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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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(* bool -> int -> int -> int -> int -> int * int
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-> string * bool * Kodkod.tuple list *)
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fun tabulate_built_in_rel debug univ_card nat_card int_card j0 (x as (n, _)) =
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(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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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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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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else if Kodkod.Rel x = nat_subtract_rel then
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("nat_subtract",
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tabulate_op2 debug univ_card (nat_card, j0) j0 (op nat_minus))
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else if Kodkod.Rel x = int_subtract_rel then
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("int_subtract", tabulate_int_op2 debug univ_card (int_card, j0) (op -))
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else if Kodkod.Rel x = nat_multiply_rel then
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("nat_multiply", tabulate_nat_op2 debug univ_card (nat_card, j0) (op * ))
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else if 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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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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else if Kodkod.Rel x = int_divide_rel then
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("int_divide", tabulate_int_op2 debug univ_card (int_card, j0) isa_div)
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else if 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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else if Kodkod.Rel x = int_modulo_rel then
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("int_modulo", tabulate_int_op2 debug univ_card (int_card, j0) isa_mod)
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else if Kodkod.Rel x = nat_less_rel then
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("nat_less", tabulate_nat_op2 debug univ_card (nat_card, j0)
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(int_for_bool o op <))
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else if Kodkod.Rel x = int_less_rel then
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("int_less", tabulate_int_op2 debug univ_card (int_card, j0)
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(int_for_bool o op <))
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else if Kodkod.Rel x = gcd_rel then
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("gcd", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_gcd)
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else if 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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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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isa_norm_frac)
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else
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raise ARG ("NitpickKodkod.tabulate_built_in_rel", "unknown relation"))
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(* bool -> int -> int -> int -> int -> int * int -> Kodkod.rel_expr
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-> Kodkod.bound *)
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fun bound_for_built_in_rel debug univ_card nat_card int_card j0 x =
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let
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val (nick, ts) = tabulate_built_in_rel debug univ_card nat_card int_card
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j0 x
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in ([(x, nick)], [Kodkod.TupleSet ts]) end
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(* bool -> int -> int -> int -> int -> Kodkod.formula -> Kodkod.bound list *)
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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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o built_in_rels_in_formula
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(* Proof.context -> bool -> nut -> Kodkod.bound *)
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fun bound_for_plain_rel ctxt debug (u as FreeRel (x, T, R, nick)) =
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([(x, bound_comment ctxt debug nick T R)],
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if nick = @{const_name bisim_iterator_max} then
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case R of
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Atom (k, j0) => [Kodkod.TupleSet [Kodkod.Tuple [k - 1 + j0]]]
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| _ => raise NUT ("NitpickKodkod.bound_for_plain_rel", [u])
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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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raise NUT ("NitpickKodkod.bound_for_plain_rel", [u])
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(* Proof.context -> bool -> dtype_spec list -> nut -> Kodkod.bound *)
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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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nick)) =
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let
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val constr as {delta, epsilon, exclusive, explicit_max, ...} =
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constr_spec dtypes (original_name nick, T1)
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in
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([(x, bound_comment ctxt debug nick T R)],
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if explicit_max = 0 then
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[Kodkod.TupleSet []]
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else
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let val ts = Kodkod.TupleAtomSeq (epsilon - delta, delta + j0) in
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if R2 = Formula Neut then
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[ts] |> not exclusive ? cons (Kodkod.TupleSet [])
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else
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[Kodkod.TupleSet [],
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Kodkod.TupleProduct (ts, upper_bound_for_rep R2)]
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end)
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end
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| bound_for_sel_rel _ _ _ u =
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raise NUT ("NitpickKodkod.bound_for_sel_rel", [u])
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(* Kodkod.bound list -> Kodkod.bound list *)
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fun merge_bounds bs =
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let
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(* Kodkod.bound -> int *)
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fun arity (zs, _) = fst (fst (hd zs))
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(* Kodkod.bound list -> Kodkod.bound -> Kodkod.bound list
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-> Kodkod.bound list *)
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fun add_bound ds b [] = List.revAppend (ds, [b])
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| add_bound ds b (c :: cs) =
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if arity b = arity c andalso snd b = snd c then
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List.revAppend (ds, (fst c @ fst b, snd c) :: cs)
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else
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add_bound (c :: ds) b cs
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in fold (add_bound []) bs [] end
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(* int -> int -> Kodkod.rel_expr list *)
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fun unary_var_seq j0 n = map (curry Kodkod.Var 1) (index_seq j0 n)
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(* int list -> Kodkod.rel_expr *)
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val singleton_from_combination = foldl1 Kodkod.Product o map Kodkod.Atom
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(* rep -> Kodkod.rel_expr list *)
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fun all_singletons_for_rep R =
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if is_lone_rep R then
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all_combinations_for_rep R |> map singleton_from_combination
