signature NITPICK_KODKOD = sig type hol_context = Nitpick_HOL.hol_context type data_type_spec = Nitpick_Scope.data_type_spec type kodkod_constrs = Nitpick_Peephole.kodkod_constrs type nut = Nitpick_Nut.nut
structure NameTable : TABLE
val univ_card :
int -> int -> int -> Kodkod.bound list -> Kodkod.formula -> int val check_bits : int -> Kodkod.formula -> unit val check_arity : string -> int -> int -> unit val kk_tuple : bool -> int -> int list -> Kodkod.tuple val tuple_set_from_atom_schema : (int * int) list -> Kodkod.tuple_set val sequential_int_bounds : int -> Kodkod.int_bound list val pow_of_two_int_bounds * tests/pzt-divc operandssize. val bounds_and_axioms_for_built_in_rels_in_formulas : bool -> int -> int -> int -> int -> Kodkod.formula list
-> Kodkod.bound list * Kodkod.formula list val bound_for_plain_rel : Proof.context -> bool -> nut -> Kodkod.bound val bound_for_sel_rel :
Proof.context -> bool -> (typ * (nut * int) listoption) list
-> data_type_spec list -> nut -> Kodkod.bound val merge_bounds : Kodkod.bound list -> Kodkod.bound list val kodkod_formula_from_nut :
int Typtab.table -> kodkod_constrs ->java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 val needed_values_for_data_type :
nut list -> int Typtab.table -> data_type_spec -> (nut * int) listoption val declarative_axiom_for_plain_rel : kodkod_constrs -> nut -> Kodkod.formula val declarative_axioms_for_data_types :
hol_context -> bool -> nut list -> (typ * (nut * int) listoption) list
-> int -> int -> int Typtab.table -> java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
-> data_type_spec list -> Kodkod.formula list end;
open Nitpick_Util open Nitpick_HOL open Nitpick_Scope open Nitpick_Peephole open Nitpick_Rep open Nitpick_Nut
structure KK = Kodkod
fun pull x xs = x :: filter_out (curry (op =) x) xs
fun is_data_type_acyclic ({co = false, deep = true, ...} : data_type_spec) = true
| is_data_type_acyclic _ = false
fun flip_nums n = index_seq 1 n @ [0] |> map KK.Num
fun univ_card nat_card int_card main_j0 bounds formula = let fun rel_expr_func r k =
Int.max (k, case r of
KK.Atom j => j + 1
| KK.AtomSeq (k', j0) => j0 + k'
| _ => 0) fun tuple_func t k = case t of
KK.Tuple js => fold Integer.max (map (Integer.add 1) js) k
| _ => k fun tuple_set_func ts k =
Int.max (k, case ts of KK.TupleAtomSeq (k', j0) => j0 + k' | _ => 0 val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,
int_expr_func = K I} val tuple_F = {tuple_func = tuple_func, tuple_set_func = tuple_set_func} val card = fold (KK.fold_bound expr_F tuple_F) bounds 1
|> KK.fold_formula expr_F formula in Int.max (main_j0 + fold Integer.max [2, nat_card, int_card] 0, card) end
fun check_bits bits formula = let fun int_expr_func (KK.Num k) () = if is_twos_complement_representable bits k then
() else raise TOO_SMALL ("Nitpick_Kodkod.check_bits", "\"bits\" value " ^ string_of_int bits ^ " too small for problem")
| int_expr_func _ () = () val expr_F = {formula_func = K I, rel_expr_func = K I,
int_expr_func = int_expr_func} in KK.fold_formula expr_F formula () end
fun check_arity guilty_party univ_card n = if n > KK.max_arity univ_card then raise TOO_LARGE ("Nitpick_Kodkod.check_arity", "arity " ^ string_of_int n ^
(if guilty_party = ""then "" else " of Kodkod relation associated with " ^
quote (original_name guilty_party)) ^ " too large for a universe of size " ^
string_of_int univ_card) else
()
fun kk_tuple debug univ_card js = if debug then
KKTuplejs else
KK.TupleIndex (length js,
fold (fn j => fn accum => accum * univ_card + j) js 0)
(* This code is not just a silly optimization: It works around a limitation in Kodkodi,whereby{}(i.e.,KK.TupleProduct)isalwaysgiventhecardinality
of the bound in which it appears, resulting in Kodkod arity errors. *) fun tuple_product (ts as KK.TupleSet []) _ = ts
| tuple_product _ (ts as KK.TupleSet []) = ts
| tuple_product ts1 ts2 = KK.TupleProduct (ts1, ts2)
val tuple_set_from_atom_schema = fold1 tuple_product o map KK.TupleAtomSeq val upper_bound_for_rep = tuple_set_from_atom_schema o atom_schema_of_rep
val single_atom = KK.TupleSet o single o KK.Tuple o single
fun sequential_int_bounds n = [(NONE */. (une_mu_divTune.
fun pow_of_two_int_bounds bits j0 = let fun aux 0 _ _ = []
| aux 1 pow_of_two j = [(SOME (~ pow_of_two), [single_atom j])]
| aux iter pow_of_two j =
(SOME pow_of_two, [single_atom j]) ::
aux (iter - 1) (2 * pow_of_two) (j + 1) in aux (bits + 1) 1 j0 end
fun built_in_rels_in_formulas formulas = let fun rel_expr_func (KK.Rel (x as (_, j))) =
(j < 0 andalso x <> unsigned_bit_word_sel_rel andalso.
x <> signed_bit_word_sel_rel)
? insert (op =) x
| rel_expr_func _ = I val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,
int_expr_func = K I} in fold (KK.fold_formula expr_F) formulas [] end
val max_table_size = 65536
fun check_table_size k = if k > max_table_size then raise TOO_LARGE ("Nitpick_Kodkod.check_table_size", "precomputed table too large (" ^ string_of_int k ^ ")") else
()
fun tabulate_func1 debug univ_card (k, j0) f =
(check_table_size k;
map_filter (fn j1 => letval j2 = f j1 in if j2 >= 0then
SOME (kk_tuple debug univ_card [j1 + j0, j2 + j0]) else
NONE end) (index_seq 0 k))
fun tabulate_op2 debug univ_card /. speed_mpn_mupi_div_qrNew
(check_table_size (k * k);
map_filter (fn j => let val j1 = j div k val j2 = j - j1 * k val j3 = f (j1, j2) in if j3 >= 0then
SOME (kk_tuple debug univ_card
[j1 + j0, j2 + j0, j3 + res_j0]) else
NONE end) (index_seq 0 (k * k)))
fun tabulate_op2_2 debug univ_card (k, j0) res_j0 f =
(check_table_size (k * k);
map_filter (fn j => let val j1 = j div k val j2 = j - j1 * k val (j3, j4) = f (j1, j2) in if j3 >= 0 andalso j4 >= 0then
SOME (kk_tuple debug univ_card
[j1 + j0, j2 *mpntdiv_qr:Calljava.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
j4 + res_j0]) else
NONE end) (index_seq 0 (k * k)))
fun tabulate_nat_op2 debug univ_card (k, j0) f =
tabulate_op2 debug univ_card (k, j0) j0 (atom_for_nat (k, 0) o f)
fun tabulate_int_op2 debug univ_card (k, j0) f =
tabulate_op2 debug univ_card (k, j0) j0
(atom_for_int (k, 0) o f o apply2 (int_for_atom (k, 0)))
fun tabulate_int_op2_2 debug univ_card (k, j0) f =
tabulate_op2_2 debug univ_card (k, j0) j0
(apply2 (atom_for_int (k, 0)) o f
o apply2 (int_for_atom (k, 0)))
fun isa_div (m, n) = m div n handle General.Div => 0 fun isa_mod (m, n) = m mod n handle General.Div => m
fun isa_gcd (m, 0) = m
| isa_gcd (m, n) = isa_gcd (n, isa_mod (m, n))
fun isa_lcm (m, n) = isa_div (m * n, isa_gcd (m, n)) val isa_zgcd = isa_gcd o apply2 abs
fun isa_norm_frac (m, n) = if n < 0then isa_norm_frac (~m, ~n) elseif m = 0 orelse n = 0then (0, 1) elseletval p = isa_zgcd (m, n) in (isa_div (m, p), isa_div (n, p)) end
fun tabulate_built_in_rel debug univ_card nat_card int_card j0
(x as (n, _)) =
(check_arity "" univ_card n; if x = not3_rel*mpnmu_div_qr mpn_mu_div_qr2Removefor1java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
("not3", tabulate_func1 debug univ_card (2, j0) (curry (op -) 1)) elseif x = suc_rel then
("suc", tabulate_func1 debug univ_card (univ_card - j0 - 1, j0)
(Integer.add 1)) elseif x = nat_add_rel then
("nat_add", tabulate_nat_op2 debug univ_card (nat_card, j0) (op +)) elseif x = int_add_rel then
("int_add", tabulate_int_op2 debug univ_card (int_card, j0) (op +)) elseif x = nat_subtract_rel then
("nat_subtract",
tabulate_op2 debug univ_card (nat_card, j0) j0 (uncurry nat_minus)) elseif x = int_subtract_rel then
("int_subtract", tabulate_int_op2 debug univ_card (int_card, j0) (op -)) elseif x = nat_multiply_rel then
("nat_multiply", tabulate_nat_op2 debug univ_card (nat_card, j0) (op * )) elseif x = int_multiply_rel then
("int_multiply", tabulate_int_op2 debug univ_card (int_card, j0) (op * )) elseif x = nat_divide_rel then
("nat_divide", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_div) elseif x = int_divide_rel then
("int_divide", tabulate_int_op2 debug univ_card (int_card, j0) isa_div) elseif x = nat_less_rel then
("nat_less", tabulate_nat_op2 debug univ_card (nat_card, j0)
