blanchet@33982
|
1 |
(* Title: HOL/Tools/Nitpick/nitpick_kodkod.ML
|
blanchet@33192
|
2 |
Author: Jasmin Blanchette, TU Muenchen
|
blanchet@34969
|
3 |
Copyright 2008, 2009, 2010
|
blanchet@33192
|
4 |
|
blanchet@33192
|
5 |
Kodkod problem generator part of Kodkod.
|
blanchet@33192
|
6 |
*)
|
blanchet@33192
|
7 |
|
blanchet@33192
|
8 |
signature NITPICK_KODKOD =
|
blanchet@33192
|
9 |
sig
|
blanchet@35067
|
10 |
type hol_context = Nitpick_HOL.hol_context
|
blanchet@33224
|
11 |
type dtype_spec = Nitpick_Scope.dtype_spec
|
blanchet@33224
|
12 |
type kodkod_constrs = Nitpick_Peephole.kodkod_constrs
|
blanchet@33224
|
13 |
type nut = Nitpick_Nut.nut
|
blanchet@33192
|
14 |
type nfa_transition = Kodkod.rel_expr * typ
|
blanchet@33192
|
15 |
type nfa_entry = typ * nfa_transition list
|
blanchet@33192
|
16 |
type nfa_table = nfa_entry list
|
blanchet@33192
|
17 |
|
blanchet@33192
|
18 |
structure NameTable : TABLE
|
blanchet@33192
|
19 |
|
blanchet@33192
|
20 |
val univ_card :
|
blanchet@33192
|
21 |
int -> int -> int -> Kodkod.bound list -> Kodkod.formula -> int
|
blanchet@34121
|
22 |
val check_bits : int -> Kodkod.formula -> unit
|
blanchet@33192
|
23 |
val check_arity : int -> int -> unit
|
blanchet@33192
|
24 |
val kk_tuple : bool -> int -> int list -> Kodkod.tuple
|
blanchet@33192
|
25 |
val tuple_set_from_atom_schema : (int * int) list -> Kodkod.tuple_set
|
blanchet@33192
|
26 |
val sequential_int_bounds : int -> Kodkod.int_bound list
|
blanchet@34121
|
27 |
val pow_of_two_int_bounds : int -> int -> int -> Kodkod.int_bound list
|
blanchet@33192
|
28 |
val bounds_for_built_in_rels_in_formula :
|
blanchet@33192
|
29 |
bool -> int -> int -> int -> int -> Kodkod.formula -> Kodkod.bound list
|
blanchet@33192
|
30 |
val bound_for_plain_rel : Proof.context -> bool -> nut -> Kodkod.bound
|
blanchet@33192
|
31 |
val bound_for_sel_rel :
|
blanchet@33192
|
32 |
Proof.context -> bool -> dtype_spec list -> nut -> Kodkod.bound
|
blanchet@33192
|
33 |
val merge_bounds : Kodkod.bound list -> Kodkod.bound list
|
blanchet@33192
|
34 |
val declarative_axiom_for_plain_rel : kodkod_constrs -> nut -> Kodkod.formula
|
blanchet@33192
|
35 |
val declarative_axioms_for_datatypes :
|
blanchet@35067
|
36 |
hol_context -> int -> int Typtab.table -> kodkod_constrs
|
blanchet@33192
|
37 |
-> nut NameTable.table -> dtype_spec list -> Kodkod.formula list
|
blanchet@33192
|
38 |
val kodkod_formula_from_nut :
|
blanchet@34121
|
39 |
int -> int Typtab.table -> bool -> kodkod_constrs -> nut -> Kodkod.formula
|
blanchet@33192
|
40 |
end;
|
blanchet@33192
|
41 |
|
blanchet@33224
|
42 |
structure Nitpick_Kodkod : NITPICK_KODKOD =
|
blanchet@33192
|
43 |
struct
|
blanchet@33192
|
44 |
|
blanchet@33224
|
45 |
open Nitpick_Util
|
blanchet@33224
|
46 |
open Nitpick_HOL
|
blanchet@33224
|
47 |
open Nitpick_Scope
|
blanchet@33224
|
48 |
open Nitpick_Peephole
|
blanchet@33224
|
49 |
open Nitpick_Rep
|
blanchet@33224
|
50 |
open Nitpick_Nut
|
blanchet@33192
|
51 |
|
blanchet@34123
|
52 |
structure KK = Kodkod
|
blanchet@34123
|
53 |
|
blanchet@34123
|
54 |
type nfa_transition = KK.rel_expr * typ
|
blanchet@33192
|
55 |
type nfa_entry = typ * nfa_transition list
|
blanchet@33192
|
56 |
type nfa_table = nfa_entry list
|
blanchet@33192
|
57 |
|
blanchet@33192
|
58 |
structure NfaGraph = Graph(type key = typ val ord = TermOrd.typ_ord)
|
blanchet@33192
|
59 |
|
blanchet@34123
|
60 |
(* int -> KK.int_expr list *)
|
blanchet@34123
|
61 |
fun flip_nums n = index_seq 1 n @ [0] |> map KK.Num
|
blanchet@33192
|
62 |
|
blanchet@34123
|
63 |
(* int -> int -> int -> KK.bound list -> KK.formula -> int *)
|
blanchet@33192
|
64 |
fun univ_card nat_card int_card main_j0 bounds formula =
|
blanchet@33192
|
65 |
let
|
blanchet@34123
|
66 |
(* KK.rel_expr -> int -> int *)
|
blanchet@33192
|
67 |
fun rel_expr_func r k =
|
blanchet@33192
|
68 |
Int.max (k, case r of
|
blanchet@34123
|
69 |
KK.Atom j => j + 1
|
blanchet@34123
|
70 |
| KK.AtomSeq (k', j0) => j0 + k'
|
blanchet@33192
|
71 |
| _ => 0)
|
blanchet@34123
|
72 |
(* KK.tuple -> int -> int *)
|
blanchet@33192
|
73 |
fun tuple_func t k =
|
blanchet@33192
|
74 |
case t of
|
blanchet@34123
|
75 |
KK.Tuple js => fold Integer.max (map (Integer.add 1) js) k
|
blanchet@33192
|
76 |
| _ => k
|
blanchet@34123
|
77 |
(* KK.tuple_set -> int -> int *)
|
blanchet@33192
|
78 |
fun tuple_set_func ts k =
|
blanchet@34123
|
79 |
Int.max (k, case ts of KK.TupleAtomSeq (k', j0) => j0 + k' | _ => 0)
|
blanchet@33192
|
80 |
val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,
|
blanchet@33192
|
81 |
int_expr_func = K I}
|
blanchet@33192
|
82 |
val tuple_F = {tuple_func = tuple_func, tuple_set_func = tuple_set_func}
|
blanchet@34123
|
83 |
val card = fold (KK.fold_bound expr_F tuple_F) bounds 1
|
blanchet@34123
|
84 |
|> KK.fold_formula expr_F formula
|
blanchet@33192
|
85 |
in Int.max (main_j0 + fold Integer.max [2, nat_card, int_card] 0, card) end
|
blanchet@33192
|
86 |
|
blanchet@34123
|
87 |
(* int -> KK.formula -> unit *)
|
blanchet@34121
|
88 |
fun check_bits bits formula =
|
blanchet@34121
|
89 |
let
|
blanchet@34123
|
90 |
(* KK.int_expr -> unit -> unit *)
|
blanchet@34123
|
91 |
fun int_expr_func (KK.Num k) () =
|
blanchet@34121
|
92 |
if is_twos_complement_representable bits k then
|
blanchet@34121
|
93 |
()
|
blanchet@34121
|
94 |
else
|
blanchet@34121
|
95 |
raise TOO_SMALL ("Nitpick_Kodkod.check_bits",
|
blanchet@34121
|
96 |
"\"bits\" value " ^ string_of_int bits ^
|
blanchet@34121
|
97 |
" too small for problem")
|
blanchet@34121
|
98 |
| int_expr_func _ () = ()
|
blanchet@34121
|
99 |
val expr_F = {formula_func = K I, rel_expr_func = K I,
|
blanchet@34121
|
100 |
int_expr_func = int_expr_func}
|
blanchet@34123
|
101 |
in KK.fold_formula expr_F formula () end
|
blanchet@33192
|
102 |
|
blanchet@33192
|
103 |
(* int -> int -> unit *)
|
blanchet@33192
|
104 |
fun check_arity univ_card n =
|
blanchet@34123
|
105 |
if n > KK.max_arity univ_card then
|
blanchet@34121
|
106 |
raise TOO_LARGE ("Nitpick_Kodkod.check_arity",
|
blanchet@34121
|
107 |
"arity " ^ string_of_int n ^ " too large for universe of \
|
blanchet@34121
|
108 |
\cardinality " ^ string_of_int univ_card)
|
blanchet@33192
|
109 |
else
|
blanchet@33192
|
110 |
()
|
blanchet@33192
|
111 |
|
blanchet@34123
|
112 |
(* bool -> int -> int list -> KK.tuple *)
|
blanchet@33192
|
113 |
fun kk_tuple debug univ_card js =
|
blanchet@33192
|
114 |
if debug then
|
blanchet@34123
|
115 |
KK.Tuple js
|
blanchet@33192
|
116 |
else
|
blanchet@34123
|
117 |
KK.TupleIndex (length js,
|
blanchet@34123
|
118 |
fold (fn j => fn accum => accum * univ_card + j) js 0)
|
blanchet@33192
|
119 |
|
blanchet@34123
|
120 |
(* (int * int) list -> KK.tuple_set *)
|
blanchet@34123
|
121 |
val tuple_set_from_atom_schema = foldl1 KK.TupleProduct o map KK.TupleAtomSeq
|
blanchet@34123
|
122 |
(* rep -> KK.tuple_set *)
|
blanchet@33192
|
123 |
val upper_bound_for_rep = tuple_set_from_atom_schema o atom_schema_of_rep
|
blanchet@33192
|
124 |
|
blanchet@34123
|
125 |
(* int -> KK.tuple_set *)
|
blanchet@34123
|
126 |
val single_atom = KK.TupleSet o single o KK.Tuple o single
|
blanchet@34123
|
127 |
(* int -> KK.int_bound list *)
|
blanchet@34121
|
128 |
fun sequential_int_bounds n = [(NONE, map single_atom (index_seq 0 n))]
|
blanchet@34123
|
129 |
(* int -> int -> KK.int_bound list *)
|
blanchet@34121
|
130 |
fun pow_of_two_int_bounds bits j0 univ_card =
|
blanchet@34121
|
131 |
let
|
blanchet@34123
|
132 |
(* int -> int -> int -> KK.int_bound list *)
|
blanchet@34121
|
133 |
fun aux 0 _ _ = []
|
blanchet@34121
|
134 |
| aux 1 pow_of_two j =
|
blanchet@34121
|
135 |
if j < univ_card then [(SOME (~ pow_of_two), [single_atom j])] else []
|
blanchet@34121
|
136 |
| aux iter pow_of_two j =
|
blanchet@34121
|
137 |
(SOME pow_of_two, [single_atom j]) ::
|
blanchet@34121
|
138 |
aux (iter - 1) (2 * pow_of_two) (j + 1)
|
blanchet@34121
|
139 |
in aux (bits + 1) 1 j0 end
|
blanchet@33192
|
140 |
|
blanchet@34123
|
141 |
(* KK.formula -> KK.n_ary_index list *)
|
blanchet@33192
|
142 |
fun built_in_rels_in_formula formula =
|
blanchet@33192
|
143 |
let
|
blanchet@34123
|
144 |
(* KK.rel_expr -> KK.n_ary_index list -> KK.n_ary_index list *)
|
blanchet@34123
|
145 |
fun rel_expr_func (r as KK.Rel (x as (n, j))) =
|
blanchet@34121
|
146 |
if x = unsigned_bit_word_sel_rel orelse x = signed_bit_word_sel_rel then
|
blanchet@34121
|
147 |
I
|
blanchet@34121
|
148 |
else
|
blanchet@34121
|
149 |
(case AList.lookup (op =) (#rels initial_pool) n of
|
blanchet@34121
|
150 |
SOME k => j < k ? insert (op =) x
|
blanchet@34121
|
151 |
| NONE => I)
|
blanchet@34121
|
152 |
| rel_expr_func _ = I
|
blanchet@33192
|
153 |
val expr_F = {formula_func = K I, rel_expr_func = rel_expr_func,
|
blanchet@33192
|
154 |
int_expr_func = K I}
|
blanchet@34123
|
155 |
in KK.fold_formula expr_F formula [] end
|
blanchet@33192
|
156 |
|
blanchet@33192
|
157 |
val max_table_size = 65536
|
blanchet@33192
|
158 |
|
blanchet@33192
|
159 |
(* int -> unit *)
|
blanchet@33192
|
160 |
fun check_table_size k =
|
blanchet@33192
|
161 |
if k > max_table_size then
|
blanchet@34121
|
162 |
raise TOO_LARGE ("Nitpick_Kodkod.check_table_size",
|
blanchet@34121
|
163 |
"precomputed table too large (" ^ string_of_int k ^ ")")
|
blanchet@33192
|
164 |
else
|
blanchet@33192
|
165 |
()
|
blanchet@33192
|
166 |
|
blanchet@34123
|
167 |
(* bool -> int -> int * int -> (int -> int) -> KK.tuple list *)
|
blanchet@33192
|
168 |
fun tabulate_func1 debug univ_card (k, j0) f =
|
blanchet@33192
|
169 |
(check_table_size k;
|
blanchet@33192
|
170 |
map_filter (fn j1 => let val j2 = f j1 in
|
blanchet@33192
|
171 |
if j2 >= 0 then
|
blanchet@33192
|
172 |
SOME (kk_tuple debug univ_card [j1 + j0, j2 + j0])
|
blanchet@33192
|
173 |
else
|
blanchet@33192
|
174 |
NONE
|
blanchet@33192
|
175 |
end) (index_seq 0 k))
|
blanchet@34123
|
176 |
(* bool -> int -> int * int -> int -> (int * int -> int) -> KK.tuple list *)
|
blanchet@33192
|
177 |
fun tabulate_op2 debug univ_card (k, j0) res_j0 f =
|
blanchet@33192
|
178 |
(check_table_size (k * k);
|
blanchet@33192