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else
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raise REP ("NitpickKodkod.all_singletons_for_rep", [R])
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325 |
(* Kodkod.rel_expr -> Kodkod.rel_expr list *)
|
|
326 |
fun unpack_products (Kodkod.Product (r1, r2)) =
|
|
327 |
unpack_products r1 @ unpack_products r2
|
|
328 |
| unpack_products r = [r]
|
|
329 |
fun unpack_joins (Kodkod.Join (r1, r2)) = unpack_joins r1 @ unpack_joins r2
|
|
330 |
| unpack_joins r = [r]
|
|
331 |
|
|
332 |
(* rep -> Kodkod.rel_expr *)
|
|
333 |
val empty_rel_for_rep = empty_n_ary_rel o arity_of_rep
|
|
334 |
fun full_rel_for_rep R =
|
|
335 |
case atom_schema_of_rep R of
|
|
336 |
[] => raise REP ("NitpickKodkod.full_rel_for_rep", [R])
|
|
337 |
| schema => foldl1 Kodkod.Product (map Kodkod.AtomSeq schema)
|
|
338 |
|
|
339 |
(* int -> int list -> Kodkod.decl list *)
|
|
340 |
fun decls_for_atom_schema j0 schema =
|
|
341 |
map2 (fn j => fn x => Kodkod.DeclOne ((1, j), Kodkod.AtomSeq x))
|
|
342 |
(index_seq j0 (length schema)) schema
|
|
343 |
|
|
344 |
(* The type constraint below is a workaround for a Poly/ML bug. *)
|
|
345 |
|
|
346 |
(* FIXME: clean up *)
|
|
347 |
(* kodkod_constrs -> rep -> Kodkod.rel_expr -> Kodkod.formula *)
|
|
348 |
fun d_n_ary_function ({kk_all, kk_join, kk_lone, kk_one, ...} : kodkod_constrs)
|
|
349 |
R r =
|
|
350 |
let val body_R = body_rep R in
|
|
351 |
if is_lone_rep body_R then
|
|
352 |
let
|
|
353 |
val binder_schema = atom_schema_of_reps (binder_reps R)
|
|
354 |
val body_schema = atom_schema_of_rep body_R
|
|
355 |
val one = is_one_rep body_R
|
|
356 |
val opt_x = case r of Kodkod.Rel x => SOME x | _ => NONE
|
|
357 |
in
|
|
358 |
if opt_x <> NONE andalso length binder_schema = 1
|
|
359 |
andalso length body_schema = 1 then
|
|
360 |
(if one then Kodkod.Function else Kodkod.Functional)
|
|
361 |
(the opt_x, Kodkod.AtomSeq (hd binder_schema),
|
|
362 |
Kodkod.AtomSeq (hd body_schema))
|
|
363 |
else
|
|
364 |
let
|
|
365 |
val decls = decls_for_atom_schema ~1 binder_schema
|
|
366 |
val vars = unary_var_seq ~1 (length binder_schema)
|
|
367 |
val kk_xone = if one then kk_one else kk_lone
|
|
368 |
in kk_all decls (kk_xone (fold kk_join vars r)) end
|
|
369 |
end
|
|
370 |
else
|
|
371 |
Kodkod.True
|
|
372 |
end
|
|
373 |
fun kk_n_ary_function kk R (r as Kodkod.Rel _) =
|
|
374 |
(* FIXME: weird test *)
|
|
375 |
if not (is_opt_rep R) then
|
|
376 |
if r = suc_rel then
|
|
377 |
Kodkod.False
|
|
378 |
else if r = nat_add_rel then
|
|
379 |
formula_for_bool (card_of_rep (body_rep R) = 1)
|
|
380 |
else if r = nat_multiply_rel then
|
|
381 |
formula_for_bool (card_of_rep (body_rep R) <= 2)
|
|
382 |
else
|
|
383 |
d_n_ary_function kk R r
|
|
384 |
else if r = nat_subtract_rel then
|
|
385 |
Kodkod.True
|
|
386 |
else
|
|
387 |
d_n_ary_function kk R r
|
|
388 |
| kk_n_ary_function kk R r = d_n_ary_function kk R r
|
|
389 |
|
|
390 |
(* kodkod_constrs -> Kodkod.rel_expr list -> Kodkod.formula *)
|
|
391 |
fun kk_disjoint_sets _ [] = Kodkod.True
|
|
392 |
| kk_disjoint_sets (kk as {kk_and, kk_no, kk_intersect, ...} : kodkod_constrs)
|
|
393 |
(r :: rs) =
|
|
394 |
fold (kk_and o kk_no o kk_intersect r) rs (kk_disjoint_sets kk rs)
|
|
395 |
|
|
396 |
(* int -> kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr)
|
|
397 |
-> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
398 |
fun basic_rel_let j ({kk_rel_let, ...} : kodkod_constrs) f r =
|
|
399 |
if inline_rel_expr r then
|
|
400 |
f r
|
|
401 |
else
|
|
402 |
let val x = (Kodkod.arity_of_rel_expr r, j) in
|
|
403 |
kk_rel_let [Kodkod.AssignRelReg (x, r)] (f (Kodkod.RelReg x))
|
|
404 |
end
|
|
405 |
|
|
406 |
(* kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr) -> Kodkod.rel_expr
|
|
407 |
-> Kodkod.rel_expr *)
|
|
408 |
val single_rel_let = basic_rel_let 0
|
|
409 |
(* kodkod_constrs -> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)
|
|
410 |
-> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
411 |
fun double_rel_let kk f r1 r2 =
|
|
412 |
single_rel_let kk (fn r1 => basic_rel_let 1 kk (f r1) r2) r1
|
|
413 |
(* kodkod_constrs
|
|
414 |
-> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)
|
|
415 |
-> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr
|
|
416 |
-> Kodkod.rel_expr *)
|
|
417 |
fun triple_rel_let kk f r1 r2 r3 =
|
|
418 |
double_rel_let kk (fn r1 => fn r2 => basic_rel_let 2 kk (f r1 r2) r3) r1 r2
|
|
419 |
|
|
420 |
(* kodkod_constrs -> int -> Kodkod.formula -> Kodkod.rel_expr *)
|
|
421 |
fun atom_from_formula ({kk_rel_if, ...} : kodkod_constrs) j0 f =
|
|
422 |
kk_rel_if f (Kodkod.Atom (j0 + 1)) (Kodkod.Atom j0)
|
|
423 |
(* kodkod_constrs -> rep -> Kodkod.formula -> Kodkod.rel_expr *)
|
|
424 |
fun rel_expr_from_formula kk R f =
|
|
425 |
case unopt_rep R of
|
|
426 |
Atom (2, j0) => atom_from_formula kk j0 f
|
|
427 |
| _ => raise REP ("NitpickKodkod.rel_expr_from_formula", [R])
|
|
428 |
|
|
429 |
(* kodkod_cotrs -> int -> int -> Kodkod.rel_expr -> Kodkod.rel_expr list *)
|
|
430 |
fun unpack_vect_in_chunks ({kk_project_seq, ...} : kodkod_constrs) chunk_arity
|
|
431 |
num_chunks r =
|
|
432 |
List.tabulate (num_chunks, fn j => kk_project_seq r (j * chunk_arity)
|
|
433 |
chunk_arity)
|
|
434 |
|
|
435 |
(* kodkod_constrs -> bool -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr
|
|
436 |
-> Kodkod.rel_expr *)
|
|
437 |
fun kk_n_fold_join
|
|
438 |
(kk as {kk_intersect, kk_product, kk_join, kk_project_seq, ...}) one R1
|
|
439 |
res_R r1 r2 =
|
|
440 |
case arity_of_rep R1 of
|
|
441 |
1 => kk_join r1 r2
|
|
442 |
| arity1 =>
|
|
443 |
let
|
|
444 |
val unpacked_rs1 =
|
|
445 |
if inline_rel_expr r1 then unpack_vect_in_chunks kk 1 arity1 r1
|
|
446 |
else unpack_products r1
|
|
447 |
in
|
|
448 |
if one andalso length unpacked_rs1 = arity1 then
|
|
449 |
fold kk_join unpacked_rs1 r2
|
|
450 |
else
|
|
451 |
kk_project_seq
|
|
452 |
(kk_intersect (kk_product r1 (full_rel_for_rep res_R)) r2)
|
|
453 |
arity1 (arity_of_rep res_R)
|
|
454 |
end
|
|
455 |
|
|
456 |
(* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr list
|
|
457 |
-> Kodkod.rel_expr list -> Kodkod.rel_expr *)
|
|
458 |
fun kk_case_switch (kk as {kk_union, kk_product, ...}) R1 R2 r rs1 rs2 =
|
|
459 |
if rs1 = rs2 then r
|
|
460 |
else kk_n_fold_join kk true R1 R2 r (fold1 kk_union (map2 kk_product rs1 rs2))
|
|
461 |
|
|
462 |
val lone_rep_fallback_max_card = 4096
|
|
463 |
val some_j0 = 0
|
|
464 |
|
|
465 |
(* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
466 |
fun lone_rep_fallback kk new_R old_R r =
|
|
467 |
if old_R = new_R then
|
|
468 |
r
|
|
469 |
else
|
|
470 |
let val card = card_of_rep old_R in
|
|
471 |
if is_lone_rep old_R andalso is_lone_rep new_R
|
|
472 |
andalso card = card_of_rep new_R then
|
|
473 |
if card >= lone_rep_fallback_max_card then
|
|
474 |
raise LIMIT ("NitpickKodkod.lone_rep_fallback",
|
|
475 |
"too high cardinality (" ^ string_of_int card ^ ")")
|
|
476 |
else
|
|
477 |
kk_case_switch kk old_R new_R r (all_singletons_for_rep old_R)
|
|
478 |
(all_singletons_for_rep new_R)
|
|
479 |
else
|
|
480 |
raise REP ("NitpickKodkod.lone_rep_fallback", [old_R, new_R])
|
|
481 |
end
|
|
482 |
(* kodkod_constrs -> int * int -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
483 |
and atom_from_rel_expr kk (x as (k, j0)) old_R r =
|
|
484 |
case old_R of
|
|
485 |
Func (R1, R2) =>
|
|
486 |
let
|
|
487 |
val dom_card = card_of_rep R1
|
|
488 |
val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
|
|
489 |
in
|
|
490 |
atom_from_rel_expr kk x (Vect (dom_card, R2'))
|
|
491 |
(vect_from_rel_expr kk dom_card R2' old_R r)
|
|
492 |
end
|
|
493 |
| Opt _ => raise REP ("NitpickKodkod.atom_from_rel_expr", [old_R])
|
|
494 |
| _ => lone_rep_fallback kk (Atom x) old_R r
|
|
495 |
(* kodkod_constrs -> rep list -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
496 |
and struct_from_rel_expr kk Rs old_R r =
|
|
497 |
case old_R of
|
|
498 |
Atom _ => lone_rep_fallback kk (Struct Rs) old_R r
|
|
499 |
| Struct Rs' =>
|
|
500 |
let
|
|
501 |
val Rs = filter (not_equal Unit) Rs
|
|
502 |
val Rs' = filter (not_equal Unit) Rs'
|
|
503 |
in
|
|
504 |
if Rs' = Rs then
|
|
505 |
r
|
|
506 |
else if map card_of_rep Rs' = map card_of_rep Rs then
|
|
507 |
let
|
|
508 |
val old_arities = map arity_of_rep Rs'
|
|
509 |
val old_offsets = offset_list old_arities
|
|
510 |
val old_rs = map2 (#kk_project_seq kk r) old_offsets old_arities
|
|
511 |
in
|
|
512 |
fold1 (#kk_product kk)
|
|
513 |
(map3 (rel_expr_from_rel_expr kk) Rs Rs' old_rs)
|
|
514 |
end
|
|
515 |
else
|
|
516 |
lone_rep_fallback kk (Struct Rs) old_R r
|
|
517 |
end
|
|
518 |
| _ => raise REP ("NitpickKodkod.struct_from_rel_expr", [old_R])
|
|
519 |
(* kodkod_constrs -> int -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
520 |
and vect_from_rel_expr kk k R old_R r =
|
|
521 |
case old_R of
|
|
522 |
Atom _ => lone_rep_fallback kk (Vect (k, R)) old_R r
|
|
523 |
| Vect (k', R') =>
|
|
524 |
if k = k' andalso R = R' then r
|
|
525 |
else lone_rep_fallback kk (Vect (k, R)) old_R r
|
|
526 |