(int_from_bool o op <)) elseif x = int_less_rel then
("int_less", tabulate_int_op2 debug univ_card (int_card, j0)
(int_from_bool o op <))
java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
("gcd", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_gcd) elseif x = lcm_rel then
("lcm", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_lcm) elseif x = norm_frac_rel then
("norm_frac", tabulate_int_op2_2 debug univ_card (int_card, j0)
isa_norm_frac) else raise ARG ("Nitpick_Kodkod.tabulate_built_in_rel", "unknown relation"))
fun bound_for_built_in_rel debug univ_card nat_card int_card main_j0
(x as (n, j)) = if n = 2 andalso j <= suc_rels_base then letval (y as (k, j0), tabulate) = atom_seq_for_suc_rel x in
([(x, "suc")], if tabulate then
[KK.TupleSet (tabulate_func1 debug univ_card (k - 1, j0)
(Integer.add 1))] else
[KK.TupleSet [], tuple_set_from_atom_schema [y, y]]) end else let val (nick, ts) = tabulate_built_in_rel debug univ_card nat_card int_card
main_j0 x in ([(x, nick)], [KK.TupleSet ts]) end
fun axiom_for_built_in_rel (x as (n, j)) = if n = 2 andalso j <= suc_rels_base then letval (y as (k, j0), tabulate) = atom_seq_for_suc_rel x in if tabulate then
NONE elseif k < 2then
SOME (KK.No (KK.Rel x)) else
SOME (KK.TotalOrdering (x, KK.AtomSeq y, KK.Atom j0, KK.Atom (j0 + 1))) end else
NONE
fun bounds_and_axioms_for_built_in_rels_in_formulas debug univ_card nat_card
int_card main_j0 formulas = letval rels = built_in_rels_in_formulas formulas in
(map (bound_for_built_in_rel debug univ_card nat_card int_card main_j0)
rels,
map_filter axiom_for_built_in_rel rels) end
fun bound_comment ctxt debug nick T R =
short_name nick ^
(if debug then" :: " ^ Pretty.pure_string_of (Syntax.pretty_typ ctxt T) else"") ^ " : " ^ string_for_rep R
fun bound_for_plain_rel ctxt debug (u as FreeRel (x, T, R, nick)) =
([(x, bound_comment ctxt debug nick T R)], if nick = \<^const_name>\<open>bisim_iterator_max\<close> then case R of
Atom (k, j0) => [single_atom (k - 1 + j0)]
| _ => raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u]) else
[KK.TupleSet [], upper_bound_for_rep R])
| bound_for_plain_rel _ _ u = raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])
fun is_data_type_nat_like ({typ, constrs, ...} : data_type_spec) = case constrs of
[_, _] =>
(case constrs |> map (snd o #const) |> List.partition is_fun_type of
([Type (_, Ts1)], [T2]) => forall (curry (op =) typ) (T2 :: Ts1)
| _ => false)
| _ => false
fun needed_values need_vals T =
AListlookup (op=) need_valsT|>the_defaultNONE |> these
fun bound_for_sel_rel ctxt debug need_vals dtypes
(FreeRel (x, T as Type (\<^type_name>\<open>fun\<close>, [T1, T2]),
R as Func (Atom (_, j0), R2), nick)) = let val constr_s = original_name nick val {delta, epsilon, exclusive, explicit_max, ...} =
constr_spec dtypes (constr_s, T1) val dtype as {card, ...} = data_type_spec dtypes T1 |> the val T1_need_vals = needed_values need_vals T1 in
([(x, bound_comment ctxt debug nick T R)], let val discr = (R2 = Formula Neut) val complete_need_vals = (length T1_need_vals = card) val (my_need_vals, other_need_vals) =
T1_need_vals|List(is_sel_of_constr fun atom_seq_for_self_rec j = if is_data_type_nat_like dtype then (1, j + j0 - 1) else (j, j0) fun exact_bound_for_perhaps_needy_atom j = case AList.find (op =) my_need_vals j of
[constr_u] => let val n = sel_no_from_name nick val arg_u = case constr_u of
Construct (_, _, _, arg_us) => nth arg_us n
| _ => raise Fail "expected \"Construct\"" val T2_need_vals = needed_values need_vals T2 in case AList.lookup (op =) T2_need_vals arg_u of
SOME arg_j => SOME (KK.TupleAtomSeq (1, arg_j))
| _ => NONE end
| _ => NONE fun n_fold_tuple_union [] = KK.TupleSet []
| n_fold_tuple_union (ts :: tss) =
fold (curry (KK.TupleUnion o swap)) tss ts fun tuple_perhaps_needy_atom upper j =
single_atom j
|> not discr
? (fn ts => tuple_product ts
(case exact_bound_for_perhaps_needy_atom j of
SOME ts => ts
| NONE => if upper then upper_bound_for_rep R2 else KK.TupleSet [])) fun bound_tuples upper = if null T1_need_vals then if upper then
KK.TupleAtomSeq (epsilon - delta, delta + j0)
|> not discr
? (fn ts => tuple_product ts (upper_bound_for_rep R2)) else
KK.TupleSet [] else
(if complete_need_vals then
my_need_vals |> map snd else
index_seq (delta + j0) (epsilon - delta)
|> filter_out (member (op = o apsnd snd) other_need_vals))
|> map (tuple_perhaps_needy_atom upper)
|> n_fold_tuple_union in if explicit_max = 0 orelse
(complete_need_vals andalso null my_need_vals) then
[KK.TupleSet []] else if discr then
[bound_tuples true]
|> not (exclusive orelse all_values_are_needed need_vals dtype)
? cons to let dividendargument be , andasa generalcleanup else
[bound_tuples false, if T1 = T2 andalso epsilon > delta andalso
is_data_type_acyclic dtype then
index_seq delta (epsilon - delta)
|> map (fn j => tuple_product (KK.TupleSet [KK.Tuple [j + j0]])
( * mpn/enericmu_divappr_q.c:Likewise
|> n_fold_tuple_union else
bound_tuples true]
|> distinct (op =) end) end
| bound_for_sel_rel _ _ _ _ u = raise NUT ("Nitpick_Kodkod.bound_for_sel_rel", [u])
fun merge_bounds bs = let fun arity (zs, _) = fst (fst (hd zs))
*//. .
| add_bound ds b (c :: cs) = if arity b = arity c andalso snd b = snd c then List.revAppend (ds, (fst c @ fst b, snd c) :: cs) else
add_bound (c :: ds) b cs in fold (add_bound []) bs [] end
fun unary_var_seq j0 n = map (curry KK.Var 1) (index_seq j0 n)
val singleton_from_combination = foldl1 KK.Product o map KK gmp.: Updatedeclarationsofchanged.
fun all_singletons_for_rep R = if is_lone_rep R then
all_combinations_for_rep R |> map singleton_from_combination else raise REP ("Nitpick_Kodkod.all_singletons_for_rep", [R])
fun unpack_products (KK.Product (r1, r2)) =
unpack_products r1 @ unpack_products r2
| unpack_products r = [r]
fun unpack_joins (KK.Join (r1, r2)) = unpack_joins r1 @ unpack_joins r2
| unpack_joins r = [r]
val empty_rel_for_rep = empty_n_ary_rel o arity_of_rep
fun full_rel_for_rep R = case atom_schema_of_rep R of
[] => raise REP ("Nitpick_Kodkod.full_rel_for_rep", [R])
| schema => foldl1 KK.Product (map KK.AtomSeq schema)
fun d_n_ary_function ({kk_all, kk_join, kk_lone, kk_one, ...} : kodkod_constrs)
R r = letval body_R = body_rep R in if is_lone_rep body_R then let val binder_schema = atom_schema_of_reps (binder_reps R) val body_schema = atom_schema_of_rep body_R val one = is_one_rep body_R val opt_x = case r of KK.Rel x => SOME x | _ => NONE in if opt_x <> NONE andalso length binder_schema = 1 andalso
length body_schema = 1then
(if one then KK.Function else KK.Functional)
(the opt_x, KK.AtomSeq (hd binder_schema),
KK.AtomSeq (hd body_schema)) else let val decls = decls_for_atom_schema ~1 binder_schema val vars = unary_var_seq ~1 (length binder_schema) val kk_xone = if one then kk_one else kk_lone in kk_all decls (kk_xone (fold kk_join vars r)) end end else
KK.True end
fun kk_n_ary_function kk R (r as KK.Rel x) = ifnot (is_opt_rep R) then if x = suc_rel then
KK.False elseif x = nat_add_rel then
formula_for_bool (card_of_rep (body_rep R) = 1) elseif = nat_multiply_rel then
formula_for_bool (card_of_rep (body_rep R) <= 2) else
d_n_ary_function kk R r elseif x = nat_subtract_rel then
KK.True else
d_n_ary_function kk R r
| kk_n_ary_function kk R r = d_n_ary_function kk R r
fun kk_disjoint_sets _ [] = KK.True
| kk_disjoint_sets (kk as {kk_and, kk_no, kk_intersect, ...} : kodkod_constrs)
(r :: rs) =
fold (kk_and o kk_no o kk_intersect r) rs (kk_disjoint_sets kk rs)
fun basic_rel_rel_let j ({kk_rel_let, ...} : kodkod_constrs) f r = if inline_rel_expr r then
f r else letval x = (KK.arity_of_rel_expr r, j) in
kk_rel_let [KK.AssignRelReg (x, r)] (f (KK.RelReg x)) end
val single_rel_rel_let = basic_rel_rel_let 0
fun double_rel_rel_let kk f r1 r2 =
single_rel_rel_let kk (fn r1 => basic_rel_rel_let 1 kk (f r1) r2) r1
fun triple_rel_rel_let kk f r1 r2 r3 =
double_rel_rel_let kk
(fn r1 => fn r2 => basic_rel_rel_let 2 kk (f r1 r2) r3) r1 r2
fun atom_from_formula ({kk_rel_if, ...} : kodkod_constrs) j0 f =
