Kodkod.Join (r1, r2)) = unpack_joins r1 @ unpack_joins r2
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   330
  | unpack_joins r = [r]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   331
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   332
(* rep -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   333
val empty_rel_for_rep = empty_n_ary_rel o arity_of_rep
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parents:
diff changeset
   334
fun full_rel_for_rep R =
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parents:
diff changeset
   335
  case atom_schema_of_rep R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   336
    [] => raise REP ("NitpickKodkod.full_rel_for_rep", [R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   337
  | schema => foldl1 Kodkod.Product (map Kodkod.AtomSeq schema)
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   338
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   339
(* int -> int list -> Kodkod.decl list *)
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parents:
diff changeset
   340
fun decls_for_atom_schema j0 schema =
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parents:
diff changeset
   341
  map2 (fn j => fn x => Kodkod.DeclOne ((1, j), Kodkod.AtomSeq x))
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   342
       (index_seq j0 (length schema)) schema
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parents:
diff changeset
   343
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   344
(* The type constraint below is a workaround for a Poly/ML bug. *)
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   345
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   346
(* FIXME: clean up *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   347
(* kodkod_constrs -> rep -> Kodkod.rel_expr -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   348
fun d_n_ary_function ({kk_all, kk_join, kk_lone, kk_one, ...} : kodkod_constrs)
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   349
                     R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   350
  let val body_R = body_rep R in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   351
    if is_lone_rep body_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   352
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   353
        val binder_schema = atom_schema_of_reps (binder_reps R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   354
        val body_schema = atom_schema_of_rep body_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   355
        val one = is_one_rep body_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   356
        val opt_x = case r of Kodkod.Rel x => SOME x | _ => NONE
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   357
      in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   358
        if opt_x <> NONE andalso length binder_schema = 1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   359
           andalso length body_schema = 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   360
          (if one then Kodkod.Function else Kodkod.Functional)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   361
              (the opt_x, Kodkod.AtomSeq (hd binder_schema),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   362
               Kodkod.AtomSeq (hd body_schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   363
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   364
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   365
            val decls = decls_for_atom_schema ~1 binder_schema
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   366
            val vars = unary_var_seq ~1 (length binder_schema)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   367
            val kk_xone = if one then kk_one else kk_lone
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   368
          in kk_all decls (kk_xone (fold kk_join vars r)) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   369
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   370
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   371
      Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   372
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   373
fun kk_n_ary_function kk R (r as Kodkod.Rel _) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   374
    (* FIXME: weird test *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   375
    if not (is_opt_rep R) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   376
      if r = suc_rel then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   377
        Kodkod.False
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   378
      else if r = nat_add_rel then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   379
        formula_for_bool (card_of_rep (body_rep R) = 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   380
      else if r = nat_multiply_rel then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   381
        formula_for_bool (card_of_rep (body_rep R) <= 2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   382
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   383
        d_n_ary_function kk R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   384
    else if r = nat_subtract_rel then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   385
      Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   386
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   387
      d_n_ary_function kk R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   388
  | kk_n_ary_function kk R r = d_n_ary_function kk R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   389
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   390
(* kodkod_constrs -> Kodkod.rel_expr list -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   391
fun kk_disjoint_sets _ [] = Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   392
  | kk_disjoint_sets (kk as {kk_and, kk_no, kk_intersect, ...} : kodkod_constrs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   393
                     (r :: rs) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   394
    fold (kk_and o kk_no o kk_intersect r) rs (kk_disjoint_sets kk rs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   395
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   396
(* int -> kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   397
   -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   398
fun basic_rel_let j ({kk_rel_let, ...} : kodkod_constrs) f r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   399
  if inline_rel_expr r then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   400
    f r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   401
  else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   402
    let val x = (Kodkod.arity_of_rel_expr r, j) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   403
      kk_rel_let [Kodkod.AssignRelReg (x, r)] (f (Kodkod.RelReg x))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   404
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   405
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   406
(* kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr) -> Kodkod.rel_expr
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   407
   -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   408
val single_rel_let = basic_rel_let 0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   409
(* kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   410
   -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   411
fun double_rel_let kk f r1 r2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   412
  single_rel_let kk (fn r1 => basic_rel_let 1 kk (f r1) r2) r1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   413
(* kodkod_constrs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   414
   -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   415
   -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   416
   -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   417
fun triple_rel_let kk f r1 r2 r3 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   418
  double_rel_let kk (fn r1 => fn r2 => basic_rel_let 2 kk (f r1 r2) r3) r1 r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   419
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   420
(* kodkod_constrs -> int -> Kodkod.formula -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   421
fun atom_from_formula ({kk_rel_if, ...} : kodkod_constrs) j0 f =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   422
  kk_rel_if f (Kodkod.Atom (j0 + 1)) (Kodkod.Atom j0)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   423
(* kodkod_constrs -> rep -> Kodkod.formula -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   424
fun rel_expr_from_formula kk R f =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   425
  case unopt_rep R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   426
    Atom (2, j0) => atom_from_formula kk j0 f
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   427
  | _ => raise REP ("NitpickKodkod.rel_expr_from_formula", [R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   428
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   429
(* kodkod_cotrs -> int -> int -> Kodkod.rel_expr -> Kodkod.rel_expr list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   430
fun unpack_vect_in_chunks ({kk_project_seq, ...} : kodkod_constrs) chunk_arity
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   431
                          num_chunks r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   432
  List.tabulate (num_chunks, fn j => kk_project_seq r (j * chunk_arity)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   433
                                                    chunk_arity)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   434
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   435
(* kodkod_constrs -> bool -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   436
   -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   437
fun kk_n_fold_join
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   438
        (kk as {kk_intersect, kk_product, kk_join, kk_project_seq, ...}) one R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   439
        res_R r1 r2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   440
  case arity_of_rep R1 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   441
    1 => kk_join r1 r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   442
  | arity1 =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   443
    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   444
      val unpacked_rs1 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   445
        if inline_rel_expr r1 then unpack_vect_in_chunks kk 1 arity1 r1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   446
        else unpack_products r1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   447
    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   448
      if one andalso length unpacked_rs1 = arity1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   449
        fold kk_join unpacked_rs1 r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   450
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   451
        kk_project_seq
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   452
            (kk_intersect (kk_product r1 (full_rel_for_rep res_R)) r2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   453
            arity1 (arity_of_rep res_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   454
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   455
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   456
(* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr list
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   457
   -> Kodkod.rel_expr list -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   458
fun kk_case_switch (kk as {kk_union, kk_product, ...}) R1 R2 r rs1 rs2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   459
  if rs1 = rs2 then r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   460
  else kk_n_fold_join kk true R1 R2 r (fold1 kk_union (map2 kk_product rs1 rs2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   461
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   462
val lone_rep_fallback_max_card = 4096
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   463
val some_j0 = 0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   464
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   465
(* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   466
fun lone_rep_fallback kk new_R old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   467
  if old_R = new_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   468
    r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   469