| Func (R1, Formula Neut) =>
|
|
527 |
if k = card_of_rep R1 then
|
|
528 |
fold1 (#kk_product kk)
|
|
529 |
(map (fn arg_r =>
|
|
530 |
rel_expr_from_formula kk R (#kk_subset kk arg_r r))
|
|
531 |
(all_singletons_for_rep R1))
|
|
532 |
else
|
|
533 |
raise REP ("NitpickKodkod.vect_from_rel_expr", [old_R])
|
|
534 |
| Func (Unit, R2) => rel_expr_from_rel_expr kk R R2 r
|
|
535 |
| Func (R1, R2) =>
|
|
536 |
fold1 (#kk_product kk)
|
|
537 |
(map (fn arg_r =>
|
|
538 |
rel_expr_from_rel_expr kk R R2
|
|
539 |
(kk_n_fold_join kk true R1 R2 arg_r r))
|
|
540 |
(all_singletons_for_rep R1))
|
|
541 |
| _ => raise REP ("NitpickKodkod.vect_from_rel_expr", [old_R])
|
|
542 |
(* kodkod_constrs -> rep -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
543 |
and func_from_no_opt_rel_expr kk R1 R2 (Atom x) r =
|
|
544 |
let
|
|
545 |
val dom_card = card_of_rep R1
|
|
546 |
val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
|
|
547 |
in
|
|
548 |
func_from_no_opt_rel_expr kk R1 R2 (Vect (dom_card, R2'))
|
|
549 |
(vect_from_rel_expr kk dom_card R2' (Atom x) r)
|
|
550 |
end
|
|
551 |
| func_from_no_opt_rel_expr kk Unit R2 old_R r =
|
|
552 |
(case old_R of
|
|
553 |
Vect (k, R') => rel_expr_from_rel_expr kk R2 R' r
|
|
554 |
| Func (Unit, R2') => rel_expr_from_rel_expr kk R2 R2' r
|
|
555 |
| Func (Atom (1, _), Formula Neut) =>
|
|
556 |
(case unopt_rep R2 of
|
|
557 |
Atom (2, j0) => atom_from_formula kk j0 (#kk_some kk r)
|
|
558 |
| _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
|
|
559 |
[old_R, Func (Unit, R2)]))
|
|
560 |
| Func (R1', R2') =>
|
|
561 |
rel_expr_from_rel_expr kk R2 R2' (#kk_project_seq kk r (arity_of_rep R1')
|
|
562 |
(arity_of_rep R2'))
|
|
563 |
| _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
|
|
564 |
[old_R, Func (Unit, R2)]))
|
|
565 |
| func_from_no_opt_rel_expr kk R1 (Formula Neut) old_R r =
|
|
566 |
(case old_R of
|
|
567 |
Vect (k, Atom (2, j0)) =>
|
|
568 |
let
|
|
569 |
val args_rs = all_singletons_for_rep R1
|
|
570 |
val vals_rs = unpack_vect_in_chunks kk 1 k r
|
|
571 |
(* Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
572 |
fun empty_or_singleton_set_for arg_r val_r =
|
|
573 |
#kk_join kk val_r (#kk_product kk (Kodkod.Atom (j0 + 1)) arg_r)
|
|
574 |
in
|
|
575 |
fold1 (#kk_union kk) (map2 empty_or_singleton_set_for args_rs vals_rs)
|
|
576 |
end
|
|
577 |
| Func (R1', Formula Neut) =>
|
|
578 |
if R1 = R1' then
|
|
579 |
r
|
|
580 |
else
|
|
581 |
let
|
|
582 |
val schema = atom_schema_of_rep R1
|
|
583 |
val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
|
|
584 |
|> rel_expr_from_rel_expr kk R1' R1
|
|
585 |
in
|
|
586 |
#kk_comprehension kk (decls_for_atom_schema ~1 schema)
|
|
587 |
(#kk_subset kk r1 r)
|
|
588 |
end
|
|
589 |
| Func (Unit, (Atom (2, j0))) =>
|
|
590 |
#kk_rel_if kk (#kk_rel_eq kk r (Kodkod.Atom (j0 + 1)))
|
|
591 |
(full_rel_for_rep R1) (empty_rel_for_rep R1)
|
|
592 |
| Func (R1', Atom (2, j0)) =>
|
|
593 |
func_from_no_opt_rel_expr kk R1 (Formula Neut)
|
|
594 |
(Func (R1', Formula Neut)) (#kk_join kk r (Kodkod.Atom (j0 + 1)))
|
|
595 |
| _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
|
|
596 |
[old_R, Func (R1, Formula Neut)]))
|
|
597 |
| func_from_no_opt_rel_expr kk R1 R2 old_R r =
|
|
598 |
case old_R of
|
|
599 |
Vect (k, R) =>
|
|
600 |
let
|
|
601 |
val args_rs = all_singletons_for_rep R1
|
|
602 |
val vals_rs = unpack_vect_in_chunks kk (arity_of_rep R) k r
|
|
603 |
|> map (rel_expr_from_rel_expr kk R2 R)
|
|
604 |
in fold1 (#kk_union kk) (map2 (#kk_product kk) args_rs vals_rs) end
|
|
605 |
| Func (R1', Formula Neut) =>
|
|
606 |
(case R2 of
|
|
607 |
Atom (x as (2, j0)) =>
|
|
608 |
let val schema = atom_schema_of_rep R1 in
|
|
609 |
if length schema = 1 then
|
|
610 |
#kk_override kk (#kk_product kk (Kodkod.AtomSeq (hd schema))
|
|
611 |
(Kodkod.Atom j0))
|
|
612 |
(#kk_product kk r (Kodkod.Atom (j0 + 1)))
|
|
613 |
else
|
|
614 |
let
|
|
615 |
val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
|
|
616 |
|> rel_expr_from_rel_expr kk R1' R1
|
|
617 |
val r2 = Kodkod.Var (1, ~(length schema) - 1)
|
|
618 |
val r3 = atom_from_formula kk j0 (#kk_subset kk r1 r)
|
|
619 |
in
|
|
620 |
#kk_comprehension kk (decls_for_atom_schema ~1 (schema @ [x]))
|
|
621 |
(#kk_rel_eq kk r2 r3)
|
|
622 |
end
|
|
623 |
end
|
|
624 |
| _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
|
|
625 |
[old_R, Func (R1, R2)]))
|
|
626 |
| Func (Unit, R2') =>
|
|
627 |
let val j0 = some_j0 in
|
|
628 |
func_from_no_opt_rel_expr kk R1 R2 (Func (Atom (1, j0), R2'))
|
|
629 |
(#kk_product kk (Kodkod.Atom j0) r)
|
|
630 |
end
|
|
631 |
| Func (R1', R2') =>
|
|
632 |
if R1 = R1' andalso R2 = R2' then
|
|
633 |
r
|
|
634 |
else
|
|
635 |
let
|
|
636 |
val dom_schema = atom_schema_of_rep R1
|
|
637 |
val ran_schema = atom_schema_of_rep R2
|
|
638 |
val dom_prod = fold1 (#kk_product kk)
|
|
639 |
(unary_var_seq ~1 (length dom_schema))
|
|
640 |
|> rel_expr_from_rel_expr kk R1' R1
|
|
641 |
val ran_prod = fold1 (#kk_product kk)
|
|
642 |
(unary_var_seq (~(length dom_schema) - 1)
|
|
643 |
(length ran_schema))
|
|
644 |
|> rel_expr_from_rel_expr kk R2' R2
|
|
645 |
val app = kk_n_fold_join kk true R1' R2' dom_prod r
|
|
646 |
in
|
|
647 |
#kk_comprehension kk (decls_for_atom_schema ~1
|
|
648 |
(dom_schema @ ran_schema))
|
|
649 |
(#kk_subset kk ran_prod app)
|
|
650 |
end
|
|
651 |
| _ => raise REP ("NitpickKodkod.func_from_no_opt_rel_expr",
|
|
652 |
[old_R, Func (R1, R2)])
|
|
653 |
(* kodkod_constrs -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
654 |
and rel_expr_from_rel_expr kk new_R old_R r =
|
|
655 |
let
|
|
656 |
val unopt_old_R = unopt_rep old_R
|
|
657 |
val unopt_new_R = unopt_rep new_R
|
|
658 |
in
|
|
659 |
if unopt_old_R <> old_R andalso unopt_new_R = new_R then
|
|
660 |
raise REP ("NitpickKodkod.rel_expr_from_rel_expr", [old_R, new_R])
|
|
661 |
else if unopt_new_R = unopt_old_R then
|
|
662 |
r
|
|
663 |
else
|
|
664 |
(case unopt_new_R of
|
|
665 |
Atom x => atom_from_rel_expr kk x
|
|
666 |
| Struct Rs => struct_from_rel_expr kk Rs
|
|
667 |
| Vect (k, R') => vect_from_rel_expr kk k R'
|
|
668 |
| Func (R1, R2) => func_from_no_opt_rel_expr kk R1 R2
|
|
669 |
| _ => raise REP ("NitpickKodkod.rel_expr_from_rel_expr",
|
|
670 |
[old_R, new_R]))
|
|
671 |
unopt_old_R r
|
|
672 |
end
|
|
673 |
(* kodkod_constrs -> rep -> rep -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
674 |
and rel_expr_to_func kk R1 R2 = rel_expr_from_rel_expr kk (Func (R1, R2))
|
|
675 |
|
|
676 |
(* kodkod_constrs -> nut -> Kodkod.formula *)
|
|
677 |
fun declarative_axiom_for_plain_rel kk (FreeRel (x, _, R as Func _, nick)) =
|
|
678 |
kk_n_ary_function kk (R |> nick = @{const_name List.set} ? unopt_rep)
|
|
679 |
(Kodkod.Rel x)
|
|
680 |
| declarative_axiom_for_plain_rel ({kk_lone, kk_one, ...} : kodkod_constrs)
|
|
681 |
(FreeRel (x, _, R, _)) =
|
|
682 |
if is_one_rep R then kk_one (Kodkod.Rel x)
|
|
683 |
else if is_lone_rep R andalso card_of_rep R > 1 then kk_lone (Kodkod.Rel x)
|
|
684 |
else Kodkod.True
|
|
685 |
| declarative_axiom_for_plain_rel _ u =
|
|
686 |
raise NUT ("NitpickKodkod.declarative_axiom_for_plain_rel", [u])
|
|
687 |
|
|
688 |
(* nut NameTable.table -> styp -> Kodkod.rel_expr * rep * int *)
|
|
689 |
fun const_triple rel_table (x as (s, T)) =
|
|
690 |
case the_name rel_table (ConstName (s, T, Any)) of
|
|
691 |
FreeRel ((n, j), _, R, _) => (Kodkod.Rel (n, j), R, n)
|
|
692 |
| _ => raise TERM ("NitpickKodkod.const_triple", [Const x])
|
|
693 |
|
|
694 |
(* nut NameTable.table -> styp -> Kodkod.rel_expr *)
|
|
695 |
fun discr_rel_expr rel_table = #1 o const_triple rel_table o discr_for_constr
|
|
696 |
|
|
697 |
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
|
698 |
-> styp -> int -> nfa_transition list *)
|
|
699 |
fun nfa_transitions_for_sel ext_ctxt ({kk_project, ...} : kodkod_constrs)
|
|
700 |
rel_table (dtypes : dtype_spec list) constr_x n =
|
|
701 |
let
|
|
702 |
val x as (_, T) = boxed_nth_sel_for_constr ext_ctxt constr_x n
|
|
703 |
val (r, R, arity) = const_triple rel_table x
|
|
704 |
val type_schema = type_schema_of_rep T R
|
|
705 |
in
|
|
706 |
map_filter (fn (j, T) =>
|
|
707 |
if forall (not_equal T o #typ) dtypes then NONE
|
|
708 |
else SOME (kk_project r (map Kodkod.Num [0, j]), T))
|
|
709 |
(index_seq 1 (arity - 1) ~~ tl type_schema)
|
|
710 |
end
|
|
711 |
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
|
712 |
-> styp -> nfa_transition list *)
|
|
713 |
fun nfa_transitions_for_constr ext_ctxt kk rel_table dtypes (x as (_, T)) =
|
|
714 |
maps (nfa_transitions_for_sel ext_ctxt kk rel_table dtypes x)
|
|
715 |
(index_seq 0 (num_sels_for_constr_type T))
|
|
716 |
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
|
717 |
-> dtype_spec -> nfa_entry option *)
|
|
718 |
fun nfa_entry_for_datatype _ _ _ _ ({co = true, ...} : dtype_spec) = NONE
|
|
719 |
| nfa_entry_for_datatype ext_ctxt kk rel_table dtypes
|
|
720 |
({typ, constrs, ...} : dtype_spec) =
|
|
721 |
SOME (typ, maps (nfa_transitions_for_constr ext_ctxt kk rel_table dtypes
|
|
722 |
o #const) constrs)
|
|
723 |
|
|
724 |
val empty_rel = Kodkod.Product (Kodkod.None, Kodkod.None)