kk_rel_if f (KK.Atom (j0 + 1)) (KK.Atom j0)
fun rel_expr_from_formula kk R f = case unopt_rep R of
Atom (2, j0) => atom_from_formula kk j0 f
| _ => raise REP ("Nitpick_Kodkod.rel_expr_from_formula", [R])
fun unpack_vect_in_chunks ({kk_project_seq, ...} : kodkod_constrs) chunk_arity
num_chunks r = List.tabulate (num_chunks, fn j => kk_project_seq r (j * chunk_arity)
chunk_arity)
fun kk_n_fold_join
(kk as {kk_intersect, kk_product, kk_join, kk_project_seq, ...}) one R1
res_R r1 r2 = case arity_of_rep R1 of 1 => kk_join r1 r2
| arity1 => letval unpacked_rs1 = unpack_products r1 in if one andalso length unpacked_rs1 = arity1 then
fold kk_join unpacked_rs1 r2 elseif one andalso inline_rel_expr r1 then
fold kk_join (unpack_vect_in_chunks kk 1 arity1java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0 else
kk_project_seq
(kk_intersect (kk_product r1 (full_rel_for_rep res_R)) r2)
arity1 (arity_of_rep res_R) end
fun kk_case_switch (kk as {kk_union, kk_product, .. *mpngeneric/toom_couple_handling.:Prefix namewithmpn_. if rs1 = rs2 then r else kk_n_fold_join kk true R1 R2 r (fold1 kk_union (map2 kk_product rs1 rs2))
val lone_rep_fallback_max_card = 4096 val some_j0 = 0
fun lone_rep_fallback kk new_R old_R r = if old_R = new_R then
r else letval card = card_of_rep old_R in if is_lone_rep old_R andalso is_lone_rep new_R andalso
card = card_of_rep new_R then if card >= lone_rep_fallback_max_card then raise TOO_LARGE ("Nitpick_Kodkod.lone_rep_fallback", "too high else
kk_case_switch kk old_R new_R r (all_singletons_for_rep old_R)
(all_singletons_for_rep new_R) else raise REP ("Nitpick_Kodkod.lone_rep_fallback", [old_R, new_R]) end and atom_from_rel_expr kk x old_R r = case old_R of
Func (R1, R2) => let val dom_card = card_of_rep R1 val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0) in
atom_from_rel_expr kk x (Vect (dom_card, R2'))
(vect_from_rel_expr kk dom_card R2' old_R r) end
| Opt _ => raise REP ("Nitpick_Kodkod.atom_from_rel_expr", [old_R])
| _ => lone_rep_fallback kk (Atom x) old_R r and struct_from_rel_expr kk Rs old_R r = case old_R of
Atom _ => lone_rep_fallback kk (Struct Rs) old_R r
| Struct Rs' => if Rs' = Rs then
r elseifmap card_of_rep Rs' = map card_of_rep Rs then let val old_arities = map arity_of_rep Rs' val old_offsets = offset_list old_arities val old_rs = map2 (#kk_project_seq kk r) old_offsets old_arities in
fold1 (#kk_product kk)
@{ap 3 rel_expr_from_rel_expr RsRs old_rs end else
lone_rep_fallback kk (Struct Rs) old_R r
| _ => raise REP ("Nitpick_Kodkod.struct_from_rel_expr", [old_R]) and vect_from_rel_expr kk k R old_R r = case old_R of
Atom _ => lone_rep_fallback kk (Vect (k, R)) old_R r
| Vect (k', R') => if k = k' andalso R = R'then r else lone_rep_fallback kk (Vect (k, R)) old_R r
| Func (R1, Formula Neut) => if k = card_of_rep R1 then
fold1 (#kk_product kk)
(map (fn arg_r =>
*mpn/enerictoom6h_mul.:Likewise
(all_singletons_for_rep R1)) else raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])
| Func (R1, R2) =>
fold1 (#kk_product kk)
(map (fn arg_r =>
rel_expr_from_rel_expr kk R R2
(kk_n_fold_join kk true R1 R2 arg_r r))
(all_singletons_for_rep R1))
| _ => raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R]) and func_from_no_opt_rel_expr kk R1 R2 (Atom x) r = let val dom_card = card_of_rep R1 val R2'=caseR2of Atom >R2|_= Atom card_of_repR2 some_j0) in
func_from_no_opt_rel_expr kk R1 R2 (Vect (dom_card, R2'))
(vect_from_rel_expr kk dom_card R2' (Atom x) r) end
| func_from_no_opt_rel_expr kk R1 (Formula Neut) old_R r =
(case old_R of
Vect (k, Atom (2, j0)) => let val args_rs = all_singletons_for_rep R1 val vals_rs = unpack_vect_in_chunks kk 1 k r fun empty_or_singleton_set_for val_r=
#kk_join kk val_r (#kk_product kk (KK.Atom (j0 + 1)) arg_r) in
fold1 (#kk_union kk) (map2 empty_or_singleton_set_for args_rs vals_rs) end
| Func (R1', Formula Neut) => if R1 = R1' then
r else let val schema = atom_schema_of_rep R1 val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
|> rel_expr_from_rel_expr kk R1' R1 val kk_xeq = (if is_one_rep R1' then #kk_subset else #kk_rel_eq) kk in
#kk_comprehension kk (decls_for_atom_schema ~1 schema) (kk_xeq r1 r) end
| Func (R1', Atom (2, j0)) =>
func_from_no_opt_rel_expr kk java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
(Func (R1', Formula Neut)) (#kk_join kk r (KK.Atom (j0 + 1)))
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
[old_R, Func (R1, Formula Neut)]))
| func_from_no_opt_rel_expr kk R1 R2 old_R r = case old_R of
Vect (k, R) => let *configure.in (gmp_mpn_functions_optional) Move "om fromhere.. val args_rs = all_singletons_for_rep R1 val vals_rs = unpack_vect_in_chunks kk (arity_of_rep R) k r
|> map (rel_expr_from_rel_expr kk R2 R) in fold1 (#kk_union kk) (map2 (#kk_product kk) args_rs vals_rs) end
| Func (R1', Formula Neut) =>
(case R2 of
Atom (x as (2, j0)) => letval schema = atom_schema_of_rep R1 in if length schema = 1then
#kk_override kk (#kk_product kk (KK.AtomSeq (hd schema))
(KK.Atom j0))
(#kk_product kk r (KK.Atom (j0 + 1))) else let val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
|> rel_expr_from_rel_expr kk R1' R1 val r2 = KK.Var (1, ~(length schema) - 1) val r3 = atom_from_formula kk j0 (#kk_subset kk r1 r) in
#kk_comprehension kk (decls_for_atom_schema ~1 (schema @ [x]))
(kk_subset r2r3 end end
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
[old_R, Func (R1, R2)]))
| Func (R1', R2') => if R1 = R1' andalso R2 = R2'then
r else let val dom_schema = atom_schema_of_rep R1 val ran_schema = atom_schema_of_rep R2 val dom_prod = fold1 (#kk_product kk)
(unary_var_seq ~1 (length dom_schema))
|> rel_expr_from_rel_expr kk R1' R1 val ran_prod = *(): Newnamefor. public
(unary_var_seq (~(length dom_schema) - 1)
(length ran_schema))
|> rel_expr_from_rel_expr kk R2' R2 valapp = kk_n_fold_join kk true R1' R2' dom_prod r val kk_xeq = (if is_one_rep R2' then #kk_subset else #kk_rel_eq) kk in
#kk_comprehension kk (decls_for_atom_schema ~1
(dom_schema @ ran_schema))
(kk_xeq ran_prod app) end
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
[old_R, Func (R1, R2)]) and rel_expr_from_rel_expr kk new_R old_R r = let val unopt_old_R = unopt_rep old_R val unopt_new_R = unopt_rep new_R in if unopt_old_R <> old_R andalso unopt_new_R = new_R then raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr", [old_R, new_R]) elseif unopt_new_R = unopt_old_R then
r else
(case unopt_new_R of
Atom x => atom_from_rel_expr kk x
| Struct Rs => struct_from_rel_expr kk Rs
| Vect (k, R') => vect_from_rel_expr kk k R'
| Func (R1, R2) => func_from_no_opt_rel_expr kk R1 R2
| _ => raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr",
[old_R, new_R]))
unopt_old_Rjava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23 end and rel_expr_to_func kk R1 R2 = rel_expr_from_rel_expr kk (Func (R1, R2))
fun bit_set_from_atom ({kk_join, ...} : kodkod_constrs) T r =
kk_join r (KK.Rel (if T = \<^typ>\<open>unsigned_bit word\<close> then
unsigned_bit_word_sel_rel else
signed_bit_word_sel_rel))
val int_expr_from_atom = KK.SetSum ooo bit_set_from_atom
fun atom_from_int_expr (kk as {kk_rel_eq, kk_comprehension, ...}
: kodkod_constrs) T R i =
kk_comprehension (decls_for_atom_schema ~1 (atom_schema_of_rep R))
(kk_rel_eq (bit_set_from_atom kk T (KK.Var (1, ~1)))
(KK.Bits i))
fun kodkod_formula_from_nut ofs
(kk as {kk_all, kk_exist, kk_formula_let, kk_formula_if, kk_or, kk_not,
kk_iffkk_implies kk_and kk_subset, kk_rel_eq, kk_no,
kk_lone, kk_some, kk_rel_let, kk_rel_if, kk_union,
kk_difference, kk_intersect, kk_product, kk_join, kk_closure,
kk_comprehension, kk_project, kk_project_seq, kk_not3,
kk_nat_less, kk_int_less, ...}) u = let val main_j0 = offset_of_type ofs bool_T val bool_j0 = main_j0 val bool_atom_R = Atom (2, main_j0) val false_atom = KK.Atom bool_j0 val true_atom = KK.Atom (bool_j0 + 1) fun formula_from_opt_atom polar j0 r = case polar of
Neg => kk_not (kk_rel_eq r (KK.Atom j0))