  else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   470
    let val card = card_of_rep old_R in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   471
      if is_lone_rep old_R andalso is_lone_rep new_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   472
         andalso card = card_of_rep new_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   473
        if card >= lone_rep_fallback_max_card then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   474
          raise LIMIT ("NitpickKodkod.lone_rep_fallback",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   475
                       "too high cardinality (" ^ string_of_int card ^ ")")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   476
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   477
          kk_case_switch kk old_R new_R r (all_singletons_for_rep old_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   478
                         (all_singletons_for_rep new_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   479
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   480
        raise REP ("NitpickKodkod.lone_rep_fallback", [old_R, new_R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   481
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   482
(* kodkod_constrs -> int * int -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   483
and atom_from_rel_expr kk (x as (k, j0)) old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   484
  case old_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   485
    Func (R1, R2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   486
    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   487
      val dom_card = card_of_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   488
      val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   489
    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   490
      atom_from_rel_expr kk x (Vect (dom_card, R2'))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   491
                         (vect_from_rel_expr kk dom_card R2' old_R r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   492
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   493
  | Opt _ => raise REP ("NitpickKodkod.atom_from_rel_expr", [old_R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   494
  | _ => lone_rep_fallback kk (Atom x) old_R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   495
(* kodkod_constrs -> rep list -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   496
and struct_from_rel_expr kk Rs old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   497
  case old_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   498
    Atom _ => lone_rep_fallback kk (Struct Rs) old_R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   499
  | Struct Rs' =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   500
    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   501
      val Rs = filter (not_equal Unit) Rs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   502
      val Rs' = filter (not_equal Unit) Rs'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   503
    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   504
      if Rs' = Rs then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   505
        r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   506
      else if map card_of_rep Rs' = map card_of_rep Rs then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   507
        let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   508
          val old_arities = map arity_of_rep Rs'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   509
          val old_offsets = offset_list old_arities
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   510
          val old_rs = map2 (#kk_project_seq kk r) old_offsets old_arities
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   511
        in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   512
          fold1 (#kk_product kk)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   513
                (map3 (rel_expr_from_rel_expr kk) Rs Rs' old_rs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   514
        end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   515
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   516
        lone_rep_fallback kk (Struct Rs) old_R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   517
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   518
  | _ => raise REP ("NitpickKodkod.struct_from_rel_expr", [old_R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   519
(* kodkod_constrs -> int -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   520
and vect_from_rel_expr kk k R old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   521
  case old_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   522
    Atom _ => lone_rep_fallback kk (Vect (k, R)) old_R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   523
  | Vect (k', R') =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   524
    if k = k' andalso R = R' then r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   525
    else lone_rep_fallback kk (Vect (k, R)) old_R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   526
  | Func (R1, Formula Neut) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   527
    if k = card_of_rep R1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   528
      fold1 (#kk_product kk)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   529
            (map (fn arg_r =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   530
                     rel_expr_from_formula kk R (#kk_subset kk arg_r r))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   531
                 (all_singletons_for_rep R1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   532
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   533
      raise REP ("NitpickKodkod.vect_from_rel_expr", [old_R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   534
  | Func (Unit, R2) => rel_expr_from_rel_expr kk R R2 r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   535
  | Func (R1, R2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   536
    fold1 (#kk_product kk)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   537
          (map (fn arg_r =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   538
                   rel_expr_from_rel_expr kk R R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   539
                                         (kk_n_fold_join kk true R1 R2 arg_r r))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   540
               (all_singletons_for_rep R1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   541
  | _ => raise REP ("NitpickKodkod.vect_from_rel_expr", [old_R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   542
(* kodkod_constrs -> rep -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   543
and func_from_no_opt_rel_expr kk R1 R2 (Atom x) r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   544
    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   545
      val dom_card = card_of_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   546
      val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   547
    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   548
      func_from_no_opt_rel_expr kk R1 R2 (Vect (dom_card, R2'))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   549
                                (vect_from_rel_expr kk dom_card R2' (Atom x) r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   550
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   551
  | func_from_no_opt_rel_expr kk Unit R2 old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   552
    (case old_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   553
       Vect (k, R') => rel_expr_from_rel_expr kk R2 R' r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   554
     | Func (Unit, R2') => rel_expr_from_rel_expr kk R2 R2' r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   555
     | Func (Atom (1, _), Formula Neut) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   556
       (case unopt_rep R2 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   557
          Atom (2, j0) => atom_from_formula kk j0 (#kk_some kk r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   558
        | _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   559
                          [old_R, Func (Unit, R2)]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   560
     | Func (R1', R2') =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   561
       rel_expr_from_rel_expr kk R2 R2' (#kk_project_seq kk r (arity_of_rep R1')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   562
                              (arity_of_rep R2'))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   563
     | _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   564
                       [old_R, Func (Unit, R2)]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   565
  | func_from_no_opt_rel_expr kk R1 (Formula Neut) old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   566
    (case old_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   567
       Vect (k, Atom (2, j0)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   568
       let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   569
         val args_rs = all_singletons_for_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   570
         val vals_rs = unpack_vect_in_chunks kk 1 k r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   571
         (* Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   572
         fun empty_or_singleton_set_for arg_r val_r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   573
           #kk_join kk val_r (#kk_product kk (Kodkod.Atom (j0 + 1)) arg_r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   574
       in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   575
         fold1 (#kk_union kk) (map2 empty_or_singleton_set_for args_rs vals_rs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   576
       end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   577
     | Func (R1', Formula Neut) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   578
       if R1 = R1' then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   579
         r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   580
       else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   581
         let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   582
           val schema = atom_schema_of_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   583
           val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   584
                    |> rel_expr_from_rel_expr kk R1' R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   585
         in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   586
           #kk_comprehension kk (decls_for_atom_schema ~1 schema)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   587
                                (#kk_subset kk r1 r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   588
         end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   589
     | Func (Unit, (Atom (2, j0))) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   590
       #kk_rel_if kk (#kk_rel_eq kk r (Kodkod.Atom (j0 + 1)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   591
                  (full_rel_for_rep R1) (empty_rel_for_rep R1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   592
     | Func (R1', Atom (2, j0)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   593
       func_from_no_opt_rel_expr kk R1 (Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   594
           (Func (R1', Formula Neut)) (#kk_join kk r (Kodkod.Atom (j0 + 1)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   595
     | _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   596
                       [old_R, Func (R1, Formula Neut)]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   597
  | func_from_no_opt_rel_expr kk R1 R2 old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   598
    case old_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   599
      Vect (k, R) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   600
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   601
        val args_rs = all_singletons_for_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   602
        val vals_rs = unpack_vect_in_chunks kk (arity_of_rep R) k r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   603
                      |> map (rel_expr_from_rel_expr kk R2 R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   604
      in fold1 (#kk_union kk) (map2 (#kk_product kk) args_rs vals_rs) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   605