|
|
725 |
|
|
726 |
(* nfa_table -> typ -> typ -> Kodkod.rel_expr list *)
|
|
727 |
fun direct_path_rel_exprs nfa start final =
|
|
728 |
case AList.lookup (op =) nfa final of
|
|
729 |
SOME trans => map fst (filter (equal start o snd) trans)
|
|
730 |
| NONE => []
|
|
731 |
(* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> Kodkod.rel_expr *)
|
|
732 |
and any_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start final =
|
|
733 |
fold kk_union (direct_path_rel_exprs nfa start final)
|
|
734 |
(if start = final then Kodkod.Iden else empty_rel)
|
|
735 |
| any_path_rel_expr (kk as {kk_union, ...}) nfa (q :: qs) start final =
|
|
736 |
kk_union (any_path_rel_expr kk nfa qs start final)
|
|
737 |
(knot_path_rel_expr kk nfa qs start q final)
|
|
738 |
(* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> typ
|
|
739 |
-> Kodkod.rel_expr *)
|
|
740 |
and knot_path_rel_expr (kk as {kk_join, kk_reflexive_closure, ...}) nfa qs start
|
|
741 |
knot final =
|
|
742 |
kk_join (kk_join (any_path_rel_expr kk nfa qs knot final)
|
|
743 |
(kk_reflexive_closure (loop_path_rel_expr kk nfa qs knot)))
|
|
744 |
(any_path_rel_expr kk nfa qs start knot)
|
|
745 |
(* kodkod_constrs -> nfa_table -> typ list -> typ -> Kodkod.rel_expr *)
|
|
746 |
and loop_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start =
|
|
747 |
fold kk_union (direct_path_rel_exprs nfa start start) empty_rel
|
|
748 |
| loop_path_rel_expr (kk as {kk_union, kk_closure, ...}) nfa (q :: qs) start =
|
|
749 |
if start = q then
|
|
750 |
kk_closure (loop_path_rel_expr kk nfa qs start)
|
|
751 |
else
|
|
752 |
kk_union (loop_path_rel_expr kk nfa qs start)
|
|
753 |
(knot_path_rel_expr kk nfa qs start q start)
|
|
754 |
|
|
755 |
(* nfa_table -> unit NfaGraph.T *)
|
|
756 |
fun graph_for_nfa nfa =
|
|
757 |
let
|
|
758 |
(* typ -> unit NfaGraph.T -> unit NfaGraph.T *)
|
|
759 |
fun new_node q = perhaps (try (NfaGraph.new_node (q, ())))
|
|
760 |
(* nfa_table -> unit NfaGraph.T -> unit NfaGraph.T *)
|
|
761 |
fun add_nfa [] = I
|
|
762 |
| add_nfa ((_, []) :: nfa) = add_nfa nfa
|
|
763 |
| add_nfa ((q, ((_, q') :: transitions)) :: nfa) =
|
|
764 |
add_nfa ((q, transitions) :: nfa) o NfaGraph.add_edge (q, q') o
|
|
765 |
new_node q' o new_node q
|
|
766 |
in add_nfa nfa NfaGraph.empty end
|
|
767 |
|
|
768 |
(* nfa_table -> nfa_table list *)
|
|
769 |
fun strongly_connected_sub_nfas nfa =
|
|
770 |
nfa |> graph_for_nfa |> NfaGraph.strong_conn
|
|
771 |
|> map (fn keys => filter (member (op =) keys o fst) nfa)
|
|
772 |
|
|
773 |
(* dtype_spec list -> kodkod_constrs -> nfa_table -> typ -> Kodkod.formula *)
|
|
774 |
fun acyclicity_axiom_for_datatype dtypes kk nfa start =
|
|
775 |
#kk_no kk (#kk_intersect kk
|
|
776 |
(loop_path_rel_expr kk nfa (map fst nfa) start) Kodkod.Iden)
|
|
777 |
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
|
778 |
-> Kodkod.formula list *)
|
|
779 |
fun acyclicity_axioms_for_datatypes ext_ctxt kk rel_table dtypes =
|
|
780 |
map_filter (nfa_entry_for_datatype ext_ctxt kk rel_table dtypes) dtypes
|
|
781 |
|> strongly_connected_sub_nfas
|
|
782 |
|> maps (fn nfa => map (acyclicity_axiom_for_datatype dtypes kk nfa o fst)
|
|
783 |
nfa)
|
|
784 |
|
|
785 |
(* extended_context -> int -> kodkod_constrs -> nut NameTable.table
|
|
786 |
-> Kodkod.rel_expr -> constr_spec -> int -> Kodkod.formula *)
|
|
787 |
fun sel_axiom_for_sel ext_ctxt j0
|
|
788 |
(kk as {kk_all, kk_implies, kk_formula_if, kk_subset, kk_rel_eq, kk_no,
|
|
789 |
kk_join, kk_project, ...}) rel_table dom_r
|
|
790 |
({const, delta, epsilon, exclusive, explicit_max, ...} : constr_spec)
|
|
791 |
n =
|
|
792 |
let
|
|
793 |
val x as (_, T) = boxed_nth_sel_for_constr ext_ctxt const n
|
|
794 |
val (r, R, arity) = const_triple rel_table x
|
|
795 |
val R2 = dest_Func R |> snd
|
|
796 |
val z = (epsilon - delta, delta + j0)
|
|
797 |
in
|
|
798 |
if exclusive then
|
|
799 |
kk_n_ary_function kk (Func (Atom z, R2)) r
|
|
800 |
else
|
|
801 |
let val r' = kk_join (Kodkod.Var (1, 0)) r in
|
|
802 |
kk_all [Kodkod.DeclOne ((1, 0), Kodkod.AtomSeq z)]
|
|
803 |
(kk_formula_if (kk_subset (Kodkod.Var (1, 0)) dom_r)
|
|
804 |
(kk_n_ary_function kk R2 r')
|
|
805 |
(kk_no r'))
|
|
806 |
end
|
|
807 |
end
|
|
808 |
(* extended_context -> int -> kodkod_constrs -> nut NameTable.table
|
|
809 |
-> constr_spec -> Kodkod.formula list *)
|
|
810 |
fun sel_axioms_for_constr ext_ctxt j0 kk rel_table
|
|
811 |
(constr as {const, delta, epsilon, explicit_max, ...}) =
|
|
812 |
let
|
|
813 |
val honors_explicit_max =
|
|
814 |
explicit_max < 0 orelse epsilon - delta <= explicit_max
|
|
815 |
in
|
|
816 |
if explicit_max = 0 then
|
|
817 |
[formula_for_bool honors_explicit_max]
|
|
818 |
else
|
|
819 |
let
|
|
820 |
val ran_r = discr_rel_expr rel_table const
|
|
821 |
val max_axiom =
|
|
822 |
if honors_explicit_max then Kodkod.True
|
|
823 |
else Kodkod.LE (Kodkod.Cardinality ran_r, Kodkod.Num explicit_max)
|
|
824 |
in
|
|
825 |
max_axiom ::
|
|
826 |
map (sel_axiom_for_sel ext_ctxt j0 kk rel_table ran_r constr)
|
|
827 |
(index_seq 0 (num_sels_for_constr_type (snd const)))
|
|
828 |
end
|
|
829 |
end
|
|
830 |
(* extended_context -> int -> kodkod_constrs -> nut NameTable.table
|
|
831 |
-> dtype_spec -> Kodkod.formula list *)
|
|
832 |
fun sel_axioms_for_datatype ext_ctxt j0 kk rel_table
|
|
833 |
({constrs, ...} : dtype_spec) =
|
|
834 |
maps (sel_axioms_for_constr ext_ctxt j0 kk rel_table) constrs
|
|
835 |
|
|
836 |
(* extended_context -> kodkod_constrs -> nut NameTable.table -> constr_spec
|
|
837 |
-> Kodkod.formula list *)
|
|
838 |
fun uniqueness_axiom_for_constr ext_ctxt
|
|
839 |
({kk_all, kk_implies, kk_and, kk_rel_eq, kk_lone, kk_join, ...}
|
|
840 |
: kodkod_constrs) rel_table ({const, ...} : constr_spec) =
|
|
841 |
let
|
|
842 |
(* Kodkod.rel_expr -> Kodkod.formula *)
|
|
843 |
fun conjunct_for_sel r =
|
|
844 |
kk_rel_eq (kk_join (Kodkod.Var (1, 0)) r)
|
|
845 |
(kk_join (Kodkod.Var (1, 1)) r)
|
|
846 |
val num_sels = num_sels_for_constr_type (snd const)
|
|
847 |
val triples = map (const_triple rel_table
|
|
848 |
o boxed_nth_sel_for_constr ext_ctxt const)
|
|
849 |
(~1 upto num_sels - 1)
|
|
850 |
val j0 = case triples |> hd |> #2 of
|
|
851 |
Func (Atom (_, j0), _) => j0
|
|
852 |
| R => raise REP ("NitpickKodkod.uniqueness_axiom_for_constr", [R])
|
|
853 |
val set_r = triples |> hd |> #1
|
|
854 |
in
|
|
855 |
if num_sels = 0 then
|
|
856 |
kk_lone set_r
|
|
857 |
else
|
|
858 |
kk_all (map (Kodkod.DeclOne o rpair set_r o pair 1) [0, 1])
|
|
859 |
(kk_implies
|
|
860 |
(fold1 kk_and (map (conjunct_for_sel o #1) (tl triples)))
|
|
861 |
(kk_rel_eq (Kodkod.Var (1, 0)) (Kodkod.Var (1, 1))))
|
|
862 |
end
|
|
863 |
(* extended_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec
|
|
864 |
-> Kodkod.formula list *)
|
|
865 |
fun uniqueness_axioms_for_datatype ext_ctxt kk rel_table
|
|
866 |
({constrs, ...} : dtype_spec) =
|
|
867 |
map (uniqueness_axiom_for_constr ext_ctxt kk rel_table) constrs
|
|
868 |
|
|
869 |
(* constr_spec -> int *)
|
|
870 |
fun effective_constr_max ({delta, epsilon, ...} : constr_spec) = epsilon - delta
|
|
871 |
(* int -> kodkod_constrs -> nut NameTable.table -> dtype_spec
|
|
872 |
-> Kodkod.formula list *)
|
|
873 |
fun partition_axioms_for_datatype j0 (kk as {kk_rel_eq, kk_union, ...})
|
|
874 |
rel_table
|
|
875 |
({card, constrs, ...} : dtype_spec) =
|
|
876 |
if forall #exclusive constrs then
|
|
877 |
[Integer.sum (map effective_constr_max constrs) = card |> formula_for_bool]
|
|
878 |
else
|
|
879 |
let val rs = map (discr_rel_expr rel_table o #const) constrs in
|
|
880 |
[kk_rel_eq (fold1 kk_union rs) (Kodkod.AtomSeq (card, j0)),
|
|
881 |
kk_disjoint_sets kk rs]
|
|
882 |
end
|
|
883 |
|
|
884 |
(* extended_context -> int Typtab.table -> kodkod_constrs -> nut NameTable.table
|
|
885 |
-> dtype_spec -> Kodkod.formula list *)
|
|
886 |
fun other_axioms_for_datatype ext_ctxt ofs kk rel_table (dtype as {typ, ...}) =
|
|
887 |
let val j0 = offset_of_type ofs typ in
|
|
888 |
sel_axioms_for_datatype ext_ctxt j0 kk rel_table dtype @
|
|
889 |
uniqueness_axioms_for_datatype ext_ctxt kk rel_table dtype @
|
|
890 |
partition_axioms_for_datatype j0 kk rel_table dtype
|
|
891 |
end
|
|
892 |
|
|
893 |
(* extended_context -> int Typtab.table -> kodkod_constrs -> nut NameTable.table
|
|
894 |
-> dtype_spec list -> Kodkod.formula list *)
|
|
895 |
fun declarative_axioms_for_datatypes ext_ctxt ofs kk rel_table dtypes =
|
|
896 |
acyclicity_axioms_for_datatypes ext_ctxt kk rel_table dtypes @
|
|
897 |
maps (other_axioms_for_datatype ext_ctxt ofs kk rel_table) dtypes
|
|
898 |
|
|
899 |
(* int Typtab.table -> bool -> kodkod_constrs -> nut -> Kodkod.formula *)
|
|
900 |
fun kodkod_formula_from_nut ofs liberal
|
|
901 |
(kk as {kk_all, kk_exist, kk_formula_let, kk_formula_if, kk_or, kk_not,
|
|
902 |
kk_iff, kk_implies, kk_and, kk_subset, kk_rel_eq, kk_no, kk_one,
|
|
903 |
kk_some, kk_rel_let, kk_rel_if, kk_union, kk_difference,
|
|
904 |
kk_intersect, kk_product, kk_join, kk_closure, kk_comprehension,
|
|
905 |
kk_project, kk_project_seq, kk_not3, kk_nat_less, kk_int_less,