|
179 |
map_filter (fn j => let
|
blanchet@33192
|
180 |
val j1 = j div k
|
blanchet@33192
|
181 |
val j2 = j - j1 * k
|
blanchet@33192
|
182 |
val j3 = f (j1, j2)
|
blanchet@33192
|
183 |
in
|
blanchet@33192
|
184 |
if j3 >= 0 then
|
blanchet@33192
|
185 |
SOME (kk_tuple debug univ_card
|
blanchet@33192
|
186 |
[j1 + j0, j2 + j0, j3 + res_j0])
|
blanchet@33192
|
187 |
else
|
blanchet@33192
|
188 |
NONE
|
blanchet@33192
|
189 |
end) (index_seq 0 (k * k)))
|
blanchet@33192
|
190 |
(* bool -> int -> int * int -> int -> (int * int -> int * int)
|
blanchet@34123
|
191 |
-> KK.tuple list *)
|
blanchet@33192
|
192 |
fun tabulate_op2_2 debug univ_card (k, j0) res_j0 f =
|
blanchet@33192
|
193 |
(check_table_size (k * k);
|
blanchet@33192
|
194 |
map_filter (fn j => let
|
blanchet@33192
|
195 |
val j1 = j div k
|
blanchet@33192
|
196 |
val j2 = j - j1 * k
|
blanchet@33192
|
197 |
val (j3, j4) = f (j1, j2)
|
blanchet@33192
|
198 |
in
|
blanchet@33192
|
199 |
if j3 >= 0 andalso j4 >= 0 then
|
blanchet@33192
|
200 |
SOME (kk_tuple debug univ_card
|
blanchet@33192
|
201 |
[j1 + j0, j2 + j0, j3 + res_j0,
|
blanchet@33192
|
202 |
j4 + res_j0])
|
blanchet@33192
|
203 |
else
|
blanchet@33192
|
204 |
NONE
|
blanchet@33192
|
205 |
end) (index_seq 0 (k * k)))
|
blanchet@34123
|
206 |
(* bool -> int -> int * int -> (int * int -> int) -> KK.tuple list *)
|
blanchet@33192
|
207 |
fun tabulate_nat_op2 debug univ_card (k, j0) f =
|
blanchet@33192
|
208 |
tabulate_op2 debug univ_card (k, j0) j0 (atom_for_nat (k, 0) o f)
|
blanchet@33192
|
209 |
fun tabulate_int_op2 debug univ_card (k, j0) f =
|
blanchet@33192
|
210 |
tabulate_op2 debug univ_card (k, j0) j0
|
blanchet@33192
|
211 |
(atom_for_int (k, 0) o f o pairself (int_for_atom (k, 0)))
|
blanchet@34123
|
212 |
(* bool -> int -> int * int -> (int * int -> int * int) -> KK.tuple list *)
|
blanchet@33192
|
213 |
fun tabulate_int_op2_2 debug univ_card (k, j0) f =
|
blanchet@33192
|
214 |
tabulate_op2_2 debug univ_card (k, j0) j0
|
blanchet@33192
|
215 |
(pairself (atom_for_int (k, 0)) o f
|
blanchet@33192
|
216 |
o pairself (int_for_atom (k, 0)))
|
blanchet@33192
|
217 |
|
blanchet@33192
|
218 |
(* int * int -> int *)
|
blanchet@33192
|
219 |
fun isa_div (m, n) = m div n handle General.Div => 0
|
blanchet@33192
|
220 |
fun isa_mod (m, n) = m mod n handle General.Div => m
|
blanchet@33192
|
221 |
fun isa_gcd (m, 0) = m
|
blanchet@33192
|
222 |
| isa_gcd (m, n) = isa_gcd (n, isa_mod (m, n))
|
blanchet@33192
|
223 |
fun isa_lcm (m, n) = isa_div (m * n, isa_gcd (m, n))
|
blanchet@33192
|
224 |
val isa_zgcd = isa_gcd o pairself abs
|
blanchet@33192
|
225 |
(* int * int -> int * int *)
|
blanchet@33192
|
226 |
fun isa_norm_frac (m, n) =
|
blanchet@33192
|
227 |
if n < 0 then isa_norm_frac (~m, ~n)
|
blanchet@33192
|
228 |
else if m = 0 orelse n = 0 then (0, 1)
|
blanchet@33192
|
229 |
else let val p = isa_zgcd (m, n) in (isa_div (m, p), isa_div (n, p)) end
|
blanchet@33192
|
230 |
|
blanchet@33192
|
231 |
(* bool -> int -> int -> int -> int -> int * int
|
blanchet@34123
|
232 |
-> string * bool * KK.tuple list *)
|
blanchet@33192
|
233 |
fun tabulate_built_in_rel debug univ_card nat_card int_card j0 (x as (n, _)) =
|
blanchet@33192
|
234 |
(check_arity univ_card n;
|
blanchet@34121
|
235 |
if x = not3_rel then
|
blanchet@33192
|
236 |
("not3", tabulate_func1 debug univ_card (2, j0) (curry (op -) 1))
|
blanchet@34121
|
237 |
else if x = suc_rel then
|
blanchet@33192
|
238 |
("suc", tabulate_func1 debug univ_card (univ_card - j0 - 1, j0)
|
blanchet@33192
|
239 |
(Integer.add 1))
|
blanchet@34121
|
240 |
else if x = nat_add_rel then
|
blanchet@33192
|
241 |
("nat_add", tabulate_nat_op2 debug univ_card (nat_card, j0) (op +))
|
blanchet@34121
|
242 |
else if x = int_add_rel then
|
blanchet@33192
|
243 |
("int_add", tabulate_int_op2 debug univ_card (int_card, j0) (op +))
|
blanchet@34121
|
244 |
else if x = nat_subtract_rel then
|
blanchet@33192
|
245 |
("nat_subtract",
|
blanchet@33705
|
246 |
tabulate_op2 debug univ_card (nat_card, j0) j0 (uncurry nat_minus))
|
blanchet@34121
|
247 |
else if x = int_subtract_rel then
|
blanchet@33192
|
248 |
("int_subtract", tabulate_int_op2 debug univ_card (int_card, j0) (op -))
|
blanchet@34121
|
249 |
else if x = nat_multiply_rel then
|
blanchet@33192
|
250 |
("nat_multiply", tabulate_nat_op2 debug univ_card (nat_card, j0) (op * ))
|
blanchet@34121
|
251 |
else if x = int_multiply_rel then
|
blanchet@33192
|
252 |
("int_multiply", tabulate_int_op2 debug univ_card (int_card, j0) (op * ))
|
blanchet@34121
|
253 |
else if x = nat_divide_rel then
|
blanchet@33192
|
254 |
("nat_divide", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_div)
|
blanchet@34121
|
255 |
else if x = int_divide_rel then
|
blanchet@33192
|
256 |
("int_divide", tabulate_int_op2 debug univ_card (int_card, j0) isa_div)
|
blanchet@34121
|
257 |
else if x = nat_less_rel then
|
blanchet@33192
|
258 |
("nat_less", tabulate_nat_op2 debug univ_card (nat_card, j0)
|
blanchet@33192
|
259 |
(int_for_bool o op <))
|
blanchet@34121
|
260 |
else if x = int_less_rel then
|
blanchet@33192
|
261 |
("int_less", tabulate_int_op2 debug univ_card (int_card, j0)
|
blanchet@33192
|
262 |
(int_for_bool o op <))
|
blanchet@34121
|
263 |
else if x = gcd_rel then
|
blanchet@33192
|
264 |
("gcd", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_gcd)
|
blanchet@34121
|
265 |
else if x = lcm_rel then
|
blanchet@33192
|
266 |
("lcm", tabulate_nat_op2 debug univ_card (nat_card, j0) isa_lcm)
|
blanchet@34121
|
267 |
else if x = norm_frac_rel then
|
blanchet@33192
|
268 |
("norm_frac", tabulate_int_op2_2 debug univ_card (int_card, j0)
|
blanchet@33192
|
269 |
isa_norm_frac)
|
blanchet@33192
|
270 |
else
|
blanchet@33224
|
271 |
raise ARG ("Nitpick_Kodkod.tabulate_built_in_rel", "unknown relation"))
|
blanchet@33192
|
272 |
|
blanchet@34123
|
273 |
(* bool -> int -> int -> int -> int -> int * int -> KK.rel_expr -> KK.bound *)
|
blanchet@33192
|
274 |
fun bound_for_built_in_rel debug univ_card nat_card int_card j0 x =
|
blanchet@33192
|
275 |
let
|
blanchet@33192
|
276 |
val (nick, ts) = tabulate_built_in_rel debug univ_card nat_card int_card
|
blanchet@33192
|
277 |
j0 x
|
blanchet@34123
|
278 |
in ([(x, nick)], [KK.TupleSet ts]) end
|
blanchet@33192
|
279 |
|
blanchet@34123
|
280 |
(* bool -> int -> int -> int -> int -> KK.formula -> KK.bound list *)
|
blanchet@33192
|
281 |
fun bounds_for_built_in_rels_in_formula debug univ_card nat_card int_card j0 =
|
blanchet@33192
|
282 |
map (bound_for_built_in_rel debug univ_card nat_card int_card j0)
|
blanchet@33192
|
283 |
o built_in_rels_in_formula
|
blanchet@33192
|
284 |
|
blanchet@34121
|
285 |
(* Proof.context -> bool -> string -> typ -> rep -> string *)
|
blanchet@34121
|
286 |
fun bound_comment ctxt debug nick T R =
|
blanchet@34121
|
287 |
short_name nick ^
|
blanchet@34969
|
288 |
(if debug then " :: " ^ unyxml (Syntax.string_of_typ ctxt T) else "") ^
|
blanchet@34969
|
289 |
" : " ^ string_for_rep R
|
blanchet@34121
|
290 |
|
blanchet@34123
|
291 |
(* Proof.context -> bool -> nut -> KK.bound *)
|
blanchet@33192
|
292 |
fun bound_for_plain_rel ctxt debug (u as FreeRel (x, T, R, nick)) =
|
blanchet@33192
|
293 |
([(x, bound_comment ctxt debug nick T R)],
|
blanchet@33192
|
294 |
if nick = @{const_name bisim_iterator_max} then
|
blanchet@33192
|
295 |
case R of
|
blanchet@34121
|
296 |
Atom (k, j0) => [single_atom (k - 1 + j0)]
|
blanchet@33224
|
297 |
| _ => raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])
|
blanchet@33192
|
298 |
else
|
blanchet@34123
|
299 |
[KK.TupleSet [], upper_bound_for_rep R])
|
blanchet@33192
|
300 |
| bound_for_plain_rel _ _ u =
|
blanchet@33224
|
301 |
raise NUT ("Nitpick_Kodkod.bound_for_plain_rel", [u])
|
blanchet@33192
|
302 |
|
blanchet@34123
|
303 |
(* Proof.context -> bool -> dtype_spec list -> nut -> KK.bound *)
|
blanchet@33192
|
304 |
fun bound_for_sel_rel ctxt debug dtypes
|
blanchet@33192
|
305 |
(FreeRel (x, T as Type ("fun", [T1, T2]), R as Func (Atom (_, j0), R2),
|
blanchet@33192
|
306 |
nick)) =
|
blanchet@33192
|
307 |
let
|
blanchet@33192
|
308 |
val constr as {delta, epsilon, exclusive, explicit_max, ...} =
|
blanchet@33192
|
309 |
constr_spec dtypes (original_name nick, T1)
|
blanchet@33192
|
310 |
in
|
blanchet@33192
|
311 |
([(x, bound_comment ctxt debug nick T R)],
|
blanchet@33192
|
312 |
if explicit_max = 0 then
|
blanchet@34123
|
313 |
[KK.TupleSet []]
|
blanchet@33192
|
314 |
else
|
blanchet@34123
|
315 |
let val ts = KK.TupleAtomSeq (epsilon - delta, delta + j0) in
|
blanchet@33192
|
316 |
if R2 = Formula Neut then
|
blanchet@34123
|
317 |
[ts] |> not exclusive ? cons (KK.TupleSet [])
|
blanchet@33192
|
318 |
else
|
blanchet@35069
|
319 |
[KK.TupleSet [],
|
blanchet@35075
|
320 |
if (* ### exclusive andalso*) T1 = T2 andalso epsilon > delta then
|
blanchet@35069
|
321 |
index_seq delta (epsilon - delta)
|
blanchet@35069
|
322 |
|> map (fn j =>
|
blanchet@35069
|
323 |
KK.TupleProduct (KK.TupleSet [Kodkod.Tuple [j + j0]],
|
blanchet@35069
|
324 |
KK.TupleAtomSeq (j, j0)))
|
blanchet@35069
|
325 |
|> foldl1 KK.TupleUnion
|
blanchet@35069
|
326 |
else
|
blanchet@35069
|
327 |
KK.TupleProduct (ts, upper_bound_for_rep R2)]
|
blanchet@33192
|
328 |
end)
|
blanchet@33192
|
329 |
end
|
blanchet@33192
|
330 |
| bound_for_sel_rel _ _ _ u =
|
blanchet@33224
|
331 |
raise NUT ("Nitpick_Kodkod.bound_for_sel_rel", [u])
|
blanchet@33192
|
332 |
|
blanchet@34123
|
333 |
(* KK.bound list -> KK.bound list *)
|
blanchet@33192
|
334 |
fun merge_bounds bs =
|
blanchet@33192
|
335 |
let
|
blanchet@34123
|
336 |
(* KK.bound -> int *)
|
blanchet@33192
|
337 |
fun arity (zs, _) = fst (fst (hd zs))
|
blanchet@34123
|
338 |
(* KK.bound list -> KK.bound -> KK.bound list -> KK.bound list *)
|
blanchet@33192
|
339 |
fun add_bound ds b [] = List.revAppend (ds, [b])
|
blanchet@33192
|
340 |
| add_bound ds b (c :: cs) =
|
blanchet@33192
|
341 |
if arity b = arity c andalso snd b = snd c then
|
blanchet@33192
|
342 |
List.revAppend (ds, (fst c @ fst b, snd c) :: cs)
|
blanchet@33192
|
343 |
else
|