    | Func (R1', Formula Neut) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   606
      (case R2 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   607
         Atom (x as (2, j0)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   608
         let val schema = atom_schema_of_rep R1 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   609
           if length schema = 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   610
             #kk_override kk (#kk_product kk (Kodkod.AtomSeq (hd schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   611
                                             (Kodkod.Atom j0))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   612
                             (#kk_product kk r (Kodkod.Atom (j0 + 1)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   613
           else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   614
             let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   615
               val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   616
                        |> rel_expr_from_rel_expr kk R1' R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   617
               val r2 = Kodkod.Var (1, ~(length schema) - 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   618
               val r3 = atom_from_formula kk j0 (#kk_subset kk r1 r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   619
             in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   620
               #kk_comprehension kk (decls_for_atom_schema ~1 (schema @ [x]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   621
                                 (#kk_rel_eq kk r2 r3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   622
             end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   623
           end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   624
         | _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   625
                           [old_R, Func (R1, R2)]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   626
    | Func (Unit, R2') =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   627
      let val j0 = some_j0 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   628
        func_from_no_opt_rel_expr kk R1 R2 (Func (Atom (1, j0), R2'))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   629
                                  (#kk_product kk (Kodkod.Atom j0) r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   630
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   631
    | Func (R1', R2') =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   632
      if R1 = R1' andalso R2 = R2' then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   633
        r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   634
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   635
        let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   636
          val dom_schema = atom_schema_of_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   637
          val ran_schema = atom_schema_of_rep R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   638
          val dom_prod = fold1 (#kk_product kk)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   639
                               (unary_var_seq ~1 (length dom_schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   640
                         |> rel_expr_from_rel_expr kk R1' R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   641
          val ran_prod = fold1 (#kk_product kk)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   642
                               (unary_var_seq (~(length dom_schema) - 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   643
                                              (length ran_schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   644
                         |> rel_expr_from_rel_expr kk R2' R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   645
          val app = kk_n_fold_join kk true R1' R2' dom_prod r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   646
        in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   647
          #kk_comprehension kk (decls_for_atom_schema ~1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   648
                                                      (dom_schema @ ran_schema))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   649
                               (#kk_subset kk ran_prod app)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   650
        end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   651
    | _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   652
                      [old_R, Func (R1, R2)])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   653
(* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   654
and rel_expr_from_rel_expr kk new_R old_R r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   655
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   656
    val unopt_old_R = unopt_rep old_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   657
    val unopt_new_R = unopt_rep new_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   658
  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   659
    if unopt_old_R <> old_R andalso unopt_new_R = new_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   660
      raise REP ("NitpickKodkod.rel_expr_from_rel_expr", [old_R, new_R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   661
    else if unopt_new_R = unopt_old_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   662
      r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   663
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   664
      (case unopt_new_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   665
         Atom x => atom_from_rel_expr kk x
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   666
       | Struct Rs => struct_from_rel_expr kk Rs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   667
       | Vect (k, R') => vect_from_rel_expr kk k R'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   668
       | Func (R1, R2) => func_from_no_opt_rel_expr kk R1 R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   669
       | _ => raise REP ("NitpickKodkod.rel_expr_from_rel_expr",
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   670
                         [old_R, new_R]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   671
          unopt_old_R r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   672
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   673
(* kodkod_constrs -> rep -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   674
and rel_expr_to_func kk R1 R2 = rel_expr_from_rel_expr kk (Func (R1, R2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   675
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   676
(* kodkod_constrs -> nut -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   677
fun declarative_axiom_for_plain_rel kk (FreeRel (x, _, R as Func _, nick)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   678
    kk_n_ary_function kk (R |> nick = @{const_name List.set} ? unopt_rep)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   679
                      (Kodkod.Rel x)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   680
  | declarative_axiom_for_plain_rel ({kk_lone, kk_one, ...} : kodkod_constrs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   681
                                    (FreeRel (x, _, R, _)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   682
    if is_one_rep R then kk_one (Kodkod.Rel x)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   683
    else if is_lone_rep R andalso card_of_rep R > 1 then kk_lone (Kodkod.Rel x)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   684
    else Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   685
  | declarative_axiom_for_plain_rel _ u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   686
    raise NUT ("NitpickKodkod.declarative_axiom_for_plain_rel", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   687
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   688
(* nut NameTable.table -> styp -> Kodkod.rel_expr * rep * int *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   689
fun const_triple rel_table (x as (s, T)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   690
  case the_name rel_table (ConstName (s, T, Any)) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   691
    FreeRel ((n, j), _, R, _) => (Kodkod.Rel (n, j), R, n)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   692
  | _ => raise TERM ("NitpickKodkod.const_triple", [Const x])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   693
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   694
(* nut NameTable.table -> styp -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   695
fun discr_rel_expr rel_table = #1 o const_triple rel_table o discr_for_constr
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   696
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   697
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   698
   -> styp -> int -> nfa_transition list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   699
fun nfa_transitions_for_sel ext_ctxt ({kk_project, ...} : kodkod_constrs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   700
                            rel_table (dtypes : dtype_spec list) constr_x n =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   701
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   702
    val x as (_, T) = boxed_nth_sel_for_constr ext_ctxt constr_x n
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   703
    val (r, R, arity) = const_triple rel_table x
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   704
    val type_schema = type_schema_of_rep T R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   705
  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   706
    map_filter (fn (j, T) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   707
                   if forall (not_equal T o #typ) dtypes then NONE
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   708
                   else SOME (kk_project r (map Kodkod.Num [0, j]), T))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   709
               (index_seq 1 (arity - 1) ~~ tl type_schema)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   710
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   711
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   712
   -> styp -> nfa_transition list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   713
fun nfa_transitions_for_constr ext_ctxt kk rel_table dtypes (x as (_, T)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   714
  maps (nfa_transitions_for_sel ext_ctxt kk rel_table dtypes x)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   715
       (index_seq 0 (num_sels_for_constr_type T))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   716
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   717
   -> dtype_spec -> nfa_entry option *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   718
fun nfa_entry_for_datatype _ _ _ _ ({co = true, ...} : dtype_spec) = NONE
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   719
  | nfa_entry_for_datatype ext_ctxt kk rel_table dtypes
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   720
                           ({typ, constrs, ...} : dtype_spec) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   721
    SOME (typ, maps (nfa_transitions_for_constr ext_ctxt kk rel_table dtypes
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   722
                     o #const) constrs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   723
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   724
val empty_rel = Kodkod.Product (Kodkod.None, Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   725
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   726
(* nfa_table -> typ -> typ -> Kodkod.rel_expr list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   727
fun direct_path_rel_exprs nfa start final =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   728
  case AList.lookup (op =) nfa final of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   729
    SOME trans => map fst (filter (equal start o snd) trans)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   730
  | NONE => []
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   731
(* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   732
and any_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start final =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   733
    fold kk_union (direct_path_rel_exprs nfa start final)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   734
         (if start = final then Kodkod.Iden else empty_rel)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   735