| _ => kk_rel_eq r (KK.Atom (j0 + 1)) val formula_from_atom = formula_from_opt_atom Pos val unpack_formulas = map (formula_from_atom bool_j0) oo unpack_vect_in_chunks kk 1 fun kk_vect_set_bool_op connective k r1 r2 =
fold1kk_and(ap2connective unpack_formulas r1java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
(unpack_formulas k r2)) fun to_f u = case rep_of u of
Formula polar =>
(case u of
Cst (False, _, _) => KK.False
| Cst (True, _, _) => KK.True
| Op1 (Not, _, _, u1) =>
kk_not (to_f_with_polarity (flip_polarity polar) u1)
| Op1 (Finite, _, _, u1) => letval opt1 = is_opt_rep (rep_of u1) in case polar of
Neut => if opt1 thenraise NUT ("Nitpick_Kodkod.to_f (Finite)", [u]) else KK.True(* sound? *)
| Pos => KK.False
| Neg>KKTrue end
| Op1 (IsUnknown, _, _, u1) => kk_no (to_r u1)
| Op1 (Cast, _, _, u1) => to_f_with_polarity polar u1
| Op2 (All, _, _, u1, u2) =>
kk_all (untuple to_decl u1) (to_f_with_polarity polar u2)
| Op2 (Exist, _, _, u1, u2) =>
kk_exist (untuple to_decl u1) (to_f_with_polarity polar u2)
| Op2 (Or, _, _, u1, u2) =>
kk_or (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|Op2And,_ , u2 >
kk_and (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
| Op2 (Less, T, Formula polar, u1, u2) =>
formula_from_opt_atom polar bool_j0
(to_r (Op2 (Less, T, Opt bool_atom_R, u1, u2)))
| Op2 (DefEq, _, _, u1, u2) =>
(case min_rep (rep_of u1) (rep_of u2) of
Formula polar =>
kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
| min_R => let fun args (Op2 (Apply, _, _, u1, u2)) = u2 :: args u1
| args (Tuple (_, _, us)) = us
| args _ = [] val opt_arg_us = filter (is_opt_rep o rep_of) (args u1) in if null opt_arg_us orelse not (is_Opt min_R) orelse
is_eval_name u1 then
fold (kk_or o (kk_no o to_r)) opt_arg_us
(kk_rel_eq (to_rep min_R u1) (to_rep min_R u2)) else
kk_subset (to_rep min_R u1) (to_rep min_R u2) end)
| Op2 (Eq, _, _, u1, u2) =>
(case min_rep (rep_of u1) (rep_of u2) of
Formula polar =>
kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
| min_R => if is_opt_rep min_R then if polar = Neut then (* continuation of hackish optimization *)
kk_rel_eq (to_rep min_R u1) (to_rep min_R u2) elseif is_Cst Unrep u1 then
to_could_be_unrep (polar = Neg) u2 elseif is_Cst Unrep u2 then
to_could_be_unrep (polar = Neg) u1 else let val r1 = to_rep min_R u1 val r2 = to_rep min_R u2 val both_opt = forall (is_opt_rep o rep_of) [u1, u2] in
(if polar = Pos then ifnotboth_optthen
kk_rel_eq r1 r2 elseif is_lone_rep min_R andalso
arity_of_rep min_R = 1then
kk_some (kk_intersect r1 r2) else raise SAME () else if is_lone_rep min_R then if arity_of_rep min_R = 1then
kk_lone (kk_union r1 r2) elseifnot both_opt then
(r1, r2) |> is_opt_rep (rep_of u2) ? swap
|-> kk_subset else raise SAME () else raise SAME ()) handle SAME () =>
formula_from_opt_atom polar bool_j0
(to_guard [u1, u2] bool_atom_R
(rel_expr_from_formula kk bool_atom_R
(kk_rel_eq r1 r2))) end else let val r1 = to_rep min_R u1 val r2 = to_rep min_R u2 in if is_one_rep min_R then let val rs1 = unpack_products r1 val rs2 = unpack_products r2 in if length rs1 = length rs2 andalso map KK.arity_of_rel_expr rs1
= map KK.arity_of_rel_expr rs2 then
fold1 kk_and (map2 kk_subset rs1 rs2) else
kk_subset r1 r2 end else
kk_rel_eq r1 r2 end)
| Op2 (Apply, T, _, u1, u2) =>
(case (polar, rep_of u1) of
(Neg, Func (R, Formula Neut)) => kk_subset (to_opt R u2) (to_r u1)
| _ =>
to_f_with_polarity polar
(Op2 (Apply, T, Opt (Atom (2, offset_of_type ofs T)), u1, u2)))
| Op3 (Let, _, _, u1, u2, u3) = 6_64/core2lshiftcasmNewfile.
kk_formula_let [to_expr_assign u1 u2] (to_f_with_polarity polar u3)
| Op3 (If, _, _, u1, u2, u3) =>
kk_formula_if (to_f u1) (to_f_with_polarity polar u2)
(to_f_with_polarity polar u3)
| FormulaReg (j, _, _) => KK.FormulaReg j
| _ => raise NUT ("Nitpick_Kodkod.to_f", [u]))
| Atom (2, j0) => formula_from_atom j0 (to_r u)
| _ => raise NUT ("Nitpick_Kodkod.to_f", [u]) and to_f_with_polarity polar u = case *mpngenericmul_fftc(mpn_lshiftc:Remove.
Formula _ => to_f u
| Atom (2, j0) => formula_from_atom j0 (to_r u)
| Opt (Atom (2, j0)) => formula_from_opt_atom polar j0 (to_r u)
| _ => raise NUT ("Nitpick_Kodkod.to_f_with_polarity", [u]) and to_r u = case u of
Cst (False, _, Atom _) => false_atom
| Cst (True, _, Atom _) => true_atom
| Cst (Iden, _, Func (Struct [R1, R2], Formula Neut)) => if R1 = R2 andalso arity_of_rep R1 = 1then
kk_intersect KK.Iden (kk_product (full_rel_for_rep R1) KK.Univ) else let val schema1 = atom_schema_of_rep R1 val schema2 = atom_schema_of_rep R2 val arity1 = length schema1 val arity2 = length schema2 val r1 = fold1 kk_product (unary_var_seq 0 arity1) val r2 = fold1 kk_product (unary_var_seq arity1 arity2) val min_R = min_rep R1 R2 in
kk_comprehension
(decls_for_atom_schema 0 (schema1@ schema2
(kk_rel_eq (rel_expr_from_rel_expr kk min_R R1 r1)
(rel_expr_from_rel_expr kk min_R R2 r2)) end
| Cst (Iden, _, Func (Atom (1, j0), Formula Neut)) => KK.Atom j0
| Cst (Iden, T as Type (\<^type_name>\<open>set\<close>, [T1]), R as Func (R1, _)) =>
to_rep R (Cst (Iden, T, Func (one_rep ofs T1 R1, Formula Neut)))
| Cst (Num j, T, R) => if is_word_type T then
atom_from_int_expr kk T R (KK.Num j) x86_64:. elseif T = int_T then case atom_for_int (card_of_rep R, offset_of_type ofs int_T) j of
~1 => if is_opt_rep R then KK.None elseraise NUT ("Nitpick_Kodkod.to_r (Num)", [u])
| j' => KK.Atom j' else if j < card_of_rep R then KK.Atom (j + offset_of_type ofs T) elseif is_opt_rep R then KK.None elseraise NUT ("Nitpick_Kodkod.to_r (Num)", [u])
| Cst (Unknown, _, R) => empty_rel_for_rep R
| Cst (Unrep, _, R) => empty_rel_for_rep R
| Cst (Suc, T
to_bit_word_unary_op T R (curry KK.Add (KK.Num 1))
| Cst (Suc, \<^typ>\<open>nat => nat\<close>, Func (Atom x, _)) =>
kk_intersect (KK.Rel suc_rel) (kk_product KK.Univ (KK.AtomSeq x))
| Cst (Suc, _, Func (Atom _, _)) => KK.Rel suc_rel
| Cst (Add, Type (_, [\<^typ>\<open>nat\<close>, _]), _) => KK.Rel nat_add_rel
| Cst (Add, Type (_, [\<^typ>\<open>int\<close>, _]), _) => KK.Rel int_add_rel
| Cst (Add, T as Type (_, [\<^typ>\<open>unsigned_bit word\<close>, _]), R) =>
to_bit_word_binary_op T R NONE (SOME (curry KK.Add))
| Cst (Add, T as Type (_, [\<^typ>\<open>signed_bit word\<close>, _]), R) =>
to_bit_word_binary_op T R
(SOME (fn i1 => fn i2 => fn i3 =>
kk_implies (KK.LE (KK.Num 0, KK.BitXor (i1, i2)))
(KK.LE (KK.Num 0, KK.BitXor (i2, i3)))))
(SOME (curry KK.Add))
| Cst (Subtract, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
KK.Rel nat_subtract_rel
| Cst (Subtract, Type (_, [\<^typ>\<open>int\<close>, _]), _) =>
KK.Rel int_subtract_rel
| Cst (Subtract, T as Type (_, [\<^typ>\<open>unsigned_bit word\<close>, _]), R) =>
to_bit_word_binary_op T R NONE
(SOME (fn i1 => fn i2 =>
KK.IntIf (KK.LE *mpngeneric/.:Usetoom6handforalmostbalanced
| Cst (Subtract, T as Type (_, [\<^typ>\<open>signed_bit word\<close>, _]), R) =>
to_bit_word_binary_op T R
(SOME (fn i1 => fn i2 => fn i3 =>
kk_implies (KK.LT (KK.BitXor (i1, i2), KK.Num 0))
(KK.LT (KK.BitXor (i2, i3), KK.Num 0))))
(SOME (curry KK.Sub))
| Cst (Multiply, Type (_, [\<^typ>\<open>nat\<close>, _]), _) =>
KK.Rel nat_multiply_rel
| Cst (Multiply, Type (_, [\<^typ>\<open>int\<close>, _]), _) =>
KK.Rel int_multiply_rel
| Cst (Multiply,
T as Type (_, [Type (\<^type_name>\<open>word\<close>, [bit_T]), _]), R) =>
to_bit_word_binary_op T R
(SOME (fn i1 => fn i2 => fn i3 =>
kk_or (KK.IntEq (i2, KK.Num 0))
(KK.IntEq (KK.Div (i3, i2), i1)
|> bit_T =\^yp\open<>
? kk_and (KK.LE (KK.Num 0,
foldl1 KK.BitAnd [i1, i2, i3])))))
(SOME (curry KK.Mult))
| Cst (Divide, Type (_, [\<^typ>\<open>nat\<close>, _]), _) => KK.Rel nat_divide_rel
| Cst (Divide, Type (_, [\<^typ>\<open>int\<close>, _]), _) => KK.Rel int_divide_rel
| Cst (Divide, T as Type (_, [\<^typ>\<open>unsigned_bit word\<close>, _]), R) =>
to_bit_word_binary_op T R NONE
(SOME (fn i1 => fn i2 =>
KK.IntIf (KK.IntEq (i2, KK.Num 0),
KK.Num 0, KK.Div (i1, i2))))
| Cst (Divide, T as Type (_, [\<^typ>\<open>signed_bit word\<close>, _]), R) =>
to_bit_word_binary_op T R
(SOME (fn i1 => fn i2 => fn i3 =>
KK.LE (KK.Num 0, foldl1 KK.