blanchet@33192
|
344 |
add_bound (c :: ds) b cs
|
blanchet@33192
|
345 |
in fold (add_bound []) bs [] end
|
blanchet@33192
|
346 |
|
blanchet@34123
|
347 |
(* int -> int -> KK.rel_expr list *)
|
blanchet@34123
|
348 |
fun unary_var_seq j0 n = map (curry KK.Var 1) (index_seq j0 n)
|
blanchet@33192
|
349 |
|
blanchet@34123
|
350 |
(* int list -> KK.rel_expr *)
|
blanchet@34123
|
351 |
val singleton_from_combination = foldl1 KK.Product o map KK.Atom
|
blanchet@34123
|
352 |
(* rep -> KK.rel_expr list *)
|
blanchet@33192
|
353 |
fun all_singletons_for_rep R =
|
blanchet@33192
|
354 |
if is_lone_rep R then
|
blanchet@33192
|
355 |
all_combinations_for_rep R |> map singleton_from_combination
|
blanchet@33192
|
356 |
else
|
blanchet@33224
|
357 |
raise REP ("Nitpick_Kodkod.all_singletons_for_rep", [R])
|
blanchet@33192
|
358 |
|
blanchet@34123
|
359 |
(* KK.rel_expr -> KK.rel_expr list *)
|
blanchet@34123
|
360 |
fun unpack_products (KK.Product (r1, r2)) =
|
blanchet@33192
|
361 |
unpack_products r1 @ unpack_products r2
|
blanchet@33192
|
362 |
| unpack_products r = [r]
|
blanchet@34123
|
363 |
fun unpack_joins (KK.Join (r1, r2)) = unpack_joins r1 @ unpack_joins r2
|
blanchet@33192
|
364 |
| unpack_joins r = [r]
|
blanchet@33192
|
365 |
|
blanchet@34123
|
366 |
(* rep -> KK.rel_expr *)
|
blanchet@33192
|
367 |
val empty_rel_for_rep = empty_n_ary_rel o arity_of_rep
|
blanchet@33192
|
368 |
fun full_rel_for_rep R =
|
blanchet@33192
|
369 |
case atom_schema_of_rep R of
|
blanchet@33224
|
370 |
[] => raise REP ("Nitpick_Kodkod.full_rel_for_rep", [R])
|
blanchet@34123
|
371 |
| schema => foldl1 KK.Product (map KK.AtomSeq schema)
|
blanchet@33192
|
372 |
|
blanchet@34123
|
373 |
(* int -> int list -> KK.decl list *)
|
blanchet@33192
|
374 |
fun decls_for_atom_schema j0 schema =
|
blanchet@34123
|
375 |
map2 (fn j => fn x => KK.DeclOne ((1, j), KK.AtomSeq x))
|
blanchet@33192
|
376 |
(index_seq j0 (length schema)) schema
|
blanchet@33192
|
377 |
|
blanchet@33192
|
378 |
(* The type constraint below is a workaround for a Poly/ML bug. *)
|
blanchet@33192
|
379 |
|
blanchet@34123
|
380 |
(* kodkod_constrs -> rep -> KK.rel_expr -> KK.formula *)
|
blanchet@33192
|
381 |
fun d_n_ary_function ({kk_all, kk_join, kk_lone, kk_one, ...} : kodkod_constrs)
|
blanchet@33192
|
382 |
R r =
|
blanchet@33192
|
383 |
let val body_R = body_rep R in
|
blanchet@33192
|
384 |
if is_lone_rep body_R then
|
blanchet@33192
|
385 |
let
|
blanchet@33192
|
386 |
val binder_schema = atom_schema_of_reps (binder_reps R)
|
blanchet@33192
|
387 |
val body_schema = atom_schema_of_rep body_R
|
blanchet@33192
|
388 |
val one = is_one_rep body_R
|
blanchet@34123
|
389 |
val opt_x = case r of KK.Rel x => SOME x | _ => NONE
|
blanchet@33192
|
390 |
in
|
blanchet@34923
|
391 |
if opt_x <> NONE andalso length binder_schema = 1 andalso
|
blanchet@34923
|
392 |
length body_schema = 1 then
|
blanchet@34123
|
393 |
(if one then KK.Function else KK.Functional)
|
blanchet@34123
|
394 |
(the opt_x, KK.AtomSeq (hd binder_schema),
|
blanchet@34123
|
395 |
KK.AtomSeq (hd body_schema))
|
blanchet@33192
|
396 |
else
|
blanchet@33192
|
397 |
let
|
blanchet@33192
|
398 |
val decls = decls_for_atom_schema ~1 binder_schema
|
blanchet@33192
|
399 |
val vars = unary_var_seq ~1 (length binder_schema)
|
blanchet@33192
|
400 |
val kk_xone = if one then kk_one else kk_lone
|
blanchet@33192
|
401 |
in kk_all decls (kk_xone (fold kk_join vars r)) end
|
blanchet@33192
|
402 |
end
|
blanchet@33192
|
403 |
else
|
blanchet@34123
|
404 |
KK.True
|
blanchet@33192
|
405 |
end
|
blanchet@34123
|
406 |
fun kk_n_ary_function kk R (r as KK.Rel x) =
|
blanchet@33192
|
407 |
if not (is_opt_rep R) then
|
blanchet@34121
|
408 |
if x = suc_rel then
|
blanchet@34123
|
409 |
KK.False
|
blanchet@34121
|
410 |
else if x = nat_add_rel then
|
blanchet@33192
|
411 |
formula_for_bool (card_of_rep (body_rep R) = 1)
|
blanchet@34121
|
412 |
else if x = nat_multiply_rel then
|
blanchet@33192
|
413 |
formula_for_bool (card_of_rep (body_rep R) <= 2)
|
blanchet@33192
|
414 |
else
|
blanchet@33192
|
415 |
d_n_ary_function kk R r
|
blanchet@34121
|
416 |
else if x = nat_subtract_rel then
|
blanchet@34123
|
417 |
KK.True
|
blanchet@33192
|
418 |
else
|
blanchet@33192
|
419 |
d_n_ary_function kk R r
|
blanchet@33192
|
420 |
| kk_n_ary_function kk R r = d_n_ary_function kk R r
|
blanchet@33192
|
421 |
|
blanchet@34123
|
422 |
(* kodkod_constrs -> KK.rel_expr list -> KK.formula *)
|
blanchet@34123
|
423 |
fun kk_disjoint_sets _ [] = KK.True
|
blanchet@33192
|
424 |
| kk_disjoint_sets (kk as {kk_and, kk_no, kk_intersect, ...} : kodkod_constrs)
|
blanchet@33192
|
425 |
(r :: rs) =
|
blanchet@33192
|
426 |
fold (kk_and o kk_no o kk_intersect r) rs (kk_disjoint_sets kk rs)
|
blanchet@33192
|
427 |
|
blanchet@34123
|
428 |
(* int -> kodkod_constrs -> (KK.rel_expr -> KK.rel_expr) -> KK.rel_expr
|
blanchet@34123
|
429 |
-> KK.rel_expr *)
|
blanchet@34121
|
430 |
fun basic_rel_rel_let j ({kk_rel_let, ...} : kodkod_constrs) f r =
|
blanchet@33192
|
431 |
if inline_rel_expr r then
|
blanchet@33192
|
432 |
f r
|
blanchet@33192
|
433 |
else
|
blanchet@34123
|
434 |
let val x = (KK.arity_of_rel_expr r, j) in
|
blanchet@34123
|
435 |
kk_rel_let [KK.AssignRelReg (x, r)] (f (KK.RelReg x))
|
blanchet@33192
|
436 |
end
|
blanchet@34123
|
437 |
(* kodkod_constrs -> (KK.rel_expr -> KK.rel_expr) -> KK.rel_expr
|
blanchet@34123
|
438 |
-> KK.rel_expr *)
|
blanchet@34121
|
439 |
val single_rel_rel_let = basic_rel_rel_let 0
|
blanchet@34123
|
440 |
(* kodkod_constrs -> (KK.rel_expr -> KK.rel_expr -> KK.rel_expr) -> KK.rel_expr
|
blanchet@34123
|
441 |
-> KK.rel_expr -> KK.rel_expr *)
|
blanchet@34121
|
442 |
fun double_rel_rel_let kk f r1 r2 =
|
blanchet@34121
|
443 |
single_rel_rel_let kk (fn r1 => basic_rel_rel_let 1 kk (f r1) r2) r1
|
blanchet@34123
|
444 |
(* kodkod_constrs -> (KK.rel_expr -> KK.rel_expr -> KK.rel_expr -> KK.rel_expr)
|
blanchet@34123
|
445 |
-> KK.rel_expr -> KK.rel_expr -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@34121
|
446 |
fun tripl_rel_rel_let kk f r1 r2 r3 =
|
blanchet@34121
|
447 |
double_rel_rel_let kk
|
blanchet@34121
|
448 |
(fn r1 => fn r2 => basic_rel_rel_let 2 kk (f r1 r2) r3) r1 r2
|
blanchet@33192
|
449 |
|
blanchet@34123
|
450 |
(* kodkod_constrs -> int -> KK.formula -> KK.rel_expr *)
|
blanchet@33192
|
451 |
fun atom_from_formula ({kk_rel_if, ...} : kodkod_constrs) j0 f =
|
blanchet@34123
|
452 |
kk_rel_if f (KK.Atom (j0 + 1)) (KK.Atom j0)
|
blanchet@34123
|
453 |
(* kodkod_constrs -> rep -> KK.formula -> KK.rel_expr *)
|
blanchet@33192
|
454 |
fun rel_expr_from_formula kk R f =
|
blanchet@33192
|
455 |
case unopt_rep R of
|
blanchet@33192
|
456 |
Atom (2, j0) => atom_from_formula kk j0 f
|
blanchet@33224
|
457 |
| _ => raise REP ("Nitpick_Kodkod.rel_expr_from_formula", [R])
|
blanchet@33192
|
458 |
|
blanchet@34123
|
459 |
(* kodkod_cotrs -> int -> int -> KK.rel_expr -> KK.rel_expr list *)
|
blanchet@33192
|
460 |
fun unpack_vect_in_chunks ({kk_project_seq, ...} : kodkod_constrs) chunk_arity
|
blanchet@33192
|
461 |
num_chunks r =
|
blanchet@33192
|
462 |
List.tabulate (num_chunks, fn j => kk_project_seq r (j * chunk_arity)
|
blanchet@33192
|
463 |
chunk_arity)
|
blanchet@33192
|
464 |
|
blanchet@34123
|
465 |
(* kodkod_constrs -> bool -> rep -> rep -> KK.rel_expr -> KK.rel_expr
|
blanchet@34123
|
466 |
-> KK.rel_expr *)
|
blanchet@33192
|
467 |
fun kk_n_fold_join
|
blanchet@33192
|
468 |
(kk as {kk_intersect, kk_product, kk_join, kk_project_seq, ...}) one R1
|
blanchet@33192
|
469 |
res_R r1 r2 =
|
blanchet@33192
|
470 |
case arity_of_rep R1 of
|
blanchet@33192
|
471 |
1 => kk_join r1 r2
|
blanchet@33192
|
472 |
| arity1 =>
|
blanchet@33192
|
473 |
let
|
blanchet@33192
|
474 |
val unpacked_rs1 =
|
blanchet@33192
|
475 |
if inline_rel_expr r1 then unpack_vect_in_chunks kk 1 arity1 r1
|
blanchet@33192
|
476 |
else unpack_products r1
|
blanchet@33192
|
477 |
in
|
blanchet@33192
|
478 |
if one andalso length unpacked_rs1 = arity1 then
|
blanchet@33192
|
479 |
fold kk_join unpacked_rs1 r2
|
blanchet@33192
|
480 |
else
|
blanchet@33192
|
481 |
kk_project_seq
|
blanchet@33192
|
482 |
(kk_intersect (kk_product r1 (full_rel_for_rep res_R)) r2)
|
blanchet@33192
|
483 |
arity1 (arity_of_rep res_R)
|
blanchet@33192
|
484 |
end
|
blanchet@33192
|
485 |
|
blanchet@34123
|
486 |
(* kodkod_constrs -> rep -> rep -> KK.rel_expr -> KK.rel_expr list
|
blanchet@34123
|
487 |
-> KK.rel_expr list -> KK.rel_expr *)
|
blanchet@33192
|
488 |
fun kk_case_switch (kk as {kk_union, kk_product, ...}) R1 R2 r rs1 rs2 =
|
blanchet@33192
|
489 |
if rs1 = rs2 then r
|
blanchet@33192
|
490 |
else kk_n_fold_join kk true R1 R2 r (fold1 kk_union (map2 kk_product rs1 rs2))
|
blanchet@33192
|
491 |
|
blanchet@33192
|
492 |
val lone_rep_fallback_max_card = 4096
|
blanchet@33192
|
493 |
val some_j0 = 0
|
blanchet@33192
|
494 |
|
blanchet@34123
|
495 |
(* kodkod_constrs -> rep -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
496 |
fun lone_rep_fallback kk new_R old_R r =
|
blanchet@33192
|
497 |
if old_R = new_R then
|
blanchet@33192
|
498 |
r
|
blanchet@33192
|
499 |
else
|
blanchet@33192
|
500 |
let val card = card_of_rep old_R in
|
blanchet@34923
|
501 |
if is_lone_rep old_R andalso is_lone_rep new_R andalso
|
blanchet@34923
|
502 |
card = card_of_rep new_R then
|
blanchet@33192
|
503 |
if card >= lone_rep_fallback_max_card then
|
blanchet@34121
|
504 |
raise TOO_LARGE ("Nitpick_Kodkod.lone_rep_fallback",
|
blanchet@34121
|
505 |
"too high cardinality (" ^ string_of_int card ^ ")")
|
blanchet@33192
|
506 |
else
|
blanchet@33192
|
507 |
kk_case_switch kk old_R new_R r (all_singletons_for_rep old_R)
|
blanchet@33192
|
508 |
(all_singletons_for_rep new_R)
|
blanchet@33192
|
509 |
else
|
blanchet@33224
|
510 |
raise REP ("Nitpick_Kodkod.lone_rep_fallback", [old_R, new_R])
|
blanchet@33192
|
511 |
end
|
blanchet@34123
|
512 |
(* kodkod_constrs -> int * int -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
513 |
and atom_from_rel_expr kk (x as (k, j0)) old_R r =
|
blanchet@33192
|
514 |
case old_R of
|