  | any_path_rel_expr (kk as {kk_union, ...}) nfa (q :: qs) start final =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   736
    kk_union (any_path_rel_expr kk nfa qs start final)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   737
             (knot_path_rel_expr kk nfa qs start q final)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   738
(* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> typ
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   739
   -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   740
and knot_path_rel_expr (kk as {kk_join, kk_reflexive_closure, ...}) nfa qs start
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   741
                       knot final =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   742
  kk_join (kk_join (any_path_rel_expr kk nfa qs knot final)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   743
                   (kk_reflexive_closure (loop_path_rel_expr kk nfa qs knot)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   744
          (any_path_rel_expr kk nfa qs start knot)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   745
(* kodkod_constrs -> nfa_table -> typ list -> typ -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   746
and loop_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   747
    fold kk_union (direct_path_rel_exprs nfa start start) empty_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   748
  | loop_path_rel_expr (kk as {kk_union, kk_closure, ...}) nfa (q :: qs) start =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   749
    if start = q then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   750
      kk_closure (loop_path_rel_expr kk nfa qs start)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   751
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   752
      kk_union (loop_path_rel_expr kk nfa qs start)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   753
               (knot_path_rel_expr kk nfa qs start q start)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   754
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   755
(* nfa_table -> unit NfaGraph.T *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   756
fun graph_for_nfa nfa =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   757
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   758
    (* typ -> unit NfaGraph.T -> unit NfaGraph.T *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   759
    fun new_node q = perhaps (try (NfaGraph.new_node (q, ())))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   760
    (* nfa_table -> unit NfaGraph.T -> unit NfaGraph.T *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   761
    fun add_nfa [] = I
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   762
      | add_nfa ((_, []) :: nfa) = add_nfa nfa
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   763
      | add_nfa ((q, ((_, q') :: transitions)) :: nfa) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   764
        add_nfa ((q, transitions) :: nfa) o NfaGraph.add_edge (q, q') o
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   765
        new_node q' o new_node q
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   766
  in add_nfa nfa NfaGraph.empty end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   767
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   768
(* nfa_table -> nfa_table list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   769
fun strongly_connected_sub_nfas nfa =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   770
  nfa |> graph_for_nfa |> NfaGraph.strong_conn
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   771
      |> map (fn keys => filter (member (op =) keys o fst) nfa)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   772
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   773
(* dtype_spec list -> kodkod_constrs -> nfa_table -> typ -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   774
fun acyclicity_axiom_for_datatype dtypes kk nfa start =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   775
  #kk_no kk (#kk_intersect kk
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   776
                 (loop_path_rel_expr kk nfa (map fst nfa) start) Kodkod.Iden)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   777
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   778
   -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   779
fun acyclicity_axioms_for_datatypes ext_ctxt kk rel_table dtypes =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   780
  map_filter (nfa_entry_for_datatype ext_ctxt kk rel_table dtypes) dtypes
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   781
  |> strongly_connected_sub_nfas
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   782
  |> maps (fn nfa => map (acyclicity_axiom_for_datatype dtypes kk nfa o fst)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   783
                         nfa)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   784
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   785
(* extended_context -> int -> kodkod_constrs -> nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   786
   -> Kodkod.rel_expr -> constr_spec -> int -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   787
fun sel_axiom_for_sel ext_ctxt j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   788
        (kk as {kk_all, kk_implies, kk_formula_if, kk_subset, kk_rel_eq, kk_no,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   789
                kk_join, kk_project, ...}) rel_table dom_r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   790
        ({const, delta, epsilon, exclusive, explicit_max, ...} : constr_spec)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   791
        n =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   792
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   793
    val x as (_, T) = boxed_nth_sel_for_constr ext_ctxt const n
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   794
    val (r, R, arity) = const_triple rel_table x
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   795
    val R2 = dest_Func R |> snd
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   796
    val z = (epsilon - delta, delta + j0)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   797
  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   798
    if exclusive then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   799
      kk_n_ary_function kk (Func (Atom z, R2)) r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   800
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   801
      let val r' = kk_join (Kodkod.Var (1, 0)) r in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   802
        kk_all [Kodkod.DeclOne ((1, 0), Kodkod.AtomSeq z)]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   803
               (kk_formula_if (kk_subset (Kodkod.Var (1, 0)) dom_r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   804
                              (kk_n_ary_function kk R2 r')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   805
                              (kk_no r'))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   806
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   807
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   808
(* extended_context -> int -> kodkod_constrs -> nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   809
   -> constr_spec -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   810
fun sel_axioms_for_constr ext_ctxt j0 kk rel_table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   811
        (constr as {const, delta, epsilon, explicit_max, ...}) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   812
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   813
    val honors_explicit_max =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   814
      explicit_max < 0 orelse epsilon - delta <= explicit_max
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   815
  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   816
    if explicit_max = 0 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   817
      [formula_for_bool honors_explicit_max]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   818
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   819
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   820
        val ran_r = discr_rel_expr rel_table const
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   821
        val max_axiom =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   822
          if honors_explicit_max then Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   823
          else Kodkod.LE (Kodkod.Cardinality ran_r, Kodkod.Num explicit_max)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   824
      in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   825
        max_axiom ::
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   826
        map (sel_axiom_for_sel ext_ctxt j0 kk rel_table ran_r constr)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   827
            (index_seq 0 (num_sels_for_constr_type (snd const)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   828
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   829
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   830
(* extended_context -> int -> kodkod_constrs -> nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   831
   -> dtype_spec -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   832
fun sel_axioms_for_datatype ext_ctxt j0 kk rel_table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   833
                            ({constrs, ...} : dtype_spec) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   834
  maps (sel_axioms_for_constr ext_ctxt j0 kk rel_table) constrs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   835
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   836
(* extended_context -> kodkod_constrs -> nut NameTable.table -> constr_spec
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   837
   -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   838
fun uniqueness_axiom_for_constr ext_ctxt
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   839
        ({kk_all, kk_implies, kk_and, kk_rel_eq, kk_lone, kk_join, ...}
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   840
         : kodkod_constrs) rel_table ({const, ...} : constr_spec) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   841
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   842
    (* Kodkod.rel_expr -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   843
    fun conjunct_for_sel r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   844
      kk_rel_eq (kk_join (Kodkod.Var (1, 0)) r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   845
                (kk_join (Kodkod.Var (1, 1)) r)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   846
    val num_sels = num_sels_for_constr_type (snd const)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   847
    val triples = map (const_triple rel_table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   848
                       o boxed_nth_sel_for_constr ext_ctxt const)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   849
                      (~1 upto num_sels - 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   850
    val j0 = case triples |> hd |> #2 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   851
               Func (Atom (_, j0), _) => j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   852
             | R => raise REP ("NitpickKodkod.uniqueness_axiom_for_constr", [R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   853
    val set_r = triples |> hd |> #1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   854
  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   855
    if num_sels = 0 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   856
      kk_lone set_r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   857
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   858
      kk_all (map (Kodkod.DeclOne o rpair set_r o pair 1) [0, 1])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   859
             (kk_implies
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   860
                  (fold1 kk_and (map (conjunct_for_sel o #1) (tl triples)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   861
                  (kk_rel_eq (Kodkod.Var (1, 0)) (Kodkod.Var (1, 1))))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   862
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   863
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   864
   -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   865
fun uniqueness_axioms_for_datatype ext_ctxt kk rel_table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   866