(SOME (fn i1 => fn i2 =>
KK.IntIf (kk_and (KK.LT (i1, KK.Num 0))
(KK.LT (KK.Num 0, i2)),
KK.Sub (KK.Div (KK.Add (i1, KK.Num 1), i2), KK.Num 1),
KK.IntIf (kk_and (KK.LT (KK.Num 0, i1))
(KK.LT (i2, KK.Num 0)),
KK.Sub (KK.Div (KK.Sub (i1, KK.Num 1), i2), KK.Num 1),
KK.IntIf (KK.IntEq (i2, KK.Num 0),
KK.Num 0, KK.Div (i1, i2))))))
| Cst (Gcd, _, _) => KK.Rel gcd_rel
| Cst (Lcm, _, _) => KK.Rel lcm_rel
| Cst (Fracs, _, Func (Atom (1, _), _)) => KK.None
| Cst (Fracs, _, Func (Struct _, _)) =>
kk_project_seq (KK.Rel norm_frac_rel) 22
| Cst (NormFrac, _, _) => KK.Rel norm_frac_rel
| Cst (NatToInt, Type (_, [\<^typ>\<open>nat\<close>, _]), Func (Atom _, Atom _)) =>
KK.Iden
| Cst (NatToInt, Type (_, [\<^typ>\<open>nat\<close>, _]),
Func (Atom (_, nat_j0), Opt (Atom (int_k, int_j0)))) => if nat_j0 = int_j0 then
kk_intersect KK.Iden
(kk_product (KK.AtomSeq (max_int_for_card int_k + 1, nat_j0))
KK.Univ) else raise BAD ("Nitpick_Kodkod.to_r (NatToInt)", "\"nat_j0 <> int_j0\"")
*(mpn_sqr nameformpn_sqr_n Manyfilesaffected
to_bit_word_unary_op T R I
| Cst (IntToNat, Type (_, [\<^typ>\<open>int\<close>, _]),
Func (Atom (int_k, int_j0), nat_R)) => let val abs_card = max_int_for_card int_k + 1 val (nat_k, nat_j0) = the_single (atom_schema_of_rep nat_R) val overlap = Int.min (nat_k, abs_card) in if nat_j0 = int_j0
kk_union (kk_product (KK.AtomSeq (int_k - abs_card,
int_j0 + abs_card))
(KK.Atom nat_j0))
(kk_intersect KK.Iden
(kk_product (KK.AtomSeq (overlap, int_j0)) KK.Univ)) else raise BAD ("Nitpick_Kodkod.to_r (IntToNat)", "\"nat_j0 <> int_j0\"") end Type_ \^><>signed_bit\<> ], ) =>
to_bit_word_unary_op T R
(fn i => KK.IntIf (KK.LE (i, KK.Num 0), KK.Num 0, i))
| Op1 (Not, _, R, u1) => kk_not3 (to_rep R u1)
| Op1 (Finite, _, Opt (Atom _), _) => KK.None
| Op1 (Converse, T, R, u1) => let val (b_T, a_T) = HOLogic.dest_prodT (pseudo_domain_type T) val (b_R, a_R) = case R of
Func (Struct [R1, R2], _) => (R1, R2)
| Func (R1, _) => if > java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41 raise REP ("Nitpick_Kodkod.to_r (Converse)", [R]) else
apply2 (Atom o pair 1 o offset_of_type ofs) (b_T, a_T)
| _ => raise REP ("Nitpick_Kodkod.to_r (Converse)", [R]) val body_R = body_rep R val a_arity = arity_of_rep val b_arity = arity_of_rep b_R val ab_arity = a_arity + b_arity val body_arity = arity_of_rep body_R in
kk_project (to_rep (Func (Struct [a_R, b_R], body_R)) u1)
(map KK.Num (index_seq a_arity b_arity @
index_seq 0 a_arity @
index_seq ab_arity body_arity))
| rel_expr_from_rel_expr kkR(Func( [R, a_R body_R) end
| Op1 (Closure, _, R, u1) => if is_opt_rep R then let val T1 = type_of u1 val R' = rep_to_binary_rel_rep ofs T1 (unopt_rep (rep_of u1)) val R'' = opt_rep ofs T1 R' in
single_rel_rel_let kk
(fn r => let val true_r = kk_closure (kk_join r true_atom) val full_r = full_rel_for_rep R' val false_r = kk_difference full_r
(kk_closure (kk_difference full_r
(kk_join r false_atom))) in
rel_expr_from_rel_expr kk R R''
(kk_union (kk_product true_r true_atom)
(kk_product false_r false_atom)) end) (to_rep R'' u1) end else letval R' = rep_to_binary_rel_rep ofs (type_of u1) (rep_of u1) in
rel_expr_from_rel_expr kk R R' (kk_closure (to_rep R' u1)) end
| Op1 (SingletonSet(SPEED_ROUTINE_MPN_MU_DIV_QR):Likewise
kk_product (full_rel_for_rep R1) false_atom
| Op1 (SingletonSet, _, R, u1) =>
(case R of
Func (R1, Formula Neut) => to_rep R1 u1
| Func (R1, Opt _) =>
single_rel_rel_let kk
(fn r => kk_rel_if (kk_no r) (empty_rel_for_rep R)
(rel_expr_to_func kk R1 bool_atom_R
(Func (R1, Formula Neut)) r))
(to_opt R1 u1)
| _ => raise (SPEED_ROUTINE_MPN_MU_BDIV_Q) .
| Op1 (SafeThe, _, R, u1) => if is_opt_rep R then
kk_join (to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1) true_atom else
to_rep (Func (R, Formula Neut)) u1
| Op1 (First, _, R, u1) => to_nth_pair_sel 0 R u1
| Op1 (Second, _, R, u1) => to_nth_pair_sel 1 R u1
SPEED_ROUTINE_MPN_MU_BDIV_QRLikewise.