blanchet@33192
|
515 |
Func (R1, R2) =>
|
blanchet@33192
|
516 |
let
|
blanchet@33192
|
517 |
val dom_card = card_of_rep R1
|
blanchet@33192
|
518 |
val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
|
blanchet@33192
|
519 |
in
|
blanchet@33192
|
520 |
atom_from_rel_expr kk x (Vect (dom_card, R2'))
|
blanchet@33192
|
521 |
(vect_from_rel_expr kk dom_card R2' old_R r)
|
blanchet@33192
|
522 |
end
|
blanchet@33224
|
523 |
| Opt _ => raise REP ("Nitpick_Kodkod.atom_from_rel_expr", [old_R])
|
blanchet@33192
|
524 |
| _ => lone_rep_fallback kk (Atom x) old_R r
|
blanchet@34123
|
525 |
(* kodkod_constrs -> rep list -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
526 |
and struct_from_rel_expr kk Rs old_R r =
|
blanchet@33192
|
527 |
case old_R of
|
blanchet@33192
|
528 |
Atom _ => lone_rep_fallback kk (Struct Rs) old_R r
|
blanchet@33192
|
529 |
| Struct Rs' =>
|
blanchet@33192
|
530 |
let
|
blanchet@33192
|
531 |
val Rs = filter (not_equal Unit) Rs
|
blanchet@33192
|
532 |
val Rs' = filter (not_equal Unit) Rs'
|
blanchet@33192
|
533 |
in
|
blanchet@33192
|
534 |
if Rs' = Rs then
|
blanchet@33192
|
535 |
r
|
blanchet@33192
|
536 |
else if map card_of_rep Rs' = map card_of_rep Rs then
|
blanchet@33192
|
537 |
let
|
blanchet@33192
|
538 |
val old_arities = map arity_of_rep Rs'
|
blanchet@33192
|
539 |
val old_offsets = offset_list old_arities
|
blanchet@33192
|
540 |
val old_rs = map2 (#kk_project_seq kk r) old_offsets old_arities
|
blanchet@33192
|
541 |
in
|
blanchet@33192
|
542 |
fold1 (#kk_product kk)
|
blanchet@33192
|
543 |
(map3 (rel_expr_from_rel_expr kk) Rs Rs' old_rs)
|
blanchet@33192
|
544 |
end
|
blanchet@33192
|
545 |
else
|
blanchet@33192
|
546 |
lone_rep_fallback kk (Struct Rs) old_R r
|
blanchet@33192
|
547 |
end
|
blanchet@33224
|
548 |
| _ => raise REP ("Nitpick_Kodkod.struct_from_rel_expr", [old_R])
|
blanchet@34123
|
549 |
(* kodkod_constrs -> int -> rep -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
550 |
and vect_from_rel_expr kk k R old_R r =
|
blanchet@33192
|
551 |
case old_R of
|
blanchet@33192
|
552 |
Atom _ => lone_rep_fallback kk (Vect (k, R)) old_R r
|
blanchet@33192
|
553 |
| Vect (k', R') =>
|
blanchet@33192
|
554 |
if k = k' andalso R = R' then r
|
blanchet@33192
|
555 |
else lone_rep_fallback kk (Vect (k, R)) old_R r
|
blanchet@33192
|
556 |
| Func (R1, Formula Neut) =>
|
blanchet@33192
|
557 |
if k = card_of_rep R1 then
|
blanchet@33192
|
558 |
fold1 (#kk_product kk)
|
blanchet@33192
|
559 |
(map (fn arg_r =>
|
blanchet@33192
|
560 |
rel_expr_from_formula kk R (#kk_subset kk arg_r r))
|
blanchet@33192
|
561 |
(all_singletons_for_rep R1))
|
blanchet@33192
|
562 |
else
|
blanchet@33224
|
563 |
raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])
|
blanchet@33192
|
564 |
| Func (Unit, R2) => rel_expr_from_rel_expr kk R R2 r
|
blanchet@33192
|
565 |
| Func (R1, R2) =>
|
blanchet@33192
|
566 |
fold1 (#kk_product kk)
|
blanchet@33192
|
567 |
(map (fn arg_r =>
|
blanchet@33192
|
568 |
rel_expr_from_rel_expr kk R R2
|
blanchet@33192
|
569 |
(kk_n_fold_join kk true R1 R2 arg_r r))
|
blanchet@33192
|
570 |
(all_singletons_for_rep R1))
|
blanchet@33224
|
571 |
| _ => raise REP ("Nitpick_Kodkod.vect_from_rel_expr", [old_R])
|
blanchet@34123
|
572 |
(* kodkod_constrs -> rep -> rep -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
573 |
and func_from_no_opt_rel_expr kk R1 R2 (Atom x) r =
|
blanchet@33192
|
574 |
let
|
blanchet@33192
|
575 |
val dom_card = card_of_rep R1
|
blanchet@33192
|
576 |
val R2' = case R2 of Atom _ => R2 | _ => Atom (card_of_rep R2, some_j0)
|
blanchet@33192
|
577 |
in
|
blanchet@33192
|
578 |
func_from_no_opt_rel_expr kk R1 R2 (Vect (dom_card, R2'))
|
blanchet@33192
|
579 |
(vect_from_rel_expr kk dom_card R2' (Atom x) r)
|
blanchet@33192
|
580 |
end
|
blanchet@33192
|
581 |
| func_from_no_opt_rel_expr kk Unit R2 old_R r =
|
blanchet@33192
|
582 |
(case old_R of
|
blanchet@33192
|
583 |
Vect (k, R') => rel_expr_from_rel_expr kk R2 R' r
|
blanchet@33192
|
584 |
| Func (Unit, R2') => rel_expr_from_rel_expr kk R2 R2' r
|
blanchet@33192
|
585 |
| Func (Atom (1, _), Formula Neut) =>
|
blanchet@33192
|
586 |
(case unopt_rep R2 of
|
blanchet@33192
|
587 |
Atom (2, j0) => atom_from_formula kk j0 (#kk_some kk r)
|
blanchet@33224
|
588 |
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
|
blanchet@33192
|
589 |
[old_R, Func (Unit, R2)]))
|
blanchet@33192
|
590 |
| Func (R1', R2') =>
|
blanchet@33192
|
591 |
rel_expr_from_rel_expr kk R2 R2' (#kk_project_seq kk r (arity_of_rep R1')
|
blanchet@33192
|
592 |
(arity_of_rep R2'))
|
blanchet@33224
|
593 |
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
|
blanchet@33192
|
594 |
[old_R, Func (Unit, R2)]))
|
blanchet@33192
|
595 |
| func_from_no_opt_rel_expr kk R1 (Formula Neut) old_R r =
|
blanchet@33192
|
596 |
(case old_R of
|
blanchet@33192
|
597 |
Vect (k, Atom (2, j0)) =>
|
blanchet@33192
|
598 |
let
|
blanchet@33192
|
599 |
val args_rs = all_singletons_for_rep R1
|
blanchet@33192
|
600 |
val vals_rs = unpack_vect_in_chunks kk 1 k r
|
blanchet@34123
|
601 |
(* KK.rel_expr -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
602 |
fun empty_or_singleton_set_for arg_r val_r =
|
blanchet@34123
|
603 |
#kk_join kk val_r (#kk_product kk (KK.Atom (j0 + 1)) arg_r)
|
blanchet@33192
|
604 |
in
|
blanchet@33192
|
605 |
fold1 (#kk_union kk) (map2 empty_or_singleton_set_for args_rs vals_rs)
|
blanchet@33192
|
606 |
end
|
blanchet@33192
|
607 |
| Func (R1', Formula Neut) =>
|
blanchet@33192
|
608 |
if R1 = R1' then
|
blanchet@33192
|
609 |
r
|
blanchet@33192
|
610 |
else
|
blanchet@33192
|
611 |
let
|
blanchet@33192
|
612 |
val schema = atom_schema_of_rep R1
|
blanchet@33192
|
613 |
val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
|
blanchet@33192
|
614 |
|> rel_expr_from_rel_expr kk R1' R1
|
blanchet@33573
|
615 |
val kk_xeq = (if is_one_rep R1' then #kk_subset else #kk_rel_eq) kk
|
blanchet@33192
|
616 |
in
|
blanchet@33573
|
617 |
#kk_comprehension kk (decls_for_atom_schema ~1 schema) (kk_xeq r1 r)
|
blanchet@33192
|
618 |
end
|
blanchet@33192
|
619 |
| Func (Unit, (Atom (2, j0))) =>
|
blanchet@34123
|
620 |
#kk_rel_if kk (#kk_rel_eq kk r (KK.Atom (j0 + 1)))
|
blanchet@33192
|
621 |
(full_rel_for_rep R1) (empty_rel_for_rep R1)
|
blanchet@33192
|
622 |
| Func (R1', Atom (2, j0)) =>
|
blanchet@33192
|
623 |
func_from_no_opt_rel_expr kk R1 (Formula Neut)
|
blanchet@34123
|
624 |
(Func (R1', Formula Neut)) (#kk_join kk r (KK.Atom (j0 + 1)))
|
blanchet@33224
|
625 |
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
|
blanchet@33192
|
626 |
[old_R, Func (R1, Formula Neut)]))
|
blanchet@33192
|
627 |
| func_from_no_opt_rel_expr kk R1 R2 old_R r =
|
blanchet@33192
|
628 |
case old_R of
|
blanchet@33192
|
629 |
Vect (k, R) =>
|
blanchet@33192
|
630 |
let
|
blanchet@33192
|
631 |
val args_rs = all_singletons_for_rep R1
|
blanchet@33192
|
632 |
val vals_rs = unpack_vect_in_chunks kk (arity_of_rep R) k r
|
blanchet@33192
|
633 |
|> map (rel_expr_from_rel_expr kk R2 R)
|
blanchet@33192
|
634 |
in fold1 (#kk_union kk) (map2 (#kk_product kk) args_rs vals_rs) end
|
blanchet@33192
|
635 |
| Func (R1', Formula Neut) =>
|
blanchet@33192
|
636 |
(case R2 of
|
blanchet@33192
|
637 |
Atom (x as (2, j0)) =>
|
blanchet@33192
|
638 |
let val schema = atom_schema_of_rep R1 in
|
blanchet@33192
|
639 |
if length schema = 1 then
|
blanchet@34123
|
640 |
#kk_override kk (#kk_product kk (KK.AtomSeq (hd schema))
|
blanchet@34123
|
641 |
(KK.Atom j0))
|
blanchet@34123
|
642 |
(#kk_product kk r (KK.Atom (j0 + 1)))
|
blanchet@33192
|
643 |
else
|
blanchet@33192
|
644 |
let
|
blanchet@33192
|
645 |
val r1 = fold1 (#kk_product kk) (unary_var_seq ~1 (length schema))
|
blanchet@33192
|
646 |
|> rel_expr_from_rel_expr kk R1' R1
|
blanchet@34123
|
647 |
val r2 = KK.Var (1, ~(length schema) - 1)
|
blanchet@33192
|
648 |
val r3 = atom_from_formula kk j0 (#kk_subset kk r1 r)
|
blanchet@33192
|
649 |
in
|
blanchet@33192
|
650 |
#kk_comprehension kk (decls_for_atom_schema ~1 (schema @ [x]))
|
blanchet@33573
|
651 |
(#kk_subset kk r2 r3)
|
blanchet@33192
|
652 |
end
|
blanchet@33192
|
653 |
end
|
blanchet@33224
|
654 |
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
|
blanchet@33192
|
655 |
[old_R, Func (R1, R2)]))
|
blanchet@33192
|
656 |
| Func (Unit, R2') =>
|
blanchet@33192
|
657 |
let val j0 = some_j0 in
|
blanchet@33192
|
658 |
func_from_no_opt_rel_expr kk R1 R2 (Func (Atom (1, j0), R2'))
|
blanchet@34123
|
659 |
(#kk_product kk (KK.Atom j0) r)
|
blanchet@33192
|
660 |
end
|
blanchet@33192
|
661 |
| Func (R1', R2') =>
|
blanchet@33192
|
662 |
if R1 = R1' andalso R2 = R2' then
|
blanchet@33192
|
663 |
r
|
blanchet@33192
|
664 |
else
|
blanchet@33192
|
665 |
let
|
blanchet@33192
|
666 |
val dom_schema = atom_schema_of_rep R1
|
blanchet@33192
|
667 |
val ran_schema = atom_schema_of_rep R2
|
blanchet@33192
|
668 |
val dom_prod = fold1 (#kk_product kk)
|
blanchet@33192
|
669 |
(unary_var_seq ~1 (length dom_schema))
|
blanchet@33192
|
670 |
|> rel_expr_from_rel_expr kk R1' R1
|
blanchet@33192
|
671 |
val ran_prod = fold1 (#kk_product kk)
|
blanchet@33192
|
672 |
(unary_var_seq (~(length dom_schema) - 1)
|
blanchet@33192
|
673 |
(length ran_schema))
|
blanchet@33192
|
674 |
|> rel_expr_from_rel_expr kk R2' R2
|
blanchet@33192
|
675 |
val app = kk_n_fold_join kk true R1' R2' dom_prod r
|
blanchet@33573
|
676 |
val kk_xeq = (if is_one_rep R2' then #kk_subset else #kk_rel_eq) kk
|
blanchet@33192
|
677 |
in
|
blanchet@33192
|
678 |
#kk_comprehension kk (decls_for_atom_schema ~1
|
blanchet@33192
|
679 |
(dom_schema @ ran_schema))
|
blanchet@33573
|
680 |
(kk_xeq ran_prod app)
|
blanchet@33192
|
681 |
end
|
blanchet@33224
|
682 |
| _ => raise REP ("Nitpick_Kodkod.func_from_no_opt_rel_expr",
|
blanchet@33192
|
683 |
[old_R, Func (R1, R2)])
|
blanchet@34123
|
684 |
(* kodkod_constrs -> rep -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
685 |
and rel_expr_from_rel_expr kk new_R old_R r =
|
blanchet@33192
|
686 |
let
|
blanchet@33192
|
687 |
val unopt_old_R = unopt_rep old_R
|
blanchet@33192
|
688 |