                                   ({constrs, ...} : dtype_spec) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   867
  map (uniqueness_axiom_for_constr ext_ctxt kk rel_table) constrs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   868
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   869
(* constr_spec -> int *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   870
fun effective_constr_max ({delta, epsilon, ...} : constr_spec) = epsilon - delta
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   871
(* int -> kodkod_constrs -> nut NameTable.table -> dtype_spec
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   872
   -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   873
fun partition_axioms_for_datatype j0 (kk as {kk_rel_eq, kk_union, ...})
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   874
                                  rel_table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   875
                                  ({card, constrs, ...} : dtype_spec) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   876
  if forall #exclusive constrs then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   877
    [Integer.sum (map effective_constr_max constrs) = card |> formula_for_bool]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   878
  else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   879
    let val rs = map (discr_rel_expr rel_table o #const) constrs in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   880
      [kk_rel_eq (fold1 kk_union rs) (Kodkod.AtomSeq (card, j0)),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   881
       kk_disjoint_sets kk rs]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   882
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   883
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   884
(* extended_context -> int Typtab.table -> kodkod_constrs -> nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   885
   -> dtype_spec -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   886
fun other_axioms_for_datatype ext_ctxt ofs kk rel_table (dtype as {typ, ...}) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   887
  let val j0 = offset_of_type ofs typ in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   888
    sel_axioms_for_datatype ext_ctxt j0 kk rel_table dtype @
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   889
    uniqueness_axioms_for_datatype ext_ctxt kk rel_table dtype @
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   890
    partition_axioms_for_datatype j0 kk rel_table dtype
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   891
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   892
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   893
(* extended_context -> int Typtab.table -> kodkod_constrs -> nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   894
   -> dtype_spec list -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   895
fun declarative_axioms_for_datatypes ext_ctxt ofs kk rel_table dtypes =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   896
  acyclicity_axioms_for_datatypes ext_ctxt kk rel_table dtypes @
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   897
  maps (other_axioms_for_datatype ext_ctxt ofs kk rel_table) dtypes
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   898
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   899
(* int Typtab.table -> bool -> kodkod_constrs -> nut -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   900
fun kodkod_formula_from_nut ofs liberal
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   901
        (kk as {kk_all, kk_exist, kk_formula_let, kk_formula_if, kk_or, kk_not,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   902
                kk_iff, kk_implies, kk_and, kk_subset, kk_rel_eq, kk_no, kk_one,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   903
                kk_some, kk_rel_let, kk_rel_if, kk_union, kk_difference,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   904
                kk_intersect, kk_product, kk_join, kk_closure, kk_comprehension,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   905
                kk_project, kk_project_seq, kk_not3, kk_nat_less, kk_int_less,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   906
                ...}) u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   907
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   908
    val main_j0 = offset_of_type ofs bool_T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   909
    val bool_j0 = main_j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   910
    val bool_atom_R = Atom (2, main_j0)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   911
    val false_atom = Kodkod.Atom bool_j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   912
    val true_atom = Kodkod.Atom (bool_j0 + 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   913
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   914
    (* polarity -> int -> Kodkod.rel_expr -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   915
    fun formula_from_opt_atom polar j0 r =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   916
      case polar of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   917
        Neg => kk_not (kk_rel_eq r (Kodkod.Atom j0))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   918
      | _ => kk_rel_eq r (Kodkod.Atom (j0 + 1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   919
    (* int -> Kodkod.rel_expr -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   920
    val formula_from_atom = formula_from_opt_atom Pos
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   921
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   922
    (* Kodkod.formula -> Kodkod.formula -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   923
    fun kk_notimplies f1 f2 = kk_and f1 (kk_not f2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   924
    (* Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   925
    val kk_or3 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   926
      double_rel_let kk
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   927
          (fn r1 => fn r2 =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   928
              kk_rel_if (kk_subset true_atom (kk_union r1 r2)) true_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   929
                        (kk_intersect r1 r2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   930
    val kk_and3 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   931
      double_rel_let kk
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   932
          (fn r1 => fn r2 =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   933
              kk_rel_if (kk_subset false_atom (kk_union r1 r2)) false_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   934
                        (kk_intersect r1 r2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   935
    fun kk_notimplies3 r1 r2 = kk_and3 r1 (kk_not3 r2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   936
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   937
    (* int -> Kodkod.rel_expr -> Kodkod.formula list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   938
    val unpack_formulas =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   939
      map (formula_from_atom bool_j0) oo unpack_vect_in_chunks kk 1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   940
    (* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula) -> int
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   941
       -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   942
    fun kk_vect_set_op connective k r1 r2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   943
      fold1 kk_product (map2 (atom_from_formula kk bool_j0 oo connective)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   944
                             (unpack_formulas k r1) (unpack_formulas k r2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   945
    (* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula) -> int
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   946
       -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   947
    fun kk_vect_set_bool_op connective k r1 r2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   948
      fold1 kk_and (map2 connective (unpack_formulas k r1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   949
                         (unpack_formulas k r2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   950
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   951
    (* nut -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   952
    fun to_f u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   953
      case rep_of u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   954
        Formula polar =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   955
        (case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   956
           Cst (False, _, _) => Kodkod.False
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   957
         | Cst (True, _, _) => Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   958
         | Op1 (Not, _, _, u1) => kk_not (to_f u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   959
         | Op1 (Finite, _, _, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   960
           let val opt1 = is_opt_rep (rep_of u1) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   961
             case polar of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   962
               Neut => if opt1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   963
                         raise NUT ("NitpickKodkod.to_f (Finite)", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   964
                       else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   965
                         Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   966
             | Pos => formula_for_bool (not opt1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   967
             | Neg => Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   968
           end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   969
         | Op1 (Cast, _, _, u1) => to_f_with_polarity polar u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   970
         | Op2 (All, _, _, u1, u2) => kk_all (untuple to_decl u1) (to_f u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   971
         | Op2 (Exist, _, _, u1, u2) => kk_exist (untuple to_decl u1) (to_f u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   972
         | Op2 (Or, _, _, u1, u2) => kk_or (to_f u1) (to_f u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   973
         | Op2 (And, _, _, u1, u2) => kk_and (to_f u1) (to_f u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   974
         | Op2 (Less, T, Formula polar, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   975
           formula_from_opt_atom polar bool_j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   976
               (to_r (Op2 (Less, T, Opt bool_atom_R, u1, u2)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   977
         | Op2 (Subset, _, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   978
           let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   979
             val dom_T = domain_type (type_of u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   980
             val R1 = rep_of u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   981
             val R2 = rep_of u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   982
             val (dom_R, ran_R) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   983
               case min_rep R1 R2 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   984
                 Func (Unit, R') =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   985
                 (Atom (1, offset_of_type ofs dom_T), R')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   986
               | Func Rp => Rp
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   987
               | R => (Atom (card_of_domain_from_rep 2 R,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   988
                             offset_of_type ofs dom_T),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   989
                       if is_opt_rep R then Opt bool_atom_R else Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   990
             val set_R = Func (dom_R, ran_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   991
           in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   992
             if not (is_opt_rep ran_R) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   993
               to_set_bool_op kk_implies kk_subset u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   994
             else if polar = Neut then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   995