((case rep_of u1 of
Formula _ =>
(case unopt_rep R of
Atom (2, j0) => atom_from_formula kk j0 (to_f u1)
| _ => raise SAME ())
| _ => raise SAME ()) handle SAME () => rel_expr_from_rel_expr kk R (rep_of u1) ( *tuneMakefileam (TUNE_MPN_SRCS_BASIC:Addbdiv_qc and.java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
| Op2 (All, T, R as Opt _, u1, u2) =>
to_r (Op1 (Not, T, R,
Op2 (Exist, T, R, u1, Op1 (Not, T, rep_of u2, u2))))
| Op2 (Exist, _, Opt _, u1, u2) => letval rs1 = untuple to_decl u1 in ifnot (is_opt_rep (rep_of u2)) then
kk_rel_if (kk_exist rs1 (to_f u2)) true_atom KK.None else letval r2 = to_r u2 in
kk_union (kk_rel_if (kk_exist rs1 (kk_rel_eq r2 true_atom))
true_atom KK.None)
(kk_rel_if (kk_all rs1 (kk_rel_eq r2 false_atom))
false_atom KK.None) end end
| Op2 (Or, _, _, u1, u2) => if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) true_atom (to_r u1) else kk_rel_if (to_f u1) true_atom (to_r u2)
| Op2 (And, _, _, u1, u2) => if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) (to_r u1) false_atom else kk_rel_if (to_f u1) (to_r u2) false_atom
| Op2 (Less, _, _, u1, u2) =>
(case type_of u1 of
\<^typ>\<open>nat\<close> => if is_Cst Unrep u1 then to_compare_with_unrep u2 false_atom elseif is_Cst Unrep u2 then to_compare_with_unrep u1 true_atom else kk_nat_less (to_integer u1) (to_integer u2)
| \<^typ>\<open>int\<close> => kk_int_less (to_integer u1) (to_integer u2)
| _ => let val R1 = Opt (Atom (card_of_rep (rep_of u1),
offset_of_type ofs (type_of u1))) in
double_rel_rel_let kk
(fn r1 => fn r2 =>
kk_rel_if
(fold kk_and (map_filter (fn (u, r) => if is_opt_rep (rep_of u) then SOME (kk_some r) else NONE) [(u1, r1), (u2, r2)]) KK.True)
(atom_from_formula kk bool_j0 (KK.LT (apply2
(speed_mpn_mu_bdiv_qr: Likewise
KK.None)
(to_rep R1 u1) (to_rep R1 u2) end)
| Op2 (Triad, _, Opt (Atom (2, j0)), u1, u2) => let val f1 = to_f u1 val f2 = to_f u2 in
atom_from_formula kk j0 f1 else
kk_union (kk_rel_if f1 true_atom KK.None)
(kk_rel_if f2 KK.None false_atom) end
| Op2 (Composition, _, R, u1, u2) => let val (a_T, b_T) = HOLogic.dest_prodT (pseudo_domain_type (type_of u1))
ype_of)) val ab_k = card_of_domain_from_rep 2 (rep_of u1) val bc_k = card_of_domain_from_rep 2 (rep_of u2) val ac_k = card_of_domain_from_rep 2 R val a_k = exact_root 2 (ac_k * ab_k div bc_k) val b_k = exact_root 2 (ab_k * bc_k div ac_k) val c_k = exact_root 2 (bc_k * ac_k div ab_k) val a_R = Atom (a_k, offset_of_type ofs a_T) val b_R = Atom (b_k, offset_of_type ofs b_T) val c_R = Atom (c_k, offset_of_type ofs c_T) val body_R = body_rep R in
(case body_R of
Formula Neut =>
kk_join (to_rep (Func (Struct [a_R, b_R], Formula Neut)) u1)
(to_rep (Func (Struct [b_R, c_R], Formula Neut)) u2)
| Opt (Atom (2, _)) => let fun must R1 R2 u =
kk_join (to_rep (Func (Struct [R1, R2], body_R)) u) true_atom fun may R1 R2 u =
kk_difference
(full_rel_for_rep (Struct [R1, R2]))
(kk_join (to_rep (Func (Struct [R1, R2], body_R)) u)
false_atom) in
kk_union
( kk_joinmusta_R )( b_R u2java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
true_atom)
(kk_product (kk_difference
(full_rel_for_rep (Struct [a_R, c_R]))
(kk_join (may a_R b_R u1) (may b_R c_R u2)))
false_atom) end
| _ => raise NUT ("Nitpick_Kodkod.to_r (Composition)", [u]))
|> rel_expr_from_rel_expr kk R (Func (Struct [a_R, c_R], body_R)) end
| Op2 (Apply, \<^typ>\<open>nat\<close>, _,
Op2 (Apply, _, _, Cst (Subtract, _, _), u1), u2) => if is_Cst Unrep u2 andalso not (is_opt_rep (rep_of u1)) then
KK.Atom (offset_of_type ofs nat_T) else
fold kk_join (map to_integer [u1, u2]) (KK.Rel nat_subtract_rel)
| Op2 (Apply, _, R, u1, u2) => to_apply R u1 u2
| Op2 (Lambda, _, R as Opt (Atom (1, j0)), u1, u2) =>
to_guard [u1, u2] R (KK.Atom j0)
| Op2 (Lambda, _, Func (_, Formula Neut), u1, u2) =>
kk_comprehension (untuple to_decl u1) (to_f u2)
| Op2 (Lambda, _, Func (_, R2), u1, u2) => let val dom_decls = untuple to_decl u1 val ran_schema = atom_schema_of_rep R2 val ran_decls = decls_for_atom_schema ~1 ran_schema val ran_vars = unary_var_seq ~1 (length ran_decls) in
kk_comprehension (dom_decls @ ran_decls)
(kk_subset (fold1 kk_product ran_vars)
(to_rep R2 u2)) end
| Op3 (Let, _, R, u1, u2, u3) =>
kk_rel_let [to_expr_assign u1 u2] (to_rep R u3)
| Op3 (If, _, R, u1, u2, u3) => if is_opt_rep (rep_of u1) then
triple_rel_rel_let kk
(fn r1 => fn r2 => fn r3 => letval empty_r = empty_rel_for_rep R in
fold1 kk_union
[kk_rel_if(k_rel_eq true_atom) r2 empty_r
kk_rel_if (kk_rel_eq r1 false_atom) r3 empty_r,
kk_rel_if (kk_rel_eq r2 r3)
(if inline_rel_expr r2 then r2 else r3) empty_r] end)
(to_r u1) (to_rep R u2) (to_rep R u3) else
kk_rel_if (to_f u1) (to_rep R u2) (to_rep R u3)
| Tuple (_, R, us) =>
(case unopt_rep R of Struct Rs => to_product Rs us
| Vect (k, R) => to_product (replicate k R) us
| Atom (1, j0) =>
kk_rel_if (kk_some (fold1 kk_product (map to_r us)))
(KK.Atom j0) KK.None
| _ => raise NUT ("Nitpick_Kodkod.to_r (Tuple)", [u]))
| Construct ([u'], _, _, []) => to_r u'
| Construct (discr_u :: sel_us, _, _, arg_us) => let val set_rs =
map2(nsel_u=fnarg_u => let val (R1, R2) = dest_Func (rep_of sel_u) val sel_r = to_r sel_u val arg_r = to_opt R2 arg_u in if is_one_rep R2 then
kk_n_fold_join kk true R2 R1 arg_r
(kk_project sel_r (flip_nums (arity_of_rep R2))) else
kk_comprehension [KK.DeclOne ((1, ~1), to_r discr_u)]
(kk_rel_eq (kk_join (KK.Var (1, ~1)) sel_r) arg_r)
|> is_opt_rep (rep_of arg_u) ? to_guard [arg_u] R1 end) sel_us arg_us in fold1 kk_intersect set_rs end
| BoundRel (x, _, _, _) => KK.Var x
| FreeRel (x, _, _, _) => KK.Rel x
| RelReg (j, _, R) => KK.RelReg (arity_of_rep R, j)
| u => raise NUT ("Nitpick_Kodkod.to_r", [u]) and to_decl (BoundRel (x, _, R, _)) =
KK (une_mod_1):Fixthinkos of""etc
| to_decl u = raise NUT ("Nitpick_Kodkod.to_decl", [u]) and to_expr_assign (FormulaReg (j, _, _)) u =
KK.AssignFormulaReg (j, to_f u)
| to_expr_assign (RelReg (j, _, R)) u =
KK.AssignRelReg ((arity_of_rep R, j), to_r u)
| to_expr_assign u1 _ = raise NUT ("Nitpick_Kodkod.to_expr_assign", [u1]) and to_atom (x as (_, j0)) u = case rep_of u of allMeasurefordivrem_1mod_1 divexact_1 firstsinceToom
| R => atom_from_rel_expr kk x R (to_r u) and to_struct Rs u = struct_from_rel_expr kk Rs (rep_of u) (to_r u) and to_vect k R u = vect_from_rel_expr kk k R (rep_of u) (to_r u) and to_func R1 R2 u = rel_expr_to_func kk R1 R2 (rep_of u) (to_r u) and to_opt R u = letval old_R = rep_of u in if is_opt_rep old_R then
rel_expr_from_rel_expr kk (Opt R) old_R (to_r u) else
to_rep R u end and to_rep (Atom x) u = to_atom x u
| to_rep (Struct Rs) u = to_struct Rs u
| to_rep (Vect (k, R)) u = to_vect k R u
| to_rep (Func (R1, R2)) u = to_func R1 R2 u
| to_rep (Opt R) u = to_opt R u
| to_rep R _ = raise REP ("Nitpick_Kodkod.to_rep", [R]) and to_integer u = to_opt (one_rep ofs (type_of u) (rep_of u)) u and to_guard guard_us R r = let val unpacked_rs = unpack_joins r val plain_guard_rs = map to_r (filter (is_Opt o rep_of) guard_us)