val unopt_new_R = unopt_rep new_R
|
blanchet@33192
|
689 |
in
|
blanchet@33192
|
690 |
if unopt_old_R <> old_R andalso unopt_new_R = new_R then
|
blanchet@33224
|
691 |
raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr", [old_R, new_R])
|
blanchet@33192
|
692 |
else if unopt_new_R = unopt_old_R then
|
blanchet@33192
|
693 |
r
|
blanchet@33192
|
694 |
else
|
blanchet@33192
|
695 |
(case unopt_new_R of
|
blanchet@33192
|
696 |
Atom x => atom_from_rel_expr kk x
|
blanchet@33192
|
697 |
| Struct Rs => struct_from_rel_expr kk Rs
|
blanchet@33192
|
698 |
| Vect (k, R') => vect_from_rel_expr kk k R'
|
blanchet@33192
|
699 |
| Func (R1, R2) => func_from_no_opt_rel_expr kk R1 R2
|
blanchet@33224
|
700 |
| _ => raise REP ("Nitpick_Kodkod.rel_expr_from_rel_expr",
|
blanchet@33192
|
701 |
[old_R, new_R]))
|
blanchet@33192
|
702 |
unopt_old_R r
|
blanchet@33192
|
703 |
end
|
blanchet@34123
|
704 |
(* kodkod_constrs -> rep -> rep -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
705 |
and rel_expr_to_func kk R1 R2 = rel_expr_from_rel_expr kk (Func (R1, R2))
|
blanchet@33192
|
706 |
|
blanchet@34123
|
707 |
(* kodkod_constrs -> typ -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@34121
|
708 |
fun bit_set_from_atom ({kk_join, ...} : kodkod_constrs) T r =
|
blanchet@34123
|
709 |
kk_join r (KK.Rel (if T = @{typ "unsigned_bit word"} then
|
blanchet@34123
|
710 |
unsigned_bit_word_sel_rel
|
blanchet@34123
|
711 |
else
|
blanchet@34123
|
712 |
signed_bit_word_sel_rel))
|
blanchet@34123
|
713 |
(* kodkod_constrs -> typ -> KK.rel_expr -> KK.int_expr *)
|
blanchet@34123
|
714 |
val int_expr_from_atom = KK.SetSum ooo bit_set_from_atom
|
blanchet@34123
|
715 |
(* kodkod_constrs -> typ -> rep -> KK.int_expr -> KK.rel_expr *)
|
blanchet@34121
|
716 |
fun atom_from_int_expr (kk as {kk_rel_eq, kk_comprehension, ...}
|
blanchet@34121
|
717 |
: kodkod_constrs) T R i =
|
blanchet@34121
|
718 |
kk_comprehension (decls_for_atom_schema ~1 (atom_schema_of_rep R))
|
blanchet@34123
|
719 |
(kk_rel_eq (bit_set_from_atom kk T (KK.Var (1, ~1)))
|
blanchet@34123
|
720 |
(KK.Bits i))
|
blanchet@34121
|
721 |
|
blanchet@34123
|
722 |
(* kodkod_constrs -> nut -> KK.formula *)
|
blanchet@33192
|
723 |
fun declarative_axiom_for_plain_rel kk (FreeRel (x, _, R as Func _, nick)) =
|
blanchet@33192
|
724 |
kk_n_ary_function kk (R |> nick = @{const_name List.set} ? unopt_rep)
|
blanchet@34123
|
725 |
(KK.Rel x)
|
blanchet@33192
|
726 |
| declarative_axiom_for_plain_rel ({kk_lone, kk_one, ...} : kodkod_constrs)
|
blanchet@33192
|
727 |
(FreeRel (x, _, R, _)) =
|
blanchet@34123
|
728 |
if is_one_rep R then kk_one (KK.Rel x)
|
blanchet@34123
|
729 |
else if is_lone_rep R andalso card_of_rep R > 1 then kk_lone (KK.Rel x)
|
blanchet@34123
|
730 |
else KK.True
|
blanchet@33192
|
731 |
| declarative_axiom_for_plain_rel _ u =
|
blanchet@33224
|
732 |
raise NUT ("Nitpick_Kodkod.declarative_axiom_for_plain_rel", [u])
|
blanchet@33192
|
733 |
|
blanchet@34123
|
734 |
(* nut NameTable.table -> styp -> KK.rel_expr * rep * int *)
|
blanchet@33192
|
735 |
fun const_triple rel_table (x as (s, T)) =
|
blanchet@33192
|
736 |
case the_name rel_table (ConstName (s, T, Any)) of
|
blanchet@34123
|
737 |
FreeRel ((n, j), _, R, _) => (KK.Rel (n, j), R, n)
|
blanchet@33224
|
738 |
| _ => raise TERM ("Nitpick_Kodkod.const_triple", [Const x])
|
blanchet@33192
|
739 |
|
blanchet@34123
|
740 |
(* nut NameTable.table -> styp -> KK.rel_expr *)
|
blanchet@33192
|
741 |
fun discr_rel_expr rel_table = #1 o const_triple rel_table o discr_for_constr
|
blanchet@33192
|
742 |
|
blanchet@35067
|
743 |
(* hol_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
blanchet@33192
|
744 |
-> styp -> int -> nfa_transition list *)
|
blanchet@35067
|
745 |
fun nfa_transitions_for_sel hol_ctxt ({kk_project, ...} : kodkod_constrs)
|
blanchet@33192
|
746 |
rel_table (dtypes : dtype_spec list) constr_x n =
|
blanchet@33192
|
747 |
let
|
blanchet@35067
|
748 |
val x as (_, T) = boxed_nth_sel_for_constr hol_ctxt constr_x n
|
blanchet@33192
|
749 |
val (r, R, arity) = const_triple rel_table x
|
blanchet@33192
|
750 |
val type_schema = type_schema_of_rep T R
|
blanchet@33192
|
751 |
in
|
blanchet@33192
|
752 |
map_filter (fn (j, T) =>
|
blanchet@33192
|
753 |
if forall (not_equal T o #typ) dtypes then NONE
|
blanchet@34123
|
754 |
else SOME (kk_project r (map KK.Num [0, j]), T))
|
blanchet@33192
|
755 |
(index_seq 1 (arity - 1) ~~ tl type_schema)
|
blanchet@33192
|
756 |
end
|
blanchet@35067
|
757 |
(* hol_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
blanchet@33192
|
758 |
-> styp -> nfa_transition list *)
|
blanchet@35067
|
759 |
fun nfa_transitions_for_constr hol_ctxt kk rel_table dtypes (x as (_, T)) =
|
blanchet@35067
|
760 |
maps (nfa_transitions_for_sel hol_ctxt kk rel_table dtypes x)
|
blanchet@33192
|
761 |
(index_seq 0 (num_sels_for_constr_type T))
|
blanchet@35067
|
762 |
(* hol_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
blanchet@33192
|
763 |
-> dtype_spec -> nfa_entry option *)
|
blanchet@33192
|
764 |
fun nfa_entry_for_datatype _ _ _ _ ({co = true, ...} : dtype_spec) = NONE
|
blanchet@34969
|
765 |
| nfa_entry_for_datatype _ _ _ _ {deep = false, ...} = NONE
|
blanchet@35067
|
766 |
| nfa_entry_for_datatype hol_ctxt kk rel_table dtypes {typ, constrs, ...} =
|
blanchet@35067
|
767 |
SOME (typ, maps (nfa_transitions_for_constr hol_ctxt kk rel_table dtypes
|
blanchet@33192
|
768 |
o #const) constrs)
|
blanchet@33192
|
769 |
|
blanchet@34123
|
770 |
val empty_rel = KK.Product (KK.None, KK.None)
|
blanchet@33192
|
771 |
|
blanchet@34123
|
772 |
(* nfa_table -> typ -> typ -> KK.rel_expr list *)
|
blanchet@33192
|
773 |
fun direct_path_rel_exprs nfa start final =
|
blanchet@33192
|
774 |
case AList.lookup (op =) nfa final of
|
blanchet@34118
|
775 |
SOME trans => map fst (filter (curry (op =) start o snd) trans)
|
blanchet@33192
|
776 |
| NONE => []
|
blanchet@34123
|
777 |
(* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> KK.rel_expr *)
|
blanchet@33192
|
778 |
and any_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start final =
|
blanchet@33192
|
779 |
fold kk_union (direct_path_rel_exprs nfa start final)
|
blanchet@34123
|
780 |
(if start = final then KK.Iden else empty_rel)
|
blanchet@33192
|
781 |
| any_path_rel_expr (kk as {kk_union, ...}) nfa (q :: qs) start final =
|
blanchet@33192
|
782 |
kk_union (any_path_rel_expr kk nfa qs start final)
|
blanchet@33192
|
783 |
(knot_path_rel_expr kk nfa qs start q final)
|
blanchet@33192
|
784 |
(* kodkod_constrs -> nfa_table -> typ list -> typ -> typ -> typ
|
blanchet@34123
|
785 |
-> KK.rel_expr *)
|
blanchet@33192
|
786 |
and knot_path_rel_expr (kk as {kk_join, kk_reflexive_closure, ...}) nfa qs start
|
blanchet@33192
|
787 |
knot final =
|
blanchet@33192
|
788 |
kk_join (kk_join (any_path_rel_expr kk nfa qs knot final)
|
blanchet@33192
|
789 |
(kk_reflexive_closure (loop_path_rel_expr kk nfa qs knot)))
|
blanchet@33192
|
790 |
(any_path_rel_expr kk nfa qs start knot)
|
blanchet@34123
|
791 |
(* kodkod_constrs -> nfa_table -> typ list -> typ -> KK.rel_expr *)
|
blanchet@33192
|
792 |
and loop_path_rel_expr ({kk_union, ...} : kodkod_constrs) nfa [] start =
|
blanchet@33192
|
793 |
fold kk_union (direct_path_rel_exprs nfa start start) empty_rel
|
blanchet@33192
|
794 |
| loop_path_rel_expr (kk as {kk_union, kk_closure, ...}) nfa (q :: qs) start =
|
blanchet@33192
|
795 |
if start = q then
|
blanchet@33192
|
796 |
kk_closure (loop_path_rel_expr kk nfa qs start)
|
blanchet@33192
|
797 |
else
|
blanchet@33192
|
798 |
kk_union (loop_path_rel_expr kk nfa qs start)
|
blanchet@33192
|
799 |
(knot_path_rel_expr kk nfa qs start q start)
|
blanchet@33192
|
800 |
|
blanchet@33192
|
801 |
(* nfa_table -> unit NfaGraph.T *)
|
blanchet@33192
|
802 |
fun graph_for_nfa nfa =
|
blanchet@33192
|
803 |
let
|
blanchet@33192
|
804 |
(* typ -> unit NfaGraph.T -> unit NfaGraph.T *)
|
blanchet@33192
|
805 |
fun new_node q = perhaps (try (NfaGraph.new_node (q, ())))
|
blanchet@33192
|
806 |
(* nfa_table -> unit NfaGraph.T -> unit NfaGraph.T *)
|
blanchet@33192
|
807 |
fun add_nfa [] = I
|
blanchet@33192
|
808 |
| add_nfa ((_, []) :: nfa) = add_nfa nfa
|
blanchet@33192
|
809 |
| add_nfa ((q, ((_, q') :: transitions)) :: nfa) =
|
blanchet@33192
|
810 |
add_nfa ((q, transitions) :: nfa) o NfaGraph.add_edge (q, q') o
|
blanchet@33192
|
811 |
new_node q' o new_node q
|
blanchet@33192
|
812 |
in add_nfa nfa NfaGraph.empty end
|
blanchet@33192
|
813 |
|
blanchet@33192
|
814 |
(* nfa_table -> nfa_table list *)
|
blanchet@33192
|
815 |
fun strongly_connected_sub_nfas nfa =
|
blanchet@33192
|
816 |
nfa |> graph_for_nfa |> NfaGraph.strong_conn
|
blanchet@33192
|
817 |
|> map (fn keys => filter (member (op =) keys o fst) nfa)
|
blanchet@33192
|
818 |
|
blanchet@34123
|
819 |
(* dtype_spec list -> kodkod_constrs -> nfa_table -> typ -> KK.formula *)
|
blanchet@33192
|
820 |
fun acyclicity_axiom_for_datatype dtypes kk nfa start =
|
blanchet@33192
|
821 |
#kk_no kk (#kk_intersect kk
|
blanchet@34123
|
822 |
(loop_path_rel_expr kk nfa (map fst nfa) start) KK.Iden)
|
blanchet@35067
|
823 |
(* hol_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec list
|
blanchet@34123
|
824 |
-> KK.formula list *)
|
blanchet@35067
|
825 |
fun acyclicity_axioms_for_datatypes hol_ctxt kk rel_table dtypes =
|
blanchet@35067
|
826 |
map_filter (nfa_entry_for_datatype hol_ctxt kk rel_table dtypes) dtypes
|
blanchet@33192
|
827 |
|> strongly_connected_sub_nfas
|
blanchet@33192
|
828 |
|> maps (fn nfa => map (acyclicity_axiom_for_datatype dtypes kk nfa o fst)
|
blanchet@33192
|
829 |
nfa)
|
blanchet@33192
|
830 |
|
blanchet@35067
|
831 |
(* hol_context -> int -> kodkod_constrs -> nut NameTable.table -> KK.rel_expr
|
blanchet@35067
|
832 |
-> constr_spec -> int -> KK.formula *)
|
blanchet@35067
|
833 |
fun sel_axiom_for_sel hol_ctxt j0
|
blanchet@33192
|
834 |
(kk as {kk_all, kk_implies, kk_formula_if, kk_subset, kk_rel_eq, kk_no,
|
blanchet@33982
|
835 |
kk_join, ...}) rel_table dom_r
|
blanchet@33192
|
836 |
({const, delta, epsilon, exclusive, explicit_max, ...} : constr_spec)