|
|
906 |
...}) u =
|
|
907 |
let
|
|
908 |
val main_j0 = offset_of_type ofs bool_T
|
|
909 |
val bool_j0 = main_j0
|
|
910 |
val bool_atom_R = Atom (2, main_j0)
|
|
911 |
val false_atom = Kodkod.Atom bool_j0
|
|
912 |
val true_atom = Kodkod.Atom (bool_j0 + 1)
|
|
913 |
|
|
914 |
(* polarity -> int -> Kodkod.rel_expr -> Kodkod.formula *)
|
|
915 |
fun formula_from_opt_atom polar j0 r =
|
|
916 |
case polar of
|
|
917 |
Neg => kk_not (kk_rel_eq r (Kodkod.Atom j0))
|
|
918 |
| _ => kk_rel_eq r (Kodkod.Atom (j0 + 1))
|
|
919 |
(* int -> Kodkod.rel_expr -> Kodkod.formula *)
|
|
920 |
val formula_from_atom = formula_from_opt_atom Pos
|
|
921 |
|
|
922 |
(* Kodkod.formula -> Kodkod.formula -> Kodkod.formula *)
|
|
923 |
fun kk_notimplies f1 f2 = kk_and f1 (kk_not f2)
|
|
924 |
(* Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
925 |
val kk_or3 =
|
|
926 |
double_rel_let kk
|
|
927 |
(fn r1 => fn r2 =>
|
|
928 |
kk_rel_if (kk_subset true_atom (kk_union r1 r2)) true_atom
|
|
929 |
(kk_intersect r1 r2))
|
|
930 |
val kk_and3 =
|
|
931 |
double_rel_let kk
|
|
932 |
(fn r1 => fn r2 =>
|
|
933 |
kk_rel_if (kk_subset false_atom (kk_union r1 r2)) false_atom
|
|
934 |
(kk_intersect r1 r2))
|
|
935 |
fun kk_notimplies3 r1 r2 = kk_and3 r1 (kk_not3 r2)
|
|
936 |
|
|
937 |
(* int -> Kodkod.rel_expr -> Kodkod.formula list *)
|
|
938 |
val unpack_formulas =
|
|
939 |
map (formula_from_atom bool_j0) oo unpack_vect_in_chunks kk 1
|
|
940 |
(* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula) -> int
|
|
941 |
-> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
942 |
fun kk_vect_set_op connective k r1 r2 =
|
|
943 |
fold1 kk_product (map2 (atom_from_formula kk bool_j0 oo connective)
|
|
944 |
(unpack_formulas k r1) (unpack_formulas k r2))
|
|
945 |
(* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula) -> int
|
|
946 |
-> Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula *)
|
|
947 |
fun kk_vect_set_bool_op connective k r1 r2 =
|
|
948 |
fold1 kk_and (map2 connective (unpack_formulas k r1)
|
|
949 |
(unpack_formulas k r2))
|
|
950 |
|
|
951 |
(* nut -> Kodkod.formula *)
|
|
952 |
fun to_f u =
|
|
953 |
case rep_of u of
|
|
954 |
Formula polar =>
|
|
955 |
(case u of
|
|
956 |
Cst (False, _, _) => Kodkod.False
|
|
957 |
| Cst (True, _, _) => Kodkod.True
|
|
958 |
| Op1 (Not, _, _, u1) => kk_not (to_f u1)
|
|
959 |
| Op1 (Finite, _, _, u1) =>
|
|
960 |
let val opt1 = is_opt_rep (rep_of u1) in
|
|
961 |
case polar of
|
|
962 |
Neut => if opt1 then
|
|
963 |
raise NUT ("NitpickKodkod.to_f (Finite)", [u])
|
|
964 |
else
|
|
965 |
Kodkod.True
|
|
966 |
| Pos => formula_for_bool (not opt1)
|
|
967 |
| Neg => Kodkod.True
|
|
968 |
end
|
|
969 |
| Op1 (Cast, _, _, u1) => to_f_with_polarity polar u1
|
|
970 |
| Op2 (All, _, _, u1, u2) => kk_all (untuple to_decl u1) (to_f u2)
|
|
971 |
| Op2 (Exist, _, _, u1, u2) => kk_exist (untuple to_decl u1) (to_f u2)
|
|
972 |
| Op2 (Or, _, _, u1, u2) => kk_or (to_f u1) (to_f u2)
|
|
973 |
| Op2 (And, _, _, u1, u2) => kk_and (to_f u1) (to_f u2)
|
|
974 |
| Op2 (Less, T, Formula polar, u1, u2) =>
|
|
975 |
formula_from_opt_atom polar bool_j0
|
|
976 |
(to_r (Op2 (Less, T, Opt bool_atom_R, u1, u2)))
|
|
977 |
| Op2 (Subset, _, _, u1, u2) =>
|
|
978 |
let
|
|
979 |
val dom_T = domain_type (type_of u1)
|
|
980 |
val R1 = rep_of u1
|
|
981 |
val R2 = rep_of u2
|
|
982 |
val (dom_R, ran_R) =
|
|
983 |
case min_rep R1 R2 of
|
|
984 |
Func (Unit, R') =>
|
|
985 |
(Atom (1, offset_of_type ofs dom_T), R')
|
|
986 |
| Func Rp => Rp
|
|
987 |
| R => (Atom (card_of_domain_from_rep 2 R,
|
|
988 |
offset_of_type ofs dom_T),
|
|
989 |
if is_opt_rep R then Opt bool_atom_R else Formula Neut)
|
|
990 |
val set_R = Func (dom_R, ran_R)
|
|
991 |
in
|
|
992 |
if not (is_opt_rep ran_R) then
|
|
993 |
to_set_bool_op kk_implies kk_subset u1 u2
|
|
994 |
else if polar = Neut then
|
|
995 |
raise NUT ("NitpickKodkod.to_f (Subset)", [u])
|
|
996 |
else
|
|
997 |
let
|
|
998 |
(* bool -> nut -> Kodkod.rel_expr *)
|
|
999 |
fun set_to_r widen u =
|
|
1000 |
if widen then
|
|
1001 |
kk_difference (full_rel_for_rep dom_R)
|
|
1002 |
(kk_join (to_rep set_R u) false_atom)
|
|
1003 |
else
|
|
1004 |
kk_join (to_rep set_R u) true_atom
|
|
1005 |
val widen1 = (polar = Pos andalso is_opt_rep R1)
|
|
1006 |
val widen2 = (polar = Neg andalso is_opt_rep R2)
|
|
1007 |
in kk_subset (set_to_r widen1 u1) (set_to_r widen2 u2) end
|
|
1008 |
end
|
|
1009 |
| Op2 (DefEq, _, _, u1, u2) =>
|
|
1010 |
(case min_rep (rep_of u1) (rep_of u2) of
|
|
1011 |
Unit => Kodkod.True
|
|
1012 |
| Formula polar =>
|
|
1013 |
kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|
|
1014 |
| min_R =>
|
|
1015 |
let
|
|
1016 |
(* nut -> nut list *)
|
|
1017 |
fun args (Op2 (Apply, _, _, u1, u2)) = u2 :: args u1
|
|
1018 |
| args (Tuple (_, _, us)) = us
|
|
1019 |
| args _ = []
|
|
1020 |
val opt_arg_us = filter (is_opt_rep o rep_of) (args u1)
|
|
1021 |
in
|
|
1022 |
if null opt_arg_us orelse not (is_Opt min_R)
|
|
1023 |
orelse is_eval_name u1 then
|
|
1024 |
fold (kk_or o (kk_no o to_r)) opt_arg_us
|
|
1025 |
(kk_rel_eq (to_rep min_R u1) (to_rep min_R u2))
|
|
1026 |
else
|
|
1027 |
kk_no (kk_difference (to_rep min_R u1) (to_rep min_R u2))
|
|
1028 |
end)
|
|
1029 |
| Op2 (Eq, T, R, u1, u2) =>
|
|
1030 |
(case min_rep (rep_of u1) (rep_of u2) of
|
|
1031 |
Unit => Kodkod.True
|
|
1032 |
| Formula polar =>
|
|
1033 |
kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|
|
1034 |
| min_R =>
|
|
1035 |
if is_opt_rep min_R then
|
|
1036 |
if polar = Neut then
|
|
1037 |
(* continuation of hackish optimization *)
|
|
1038 |
kk_rel_eq (to_rep min_R u1) (to_rep min_R u2)
|
|
1039 |
else if is_Cst Unrep u1 then
|
|
1040 |
to_could_be_unrep (polar = Neg) u2
|
|
1041 |
else if is_Cst Unrep u2 then
|
|
1042 |
to_could_be_unrep (polar = Neg) u1
|
|
1043 |
else
|
|
1044 |
let
|
|
1045 |
val r1 = to_rep min_R u1
|
|
1046 |
val r2 = to_rep min_R u2
|
|
1047 |
val both_opt = forall (is_opt_rep o rep_of) [u1, u2]
|
|
1048 |
in
|
|
1049 |
(if polar = Pos then
|
|
1050 |
if not both_opt then
|
|
1051 |
kk_rel_eq r1 r2
|
|
1052 |
else if is_lone_rep min_R
|
|
1053 |
andalso arity_of_rep min_R = 1 then
|
|
1054 |
kk_some (kk_intersect r1 r2)
|
|
1055 |
else
|
|
1056 |
raise SAME ()
|
|
1057 |
else
|
|
1058 |
if is_lone_rep min_R then
|
|
1059 |
if arity_of_rep min_R = 1 then
|
|
1060 |
kk_subset (kk_product r1 r2) Kodkod.Iden
|
|
1061 |
else if not both_opt then
|
|
1062 |
(r1, r2) |> is_opt_rep (rep_of u2) ? swap
|
|
1063 |
|> uncurry kk_difference |> kk_no
|
|
1064 |
else
|
|
1065 |
raise SAME ()
|
|
1066 |
else
|
|
1067 |
raise SAME ())
|
|
1068 |
handle SAME () =>
|
|
1069 |
formula_from_opt_atom polar bool_j0
|
|
1070 |
(to_guard [u1, u2] bool_atom_R
|
|
1071 |
(rel_expr_from_formula kk bool_atom_R
|
|
1072 |
(kk_rel_eq r1 r2)))
|
|
1073 |
end
|
|
1074 |
else
|
|
1075 |
let
|
|
1076 |
val r1 = to_rep min_R u1
|
|
1077 |
val r2 = to_rep min_R u2
|
|
1078 |
in
|
|
1079 |
if is_one_rep min_R then
|
|
1080 |
let
|
|
1081 |
val rs1 = unpack_products r1
|
|
1082 |
val rs2 = unpack_products r2
|
|
1083 |
in
|
|
1084 |
if length rs1 = length rs2
|
|
1085 |
andalso map Kodkod.arity_of_rel_expr rs1
|
|
1086 |
= map Kodkod.arity_of_rel_expr rs2 then
|
|
1087 |
fold1 kk_and (map2 kk_subset rs1 rs2)
|
|
1088 |
else
|
|
1089 |
kk_subset r1 r2
|
|
1090 |
end
|
|
1091 |
else
|
|
1092 |
kk_rel_eq r1 r2
|
|
1093 |
end)
|
|
1094 |
| Op2 (Apply, T, _, u1, u2) =>
|
|
1095 |
(case (polar, rep_of u1) of
|
|
1096 |
(Neg, Func (R, Formula Neut)) => kk_subset (to_opt R u2) (to_r u1)
|
|
1097 |
| _ =>
|
|
1098 |
to_f_with_polarity polar
|
|
1099 |
(Op2 (Apply, T, Opt (Atom (2, offset_of_type ofs T)), u1, u2)))
|
|
1100 |
| Op3 (Let, _, _, u1, u2, u3) =>
|
|
1101 |
kk_formula_let [to_expr_assign u1 u2] (to_f u3)
|
|
1102 |
| Op3 (If, _, _, u1, u2, u3) =>
|
|
1103 |
kk_formula_if (to_f u1) (to_f u2) (to_f u3)
|
|
1104 |
| FormulaReg (j, _, _) => Kodkod.FormulaReg j
|
|
1105 |
| _ => raise NUT ("NitpickKodkod.to_f", [u]))
|
|
1106 |
| Atom (2, j0) => formula_from_atom j0 (to_r u)
|
|
1107 |
| _ => raise NUT ("NitpickKodkod.to_f", [u])
|
|
1108 |
(* polarity -> nut -> Kodkod.formula *)
|
|
1109 |
and to_f_with_polarity polar u =
|
|
1110 |
case rep_of u of
|
|
1111 |
Formula _ => to_f u
|
|
1112 |
| Atom (2, j0) => formula_from_atom j0 (to_r u)
|
|
1113 |
| Opt (Atom (2, j0)) => formula_from_opt_atom polar j0 (to_r u)
|
|
1114 |
| _ => raise NUT ("NitpickKodkod.to_f_with_polarity", [u])
|
|
1115 |
(* nut -> Kodkod.rel_expr *)
|
|
1116 |
and to_r u =
|
|
1117 |
case u of
|
|
1118 |
Cst (False, _, Atom _) => false_atom
|
|
1119 |
| Cst (True, _, Atom _) => true_atom
|
|
1120 |
| Cst (Iden, T, Func (Struct [R1, R2], Formula Neut)) =>
|
|
1121 |
if R1 = R2 andalso arity_of_rep R1 = 1 then
|
|
1122 |
kk_intersect Kodkod.Iden (kk_product (full_rel_for_rep R1)
|
|
1123 |
Kodkod.Univ)
|
|
1124 |
else
|
|
1125 |
let
|
|
1126 |
val schema1 = atom_schema_of_rep R1
|
|
1127 |
val schema2 = atom_schema_of_rep R2
|
|
1128 |
val arity1 = length schema1
|
|
1129 |
val arity2 = length schema2
|
|
1130 |
val r1 = fold1 kk_product (unary_var_seq 0 arity1)