               raise NUT ("NitpickKodkod.to_f (Subset)", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   996
             else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   997
               let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   998
                 (* bool -> nut -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   999
                 fun set_to_r widen u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1000
                   if widen then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1001
                     kk_difference (full_rel_for_rep dom_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1002
                                   (kk_join (to_rep set_R u) false_atom)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1003
                   else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1004
                     kk_join (to_rep set_R u) true_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1005
                 val widen1 = (polar = Pos andalso is_opt_rep R1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1006
                 val widen2 = (polar = Neg andalso is_opt_rep R2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1007
               in kk_subset (set_to_r widen1 u1) (set_to_r widen2 u2) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1008
           end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1009
         | Op2 (DefEq, _, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1010
           (case min_rep (rep_of u1) (rep_of u2) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1011
              Unit => Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1012
            | Formula polar =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1013
              kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1014
            | min_R =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1015
              let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1016
                (* nut -> nut list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1017
                fun args (Op2 (Apply, _, _, u1, u2)) = u2 :: args u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1018
                  | args (Tuple (_, _, us)) = us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1019
                  | args _ = []
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1020
                val opt_arg_us = filter (is_opt_rep o rep_of) (args u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1021
              in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1022
                if null opt_arg_us orelse not (is_Opt min_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1023
                   orelse is_eval_name u1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1024
                  fold (kk_or o (kk_no o to_r)) opt_arg_us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1025
                       (kk_rel_eq (to_rep min_R u1) (to_rep min_R u2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1026
                else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1027
                  kk_no (kk_difference (to_rep min_R u1) (to_rep min_R u2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1028
              end)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1029
         | Op2 (Eq, T, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1030
           (case min_rep (rep_of u1) (rep_of u2) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1031
              Unit => Kodkod.True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1032
            | Formula polar =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1033
              kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1034
            | min_R =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1035
              if is_opt_rep min_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1036
                if polar = Neut then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1037
                  (* continuation of hackish optimization *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1038
                  kk_rel_eq (to_rep min_R u1) (to_rep min_R u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1039
                else if is_Cst Unrep u1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1040
                  to_could_be_unrep (polar = Neg) u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1041
                else if is_Cst Unrep u2 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1042
                  to_could_be_unrep (polar = Neg) u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1043
                else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1044
                  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1045
                    val r1 = to_rep min_R u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1046
                    val r2 = to_rep min_R u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1047
                    val both_opt = forall (is_opt_rep o rep_of) [u1, u2]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1048
                  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1049
                    (if polar = Pos then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1050
                       if not both_opt then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1051
                         kk_rel_eq r1 r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1052
                       else if is_lone_rep min_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1053
                               andalso arity_of_rep min_R = 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1054
                         kk_some (kk_intersect r1 r2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1055
                       else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1056
                         raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1057
                     else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1058
                       if is_lone_rep min_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1059
                         if arity_of_rep min_R = 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1060
                           kk_subset (kk_product r1 r2) Kodkod.Iden
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1061
                         else if not both_opt then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1062
                           (r1, r2) |> is_opt_rep (rep_of u2) ? swap
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1063
                                    |> uncurry kk_difference |> kk_no
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1064
                         else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1065
                           raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1066
                       else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1067
                         raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1068
                    handle SAME () =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1069
                           formula_from_opt_atom polar bool_j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1070
                               (to_guard [u1, u2] bool_atom_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1071
                                         (rel_expr_from_formula kk bool_atom_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1072
                                                            (kk_rel_eq r1 r2)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1073
                  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1074
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1075
                let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1076
                  val r1 = to_rep min_R u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1077
                  val r2 = to_rep min_R u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1078
                in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1079
                  if is_one_rep min_R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1080
                    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1081
                      val rs1 = unpack_products r1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1082
                      val rs2 = unpack_products r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1083
                    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1084
                      if length rs1 = length rs2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1085
                         andalso map Kodkod.arity_of_rel_expr rs1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1086
                                 = map Kodkod.arity_of_rel_expr rs2 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1087
                        fold1 kk_and (map2 kk_subset rs1 rs2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1088
                      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1089
                        kk_subset r1 r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1090
                    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1091
                  else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1092
                    kk_rel_eq r1 r2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1093
                end)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1094
         | Op2 (Apply, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1095
           (case (polar, rep_of u1) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1096
              (Neg, Func (R, Formula Neut)) => kk_subset (to_opt R u2) (to_r u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1097
            | _ =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1098
              to_f_with_polarity polar
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1099
                 (Op2 (Apply, T, Opt (Atom (2, offset_of_type ofs T)), u1, u2)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1100
         | Op3 (Let, _, _, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1101
           kk_formula_let [to_expr_assign u1 u2] (to_f u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1102
         | Op3 (If, _, _, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1103
           kk_formula_if (to_f u1) (to_f u2) (to_f u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1104
         | FormulaReg (j, _, _) => Kodkod.FormulaReg j
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1105
         | _ => raise NUT ("NitpickKodkod.to_f", [u]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1106
      | Atom (2, j0) => formula_from_atom j0 (to_r u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1107
      | _ => raise NUT ("NitpickKodkod.to_f", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1108
    (* polarity -> nut -> Kodkod.formula *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1109
    and to_f_with_polarity polar u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1110
      case rep_of u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1111
        Formula _ => to_f u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1112
      | Atom (2, j0) => formula_from_atom j0 (to_r u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1113
      | Opt (Atom (2, j0)) => formula_from_opt_atom polar j0 (to_r u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1114
      | _ => raise NUT ("NitpickKodkod.to_f_with_polarity", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1115
    (* nut -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1116
    and to_r u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1117
      case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1118
        Cst (False, _, Atom _) => false_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1119
      | Cst (True, _, Atom _) => true_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1120
      | Cst (Iden, T, Func (Struct [R1, R2], Formula Neut)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1121
        if R1 = R2 andalso arity_of_rep R1 = 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1122
          kk_intersect Kodkod.Iden (kk_product (full_rel_for_rep R1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1123
                                               Kodkod.Univ)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1124
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1125
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1126
            val schema1 = atom_schema_of_rep R1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1127