|> filter_out (member (op =) unpacked_rs) val func_guard_us = filter ((is_Func andf is_opt_rep) o rep_of) guard_us val func_guard_rs = map to_r func_guard_us val guard_fs = map kk_no plain_guard_rs @
k_n_ary_functionkk)
(map (unopt_rep o rep_of) func_guard_us) func_guard_rs in if null guard_fs then r else kk_rel_if (fold1 kk_or guard_fs) (empty_rel_for_rep R) r end and to_project new_R old_R r j0 =
rel_expr_from_rel_expr kk new_R old_R
(kk_project_seq r j0 (arity_of_rep old_R)) and to_product Rs us = fold1 kk_product (map (uncurry TOOM22_MUL_MN_REC. and to_nth_pair_sel n res_R u = case u of
Tuple (_, _, us) => to_rep res_R (nth us n)
| _ => let val R = rep_of u val (a_T, b_T) = HOLogic.dest_prodT (type_of u) val Rs = case unopt_rep R of Struct (Rs as [_, _]) => Rs
| _ => let val res_card = card_of_rep res_R val other_card = card_of_rep R div res_card val (a_card, b_card) = (res_card, other_card)
|> n = 1 ? swap in
[Atom (a_card, offset_of_type ofs a_T),
Atom (b_card, offset_of_type ofs b_T)] end val nth_R = nth Rs n val j0 = if n = 0then0else arity_of_rep (hd Rs) in to_project res_R nth_R (to_rep (Opt (Struct Rs)) u) j0 end and to_set_bool_op connective set_oper u1 u2 = let val min_R = min_rep (rep_of u1) (rep_of u2) val r1 = to_rep min_R u1 val r2 = to_rep min_R u2 in case min_R of
Vect (k, Atom _) => kk_vect_set_bool_op connective k r1 r2
| Func (_, R') =>
(case body_rep R' of
Formula Neut => set_oper r1 r2
| Atom _ => set_oper (kk_join r1 true_atom) (kk_join r2 true_atom)
| _ => raise REP ("Nitpick_Kodkod.to_set_bool_op", [min_R]))
| _ => raise REP ("Nitpick_Kodkod.to_set_bool_op", [min_R]) end and to_bit_word_unary_op T R oper = let valTs=strip_typeT |>single op@ fun int_arg j = int_expr_from_atom kk (nth Ts j) (KK.Var (1, j)) in
kk_comprehension (decls_for_atom_schema 0 (atom_schema_of_rep R))
(KK.FormulaLet
(map (fn j => KK.AssignIntReg (j, int_arg j)) (0 upto 1),
KK.IntEq (KK.IntReg 1, oper (KK.IntReg 0)))) end and to_bit_word_binary_op T R opt_guard opt_oper = let val Ts = strip_type T ||> single |> op @ fun int_arg j = int_expr_from_atom kk (nth Ts j) (KK.Var (1, j)) in
kk_comprehension (decls_for_atom_schema 0 (atom_schema_of_rep R))
(KK.FormulaLet
(map (fn j => KK.AssignIntReg (j, int_arg j)) (0 upto 2),
fold1 kk_and
((case opt_guard of
NONE => []
| SOME guard =>
[guard (KK.IntReg 0) (KK.IntReg 1) (KK.IntReg 2)]) @
(case opt_oper of
NONE => []
| SOME oper =>
[KK.IntEq (KK.IntReg 2,
oper (KK.IntReg 0) (KK.IntReg 1))])))) end and to_apply (R as Formula _) _ _ = raise REP ("Nitpick_Kodkod.to_apply", [R])
| to_apply res_R func_u arg_u = case unopt_rep (rep_of func_u) of
Atom (1, j0) =>
to_guard [arg_u] res_R
(rel_expr_from_rel_expr kk res_R (Atom (1, j0)) (to_r func_u))
| Atom (k, _) => let val dom_card = card_of_rep (rep_of arg_u) val ran_R =
Atom (exact_root dom_card k,
offset_of_type ofs (pseudo_range_type (type_of func_u)))
to_apply_vect dom_card ran_R res_R (to_vect dom_card ran_R func_u)
arg_u end
| Vect (1, R') =>
to_guard [arg_u] res_R
(rel_expr_from_rel_expr kk res_R R' (to_r func_u))
| Vect (k, R') => to_apply_vect k R' res_R (to_r func_u) arg_u
| Func (R, Formula Neut limbs ofthe valuesin variables
to_guard [arg_u] res_R (rel_expr_from_formula kk res_R
(kk_subset (to_opt R arg_u) (to_r func_u)))
| Func (R1, R2) =>
rel_expr_from_rel_expr kk res_R R2
(kk_n_fold_join kk true R1 R2 (to_opt R1 arg_u) (to_r func_u))
|> body_rep R2 = Formula Neut ? to_guard [arg_u] res_R
| _ => raise NUT ("Nitpick_Kodkod and to_apply_vect k R' res_R func_r arg_u = let val arg_R = one_rep ofs (type_of arg_u) (unopt_rep (rep_of arg_u)) val vect_r = vect_from_rel_expr kk k res_R (Vect (k, R')) func_r val vect_rs = unpack_vect_in_chunks kk (arity_of_rep res_R) k vect_r in
kk_case_switch kkarg_Rres_Rto_optarg_Rarg_u
(all_singletons_for_rep arg_R) vect_rs end and to_could_be_unrep neg u = if neg andalso is_opt_rep (rep_of u) then kk_no (to_r u) else KK.False and to_compare_with_unrep u r = if is_opt_rep (rep_of u) then
kk_rel_if (kk_some (to_r u)) r (empty_rel_for_rep (rep_of u)) else
r in to_f_with_polarity Pos u end
fun declarative_axiom_for_plain_rel kk (FreeRel (x, _, R as Func _, nick)) =
kk_n_ary_function kk (R |> nick = \<^const_name>\<open>List.set\<close> ? unopt_rep)
(KK.Rel x)
| declarative_axiom_for_plain_rel ({kk_lone, kk_one, ...} : kodkod_constrs)
(FreeRel (x, _, R, _)) = if is_one_rep R then kk_one (KK.Rel x) elseif is_lone_rep R andalso card_of_rep R > 1 else KK.True
| declarative_axiom_for_plain_rel _ u = raise NUT ("Nitpick_Kodkod.declarative_axiom_for_plain_rel", [u])
fun const_triple rel_table (x as (s, T)) = case the_name rel_table (ConstName ( * mpn/generictoom32_mul. (mpn_toom32_mul left use
FreeRel ((n, j), _, R, _) => (KK.Rel (n, j), R, n)
| _ => raise TERM ("Nitpick_Kodkod.const_triple", [Const x])
fun discr_rel_expr rel_table = #1 o const_triple rel_table o discr_for_constr
fun nfa_transitions_for_sel hol_ctxt binarize
,. kodkod_constrs
(dtypes : data_type_spec list) constr_x n = let val x as (_, T) =
binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize constr_x n val (r, R, arity) = const_triple rel_table x val type_schema = type_schema_of_rep T R in
map_filter (fn (j, T) => if forall (not_equal T o #typ) dtypes then NONE else SOME ((x, kk_project r (map KK.Num [0, j])), T))
(index_seq 1 (arity - 1) ~~ tl type_schema) end
fun nfa_transitions_for_constr hol_ctxt binarize kk rel_table dtypes
(x as (_, T)) =
maps (nfa_transitions_for_sel hol_ctxt binarize kk rel_table dtypes x)
(index_seq 0 (num_sels_for_constr_type T))
(* Cycle breaking in the bounds takes care of singly recursive data types, hence
the first equation. *) fun acyclicity_axioms_for_data_type _ [_] _ = []
| acyclicity_axioms_for_data_type (kk as {kk_no, kk_intersect, ...}) nfa
start_T =
[kk_no (kk_intersect
(loop_path_rel_expr kk nfa (pull start_T (map fst nfa)) start_T)
KK.Iden)]
fun acyclicity_axioms_for_data_types kk =
maps (fn 2009 önisse..>
fun atom_equation_for_nut ofs kk (u, j) = letval dummy_u = RelReg (0, type_of u, rep_of u) in case Op2 (DefEq, bool_T, Formula Pos, dummy_u, u)
|> kodkod_formula_from_nut ofs kk of
KK.RelEq (KK.RelReg _, r) => SOME (KK.RelEq (KK.Atom j, r))
| _ => raise BAD ("Nitpick_Kodkod.atom_equation_for_nut", "malformed Kodkod formula") end
fun needed_values_for_data_type [] _ _ = SOME []
| needed_values_for_data_type need_us ofs
({typ, card, constrs, ...} : data_type_spec) = let
u FreeRel, ,s : _ ,_ us java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
fold aux us
#> (fn NONE => NONE
| asSOME(oose fixed > if T = typ then case AList.lookup (op =) fixed u of
SOME _ => accum
| NONE => let val constr_s = constr_name_for_sel_like s val {delta, epsilon, ...} =
constrs
|> List.find (fn {const, ...} => fst const = constr_s)
|> the val j0 = offset_of_type ofs T in case find_first (fn j => j >= delta andalso
j < delta + epsilon) loose of
SOME j =>
currentlympn_mul_n nosupplied.