|
|
1131 |
val r2 = fold1 kk_product (unary_var_seq arity1 arity2)
|
|
1132 |
val min_R = min_rep R1 R2
|
|
1133 |
in
|
|
1134 |
kk_comprehension
|
|
1135 |
(decls_for_atom_schema 0 (schema1 @ schema2))
|
|
1136 |
(kk_rel_eq (rel_expr_from_rel_expr kk min_R R1 r1)
|
|
1137 |
(rel_expr_from_rel_expr kk min_R R2 r2))
|
|
1138 |
end
|
|
1139 |
| Cst (Iden, T, Func (Atom (1, j0), Formula Neut)) => Kodkod.Atom j0
|
|
1140 |
| Cst (Iden, T as Type ("fun", [T1, _]), R as Func (R1, _)) =>
|
|
1141 |
to_rep R (Cst (Iden, T, Func (one_rep ofs T1 R1, Formula Neut)))
|
|
1142 |
| Cst (Num j, @{typ int}, R) =>
|
|
1143 |
(case atom_for_int (card_of_rep R, offset_of_type ofs int_T) j of
|
|
1144 |
~1 => if is_opt_rep R then Kodkod.None
|
|
1145 |
else raise NUT ("NitpickKodkod.to_r (Num)", [u])
|
|
1146 |
| j' => Kodkod.Atom j')
|
|
1147 |
| Cst (Num j, T, R) =>
|
|
1148 |
if j < card_of_rep R then Kodkod.Atom (j + offset_of_type ofs T)
|
|
1149 |
else if is_opt_rep R then Kodkod.None
|
|
1150 |
else raise NUT ("NitpickKodkod.to_r", [u])
|
|
1151 |
| Cst (Unknown, _, R) => empty_rel_for_rep R
|
|
1152 |
| Cst (Unrep, _, R) => empty_rel_for_rep R
|
|
1153 |
| Cst (Suc, T, Func (Atom x, _)) =>
|
|
1154 |
if domain_type T <> nat_T then suc_rel
|
|
1155 |
else kk_intersect suc_rel (kk_product Kodkod.Univ (Kodkod.AtomSeq x))
|
|
1156 |
| Cst (Add, Type ("fun", [@{typ nat}, _]), _) => nat_add_rel
|
|
1157 |
| Cst (Add, Type ("fun", [@{typ int}, _]), _) => int_add_rel
|
|
1158 |
| Cst (Subtract, Type ("fun", [@{typ nat}, _]), _) => nat_subtract_rel
|
|
1159 |
| Cst (Subtract, Type ("fun", [@{typ int}, _]), _) => int_subtract_rel
|
|
1160 |
| Cst (Multiply, Type ("fun", [@{typ nat}, _]), _) => nat_multiply_rel
|
|
1161 |
| Cst (Multiply, Type ("fun", [@{typ int}, _]), _) => int_multiply_rel
|
|
1162 |
| Cst (Divide, Type ("fun", [@{typ nat}, _]), _) => nat_divide_rel
|
|
1163 |
| Cst (Divide, Type ("fun", [@{typ int}, _]), _) => int_divide_rel
|
|
1164 |
| Cst (Modulo, Type ("fun", [@{typ nat}, _]), _) => nat_modulo_rel
|
|
1165 |
| Cst (Modulo, Type ("fun", [@{typ int}, _]), _) => int_modulo_rel
|
|
1166 |
| Cst (Gcd, _, _) => gcd_rel
|
|
1167 |
| Cst (Lcm, _, _) => lcm_rel
|
|
1168 |
| Cst (Fracs, _, Func (Atom (1, _), _)) => Kodkod.None
|
|
1169 |
| Cst (Fracs, _, Func (Struct _, _)) =>
|
|
1170 |
kk_project_seq norm_frac_rel 2 2
|
|
1171 |
| Cst (NormFrac, _, _) => norm_frac_rel
|
|
1172 |
| Cst (NatToInt, _, Func (Atom _, Atom _)) => Kodkod.Iden
|
|
1173 |
| Cst (NatToInt, _,
|
|
1174 |
Func (Atom (nat_k, nat_j0), Opt (Atom (int_k, int_j0)))) =>
|
|
1175 |
if nat_j0 = int_j0 then
|
|
1176 |
kk_intersect Kodkod.Iden
|
|
1177 |
(kk_product (Kodkod.AtomSeq (max_int_for_card int_k + 1, nat_j0))
|
|
1178 |
Kodkod.Univ)
|
|
1179 |
else
|
|
1180 |
raise BAD ("NitpickKodkod.to_r (NatToInt)", "\"nat_j0 <> int_j0\"")
|
|
1181 |
| Cst (IntToNat, _, Func (Atom (int_k, int_j0), nat_R)) =>
|
|
1182 |
let
|
|
1183 |
val abs_card = max_int_for_card int_k + 1
|
|
1184 |
val (nat_k, nat_j0) = the_single (atom_schema_of_rep nat_R)
|
|
1185 |
val overlap = Int.min (nat_k, abs_card)
|
|
1186 |
in
|
|
1187 |
if nat_j0 = int_j0 then
|
|
1188 |
kk_union (kk_product (Kodkod.AtomSeq (int_k - abs_card,
|
|
1189 |
int_j0 + abs_card))
|
|
1190 |
(Kodkod.Atom nat_j0))
|
|
1191 |
(kk_intersect Kodkod.Iden
|
|
1192 |
(kk_product (Kodkod.AtomSeq (overlap, int_j0))
|
|
1193 |
Kodkod.Univ))
|
|
1194 |
else
|
|
1195 |
raise BAD ("NitpickKodkod.to_r (IntToNat)", "\"nat_j0 <> int_j0\"")
|
|
1196 |
end
|
|
1197 |
| Op1 (Not, _, R, u1) => kk_not3 (to_rep R u1)
|
|
1198 |
| Op1 (Finite, _, Opt (Atom _), _) => Kodkod.None
|
|
1199 |
| Op1 (Converse, T, R, u1) =>
|
|
1200 |
let
|
|
1201 |
val (b_T, a_T) = HOLogic.dest_prodT (domain_type T)
|
|
1202 |
val (b_R, a_R) =
|
|
1203 |
case R of
|
|
1204 |
Func (Struct [R1, R2], _) => (R1, R2)
|
|
1205 |
| Func (R1, _) =>
|
|
1206 |
if card_of_rep R1 <> 1 then
|
|
1207 |
raise REP ("NitpickKodkod.to_r (Converse)", [R])
|
|
1208 |
else
|
|
1209 |
pairself (Atom o pair 1 o offset_of_type ofs) (b_T, a_T)
|
|
1210 |
| _ => raise REP ("NitpickKodkod.to_r (Converse)", [R])
|
|
1211 |
val body_R = body_rep R
|
|
1212 |
val a_arity = arity_of_rep a_R
|
|
1213 |
val b_arity = arity_of_rep b_R
|
|
1214 |
val ab_arity = a_arity + b_arity
|
|
1215 |
val body_arity = arity_of_rep body_R
|
|
1216 |
in
|
|
1217 |
kk_project (to_rep (Func (Struct [a_R, b_R], body_R)) u1)
|
|
1218 |
(map Kodkod.Num (index_seq a_arity b_arity @
|
|
1219 |
index_seq 0 a_arity @
|
|
1220 |
index_seq ab_arity body_arity))
|
|
1221 |
|> rel_expr_from_rel_expr kk R (Func (Struct [b_R, a_R], body_R))
|
|
1222 |
end
|
|
1223 |
| Op1 (Closure, _, R, u1) =>
|
|
1224 |
if is_opt_rep R then
|
|
1225 |
let
|
|
1226 |
val T1 = type_of u1
|
|
1227 |
val R' = rep_to_binary_rel_rep ofs T1 (unopt_rep (rep_of u1))
|
|
1228 |
val R'' = opt_rep ofs T1 R'
|
|
1229 |
in
|
|
1230 |
single_rel_let kk
|
|
1231 |
(fn r =>
|
|
1232 |
let
|
|
1233 |
val true_r = kk_closure (kk_join r true_atom)
|
|
1234 |
val full_r = full_rel_for_rep R'
|
|
1235 |
val false_r = kk_difference full_r
|
|
1236 |
(kk_closure (kk_difference full_r
|
|
1237 |
(kk_join r false_atom)))
|
|
1238 |
in
|
|
1239 |
rel_expr_from_rel_expr kk R R''
|
|
1240 |
(kk_union (kk_product true_r true_atom)
|
|
1241 |
(kk_product false_r false_atom))
|
|
1242 |
end) (to_rep R'' u1)
|
|
1243 |
end
|
|
1244 |
else
|
|
1245 |
let val R' = rep_to_binary_rel_rep ofs (type_of u1) (rep_of u1) in
|
|
1246 |
rel_expr_from_rel_expr kk R R' (kk_closure (to_rep R' u1))
|
|
1247 |
end
|
|
1248 |
| Op1 (SingletonSet, _, Func (R1, Opt _), Cst (Unrep, _, _)) =>
|
|
1249 |
(if R1 = Unit then I else kk_product (full_rel_for_rep R1)) false_atom
|
|
1250 |
| Op1 (SingletonSet, _, R, u1) =>
|
|
1251 |
(case R of
|
|
1252 |
Func (R1, Formula Neut) => to_rep R1 u1
|
|
1253 |
| Func (Unit, Opt R) => to_guard [u1] R true_atom
|
|
1254 |
| Func (R1, R2 as Opt _) =>
|
|
1255 |
single_rel_let kk
|
|
1256 |
(fn r => kk_rel_if (kk_no r) (empty_rel_for_rep R)
|
|
1257 |
(rel_expr_to_func kk R1 bool_atom_R
|
|
1258 |
(Func (R1, Formula Neut)) r))
|
|
1259 |
(to_opt R1 u1)
|
|
1260 |
| _ => raise NUT ("NitpickKodkod.to_r (SingletonSet)", [u]))
|
|
1261 |
| Op1 (Tha, T, R, u1) =>
|
|
1262 |
if is_opt_rep R then
|
|
1263 |
kk_join (to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1) true_atom
|
|
1264 |
else
|
|
1265 |
to_rep (Func (R, Formula Neut)) u1
|
|
1266 |
| Op1 (First, T, R, u1) => to_nth_pair_sel 0 T R u1
|
|
1267 |
| Op1 (Second, T, R, u1) => to_nth_pair_sel 1 T R u1
|
|
1268 |
| Op1 (Cast, _, R, u1) =>
|
|
1269 |
((case rep_of u1 of
|
|
1270 |
Formula _ =>
|
|
1271 |
(case unopt_rep R of
|
|
1272 |
Atom (2, j0) => atom_from_formula kk j0 (to_f u1)
|
|
1273 |
| _ => raise SAME ())
|
|
1274 |
| _ => raise SAME ())
|
|
1275 |
handle SAME () => rel_expr_from_rel_expr kk R (rep_of u1) (to_r u1))
|
|
1276 |
| Op2 (All, T, R as Opt _, u1, u2) =>
|
|
1277 |
to_r (Op1 (Not, T, R,
|
|
1278 |
Op2 (Exist, T, R, u1, Op1 (Not, T, rep_of u2, u2))))
|
|
1279 |
| Op2 (Exist, T, Opt _, u1, u2) =>
|
|
1280 |
let val rs1 = untuple to_decl u1 in
|
|
1281 |
if not (is_opt_rep (rep_of u2)) then
|
|
1282 |
kk_rel_if (kk_exist rs1 (to_f u2)) true_atom Kodkod.None
|
|
1283 |
else
|
|
1284 |
let val r2 = to_r u2 in
|
|
1285 |
kk_union (kk_rel_if (kk_exist rs1 (kk_rel_eq r2 true_atom))
|
|
1286 |
true_atom Kodkod.None)
|
|
1287 |
(kk_rel_if (kk_all rs1 (kk_rel_eq r2 false_atom))
|
|
1288 |
false_atom Kodkod.None)
|
|
1289 |
end
|
|
1290 |
end
|
|
1291 |
| Op2 (Or, _, _, u1, u2) =>
|
|
1292 |
if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) true_atom (to_r u1)
|
|
1293 |
else kk_rel_if (to_f u1) true_atom (to_r u2)
|
|
1294 |
| Op2 (And, _, _, u1, u2) =>
|
|
1295 |
if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) (to_r u1) false_atom
|
|
1296 |
else kk_rel_if (to_f u1) (to_r u2) false_atom
|
|
1297 |
| Op2 (Less, _, _, u1, u2) =>
|
|
1298 |
if type_of u1 = nat_T then
|
|
1299 |
if is_Cst Unrep u1 then to_compare_with_unrep u2 false_atom
|
|
1300 |
else if is_Cst Unrep u2 then to_compare_with_unrep u1 true_atom
|
|
1301 |
else kk_nat_less (to_integer u1) (to_integer u2)
|
|
1302 |
else
|
|
1303 |
kk_int_less (to_integer u1) (to_integer u2)
|
|
1304 |
| Op2 (The, T, R, u1, u2) =>
|
|
1305 |
if is_opt_rep R then
|
|
1306 |
let val r1 = to_opt (Func (unopt_rep R, bool_atom_R)) u1 in
|
|
1307 |
kk_rel_if (kk_one (kk_join r1 true_atom)) (kk_join r1 true_atom)
|
|
1308 |
(kk_rel_if (kk_or (kk_some (kk_join r1 true_atom))
|
|
1309 |
(kk_subset (full_rel_for_rep R)
|
|
1310 |
(kk_join r1 false_atom)))
|
|
1311 |
(to_rep R u2) Kodkod.None)
|
|
1312 |
end
|
|
1313 |
else
|
|
1314 |
let val r1 = to_rep (Func (R, Formula Neut)) u1 in
|
|
1315 |
kk_rel_if (kk_one r1) r1 (to_rep R u2)
|
|
1316 |
end
|
|
1317 |
| Op2 (Eps, T, R, u1, u2) =>
|
|
1318 |
if is_opt_rep (rep_of u1) then
|
|
1319 |
let
|
|
1320 |
val r1 = to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1
|
|
1321 |
val r2 = to_rep R u2
|
|
1322 |
in
|
|
1323 |
kk_union (kk_rel_if (kk_one (kk_join r1 true_atom))
|
|
1324 |