            val schema2 = atom_schema_of_rep R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1128
            val arity1 = length schema1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1129
            val arity2 = length schema2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1130
            val r1 = fold1 kk_product (unary_var_seq 0 arity1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1131
            val r2 = fold1 kk_product (unary_var_seq arity1 arity2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1132
            val min_R = min_rep R1 R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1133
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1134
            kk_comprehension
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1135
                (decls_for_atom_schema 0 (schema1 @ schema2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1136
                (kk_rel_eq (rel_expr_from_rel_expr kk min_R R1 r1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1137
                           (rel_expr_from_rel_expr kk min_R R2 r2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1138
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1139
      | Cst (Iden, T, Func (Atom (1, j0), Formula Neut)) => Kodkod.Atom j0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1140
      | Cst (Iden, T as Type ("fun", [T1, _]), R as Func (R1, _)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1141
        to_rep R (Cst (Iden, T, Func (one_rep ofs T1 R1, Formula Neut)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1142
      | Cst (Num j, @{typ int}, R) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1143
         (case atom_for_int (card_of_rep R, offset_of_type ofs int_T) j of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1144
            ~1 => if is_opt_rep R then Kodkod.None
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1145
                  else raise NUT ("NitpickKodkod.to_r (Num)", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1146
          | j' => Kodkod.Atom j')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1147
      | Cst (Num j, T, R) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1148
        if j < card_of_rep R then Kodkod.Atom (j + offset_of_type ofs T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1149
        else if is_opt_rep R then Kodkod.None
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1150
        else raise NUT ("NitpickKodkod.to_r", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1151
      | Cst (Unknown, _, R) => empty_rel_for_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1152
      | Cst (Unrep, _, R) => empty_rel_for_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1153
      | Cst (Suc, T, Func (Atom x, _)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1154
        if domain_type T <> nat_T then suc_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1155
        else kk_intersect suc_rel (kk_product Kodkod.Univ (Kodkod.AtomSeq x))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1156
      | Cst (Add, Type ("fun", [@{typ nat}, _]), _) => nat_add_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1157
      | Cst (Add, Type ("fun", [@{typ int}, _]), _) => int_add_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1158
      | Cst (Subtract, Type ("fun", [@{typ nat}, _]), _) => nat_subtract_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1159
      | Cst (Subtract, Type ("fun", [@{typ int}, _]), _) => int_subtract_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1160
      | Cst (Multiply, Type ("fun", [@{typ nat}, _]), _) => nat_multiply_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1161
      | Cst (Multiply, Type ("fun", [@{typ int}, _]), _) => int_multiply_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1162
      | Cst (Divide, Type ("fun", [@{typ nat}, _]), _) => nat_divide_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1163
      | Cst (Divide, Type ("fun", [@{typ int}, _]), _) => int_divide_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1164
      | Cst (Modulo, Type ("fun", [@{typ nat}, _]), _) => nat_modulo_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1165
      | Cst (Modulo, Type ("fun", [@{typ int}, _]), _) => int_modulo_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1166
      | Cst (Gcd, _, _) => gcd_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1167
      | Cst (Lcm, _, _) => lcm_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1168
      | Cst (Fracs, _, Func (Atom (1, _), _)) => Kodkod.None
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1169
      | Cst (Fracs, _, Func (Struct _, _)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1170
        kk_project_seq norm_frac_rel 2 2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1171
      | Cst (NormFrac, _, _) => norm_frac_rel
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1172
      | Cst (NatToInt, _, Func (Atom _, Atom _)) => Kodkod.Iden
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1173
      | Cst (NatToInt, _,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1174
             Func (Atom (nat_k, nat_j0), Opt (Atom (int_k, int_j0)))) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1175
        if nat_j0 = int_j0 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1176
          kk_intersect Kodkod.Iden
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1177
              (kk_product (Kodkod.AtomSeq (max_int_for_card int_k + 1, nat_j0))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1178
                          Kodkod.Univ)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1179
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1180
          raise BAD ("NitpickKodkod.to_r (NatToInt)", "\"nat_j0 <> int_j0\"")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1181
      | Cst (IntToNat, _, Func (Atom (int_k, int_j0), nat_R)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1182
        let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1183
          val abs_card = max_int_for_card int_k + 1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1184
          val (nat_k, nat_j0) = the_single (atom_schema_of_rep nat_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1185
          val overlap = Int.min (nat_k, abs_card)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1186
        in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1187
          if nat_j0 = int_j0 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1188
            kk_union (kk_product (Kodkod.AtomSeq (int_k - abs_card,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1189
                                                  int_j0 + abs_card))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1190
                                 (Kodkod.Atom nat_j0))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1191
                     (kk_intersect Kodkod.Iden
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1192
                          (kk_product (Kodkod.AtomSeq (overlap, int_j0))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1193
                                      Kodkod.Univ))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1194
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1195
            raise BAD ("NitpickKodkod.to_r (IntToNat)", "\"nat_j0 <> int_j0\"")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1196
        end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1197
      | Op1 (Not, _, R, u1) => kk_not3 (to_rep R u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1198
      | Op1 (Finite, _, Opt (Atom _), _) => Kodkod.None
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1199
      | Op1 (Converse, T, R, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1200
        let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1201
          val (b_T, a_T) = HOLogic.dest_prodT (domain_type T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1202
          val (b_R, a_R) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1203
            case R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1204
              Func (Struct [R1, R2], _) => (R1, R2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1205
            | Func (R1, _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1206
              if card_of_rep R1 <> 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1207
                raise REP ("NitpickKodkod.to_r (Converse)", [R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1208
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1209
                pairself (Atom o pair 1 o offset_of_type ofs) (b_T, a_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1210
            | _ => raise REP ("NitpickKodkod.to_r (Converse)", [R])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1211
          val body_R = body_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1212
          val a_arity = arity_of_rep a_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1213
          val b_arity = arity_of_rep b_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1214
          val ab_arity = a_arity + b_arity
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1215
          val body_arity = arity_of_rep body_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1216
        in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1217
          kk_project (to_rep (Func (Struct [a_R, b_R], body_R)) u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1218
                     (map Kodkod.Num (index_seq a_arity b_arity @
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1219
                                      index_seq 0 a_arity @
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1220
                                      index_seq ab_arity body_arity))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1221
          |> rel_expr_from_rel_expr kk R (Func (Struct [b_R, a_R], body_R))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1222
        end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1223
      | Op1 (Closure, _, R, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1224
        if is_opt_rep R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1225
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1226
            val T1 = type_of u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1227
            val R' = rep_to_binary_rel_rep ofs T1 (unopt_rep (rep_of u1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1228
            val R'' = opt_rep ofs T1 R'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1229
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1230
            single_rel_let kk
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1231
                (fn r =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1232
                    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1233
                      val true_r = kk_closure (kk_join r true_atom)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1234
                      val full_r = full_rel_for_rep R'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1235
                      val false_r = kk_difference full_r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1236
                                        (kk_closure (kk_difference full_r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1237
                                                        (kk_join r false_atom)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1238
                    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1239
                      rel_expr_from_rel_expr kk R R''
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1240
                          (kk_union (kk_product true_r true_atom)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1241
                                    (kk_product false_r false_atom))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1242
                    end) (to_rep R'' u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1243
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1244
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1245
          let val R' = rep_to_binary_rel_rep ofs (type_of u1) (rep_of u1) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1246
            rel_expr_from_rel_expr kk R R' (kk_closure (to_rep R' u1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1247
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1248
      | Op1 (SingletonSet, _, Func (R1, Opt _), Cst (Unrep, _, _)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1249
        (if R1 = Unit then I else kk_product (full_rel_for_rep R1)) false_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1250
      | Op1 (SingletonSet, _, R, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1251