|
blanchet@33192
|
837 |
n =
|
blanchet@33192
|
838 |
let
|
blanchet@35067
|
839 |
val x as (_, T) = boxed_nth_sel_for_constr hol_ctxt const n
|
blanchet@33192
|
840 |
val (r, R, arity) = const_triple rel_table x
|
blanchet@33192
|
841 |
val R2 = dest_Func R |> snd
|
blanchet@33192
|
842 |
val z = (epsilon - delta, delta + j0)
|
blanchet@33192
|
843 |
in
|
blanchet@33192
|
844 |
if exclusive then
|
blanchet@33192
|
845 |
kk_n_ary_function kk (Func (Atom z, R2)) r
|
blanchet@33192
|
846 |
else
|
blanchet@34123
|
847 |
let val r' = kk_join (KK.Var (1, 0)) r in
|
blanchet@34123
|
848 |
kk_all [KK.DeclOne ((1, 0), KK.AtomSeq z)]
|
blanchet@34123
|
849 |
(kk_formula_if (kk_subset (KK.Var (1, 0)) dom_r)
|
blanchet@34123
|
850 |
(kk_n_ary_function kk R2 r') (kk_no r'))
|
blanchet@33192
|
851 |
end
|
blanchet@33192
|
852 |
end
|
blanchet@35067
|
853 |
(* hol_context -> int -> int -> kodkod_constrs -> nut NameTable.table
|
blanchet@34123
|
854 |
-> constr_spec -> KK.formula list *)
|
blanchet@35067
|
855 |
fun sel_axioms_for_constr hol_ctxt bits j0 kk rel_table
|
blanchet@33192
|
856 |
(constr as {const, delta, epsilon, explicit_max, ...}) =
|
blanchet@33192
|
857 |
let
|
blanchet@33192
|
858 |
val honors_explicit_max =
|
blanchet@33192
|
859 |
explicit_max < 0 orelse epsilon - delta <= explicit_max
|
blanchet@33192
|
860 |
in
|
blanchet@33192
|
861 |
if explicit_max = 0 then
|
blanchet@33192
|
862 |
[formula_for_bool honors_explicit_max]
|
blanchet@33192
|
863 |
else
|
blanchet@33192
|
864 |
let
|
blanchet@33192
|
865 |
val ran_r = discr_rel_expr rel_table const
|
blanchet@33192
|
866 |
val max_axiom =
|
blanchet@34121
|
867 |
if honors_explicit_max then
|
blanchet@34123
|
868 |
KK.True
|
blanchet@34121
|
869 |
else if is_twos_complement_representable bits (epsilon - delta) then
|
blanchet@34123
|
870 |
KK.LE (KK.Cardinality ran_r, KK.Num explicit_max)
|
blanchet@34121
|
871 |
else
|
blanchet@34121
|
872 |
raise TOO_SMALL ("Nitpick_Kodkod.sel_axioms_for_constr",
|
blanchet@34121
|
873 |
"\"bits\" value " ^ string_of_int bits ^
|
blanchet@34121
|
874 |
" too small for \"max\"")
|
blanchet@33192
|
875 |
in
|
blanchet@33192
|
876 |
max_axiom ::
|
blanchet@35067
|
877 |
map (sel_axiom_for_sel hol_ctxt j0 kk rel_table ran_r constr)
|
blanchet@33192
|
878 |
(index_seq 0 (num_sels_for_constr_type (snd const)))
|
blanchet@33192
|
879 |
end
|
blanchet@33192
|
880 |
end
|
blanchet@35067
|
881 |
(* hol_context -> int -> int -> kodkod_constrs -> nut NameTable.table
|
blanchet@34123
|
882 |
-> dtype_spec -> KK.formula list *)
|
blanchet@35067
|
883 |
fun sel_axioms_for_datatype hol_ctxt bits j0 kk rel_table
|
blanchet@33192
|
884 |
({constrs, ...} : dtype_spec) =
|
blanchet@35067
|
885 |
maps (sel_axioms_for_constr hol_ctxt bits j0 kk rel_table) constrs
|
blanchet@33192
|
886 |
|
blanchet@35067
|
887 |
(* hol_context -> kodkod_constrs -> nut NameTable.table -> constr_spec
|
blanchet@34123
|
888 |
-> KK.formula list *)
|
blanchet@35067
|
889 |
fun uniqueness_axiom_for_constr hol_ctxt
|
blanchet@33192
|
890 |
({kk_all, kk_implies, kk_and, kk_rel_eq, kk_lone, kk_join, ...}
|
blanchet@33192
|
891 |
: kodkod_constrs) rel_table ({const, ...} : constr_spec) =
|
blanchet@33192
|
892 |
let
|
blanchet@34123
|
893 |
(* KK.rel_expr -> KK.formula *)
|
blanchet@33192
|
894 |
fun conjunct_for_sel r =
|
blanchet@34123
|
895 |
kk_rel_eq (kk_join (KK.Var (1, 0)) r) (kk_join (KK.Var (1, 1)) r)
|
blanchet@33192
|
896 |
val num_sels = num_sels_for_constr_type (snd const)
|
blanchet@33192
|
897 |
val triples = map (const_triple rel_table
|
blanchet@35067
|
898 |
o boxed_nth_sel_for_constr hol_ctxt const)
|
blanchet@33192
|
899 |
(~1 upto num_sels - 1)
|
blanchet@33192
|
900 |
val j0 = case triples |> hd |> #2 of
|
blanchet@33192
|
901 |
Func (Atom (_, j0), _) => j0
|
blanchet@33224
|
902 |
| R => raise REP ("Nitpick_Kodkod.uniqueness_axiom_for_constr",
|
blanchet@33224
|
903 |
[R])
|
blanchet@33192
|
904 |
val set_r = triples |> hd |> #1
|
blanchet@33192
|
905 |
in
|
blanchet@33192
|
906 |
if num_sels = 0 then
|
blanchet@33192
|
907 |
kk_lone set_r
|
blanchet@33192
|
908 |
else
|
blanchet@34123
|
909 |
kk_all (map (KK.DeclOne o rpair set_r o pair 1) [0, 1])
|
blanchet@33192
|
910 |
(kk_implies
|
blanchet@33192
|
911 |
(fold1 kk_and (map (conjunct_for_sel o #1) (tl triples)))
|
blanchet@34123
|
912 |
(kk_rel_eq (KK.Var (1, 0)) (KK.Var (1, 1))))
|
blanchet@33192
|
913 |
end
|
blanchet@35067
|
914 |
(* hol_context -> kodkod_constrs -> nut NameTable.table -> dtype_spec
|
blanchet@34123
|
915 |
-> KK.formula list *)
|
blanchet@35067
|
916 |
fun uniqueness_axioms_for_datatype hol_ctxt kk rel_table
|
blanchet@33192
|
917 |
({constrs, ...} : dtype_spec) =
|
blanchet@35067
|
918 |
map (uniqueness_axiom_for_constr hol_ctxt kk rel_table) constrs
|
blanchet@33192
|
919 |
|
blanchet@33192
|
920 |
(* constr_spec -> int *)
|
blanchet@33192
|
921 |
fun effective_constr_max ({delta, epsilon, ...} : constr_spec) = epsilon - delta
|
blanchet@33192
|
922 |
(* int -> kodkod_constrs -> nut NameTable.table -> dtype_spec
|
blanchet@34123
|
923 |
-> KK.formula list *)
|
blanchet@33192
|
924 |
fun partition_axioms_for_datatype j0 (kk as {kk_rel_eq, kk_union, ...})
|
blanchet@33192
|
925 |
rel_table
|
blanchet@33192
|
926 |
({card, constrs, ...} : dtype_spec) =
|
blanchet@33192
|
927 |
if forall #exclusive constrs then
|
blanchet@33192
|
928 |
[Integer.sum (map effective_constr_max constrs) = card |> formula_for_bool]
|
blanchet@33192
|
929 |
else
|
blanchet@33192
|
930 |
let val rs = map (discr_rel_expr rel_table o #const) constrs in
|
blanchet@34123
|
931 |
[kk_rel_eq (fold1 kk_union rs) (KK.AtomSeq (card, j0)),
|
blanchet@33192
|
932 |
kk_disjoint_sets kk rs]
|
blanchet@33192
|
933 |
end
|
blanchet@33192
|
934 |
|
blanchet@35067
|
935 |
(* hol_context -> int -> int Typtab.table -> kodkod_constrs
|
blanchet@34123
|
936 |
-> nut NameTable.table -> dtype_spec -> KK.formula list *)
|
blanchet@34969
|
937 |
fun other_axioms_for_datatype _ _ _ _ _ {deep = false, ...} = []
|
blanchet@35067
|
938 |
| other_axioms_for_datatype hol_ctxt bits ofs kk rel_table
|
blanchet@34121
|
939 |
(dtype as {typ, ...}) =
|
blanchet@33549
|
940 |
let val j0 = offset_of_type ofs typ in
|
blanchet@35067
|
941 |
sel_axioms_for_datatype hol_ctxt bits j0 kk rel_table dtype @
|
blanchet@35067
|
942 |
uniqueness_axioms_for_datatype hol_ctxt kk rel_table dtype @
|
blanchet@33549
|
943 |
partition_axioms_for_datatype j0 kk rel_table dtype
|
blanchet@33549
|
944 |
end
|
blanchet@33192
|
945 |
|
blanchet@35067
|
946 |
(* hol_context -> int -> int Typtab.table -> kodkod_constrs
|
blanchet@34123
|
947 |
-> nut NameTable.table -> dtype_spec list -> KK.formula list *)
|
blanchet@35067
|
948 |
fun declarative_axioms_for_datatypes hol_ctxt bits ofs kk rel_table dtypes =
|
blanchet@35067
|
949 |
acyclicity_axioms_for_datatypes hol_ctxt kk rel_table dtypes @
|
blanchet@35067
|
950 |
maps (other_axioms_for_datatype hol_ctxt bits ofs kk rel_table) dtypes
|
blanchet@33192
|
951 |
|
blanchet@34123
|
952 |
(* int -> int Typtab.table -> bool -> kodkod_constrs -> nut -> KK.formula *)
|
blanchet@34121
|
953 |
fun kodkod_formula_from_nut bits ofs liberal
|
blanchet@33192
|
954 |
(kk as {kk_all, kk_exist, kk_formula_let, kk_formula_if, kk_or, kk_not,
|
blanchet@35069
|
955 |
kk_iff, kk_implies, kk_and, kk_subset, kk_rel_eq, kk_no,
|
blanchet@35069
|
956 |
kk_lone, kk_one, kk_some, kk_rel_let, kk_rel_if, kk_union,
|
blanchet@35069
|
957 |
kk_difference, kk_intersect, kk_product, kk_join, kk_closure,
|
blanchet@35069
|
958 |
kk_comprehension, kk_project, kk_project_seq, kk_not3,
|
blanchet@35069
|
959 |
kk_nat_less, kk_int_less, ...}) u =
|
blanchet@33192
|
960 |
let
|
blanchet@33192
|
961 |
val main_j0 = offset_of_type ofs bool_T
|
blanchet@33192
|
962 |
val bool_j0 = main_j0
|
blanchet@33192
|
963 |
val bool_atom_R = Atom (2, main_j0)
|
blanchet@34123
|
964 |
val false_atom = KK.Atom bool_j0
|
blanchet@34123
|
965 |
val true_atom = KK.Atom (bool_j0 + 1)
|
blanchet@33192
|
966 |
|
blanchet@34123
|
967 |
(* polarity -> int -> KK.rel_expr -> KK.formula *)
|
blanchet@33192
|
968 |
fun formula_from_opt_atom polar j0 r =
|
blanchet@33192
|
969 |
case polar of
|
blanchet@34123
|
970 |
Neg => kk_not (kk_rel_eq r (KK.Atom j0))
|
blanchet@34123
|
971 |
| _ => kk_rel_eq r (KK.Atom (j0 + 1))
|
blanchet@34123
|
972 |
(* int -> KK.rel_expr -> KK.formula *)
|
blanchet@33192
|
973 |
val formula_from_atom = formula_from_opt_atom Pos
|
blanchet@33192
|
974 |
|
blanchet@34123
|
975 |
(* KK.formula -> KK.formula -> KK.formula *)
|
blanchet@33192
|
976 |
fun kk_notimplies f1 f2 = kk_and f1 (kk_not f2)
|
blanchet@34123
|
977 |
(* KK.rel_expr -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
978 |
val kk_or3 =
|
blanchet@34121
|
979 |
double_rel_rel_let kk
|
blanchet@33192
|
980 |
(fn r1 => fn r2 =>
|
blanchet@33192
|
981 |
kk_rel_if (kk_subset true_atom (kk_union r1 r2)) true_atom
|
blanchet@33192
|
982 |
(kk_intersect r1 r2))
|
blanchet@33192
|
983 |
val kk_and3 =
|
blanchet@34121
|
984 |
double_rel_rel_let kk
|
blanchet@33192
|
985 |
(fn r1 => fn r2 =>
|
blanchet@33192
|
986 |
kk_rel_if (kk_subset false_atom (kk_union r1 r2)) false_atom
|
blanchet@33192
|
987 |
(kk_intersect r1 r2))
|
blanchet@33192
|
988 |
fun kk_notimplies3 r1 r2 = kk_and3 r1 (kk_not3 r2)
|
blanchet@33192
|
989 |
|
blanchet@34123
|
990 |
(* int -> KK.rel_expr -> KK.formula list *)
|
blanchet@33192
|
991 |
val unpack_formulas =
|
blanchet@33192
|
992 |
map (formula_from_atom bool_j0) oo unpack_vect_in_chunks kk 1
|
blanchet@34123
|
993 |
(* (KK.formula -> KK.formula -> KK.formula) -> int -> KK.rel_expr
|
blanchet@34123
|
994 |
-> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
995 |
fun kk_vect_set_op connective k r1 r2 =
|
blanchet@33192
|
996 |
fold1 kk_product (map2 (atom_from_formula kk bool_j0 oo connective)
|
blanchet@33192
|
997 |
(unpack_formulas k r1) (unpack_formulas k r2))
|
blanchet@34123
|
998 |
(* (KK.formula -> KK.formula -> KK.formula) -> int -> KK.rel_expr
|
blanchet@34123
|
999 |
-> KK.rel_expr -> KK.formula *)