(kk_join r1 true_atom) Kodkod.None)
|
|
1325 |
(kk_rel_if (kk_or (kk_subset r2 (kk_join r1 true_atom))
|
|
1326 |
(kk_subset (full_rel_for_rep R)
|
|
1327 |
(kk_join r1 false_atom)))
|
|
1328 |
r2 Kodkod.None)
|
|
1329 |
end
|
|
1330 |
else
|
|
1331 |
let
|
|
1332 |
val r1 = to_rep (Func (unopt_rep R, Formula Neut)) u1
|
|
1333 |
val r2 = to_rep R u2
|
|
1334 |
in
|
|
1335 |
kk_union (kk_rel_if (kk_one r1) r1 Kodkod.None)
|
|
1336 |
(kk_rel_if (kk_or (kk_no r1) (kk_subset r2 r1))
|
|
1337 |
r2 Kodkod.None)
|
|
1338 |
end
|
|
1339 |
| Op2 (Triad, T, Opt (Atom (2, j0)), u1, u2) =>
|
|
1340 |
let
|
|
1341 |
val f1 = to_f u1
|
|
1342 |
val f2 = to_f u2
|
|
1343 |
in
|
|
1344 |
if f1 = f2 then
|
|
1345 |
atom_from_formula kk j0 f1
|
|
1346 |
else
|
|
1347 |
kk_union (kk_rel_if f1 true_atom Kodkod.None)
|
|
1348 |
(kk_rel_if f2 Kodkod.None false_atom)
|
|
1349 |
end
|
|
1350 |
| Op2 (Union, _, R, u1, u2) =>
|
|
1351 |
to_set_op kk_or kk_or3 kk_union kk_union kk_intersect false R u1 u2
|
|
1352 |
| Op2 (SetDifference, _, R, u1, u2) =>
|
|
1353 |
to_set_op kk_notimplies kk_notimplies3 kk_difference kk_intersect
|
|
1354 |
kk_union true R u1 u2
|
|
1355 |
| Op2 (Intersect, _, R, u1, u2) =>
|
|
1356 |
to_set_op kk_and kk_and3 kk_intersect kk_intersect kk_union false R
|
|
1357 |
u1 u2
|
|
1358 |
| Op2 (Composition, _, R, u1, u2) =>
|
|
1359 |
let
|
|
1360 |
val (a_T, b_T) = HOLogic.dest_prodT (domain_type (type_of u2))
|
|
1361 |
val (_, c_T) = HOLogic.dest_prodT (domain_type (type_of u1))
|
|
1362 |
val ab_k = card_of_domain_from_rep 2 (rep_of u2)
|
|
1363 |
val bc_k = card_of_domain_from_rep 2 (rep_of u1)
|
|
1364 |
val ac_k = card_of_domain_from_rep 2 R
|
|
1365 |
val a_k = exact_root 2 (ac_k * ab_k div bc_k)
|
|
1366 |
val b_k = exact_root 2 (ab_k * bc_k div ac_k)
|
|
1367 |
val c_k = exact_root 2 (bc_k * ac_k div ab_k)
|
|
1368 |
val a_R = Atom (a_k, offset_of_type ofs a_T)
|
|
1369 |
val b_R = Atom (b_k, offset_of_type ofs b_T)
|
|
1370 |
val c_R = Atom (c_k, offset_of_type ofs c_T)
|
|
1371 |
val body_R = body_rep R
|
|
1372 |
in
|
|
1373 |
(case body_R of
|
|
1374 |
Formula Neut =>
|
|
1375 |
kk_join (to_rep (Func (Struct [a_R, b_R], Formula Neut)) u2)
|
|
1376 |
(to_rep (Func (Struct [b_R, c_R], Formula Neut)) u1)
|
|
1377 |
| Opt (Atom (2, _)) =>
|
|
1378 |
let
|
|
1379 |
(* Kodkod.rel_expr -> rep -> rep -> nut -> Kodkod.rel_expr *)
|
|
1380 |
fun do_nut r R1 R2 u =
|
|
1381 |
kk_join (to_rep (Func (Struct [R1, R2], body_R)) u) r
|
|
1382 |
(* Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
1383 |
fun do_term r =
|
|
1384 |
kk_product (kk_join (do_nut r a_R b_R u2)
|
|
1385 |
(do_nut r b_R c_R u1)) r
|
|
1386 |
in kk_union (do_term true_atom) (do_term false_atom) end
|
|
1387 |
| _ => raise NUT ("NitpickKodkod.to_r (Composition)", [u]))
|
|
1388 |
|> rel_expr_from_rel_expr kk R (Func (Struct [a_R, c_R], body_R))
|
|
1389 |
end
|
|
1390 |
| Op2 (Product, T, R, u1, u2) =>
|
|
1391 |
let
|
|
1392 |
val (a_T, b_T) = HOLogic.dest_prodT (domain_type T)
|
|
1393 |
val a_k = card_of_domain_from_rep 2 (rep_of u1)
|
|
1394 |
val b_k = card_of_domain_from_rep 2 (rep_of u2)
|
|
1395 |
val a_R = Atom (a_k, offset_of_type ofs a_T)
|
|
1396 |
val b_R = Atom (b_k, offset_of_type ofs b_T)
|
|
1397 |
val body_R = body_rep R
|
|
1398 |
in
|
|
1399 |
(case body_R of
|
|
1400 |
Formula Neut =>
|
|
1401 |
kk_product (to_rep (Func (a_R, Formula Neut)) u1)
|
|
1402 |
(to_rep (Func (b_R, Formula Neut)) u2)
|
|
1403 |
| Opt (Atom (2, _)) =>
|
|
1404 |
let
|
|
1405 |
(* Kodkod.rel_expr -> rep -> nut -> Kodkod.rel_expr *)
|
|
1406 |
fun do_nut r R u = kk_join (to_rep (Func (R, body_R)) u) r
|
|
1407 |
(* Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
1408 |
fun do_term r =
|
|
1409 |
kk_product (kk_product (do_nut r a_R u1) (do_nut r b_R u2)) r
|
|
1410 |
in kk_union (do_term true_atom) (do_term false_atom) end
|
|
1411 |
| _ => raise NUT ("NitpickKodkod.to_r (Product)", [u]))
|
|
1412 |
|> rel_expr_from_rel_expr kk R (Func (Struct [a_R, b_R], body_R))
|
|
1413 |
end
|
|
1414 |
| Op2 (Image, T, R, u1, u2) =>
|
|
1415 |
(case (rep_of u1, rep_of u2) of
|
|
1416 |
(Func (R11, R12), Func (R21, Formula Neut)) =>
|
|
1417 |
if R21 = R11 andalso is_lone_rep R12 then
|
|
1418 |
let
|
|
1419 |
(* Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
1420 |
fun big_join r = kk_n_fold_join kk false R21 R12 r (to_r u1)
|
|
1421 |
val core_r = big_join (to_r u2)
|
|
1422 |
val core_R = Func (R12, Formula Neut)
|
|
1423 |
in
|
|
1424 |
if is_opt_rep R12 then
|
|
1425 |
let
|
|
1426 |
val schema = atom_schema_of_rep R21
|
|
1427 |
val decls = decls_for_atom_schema ~1 schema
|
|
1428 |
val vars = unary_var_seq ~1 (length decls)
|
|
1429 |
val f = kk_some (big_join (fold1 kk_product vars))
|
|
1430 |
in
|
|
1431 |
kk_rel_if (kk_all decls f)
|
|
1432 |
(rel_expr_from_rel_expr kk R core_R core_r)
|
|
1433 |
(rel_expr_from_rel_expr kk R (opt_rep ofs T core_R)
|
|
1434 |
(kk_product core_r true_atom))
|
|
1435 |
end
|
|
1436 |
else
|
|
1437 |
rel_expr_from_rel_expr kk R core_R core_r
|
|
1438 |
end
|
|
1439 |
else
|
|
1440 |
raise NUT ("NitpickKodkod.to_r (Image)", [u1, u2])
|
|
1441 |
| _ => raise NUT ("NitpickKodkod.to_r (Image)", [u1, u2]))
|
|
1442 |
| Op2 (Apply, @{typ nat}, _,
|
|
1443 |
Op2 (Apply, _, _, Cst (Subtract, _, _), u1), u2) =>
|
|
1444 |
if is_Cst Unrep u2 andalso not (is_opt_rep (rep_of u1)) then
|
|
1445 |
Kodkod.Atom (offset_of_type ofs nat_T)
|
|
1446 |
else
|
|
1447 |
fold kk_join [to_integer u1, to_integer u2] nat_subtract_rel
|
|
1448 |
| Op2 (Apply, _, R, u1, u2) =>
|
|
1449 |
if is_Cst Unrep u2 andalso is_set_type (type_of u1)
|
|
1450 |
andalso not (is_opt_rep (rep_of u1)) then
|
|
1451 |
false_atom
|
|
1452 |
else
|
|
1453 |
to_apply R u1 u2
|
|
1454 |
| Op2 (Lambda, T, R as Opt (Atom (1, j0)), u1, u2) =>
|
|
1455 |
to_guard [u1, u2] R (Kodkod.Atom j0)
|
|
1456 |
| Op2 (Lambda, T, Func (_, Formula Neut), u1, u2) =>
|
|
1457 |
kk_comprehension (untuple to_decl u1) (to_f u2)
|
|
1458 |
| Op2 (Lambda, T, Func (_, R2), u1, u2) =>
|
|
1459 |
let
|
|
1460 |
val dom_decls = untuple to_decl u1
|
|
1461 |
val ran_schema = atom_schema_of_rep R2
|
|
1462 |
val ran_decls = decls_for_atom_schema ~1 ran_schema
|
|
1463 |
val ran_vars = unary_var_seq ~1 (length ran_decls)
|
|
1464 |
in
|
|
1465 |
kk_comprehension (dom_decls @ ran_decls)
|
|
1466 |
(kk_subset (fold1 kk_product ran_vars)
|
|
1467 |
(to_rep R2 u2))
|
|
1468 |
end
|
|
1469 |
| Op3 (Let, _, R, u1, u2, u3) =>
|
|
1470 |
kk_rel_let [to_expr_assign u1 u2] (to_rep R u3)
|
|
1471 |
| Op3 (If, _, R, u1, u2, u3) =>
|
|
1472 |
if is_opt_rep (rep_of u1) then
|
|
1473 |
triple_rel_let kk
|
|
1474 |
(fn r1 => fn r2 => fn r3 =>
|
|
1475 |
let val empty_r = empty_rel_for_rep R in
|
|
1476 |
fold1 kk_union
|
|
1477 |
[kk_rel_if (kk_rel_eq r1 true_atom) r2 empty_r,
|
|
1478 |
kk_rel_if (kk_rel_eq r1 false_atom) r3 empty_r,
|
|
1479 |
kk_rel_if (kk_rel_eq r2 r3)
|
|
1480 |
(if inline_rel_expr r2 then r2 else r3) empty_r]
|
|
1481 |
end)
|
|
1482 |
(to_r u1) (to_rep R u2) (to_rep R u3)
|
|
1483 |
else
|
|
1484 |
kk_rel_if (to_f u1) (to_rep R u2) (to_rep R u3)
|
|
1485 |
| Tuple (_, R, us) =>
|
|
1486 |
(case unopt_rep R of
|
|
1487 |
Struct Rs => to_product Rs us
|
|
1488 |
| Vect (k, R) => to_product (replicate k R) us
|
|
1489 |
| Atom (1, j0) =>
|
|
1490 |
(case filter (not_equal Unit o rep_of) us of
|
|
1491 |
[] => Kodkod.Atom j0
|
|
1492 |
| us' =>
|
|
1493 |
kk_rel_if (kk_some (fold1 kk_product (map to_r us')))
|
|
1494 |
(Kodkod.Atom j0) Kodkod.None)
|
|
1495 |
| _ => raise NUT ("NitpickKodkod.to_r (Tuple)", [u]))
|
|
1496 |
| Construct ([u'], _, _, []) => to_r u'
|
|
1497 |
| Construct (_ :: sel_us, T, R, arg_us) =>
|
|
1498 |
let
|
|
1499 |
val set_rs =
|
|
1500 |
map2 (fn sel_u => fn arg_u =>
|
|
1501 |
let
|
|
1502 |
val (R1, R2) = dest_Func (rep_of sel_u)
|
|
1503 |
val sel_r = to_r sel_u
|
|
1504 |
val arg_r = to_opt R2 arg_u
|
|
1505 |
in
|
|
1506 |
if is_one_rep R2 then
|
|
1507 |
kk_n_fold_join kk true R2 R1 arg_r
|
|
1508 |
(kk_project sel_r (flip_nums (arity_of_rep R2)))
|
|
1509 |
else
|
|
1510 |
kk_comprehension
|
|
1511 |
(decls_for_atom_schema ~1 (atom_schema_of_rep R1))
|
|
1512 |
(kk_rel_eq (kk_join (Kodkod.Var (1, ~1)) sel_r)
|
|
1513 |
arg_r)
|
|
1514 |
end) sel_us arg_us
|
|
1515 |
in fold1 kk_intersect set_rs end
|
|
1516 |
| BoundRel (x, _, _, _) => Kodkod.Var x
|
|
1517 |
| FreeRel (x, _, _, _) => Kodkod.Rel x
|
|
1518 |
| RelReg (j, _, R) => Kodkod.RelReg (arity_of_rep R, j)
|
|
1519 |
| u => raise NUT ("NitpickKodkod.to_r", [u])
|
|
1520 |
(* nut -> Kodkod.decl *)
|
|
1521 |
and to_decl (BoundRel (x, _, R, _)) =
|
|
1522 |
Kodkod.DeclOne (x, Kodkod.AtomSeq (the_single (atom_schema_of_rep R)))
|
|
1523 |
| to_decl u = raise NUT ("NitpickKodkod.to_decl", [u])
|
|
1524 |
(* nut -> Kodkod.expr_assign *)
|
|
1525 |
and to_expr_assign (FormulaReg (j, _, R)) u =
|
|
1526 |
Kodkod.AssignFormulaReg (j, to_f u)
|
|
1527 |
| to_expr_assign (RelReg (j, _, R)) u =
|
|
1528 |
Kodkod.AssignRelReg ((arity_of_rep R, j), to_r u)
|
|
1529 |
| to_expr_assign u1 _ = raise NUT ("NitpickKodkod.to_expr_assign", [u1])
|
|
1530 |