        (case R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1252
           Func (R1, Formula Neut) => to_rep R1 u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1253
         | Func (Unit, Opt R) => to_guard [u1] R true_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1254
         | Func (R1, R2 as Opt _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1255
           single_rel_let kk
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1256
               (fn r => kk_rel_if (kk_no r) (empty_rel_for_rep R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1257
                            (rel_expr_to_func kk R1 bool_atom_R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1258
                                              (Func (R1, Formula Neut)) r))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1259
               (to_opt R1 u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1260
         | _ => raise NUT ("NitpickKodkod.to_r (SingletonSet)", [u]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1261
      | Op1 (Tha, T, R, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1262
        if is_opt_rep R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1263
          kk_join (to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1) true_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1264
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1265
          to_rep (Func (R, Formula Neut)) u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1266
      | Op1 (First, T, R, u1) => to_nth_pair_sel 0 T R u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1267
      | Op1 (Second, T, R, u1) => to_nth_pair_sel 1 T R u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1268
      | Op1 (Cast, _, R, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1269
        ((case rep_of u1 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1270
            Formula _ =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1271
            (case unopt_rep R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1272
               Atom (2, j0) => atom_from_formula kk j0 (to_f u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1273
             | _ => raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1274
          | _ => raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1275
         handle SAME () => rel_expr_from_rel_expr kk R (rep_of u1) (to_r u1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1276
      | Op2 (All, T, R as Opt _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1277
        to_r (Op1 (Not, T, R,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1278
                   Op2 (Exist, T, R, u1, Op1 (Not, T, rep_of u2, u2))))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1279
      | Op2 (Exist, T, Opt _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1280
        let val rs1 = untuple to_decl u1 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1281
          if not (is_opt_rep (rep_of u2)) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1282
            kk_rel_if (kk_exist rs1 (to_f u2)) true_atom Kodkod.None
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1283
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1284
            let val r2 = to_r u2 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1285
              kk_union (kk_rel_if (kk_exist rs1 (kk_rel_eq r2 true_atom))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1286
                                  true_atom Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1287
                       (kk_rel_if (kk_all rs1 (kk_rel_eq r2 false_atom))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1288
                                  false_atom Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1289
            end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1290
        end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1291
      | Op2 (Or, _, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1292
        if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) true_atom (to_r u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1293
        else kk_rel_if (to_f u1) true_atom (to_r u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1294
      | Op2 (And, _, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1295
        if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) (to_r u1) false_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1296
        else kk_rel_if (to_f u1) (to_r u2) false_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1297
      | Op2 (Less, _, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1298
        if type_of u1 = nat_T then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1299
          if is_Cst Unrep u1 then to_compare_with_unrep u2 false_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1300
          else if is_Cst Unrep u2 then to_compare_with_unrep u1 true_atom
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1301
          else kk_nat_less (to_integer u1) (to_integer u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1302
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1303
          kk_int_less (to_integer u1) (to_integer u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1304
      | Op2 (The, T, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1305
        if is_opt_rep R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1306
          let val r1 = to_opt (Func (unopt_rep R, bool_atom_R)) u1 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1307
            kk_rel_if (kk_one (kk_join r1 true_atom)) (kk_join r1 true_atom)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1308
                      (kk_rel_if (kk_or (kk_some (kk_join r1 true_atom))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1309
                                        (kk_subset (full_rel_for_rep R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1310
                                                   (kk_join r1 false_atom)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1311
                                 (to_rep R u2) Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1312
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1313
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1314
          let val r1 = to_rep (Func (R, Formula Neut)) u1 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1315
            kk_rel_if (kk_one r1) r1 (to_rep R u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1316
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1317
      | Op2 (Eps, T, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1318
        if is_opt_rep (rep_of u1) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1319
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1320
            val r1 = to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1321
            val r2 = to_rep R u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1322
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1323
            kk_union (kk_rel_if (kk_one (kk_join r1 true_atom))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1324
                                (kk_join r1 true_atom) Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1325
                     (kk_rel_if (kk_or (kk_subset r2 (kk_join r1 true_atom))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1326
                                       (kk_subset (full_rel_for_rep R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1327
                                                  (kk_join r1 false_atom)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1328
                                r2 Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1329
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1330
        else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1331
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1332
            val r1 = to_rep (Func (unopt_rep R, Formula Neut)) u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1333
            val r2 = to_rep R u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1334
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1335
            kk_union (kk_rel_if (kk_one r1) r1 Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1336
                     (kk_rel_if (kk_or (kk_no r1) (kk_subset r2 r1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1337
                                r2 Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1338
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1339
      | Op2 (Triad, T, Opt (Atom (2, j0)), u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1340
        let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1341
          val f1 = to_f u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1342
          val f2 = to_f u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1343
        in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1344
          if f1 = f2 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1345
            atom_from_formula kk j0 f1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1346
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1347
            kk_union (kk_rel_if f1 true_atom Kodkod.None)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1348
                     (kk_rel_if f2 Kodkod.None false_atom)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1349
        end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1350
      | Op2 (Union, _, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1351
        to_set_op kk_or kk_or3 kk_union kk_union kk_intersect false R u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1352
      | Op2 (SetDifference, _, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1353
        to_set_op kk_notimplies kk_notimplies3 kk_difference kk_intersect
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1354
                  kk_union true R u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1355
      | Op2 (Intersect, _, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1356
        to_set_op kk_and kk_and3 kk_intersect kk_intersect kk_union false R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1357
                  u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1358
      | Op2 (Composition, _, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1359
        let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1360
          val (a_T, b_T) = HOLogic.dest_prodT (domain_type (type_of u2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1361
          val (_, c_T) = HOLogic.dest_prodT (domain_type (type_of u1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1362
          val ab_k = card_of_domain_from_rep 2 (rep_of u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1363
          val bc_k = card_of_domain_from_rep 2 (rep_of u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1364
          val ac_k = card_of_domain_from_rep 2 R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1365
          val a_k = exact_root 2 (ac_k * ab_k div bc_k)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1366
          val b_k = exact_root 2 (ab_k * bc_k div ac_k)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1367
          val c_k = exact_root 2 (bc_k * ac_k div ab_k)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1368
          val a_R = Atom (a_k, offset_of_type ofs a_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1369
          val b_R = Atom (b_k, offset_of_type ofs b_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1370
          val c_R = Atom (c_k, offset_of_type ofs c_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1371
          val body_R = body_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1372
        in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1373
          (case body_R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1374
             Formula Neut =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1375
             kk_join (to_rep (Func (Struct [a_R, b_R], Formula Neut)) u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1376
                     (to_rep (Func (Struct [b_R, c_R], Formula Neut)) u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1377
           | Opt (Atom (2, _)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1378
             let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1379
               (* Kodkod.rel_expr -> rep -> rep -> nut -> Kodkod.rel_expr *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1380
               fun do_nut r R1 R2 u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1381
                 kk_join (to_rep (Func (Struct [R1, R2], body_R)) u) r
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1382
               (* Kodkod.rel_expr -> Kodkod.rel_expr *)