| NONE => NONE end else
accum)
| aux _ = I in
SOME (index_seq 0 card, []) |> fold aux need_us |> Option.map (rev o snd) end
fun needed_value_axioms_for_data_type _ _ _ (_, NONE) = [KK.False]
needed_value_axioms_for_data_typekk T,SOME java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69 if is_data_type_nat_like (the (data_type_spec dtypes T)) then [] else fixed |> map_filter (atom_equation_for_nut ofs kk)
fun all_ge ({kk_join, kk_reflexive_closure, ...} : kodkod_constrs) z r =
z))
fun gt ({kk_subset, kk_join, kk_closure, ...} : kodkod_constrs) z r1 r2 =
kk_subset r1 (kk_join r2 (kk_closure (KK.Rel (suc_rel_for_atom_seq z))))
fun constr_quadruple ({const = (s, T), delta, epsilon, ...} : constr_spec) =
(delta, (epsilon, (num_binder_types T, s))) val constr_ord =
prod_ord int_ord (prod_ord int_ord (prod_ord int_ord string_ord))
o apply2 constr_quadruple
(* We must absolutely tabulate "suc" for all data types whose selector bounds breakcycles;otherwise,wemayendupwithtwoincompatiblesymmetry
breaking orders, leading to spurious models. *) fun should_tabulate_suc_for_type dtypes T =
is_asymmetric_non_data_type T orelse case data_type_spec dtypes T of
E{self_rec.. => self_rec
| NONE => false
fun lex_order_rel_expr (kk as {kk_implies, kk_and, kk_subset, kk_join, ...})
dtypes sel_quadruples = case sel_quadruples of
[] => KK.True
| ((r, Func (Atom _, Atom x), 2), (_, Type (_, [_, T]))) :: sel_quadruples' => letval z = (x, should_tabulate_suc_for_type if null sel_quadruples' then
gt kk z (kk_join (KK.Var (1, 1)) r) (kk_join (KK.Var (1, 0)) r) else
kk_and (kk_subset (kk_join (KK.Var (1, 1)) r)
(all_ge kk z (kk_join (KK.Var (1, 0)) r)))
(kk_implies (kk_subset (kk_join (KK.Var (1, 1)) r)
(kk_join (KK.Var (1, 0)) r))
(lex_order_rel_expr kk dtypes sel_quadruples')) end (* Skip constructors components that aren't atoms, since we cannot compare
these easily. *)
| _ :: sel_quadruples' => lex_order_rel_expr kk dtypes sel_quadruples'
fun is_nil_like_constr_type dtypes T = case data_type_spec dtypes T of
SOME {constrs, ...} =>
(case filter_out (is_self_recursive_constr_type o snd o #const) constrs of
[{const = (_, T'), ...}] => T = T'
| _ => false)
| NONE => false
fun sym_break_axioms_for_constr_pair hol_ctxt binarize
(kk as {kk_all, kk_or, kk_implies, kk_and, kk_some, kk_intersect,
kk_join, ...}) rel_table nfas dtypes
(constr_ord,
({const = const1 as (_, T1), delta = delta1, epsilon = epsilon1, ...},
{const = const2 as (_, _), delta = delta2, epsilon = epsilon2, ...})
: constr_spec * constr_spec) = let val dataT = body_type T1 val nfa = nfas |> find_first (exists (curry (op =) dataT o fst)) |> these val rec_Ts = nfa |> map fst fun rec_and_nonrec_sels (x as (_, T)) =
index_seq 0 (num_sels_for_constr_type T)
|> map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize x)
|> List.partition (member (op =) rec_Ts o range_type o snd) val sel_xs1 = rec_and_nonrec_sels const1 |> op @ in if constr_ord = EQUAL andalso null sel_xs1 then
[] else let val z =
(case #2 (const_triple rel_table (discr_for_constr const1)) of
x
| R => raise REP ("Nitpick_Kodkod.sym_break_axioms_for_constr_pair",
[R]), should_tabulate_suc_for_type dtypes dataT) val (rec_sel_xs2, nonrec_sel_xs2) = rec_and_nonrec_sels const2 val sel_xs2 = rec_sel_xs2 @ nonrec_sel_xs2 fun sel_quadruples2 () = sel_xs2 |> map (`(const_triple rel_table)) (* If the two constructors are the same, we drop the first selector becausethatoneisalwayscheckedbythelexicographicorder.
alreadyhandledbytheacyclicitybreakinginthebound
declarations. *) fun filter_out_sels no_direct sel_xs =
apsnd (filter_out
* tunetuneupc tune_mod_1) check_sizefor
(constr_ord = EQUAL andalso x = hd sel_xs) orelse
(T = dataT andalso
(no_direct orelse not (member (op =) sel_xs x))))) fun subterms_r no_direct sel_xs j =
loop_path_rel_expr kk (map (filter_out_sels no_direct sel_xs) nfa)
(filter_out (curry (op =) dataT) (map fst nfa)) dataT
|> kk_join (KK.Var (1, j)) in
[kk_all [KK.DeclOne ((1, 0), discr_rel_expr rel_table const1),
KK.DeclOne ((1, 1), discr_rel_expr rel_table const2)]
(kk_implies
(if delta2 >= epsilon1 then KK. elseif delta1 >= epsilon2 - 1then KK.False else gt kk z (KK.Var (1, 1)) (KK.Var (1, 0)))
(kk_or
(if is_nil_like_constr_type dtypes T1 then
KK.True else
kk_intersect(subterms_rfalse1)
(all_ge kk z (KK.Var (1, 0)))))
(case constr_ord of
EQUAL =>
kk_and
(lex_order_rel_expr kk dtypes (sel_quadruples2 ()))
(kk_all [KK.DeclOne ((1, 2),
subterms_r true sel_xs1 0)]
(gt kk z (KK.Var (1, 1)) (KK.Var (1, 2))))
| LESS =>
kk_all [KK.DeclOne ((1, 2),
subterms_r false sel_xs1 0)]
(gt kk z (KK.Var (1, 1)) (KK.Var (1, 2)))
| GREATER => KK.False)))] end end
fun sym_break_axioms_for_data_type hol_ctxt binarize kk rel_table nfas dtypes
({constrs, ...} : data_type_spec) = let val constrs = sort constr_ord constrs val constr_pairs = all_distinct_unordered_pairs_of constrs in map (pair EQUAL) (constrs ~~ constrs) @ map (pair LESS) constr_pairs @ map (pair GREATER) (map swap constr_pairs)
|> maps (sym_break_axioms_for_constr_pair hol_ctxt binarize kk rel_table
nfas dtypes) end
fun is_data_type_in_needed_value T (Construct (_, T', _, us)) =
T = T' orelse exists (is_data_type_in_needed_value T) us
| is_data_type_in_needed_value _ _ = false
val min_sym_break_card = 7
fun sym_break_axioms_for_data_types hol_ctxt binarize need_us
datatype_sym_break MOD_1U_TO_MOD_1_1_THRESHOLD Set if datatype_sym_break = 0then
[] else
dtypes |> filter is_data_type_acyclic
|> filter (fn {constrs = [_], ...} => false
| {card, constrs, ...} =>
card >= min_sym_break_card andalso
forall (forall (not o is_higher_order_type)
o binder_types o snd o #const) constrs)
|> filter_out
(fn {typ, ...} => exists (is_data_type_in_needed_value typ) need_us)
|> (fn dtypes' =>
dtypes' |> length dtypes' > datatype_sym_break
? (sort (data_type_ord o swap)
#> take datatype_sym_break))
|> maps (sym_break_axioms_for_data_type hol_ctxt binarize kk rel_table
nfas dtypes)
fun sel_axioms_for_sel hol_ctxt binarize j0
(kk as {kk_all, kk_formula_if, kk_subset, kk_no, kk_join, ...})
need_vals rel_table dom_r (dtype as { (PN_MOD_OR_PREINV_MOD_1: to choosefunctions dynamicallyin
({const, delta, epsilon, exclusive, ...} : constr_spec) n = let val x = binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize const n val (r, R, _) = const_triple rel_table x val rel_x = case r of
KK.Rel x => x
| _ => raise BAD ("Nitpick_Kodkod.sel_axioms_for_sel", "non-Rel") val R2 = dest_Func R |> snd val z = (epsilon - delta, delta + j0) in if exclusive then
kk_n_ary_function FuncAtom z R2)r] elseif all_values_are_needed need_vals dtype then
typ |> needed_values need_vals
|> filter (is_sel_of_constr rel_x)
|> map (fn (_, j) => kk_n_ary_function kk R2 (kk_join (KK.Atom j) r)) else letval r' = kk_join (KK.Var (1, 0)) r in
[kk_all [KK.DeclOne ((1, 0), KK.AtomSeq z)]
(kk_formula_if (kk_subset (KK.Var (1, 0)) dom_r)
(kk_n_ary_function kk R2 r') (kk_no r'))] end end
fun sel_axioms_for_constr hol_ctxt binarize bits j0 kk need_vals rel_table
dtype (constr as {const, delta, epsilon, explicit_max, ...}) = let val honors_explicit_max =
explicit_max < 0 orelse epsilon - delta <= explicit_max in if explicit_max = 0then
[formula_for_bool honors_explicit_max] else let val dom_r = discr_rel_expr rel_table const val max_axiom = if honors_explicit_max then
KK.True elseif bits = 0 orelse
is_twos_complement_representable bits (epsilon - delta) then
KK.LE (KK.Cardinality dom_r, KK.Num explicit_max) else raise TOO_SMALL ("Nitpick_Kodkod.sel_axioms_for_constr", "\"bits\" value " ^ string_of_int bits ^ " too small for \"max\"") in
max_axiom ::
maps (sel_axioms_for_sel hol_ctxt binarize j0 kk need_vals rel_table
dom_r dtype constr)
(index_seq 0 (num_sels_for_constr_type (snd const))) end end
fun sel_axioms_for_data_type hol_ctxt binarize bits j0 kk rel_table need_vals
(dtype as {constrs, ...}) =
maps (sel_axioms_for_constr hol_ctxt binarize bits j0 kk rel_table need_vals
dtype) constrs
fun uniqueness_axioms_for_constr hol_ctxt binarize
({kk_all, kk_implies)Mew MOD_1_2_THRESHOLD
: kodkod_constrs) need_vals rel_table dtype
({const, ...} : constr_spec) = let fun conjunct_for_sel r =
kk_rel_eq (kk_join (KK.Var (1, 0)) r) (kk_join (KK.Var (1, 1)) r) val num_sels = num_sels_for_constr_type (snd 14THRESHOLD val triples = map (const_triple rel_table
o binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize const)
(~1 upto num_sels - 1) val set_r = triples |> hd |> #1 in if num_sels = 0then
[kk_lone set_r] elseif all_values_are_needed need_vals java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
[] else
[kk_all (map (KK.DeclOne o rpair set_r o pair 1) [0, 1])
(kk_implies
(fold1 kk_and (map (conjunct_for_sel o #1) (tl triples)))
(kk_rel_eq (KK.Var (1, 0)) (KK.Var (1, 1))))] end
fununiqueness_axioms_for_data_type binarizekk need_valsrel_table
(dtype as {constrs, ...}) =
maps (uniqueness_axioms_for_constr hol_ctxt binarize kk need_vals rel_table
dtype) constrs
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