(* int * int -> nut -> Kodkod.rel_expr *)
|
|
1531 |
and to_atom (x as (k, j0)) u =
|
|
1532 |
case rep_of u of
|
|
1533 |
Formula _ => atom_from_formula kk j0 (to_f u)
|
|
1534 |
| Unit => if k = 1 then Kodkod.Atom j0
|
|
1535 |
else raise NUT ("NitpickKodkod.to_atom", [u])
|
|
1536 |
| R => atom_from_rel_expr kk x R (to_r u)
|
|
1537 |
(* rep list -> nut -> Kodkod.rel_expr *)
|
|
1538 |
and to_struct Rs u =
|
|
1539 |
case rep_of u of
|
|
1540 |
Unit => full_rel_for_rep (Struct Rs)
|
|
1541 |
| R' => struct_from_rel_expr kk Rs R' (to_r u)
|
|
1542 |
(* int -> rep -> nut -> Kodkod.rel_expr *)
|
|
1543 |
and to_vect k R u =
|
|
1544 |
case rep_of u of
|
|
1545 |
Unit => full_rel_for_rep (Vect (k, R))
|
|
1546 |
| R' => vect_from_rel_expr kk k R R' (to_r u)
|
|
1547 |
(* rep -> rep -> nut -> Kodkod.rel_expr *)
|
|
1548 |
and to_func R1 R2 u =
|
|
1549 |
case rep_of u of
|
|
1550 |
Unit => full_rel_for_rep (Func (R1, R2))
|
|
1551 |
| R' => rel_expr_to_func kk R1 R2 R' (to_r u)
|
|
1552 |
(* rep -> nut -> Kodkod.rel_expr *)
|
|
1553 |
and to_opt R u =
|
|
1554 |
let val old_R = rep_of u in
|
|
1555 |
if is_opt_rep old_R then
|
|
1556 |
rel_expr_from_rel_expr kk (Opt R) old_R (to_r u)
|
|
1557 |
else
|
|
1558 |
to_rep R u
|
|
1559 |
end
|
|
1560 |
(* rep -> nut -> Kodkod.rel_expr *)
|
|
1561 |
and to_rep (Atom x) u = to_atom x u
|
|
1562 |
| to_rep (Struct Rs) u = to_struct Rs u
|
|
1563 |
| to_rep (Vect (k, R)) u = to_vect k R u
|
|
1564 |
| to_rep (Func (R1, R2)) u = to_func R1 R2 u
|
|
1565 |
| to_rep (Opt R) u = to_opt R u
|
|
1566 |
| to_rep R _ = raise REP ("NitpickKodkod.to_rep", [R])
|
|
1567 |
(* nut -> Kodkod.rel_expr *)
|
|
1568 |
and to_integer u = to_opt (one_rep ofs (type_of u) (rep_of u)) u
|
|
1569 |
(* nut list -> rep -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
1570 |
and to_guard guard_us R r =
|
|
1571 |
let
|
|
1572 |
val unpacked_rs = unpack_joins r
|
|
1573 |
val plain_guard_rs =
|
|
1574 |
map to_r (filter (is_Opt o rep_of) guard_us)
|
|
1575 |
|> filter_out (member (op =) unpacked_rs)
|
|
1576 |
val func_guard_us =
|
|
1577 |
filter ((is_Func andf is_opt_rep) o rep_of) guard_us
|
|
1578 |
val func_guard_rs = map to_r func_guard_us
|
|
1579 |
val guard_fs =
|
|
1580 |
map kk_no plain_guard_rs @
|
|
1581 |
map2 (kk_not oo kk_n_ary_function kk)
|
|
1582 |
(map (unopt_rep o rep_of) func_guard_us) func_guard_rs
|
|
1583 |
in
|
|
1584 |
if null guard_fs then
|
|
1585 |
r
|
|
1586 |
else
|
|
1587 |
kk_rel_if (fold1 kk_or guard_fs) (empty_rel_for_rep R) r
|
|
1588 |
end
|
|
1589 |
(* rep -> rep -> Kodkod.rel_expr -> int -> Kodkod.rel_expr *)
|
|
1590 |
and to_project new_R old_R r j0 =
|
|
1591 |
rel_expr_from_rel_expr kk new_R old_R
|
|
1592 |
(kk_project_seq r j0 (arity_of_rep old_R))
|
|
1593 |
(* rep list -> nut list -> Kodkod.rel_expr *)
|
|
1594 |
and to_product Rs us =
|
|
1595 |
case map (uncurry to_opt) (filter (not_equal Unit o fst) (Rs ~~ us)) of
|
|
1596 |
[] => raise REP ("NitpickKodkod.to_product", Rs)
|
|
1597 |
| rs => fold1 kk_product rs
|
|
1598 |
(* int -> typ -> rep -> nut -> Kodkod.rel_expr *)
|
|
1599 |
and to_nth_pair_sel n res_T res_R u =
|
|
1600 |
case u of
|
|
1601 |
Tuple (_, _, us) => to_rep res_R (nth us n)
|
|
1602 |
| _ => let
|
|
1603 |
val R = rep_of u
|
|
1604 |
val (a_T, b_T) = HOLogic.dest_prodT (type_of u)
|
|
1605 |
val Rs =
|
|
1606 |
case unopt_rep R of
|
|
1607 |
Struct (Rs as [_, _]) => Rs
|
|
1608 |
| _ =>
|
|
1609 |
let
|
|
1610 |
val res_card = card_of_rep res_R
|
|
1611 |
val other_card = card_of_rep R div res_card
|
|
1612 |
val (a_card, b_card) = (res_card, other_card)
|
|
1613 |
|> n = 1 ? swap
|
|
1614 |
in
|
|
1615 |
[Atom (a_card, offset_of_type ofs a_T),
|
|
1616 |
Atom (b_card, offset_of_type ofs b_T)]
|
|
1617 |
end
|
|
1618 |
val nth_R = nth Rs n
|
|
1619 |
val j0 = if n = 0 then 0 else arity_of_rep (hd Rs)
|
|
1620 |
in
|
|
1621 |
case arity_of_rep nth_R of
|
|
1622 |
0 => to_guard [u] res_R
|
|
1623 |
(to_rep res_R (Cst (Unity, res_T, Unit)))
|
|
1624 |
| arity => to_project res_R nth_R (to_rep (Opt (Struct Rs)) u) j0
|
|
1625 |
end
|
|
1626 |
(* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula)
|
|
1627 |
-> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula) -> nut -> nut
|
|
1628 |
-> Kodkod.formula *)
|
|
1629 |
and to_set_bool_op connective set_oper u1 u2 =
|
|
1630 |
let
|
|
1631 |
val min_R = min_rep (rep_of u1) (rep_of u2)
|
|
1632 |
val r1 = to_rep min_R u1
|
|
1633 |
val r2 = to_rep min_R u2
|
|
1634 |
in
|
|
1635 |
case min_R of
|
|
1636 |
Vect (k, Atom _) => kk_vect_set_bool_op connective k r1 r2
|
|
1637 |
| Func (R1, Formula Neut) => set_oper r1 r2
|
|
1638 |
| Func (Unit, Atom (2, j0)) =>
|
|
1639 |
connective (formula_from_atom j0 r1) (formula_from_atom j0 r2)
|
|
1640 |
| Func (R1, Atom _) => set_oper (kk_join r1 true_atom)
|
|
1641 |
(kk_join r2 true_atom)
|
|
1642 |
| _ => raise REP ("NitpickKodkod.to_set_bool_op", [min_R])
|
|
1643 |
end
|
|
1644 |
(* (Kodkod.formula -> Kodkod.formula -> Kodkod.formula)
|
|
1645 |
-> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.rel_expr)
|
|
1646 |
-> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula)
|
|
1647 |
-> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula)
|
|
1648 |
-> (Kodkod.rel_expr -> Kodkod.rel_expr -> Kodkod.formula) -> bool -> rep
|
|
1649 |
-> nut -> nut -> Kodkod.rel_expr *)
|
|
1650 |
and to_set_op connective connective3 set_oper true_set_oper false_set_oper
|
|
1651 |
neg_second R u1 u2 =
|
|
1652 |
let
|
|
1653 |
val min_R = min_rep (rep_of u1) (rep_of u2)
|
|
1654 |
val r1 = to_rep min_R u1
|
|
1655 |
val r2 = to_rep min_R u2
|
|
1656 |
val unopt_R = unopt_rep R
|
|
1657 |
in
|
|
1658 |
rel_expr_from_rel_expr kk unopt_R (unopt_rep min_R)
|
|
1659 |
(case min_R of
|
|
1660 |
Opt (Vect (k, Atom _)) => kk_vect_set_op connective k r1 r2
|
|
1661 |
| Vect (k, Atom _) => kk_vect_set_op connective k r1 r2
|
|
1662 |
| Func (_, Formula Neut) => set_oper r1 r2
|
|
1663 |
| Func (Unit, _) => connective3 r1 r2
|
|
1664 |
| Func (R1, _) =>
|
|
1665 |
double_rel_let kk
|
|
1666 |
(fn r1 => fn r2 =>
|
|
1667 |
kk_union
|
|
1668 |
(kk_product
|
|
1669 |
(true_set_oper (kk_join r1 true_atom)
|
|
1670 |
(kk_join r2 (atom_for_bool bool_j0
|
|
1671 |
(not neg_second))))
|
|
1672 |
true_atom)
|
|
1673 |
(kk_product
|
|
1674 |
(false_set_oper (kk_join r1 false_atom)
|
|
1675 |
(kk_join r2 (atom_for_bool bool_j0
|
|
1676 |
neg_second)))
|
|
1677 |
false_atom))
|
|
1678 |
r1 r2
|
|
1679 |
| _ => raise REP ("NitpickKodkod.to_set_op", [min_R]))
|
|
1680 |
end
|
|
1681 |
(* rep -> rep -> Kodkod.rel_expr -> nut -> Kodkod.rel_expr *)
|
|
1682 |
and to_apply res_R func_u arg_u =
|
|
1683 |
case unopt_rep (rep_of func_u) of
|
|
1684 |
Unit =>
|
|
1685 |
let val j0 = offset_of_type ofs (type_of func_u) in
|
|
1686 |
to_guard [arg_u] res_R
|
|
1687 |
(rel_expr_from_rel_expr kk res_R (Atom (1, j0))
|
|
1688 |
(Kodkod.Atom j0))
|
|
1689 |
end
|
|
1690 |
| Atom (1, j0) =>
|
|
1691 |
to_guard [arg_u] res_R
|
|
1692 |
(rel_expr_from_rel_expr kk res_R (Atom (1, j0)) (to_r func_u))
|
|
1693 |
| Atom (k, j0) =>
|
|
1694 |
let
|
|
1695 |
val dom_card = card_of_rep (rep_of arg_u)
|
|
1696 |
val ran_R = Atom (exact_root dom_card k,
|
|
1697 |
offset_of_type ofs (range_type (type_of func_u)))
|
|
1698 |
in
|
|
1699 |
to_apply_vect dom_card ran_R res_R (to_vect dom_card ran_R func_u)
|
|
1700 |
arg_u
|
|
1701 |
end
|
|
1702 |
| Vect (1, R') =>
|
|
1703 |
to_guard [arg_u] res_R
|
|
1704 |
(rel_expr_from_rel_expr kk res_R R' (to_r func_u))
|
|
1705 |
| Vect (k, R') => to_apply_vect k R' res_R (to_r func_u) arg_u
|
|
1706 |
| Func (R, Formula Neut) =>
|
|
1707 |
to_guard [arg_u] res_R (rel_expr_from_formula kk res_R
|
|
1708 |
(kk_subset (to_opt R arg_u) (to_r func_u)))
|
|
1709 |
| Func (Unit, R2) =>
|
|
1710 |
to_guard [arg_u] res_R
|
|
1711 |
(rel_expr_from_rel_expr kk res_R R2 (to_r func_u))
|
|
1712 |
| Func (R1, R2) =>
|
|
1713 |
rel_expr_from_rel_expr kk res_R R2
|
|
1714 |
(kk_n_fold_join kk true R1 R2 (to_opt R1 arg_u) (to_r func_u))
|
|
1715 |
|> body_rep R2 = Formula Neut ? to_guard [arg_u] res_R
|
|
1716 |
| _ => raise NUT ("NitpickKodkod.to_apply", [func_u])
|
|
1717 |
(* int -> rep -> rep -> Kodkod.rel_expr -> nut *)
|
|
1718 |
and to_apply_vect k R' res_R func_r arg_u =
|
|
1719 |
let
|
|
1720 |
val arg_R = one_rep ofs (type_of arg_u) (unopt_rep (rep_of arg_u))
|
|
1721 |
val vect_r = vect_from_rel_expr kk k res_R (Vect (k, R')) func_r
|
|
1722 |
val vect_rs = unpack_vect_in_chunks kk (arity_of_rep res_R) k vect_r
|
|
1723 |
in
|
|
1724 |
kk_case_switch kk arg_R res_R (to_opt arg_R arg_u)
|
|
1725 |
(all_singletons_for_rep arg_R) vect_rs
|
|
1726 |
end
|
|
1727 |
(* bool -> nut -> Kodkod.formula *)
|
|
1728 |
and to_could_be_unrep neg u =
|
|
1729 |
if neg andalso is_opt_rep (rep_of u) then kk_no (to_r u)
|
|
1730 |
else Kodkod.False
|
|
1731 |
(* nut -> Kodkod.rel_expr -> Kodkod.rel_expr *)
|
|
1732 |
and to_compare_with_unrep u r =
|
|
1733 |
if is_opt_rep (rep_of u) then kk_rel_if (kk_some (to_r u)) r Kodkod.None
|
|
1734 |
else r
|
|
1735 |
in to_f_with_polarity Pos u end
|
|
1736 |
|
|
1737 |
end;
|