|
blanchet@33192
|
1000 |
fun kk_vect_set_bool_op connective k r1 r2 =
|
blanchet@33192
|
1001 |
fold1 kk_and (map2 connective (unpack_formulas k r1)
|
blanchet@33192
|
1002 |
(unpack_formulas k r2))
|
blanchet@33192
|
1003 |
|
blanchet@34123
|
1004 |
(* nut -> KK.formula *)
|
blanchet@33192
|
1005 |
fun to_f u =
|
blanchet@33192
|
1006 |
case rep_of u of
|
blanchet@33192
|
1007 |
Formula polar =>
|
blanchet@33192
|
1008 |
(case u of
|
blanchet@34123
|
1009 |
Cst (False, _, _) => KK.False
|
blanchet@34123
|
1010 |
| Cst (True, _, _) => KK.True
|
blanchet@33854
|
1011 |
| Op1 (Not, _, _, u1) =>
|
blanchet@33854
|
1012 |
kk_not (to_f_with_polarity (flip_polarity polar) u1)
|
blanchet@33192
|
1013 |
| Op1 (Finite, _, _, u1) =>
|
blanchet@33192
|
1014 |
let val opt1 = is_opt_rep (rep_of u1) in
|
blanchet@33192
|
1015 |
case polar of
|
blanchet@34923
|
1016 |
Neut =>
|
blanchet@34923
|
1017 |
if opt1 then raise NUT ("Nitpick_Kodkod.to_f (Finite)", [u])
|
blanchet@34923
|
1018 |
else KK.True
|
blanchet@33192
|
1019 |
| Pos => formula_for_bool (not opt1)
|
blanchet@34123
|
1020 |
| Neg => KK.True
|
blanchet@33192
|
1021 |
end
|
blanchet@34923
|
1022 |
| Op1 (IsUnknown, _, _, u1) => kk_no (to_r u1)
|
blanchet@33192
|
1023 |
| Op1 (Cast, _, _, u1) => to_f_with_polarity polar u1
|
blanchet@33854
|
1024 |
| Op2 (All, _, _, u1, u2) =>
|
blanchet@33854
|
1025 |
kk_all (untuple to_decl u1) (to_f_with_polarity polar u2)
|
blanchet@33854
|
1026 |
| Op2 (Exist, _, _, u1, u2) =>
|
blanchet@33854
|
1027 |
kk_exist (untuple to_decl u1) (to_f_with_polarity polar u2)
|
blanchet@33854
|
1028 |
| Op2 (Or, _, _, u1, u2) =>
|
blanchet@33854
|
1029 |
kk_or (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|
blanchet@33854
|
1030 |
| Op2 (And, _, _, u1, u2) =>
|
blanchet@33854
|
1031 |
kk_and (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|
blanchet@33192
|
1032 |
| Op2 (Less, T, Formula polar, u1, u2) =>
|
blanchet@33192
|
1033 |
formula_from_opt_atom polar bool_j0
|
blanchet@33192
|
1034 |
(to_r (Op2 (Less, T, Opt bool_atom_R, u1, u2)))
|
blanchet@33192
|
1035 |
| Op2 (Subset, _, _, u1, u2) =>
|
blanchet@33192
|
1036 |
let
|
blanchet@33192
|
1037 |
val dom_T = domain_type (type_of u1)
|
blanchet@33192
|
1038 |
val R1 = rep_of u1
|
blanchet@33192
|
1039 |
val R2 = rep_of u2
|
blanchet@33192
|
1040 |
val (dom_R, ran_R) =
|
blanchet@33192
|
1041 |
case min_rep R1 R2 of
|
blanchet@33192
|
1042 |
Func (Unit, R') =>
|
blanchet@33192
|
1043 |
(Atom (1, offset_of_type ofs dom_T), R')
|
blanchet@33192
|
1044 |
| Func Rp => Rp
|
blanchet@33192
|
1045 |
| R => (Atom (card_of_domain_from_rep 2 R,
|
blanchet@33192
|
1046 |
offset_of_type ofs dom_T),
|
blanchet@33192
|
1047 |
if is_opt_rep R then Opt bool_atom_R else Formula Neut)
|
blanchet@33192
|
1048 |
val set_R = Func (dom_R, ran_R)
|
blanchet@33192
|
1049 |
in
|
blanchet@33192
|
1050 |
if not (is_opt_rep ran_R) then
|
blanchet@33192
|
1051 |
to_set_bool_op kk_implies kk_subset u1 u2
|
blanchet@33192
|
1052 |
else if polar = Neut then
|
blanchet@33224
|
1053 |
raise NUT ("Nitpick_Kodkod.to_f (Subset)", [u])
|
blanchet@33192
|
1054 |
else
|
blanchet@33192
|
1055 |
let
|
blanchet@33886
|
1056 |
(* FIXME: merge with similar code below *)
|
blanchet@34123
|
1057 |
(* bool -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1058 |
fun set_to_r widen u =
|
blanchet@33192
|
1059 |
if widen then
|
blanchet@33192
|
1060 |
kk_difference (full_rel_for_rep dom_R)
|
blanchet@33192
|
1061 |
(kk_join (to_rep set_R u) false_atom)
|
blanchet@33192
|
1062 |
else
|
blanchet@33192
|
1063 |
kk_join (to_rep set_R u) true_atom
|
blanchet@33192
|
1064 |
val widen1 = (polar = Pos andalso is_opt_rep R1)
|
blanchet@33192
|
1065 |
val widen2 = (polar = Neg andalso is_opt_rep R2)
|
blanchet@33192
|
1066 |
in kk_subset (set_to_r widen1 u1) (set_to_r widen2 u2) end
|
blanchet@33192
|
1067 |
end
|
blanchet@33192
|
1068 |
| Op2 (DefEq, _, _, u1, u2) =>
|
blanchet@33192
|
1069 |
(case min_rep (rep_of u1) (rep_of u2) of
|
blanchet@34123
|
1070 |
Unit => KK.True
|
blanchet@33192
|
1071 |
| Formula polar =>
|
blanchet@33192
|
1072 |
kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|
blanchet@33192
|
1073 |
| min_R =>
|
blanchet@33192
|
1074 |
let
|
blanchet@33192
|
1075 |
(* nut -> nut list *)
|
blanchet@33192
|
1076 |
fun args (Op2 (Apply, _, _, u1, u2)) = u2 :: args u1
|
blanchet@33192
|
1077 |
| args (Tuple (_, _, us)) = us
|
blanchet@33192
|
1078 |
| args _ = []
|
blanchet@33192
|
1079 |
val opt_arg_us = filter (is_opt_rep o rep_of) (args u1)
|
blanchet@33192
|
1080 |
in
|
blanchet@34923
|
1081 |
if null opt_arg_us orelse not (is_Opt min_R) orelse
|
blanchet@34923
|
1082 |
is_eval_name u1 then
|
blanchet@33192
|
1083 |
fold (kk_or o (kk_no o to_r)) opt_arg_us
|
blanchet@33192
|
1084 |
(kk_rel_eq (to_rep min_R u1) (to_rep min_R u2))
|
blanchet@33192
|
1085 |
else
|
blanchet@34118
|
1086 |
kk_subset (to_rep min_R u1) (to_rep min_R u2)
|
blanchet@33192
|
1087 |
end)
|
blanchet@33192
|
1088 |
| Op2 (Eq, T, R, u1, u2) =>
|
blanchet@33192
|
1089 |
(case min_rep (rep_of u1) (rep_of u2) of
|
blanchet@34123
|
1090 |
Unit => KK.True
|
blanchet@33192
|
1091 |
| Formula polar =>
|
blanchet@33192
|
1092 |
kk_iff (to_f_with_polarity polar u1) (to_f_with_polarity polar u2)
|
blanchet@33192
|
1093 |
| min_R =>
|
blanchet@33192
|
1094 |
if is_opt_rep min_R then
|
blanchet@33192
|
1095 |
if polar = Neut then
|
blanchet@33192
|
1096 |
(* continuation of hackish optimization *)
|
blanchet@33192
|
1097 |
kk_rel_eq (to_rep min_R u1) (to_rep min_R u2)
|
blanchet@33192
|
1098 |
else if is_Cst Unrep u1 then
|
blanchet@33192
|
1099 |
to_could_be_unrep (polar = Neg) u2
|
blanchet@33192
|
1100 |
else if is_Cst Unrep u2 then
|
blanchet@33192
|
1101 |
to_could_be_unrep (polar = Neg) u1
|
blanchet@33192
|
1102 |
else
|
blanchet@33192
|
1103 |
let
|
blanchet@33192
|
1104 |
val r1 = to_rep min_R u1
|
blanchet@33192
|
1105 |
val r2 = to_rep min_R u2
|
blanchet@33192
|
1106 |
val both_opt = forall (is_opt_rep o rep_of) [u1, u2]
|
blanchet@33192
|
1107 |
in
|
blanchet@33192
|
1108 |
(if polar = Pos then
|
blanchet@33192
|
1109 |
if not both_opt then
|
blanchet@33192
|
1110 |
kk_rel_eq r1 r2
|
blanchet@34923
|
1111 |
else if is_lone_rep min_R andalso
|
blanchet@34923
|
1112 |
arity_of_rep min_R = 1 then
|
blanchet@33192
|
1113 |
kk_some (kk_intersect r1 r2)
|
blanchet@33192
|
1114 |
else
|
blanchet@33192
|
1115 |
raise SAME ()
|
blanchet@33192
|
1116 |
else
|
blanchet@33192
|
1117 |
if is_lone_rep min_R then
|
blanchet@33192
|
1118 |
if arity_of_rep min_R = 1 then
|
blanchet@35069
|
1119 |
kk_lone (kk_union r1 r2)
|
blanchet@33192
|
1120 |
else if not both_opt then
|
blanchet@33192
|
1121 |
(r1, r2) |> is_opt_rep (rep_of u2) ? swap
|
blanchet@34118
|
1122 |
|-> kk_subset
|
blanchet@33192
|
1123 |
else
|
blanchet@33192
|
1124 |
raise SAME ()
|
blanchet@33192
|
1125 |
else
|
blanchet@33192
|
1126 |
raise SAME ())
|
blanchet@33192
|
1127 |
handle SAME () =>
|
blanchet@33192
|
1128 |
formula_from_opt_atom polar bool_j0
|
blanchet@33192
|
1129 |
(to_guard [u1, u2] bool_atom_R
|
blanchet@33192
|
1130 |
(rel_expr_from_formula kk bool_atom_R
|
blanchet@33192
|
1131 |
(kk_rel_eq r1 r2)))
|
blanchet@33192
|
1132 |
end
|
blanchet@33192
|
1133 |
else
|
blanchet@33192
|
1134 |
let
|
blanchet@33192
|
1135 |
val r1 = to_rep min_R u1
|
blanchet@33192
|
1136 |
val r2 = to_rep min_R u2
|
blanchet@33192
|
1137 |
in
|
blanchet@33192
|
1138 |
if is_one_rep min_R then
|
blanchet@33192
|
1139 |
let
|
blanchet@33192
|
1140 |
val rs1 = unpack_products r1
|
blanchet@33192
|
1141 |
val rs2 = unpack_products r2
|
blanchet@33192
|
1142 |
in
|
blanchet@34923
|
1143 |
if length rs1 = length rs2 andalso
|
blanchet@34923
|
1144 |
map KK.arity_of_rel_expr rs1
|
blanchet@34923
|
1145 |
= map KK.arity_of_rel_expr rs2 then
|
blanchet@33192
|
1146 |
fold1 kk_and (map2 kk_subset rs1 rs2)
|
blanchet@33192
|
1147 |
else
|
blanchet@33192
|
1148 |
kk_subset r1 r2
|
blanchet@33192
|
1149 |
end
|
blanchet@33192
|
1150 |
else
|
blanchet@33192
|
1151 |
kk_rel_eq r1 r2
|
blanchet@33192
|
1152 |
end)
|
blanchet@33744
|
1153 |
| Op2 (The, T, _, u1, u2) =>
|
blanchet@33744
|
1154 |
to_f_with_polarity polar
|
blanchet@33744
|
1155 |
(Op2 (The, T, Opt (Atom (2, bool_j0)), u1, u2))
|
blanchet@33744
|
1156 |
| Op2 (Eps, T, _, u1, u2) =>
|
blanchet@33744
|
1157 |
to_f_with_polarity polar
|
blanchet@33744
|
1158 |
(Op2 (Eps, T, Opt (Atom (2, bool_j0)), u1, u2))
|
blanchet@33192
|
1159 |
| Op2 (Apply, T, _, u1, u2) =>
|
blanchet@33192
|
1160 |
(case (polar, rep_of u1) of
|
blanchet@33192
|
1161 |
(Neg, Func (R, Formula Neut)) => kk_subset (to_opt R u2) (to_r u1)
|
blanchet@33192
|
1162 |
| _ =>
|
blanchet@33192
|
1163 |
to_f_with_polarity polar
|
blanchet@33192
|
1164 |
(Op2 (Apply, T, Opt (Atom (2, offset_of_type ofs T)), u1, u2)))
|
blanchet@33192
|
1165 |
| Op3 (Let, _, _, u1, u2, u3) =>
|
blanchet@33854
|
1166 |
kk_formula_let [to_expr_assign u1 u2] (to_f_with_polarity polar u3)
|
blanchet@33192
|
1167 |
| Op3 (If, _, _, u1, u2, u3) =>
|
blanchet@33854
|
1168 |
kk_formula_if (to_f u1) (to_f_with_polarity polar u2)
|
blanchet@33854
|
1169 |
(to_f_with_polarity polar u3)
|
blanchet@34123
|
1170 |
| FormulaReg (j, _, _) => KK.FormulaReg j
|
blanchet@33224
|
1171 |
| _ => raise NUT ("Nitpick_Kodkod.to_f", [u]))
|
blanchet@33192
|
1172 |
| Atom (2, j0) => formula_from_atom j0 (to_r u)
|
blanchet@33224
|
1173 |
| _ => raise NUT ("Nitpick_Kodkod.to_f", [u])
|
blanchet@34123
|
1174 |
(* polarity -> nut -> KK.formula *)
|
blanchet@33192
|
1175 |
and to_f_with_polarity polar u =
|
blanchet@33192
|
1176 |
case rep_of u of
|
blanchet@33192
|
1177 |
Formula _ => to_f u
|
blanchet@33192
|
1178 |
| Atom (2, j0) => formula_from_atom j0 (to_r u)
|
blanchet@33192
|
1179 |
| Opt (Atom (2, j0)) => formula_from_opt_atom polar j0 (to_r u)
|
blanchet@33224
|
1180 |
| _ => raise NUT ("Nitpick_Kodkod.to_f_with_polarity", [u])
|
blanchet@34123
|
1181 |
(* nut -> KK.rel_expr *)
|
blanchet@33192
|
1182 |
and to_r u =
|
blanchet@33192
|
1183 |
case u of
|
blanchet@33192
|
1184 |
Cst (False, _, Atom _) => false_atom
|
blanchet@33192
|
1185 |
| Cst (True, _, Atom _) => true_atom
|
blanchet@33192
|
1186 |
| Cst (Iden, T, Func (Struct [R1, R2], Formula Neut)) =>
|
blanchet@33192
|
1187 |
if R1 = R2 andalso arity_of_rep R1 = 1 then
|
blanchet@34123
|
1188 |
kk_intersect KK.Iden (kk_product (full_rel_for_rep R1) KK.Univ)
|
blanchet@33192
|
1189 |
else
|
blanchet@33192
|
1190 |
let
|
blanchet@33192
|
1191 |
val schema1 = atom_schema_of_rep R1
|
blanchet@33192
|
1192 |
val schema2 = atom_schema_of_rep R2
|
blanchet@33192
|
1193 |
val arity1 = length schema1
|
blanchet@33192
|
1194 |
val arity2 = length schema2
|
blanchet@33192
|
1195 |
val r1 = fold1 kk_product (unary_var_seq 0 arity1)
|
blanchet@33192
|
1196 |
val r2 = fold1 kk_product (unary_var_seq arity1 arity2)
|
blanchet@33192
|
1197 |
val min_R = min_rep R1 R2
|
blanchet@33192
|
1198 |
in
|
blanchet@33192
|
1199 |
kk_comprehension
|
blanchet@33192
|
1200 |
(decls_for_atom_schema 0 (schema1 @ schema2))
|
blanchet@33192
|
1201 |
(kk_rel_eq (rel_expr_from_rel_expr kk min_R R1 r1)
|
blanchet@33192
|
1202 |
(rel_expr_from_rel_expr kk min_R R2 r2))
|
blanchet@33192
|
1203 |
end
|
blanchet@34123
|
1204 |
| Cst (Iden, T, Func (Atom (1, j0), Formula Neut)) => KK.Atom j0
|
blanchet@33192
|
1205 |
| Cst (Iden, T as Type ("fun", [T1, _]), R as Func (R1, _)) =>
|
blanchet@33192
|
1206 |
to_rep R (Cst (Iden, T, Func (one_rep ofs T1 R1, Formula Neut)))
|
blanchet@34121
|
1207 |
| Cst (Num j, T, R) =>
|
blanchet@34121
|
1208 |
if is_word_type T then
|
blanchet@34123
|
1209 |
atom_from_int_expr kk T R (KK.Num j)
|
blanchet@34121
|
1210 |
else if T = int_T then
|
blanchet@34121
|
1211 |
case atom_for_int (card_of_rep R, offset_of_type ofs int_T) j of
|
blanchet@34123
|
1212 |
~1 => if is_opt_rep R then KK.None
|
blanchet@33224
|
1213 |
else raise NUT ("Nitpick_Kodkod.to_r (Num)", [u])
|
blanchet@34123
|
1214 |
| j' => KK.Atom j'
|
blanchet@34121
|
1215 |
else
|
blanchet@34123
|
1216 |
if j < card_of_rep R then KK.Atom (j + offset_of_type ofs T)
|
blanchet@34123
|
1217 |
else if is_opt_rep R then KK.None
|
blanchet@34121
|
1218 |
else raise NUT ("Nitpick_Kodkod.to_r (Num)", [u])
|
blanchet@33192
|
1219 |
| Cst (Unknown, _, R) => empty_rel_for_rep R
|
blanchet@33192
|
1220 |
| Cst (Unrep, _, R) => empty_rel_for_rep R
|
blanchet@34123
|
1221 |
| Cst (Suc, T as @{typ "unsigned_bit word => unsigned_bit word"}, R) =>
|
blanchet@34123
|
1222 |
to_bit_word_unary_op T R (curry KK.Add (KK.Num 1))
|
blanchet@34123
|
1223 |
| Cst (Suc, @{typ "nat => nat"}, Func (Atom x, _)) =>
|
blanchet@34123
|
1224 |
kk_intersect (KK.Rel suc_rel) (kk_product KK.Univ (KK.AtomSeq x))
|
blanchet@34123
|
1225 |
| Cst (Suc, _, Func (Atom x, _)) => KK.Rel suc_rel
|
blanchet@34123
|
1226 |
| Cst (Add, Type ("fun", [@{typ nat}, _]), _) => KK.Rel nat_add_rel
|
blanchet@34123
|
1227 |
| Cst (Add, Type ("fun", [@{typ int}, _]), _) => KK.Rel int_add_rel
|
blanchet@34121
|
1228 |
| Cst (Add, T as Type ("fun", [@{typ "unsigned_bit word"}, _]), R) =>
|
blanchet@34123
|
1229 |
to_bit_word_binary_op T R NONE (SOME (curry KK.Add))
|
blanchet@34121
|
1230 |
| Cst (Add, T as Type ("fun", [@{typ "signed_bit word"}, _]), R) =>
|
blanchet@34121
|
1231 |
to_bit_word_binary_op T R
|
blanchet@34121
|
1232 |
(SOME (fn i1 => fn i2 => fn i3 =>
|
blanchet@34123
|
1233 |
kk_implies (KK.LE (KK.Num 0, KK.BitXor (i1, i2)))
|
blanchet@34123
|
1234 |
(KK.LE (KK.Num 0, KK.BitXor (i2, i3)))))
|
blanchet@34123
|
1235 |
(SOME (curry KK.Add))
|
blanchet@34121
|
1236 |
| Cst (Subtract, Type ("fun", [@{typ nat}, _]), _) =>
|
blanchet@34123
|
1237 |
KK.Rel nat_subtract_rel
|
blanchet@34121
|
1238 |
| Cst (Subtract, Type ("fun", [@{typ int}, _]), _) =>
|
blanchet@34123
|
1239 |
KK.Rel int_subtract_rel
|
blanchet@34121
|
1240 |
| Cst (Subtract, T as Type ("fun", [@{typ "unsigned_bit word"}, _]), R) =>
|
blanchet@34121
|
1241 |
to_bit_word_binary_op T R NONE
|
blanchet@34121
|
1242 |
(SOME (fn i1 => fn i2 =>
|
blanchet@34123
|
1243 |
KK.IntIf (KK.LE (i1, i2), KK.Num 0, KK.Sub (i1, i2))))
|
blanchet@34121
|
1244 |
| Cst (Subtract, T as Type ("fun", [@{typ "signed_bit word"}, _]), R) =>
|
blanchet@34121
|
1245 |
to_bit_word_binary_op T R
|
blanchet@34121
|
1246 |
(SOME (fn i1 => fn i2 => fn i3 =>
|
blanchet@34123
|
1247 |
kk_implies (KK.LT (KK.BitXor (i1, i2), KK.Num 0))
|
blanchet@34123
|
1248 |
(KK.LT (KK.BitXor (i2, i3), KK.Num 0))))
|
blanchet@34123
|
1249 |
(SOME (curry KK.Sub))
|
blanchet@34121
|
1250 |
| Cst (Multiply, Type ("fun", [@{typ nat}, _]), _) =>
|
blanchet@34123
|
1251 |
KK.Rel nat_multiply_rel
|
blanchet@34121
|
1252 |
| Cst (Multiply, Type ("fun", [@{typ int}, _]), _) =>
|
blanchet@34123
|
1253 |
KK.Rel int_multiply_rel
|
blanchet@34121
|
1254 |
| Cst (Multiply,
|
blanchet@34121
|
1255 |
T as Type ("fun", [Type (@{type_name word}, [bit_T]), _]), R) =>
|
blanchet@34121
|
1256 |
to_bit_word_binary_op T R
|
blanchet@34121
|
1257 |
(SOME (fn i1 => fn i2 => fn i3 =>
|
blanchet@34123
|
1258 |
kk_or (KK.IntEq (i2, KK.Num 0))
|
blanchet@34123
|
1259 |
(KK.IntEq (KK.Div (i3, i2), i1)
|
blanchet@34121
|
1260 |
|> bit_T = @{typ signed_bit}
|
blanchet@34123
|
1261 |
? kk_and (KK.LE (KK.Num 0,
|
blanchet@34123
|
1262 |
foldl1 KK.BitAnd [i1, i2, i3])))))
|
blanchet@34123
|
1263 |
(SOME (curry KK.Mult))
|
blanchet@34123
|
1264 |
| Cst (Divide, Type ("fun", [@{typ nat}, _]), _) => KK.Rel nat_divide_rel
|
blanchet@34123
|
1265 |
| Cst (Divide, Type ("fun", [@{typ int}, _]), _) => KK.Rel int_divide_rel
|
blanchet@34121
|
1266 |
| Cst (Divide, T as Type ("fun", [@{typ "unsigned_bit word"}, _]), R) =>
|
blanchet@34121
|
1267 |
to_bit_word_binary_op T R NONE
|
blanchet@34121
|
1268 |
(SOME (fn i1 => fn i2 =>
|
blanchet@34123
|
1269 |
KK.IntIf (KK.IntEq (i2, KK.Num 0),
|
blanchet@34123
|
1270 |
KK.Num 0, KK.Div (i1, i2))))
|
blanchet@34121
|
1271 |
| Cst (Divide, T as Type ("fun", [@{typ "signed_bit word"}, _]), R) =>
|
blanchet@34121
|
1272 |
to_bit_word_binary_op T R
|
blanchet@34121
|
1273 |
(SOME (fn i1 => fn i2 => fn i3 =>
|
blanchet@34123
|
1274 |
KK.LE (KK.Num 0, foldl1 KK.BitAnd [i1, i2, i3])))
|
blanchet@34121
|
1275 |
(SOME (fn i1 => fn i2 =>
|
blanchet@34123
|
1276 |
KK.IntIf (kk_and (KK.LT (i1, KK.Num 0))
|
blanchet@34123
|
1277 |
(KK.LT (KK.Num 0, i2)),
|
blanchet@34123
|
1278 |
KK.Sub (KK.Div (KK.Add (i1, KK.Num 1), i2), KK.Num 1),
|
blanchet@34123
|
1279 |
KK.IntIf (kk_and (KK.LT (KK.Num 0, i1))
|
blanchet@34123
|
1280 |
(KK.LT (i2, KK.Num 0)),
|
blanchet@34123
|
1281 |
KK.Sub (KK.Div (KK.Sub (i1, KK.Num 1), i2), KK.Num 1),
|
blanchet@34123
|
1282 |
KK.IntIf (KK.IntEq (i2, KK.Num 0),
|
blanchet@34123
|
1283 |
KK.Num 0, KK.Div (i1, i2))))))
|
blanchet@34123
|
1284 |
| Cst (Gcd, _, _) => KK.Rel gcd_rel
|
blanchet@34123
|
1285 |
| Cst (Lcm, _, _) => KK.Rel lcm_rel
|
blanchet@34123
|
1286 |
| Cst (Fracs, _, Func (Atom (1, _), _)) => KK.None
|
blanchet@33192
|
1287 |
| Cst (Fracs, _, Func (Struct _, _)) =>
|
blanchet@34123
|
1288 |
kk_project_seq (KK.Rel norm_frac_rel) 2 2
|
blanchet@34123
|
1289 |
| Cst (NormFrac, _, _) => KK.Rel norm_frac_rel
|
blanchet@34121
|
1290 |
| Cst (NatToInt, Type ("fun", [@{typ nat}, _]), Func (Atom _, Atom _)) =>
|
blanchet@34123
|
1291 |
KK.Iden
|
blanchet@34121
|
1292 |
| Cst (NatToInt, Type ("fun", [@{typ nat}, _]),
|
blanchet@33192
|
1293 |
Func (Atom (nat_k, nat_j0), Opt (Atom (int_k, int_j0)))) =>
|
blanchet@33192
|
1294 |
if nat_j0 = int_j0 then
|
blanchet@34123
|
1295 |
kk_intersect KK.Iden
|
blanchet@34123
|
1296 |
(kk_product (KK.AtomSeq (max_int_for_card int_k + 1, nat_j0))
|
blanchet@34123
|
1297 |
KK.Univ)
|
blanchet@33192
|
1298 |
else
|
blanchet@33224
|
1299 |
raise BAD ("Nitpick_Kodkod.to_r (NatToInt)", "\"nat_j0 <> int_j0\"")
|
blanchet@34121
|
1300 |
| Cst (NatToInt, T as Type ("fun", [@{typ "unsigned_bit word"}, _]), R) =>
|
blanchet@34121
|
1301 |
to_bit_word_unary_op T R I
|
blanchet@34121
|
1302 |
| Cst (IntToNat, Type ("fun", [@{typ int}, _]),
|
blanchet@34121
|
1303 |
Func (Atom (int_k, int_j0), nat_R)) =>
|
blanchet@33192
|
1304 |
let
|
blanchet@33192
|
1305 |
val abs_card = max_int_for_card int_k + 1
|
blanchet@33192
|
1306 |
val (nat_k, nat_j0) = the_single (atom_schema_of_rep nat_R)
|
blanchet@33192
|
1307 |
val overlap = Int.min (nat_k, abs_card)
|
blanchet@33192
|
1308 |
in
|
blanchet@33192
|
1309 |
if nat_j0 = int_j0 then
|
blanchet@34123
|
1310 |
kk_union (kk_product (KK.AtomSeq (int_k - abs_card,
|
blanchet@34123
|
1311 |
int_j0 + abs_card))
|
blanchet@34123
|
1312 |
(KK.Atom nat_j0))
|
blanchet@34123
|
1313 |
(kk_intersect KK.Iden
|
blanchet@34123
|
1314 |
(kk_product (KK.AtomSeq (overlap, int_j0)) KK.Univ))
|
blanchet@33192
|
1315 |
else
|
blanchet@33224
|
1316 |
raise BAD ("Nitpick_Kodkod.to_r (IntToNat)", "\"nat_j0 <> int_j0\"")
|
blanchet@33192
|
1317 |
end
|
blanchet@34121
|
1318 |
| Cst (IntToNat, T as Type ("fun", [@{typ "signed_bit word"}, _]), R) =>
|
blanchet@34121
|
1319 |
to_bit_word_unary_op T R
|
blanchet@34123
|
1320 |
(fn i => KK.IntIf (KK.LE (i, KK.Num 0), KK.Num 0, i))
|
blanchet@33192
|
1321 |
| Op1 (Not, _, R, u1) => kk_not3 (to_rep R u1)
|
blanchet@34123
|
1322 |
| Op1 (Finite, _, Opt (Atom _), _) => KK.None
|
blanchet@33192
|
1323 |
| Op1 (Converse, T, R, u1) =>
|
blanchet@33192
|
1324 |
let
|
blanchet@33192
|
1325 |
val (b_T, a_T) = HOLogic.dest_prodT (domain_type T)
|
blanchet@33192
|
1326 |
val (b_R, a_R) =
|
blanchet@33192
|
1327 |
case R of
|
blanchet@33192
|
1328 |
Func (Struct [R1, R2], _) => (R1, R2)
|
blanchet@33192
|
1329 |
| Func (R1, _) =>
|
blanchet@33192
|
1330 |
if card_of_rep R1 <> 1 then
|
blanchet@33224
|
1331 |
raise REP ("Nitpick_Kodkod.to_r (Converse)", [R])
|
blanchet@33192
|
1332 |
else
|
blanchet@33192
|
1333 |
pairself (Atom o pair 1 o offset_of_type ofs) (b_T, a_T)
|
blanchet@33224
|
1334 |
| _ => raise REP ("Nitpick_Kodkod.to_r (Converse)", [R])
|
blanchet@33192
|
1335 |
val body_R = body_rep R
|
blanchet@33192
|
1336 |
val a_arity = arity_of_rep a_R
|
blanchet@33192
|
1337 |
val b_arity = arity_of_rep b_R
|
blanchet@33192
|
1338 |
val ab_arity = a_arity + b_arity
|
blanchet@33192
|
1339 |
val body_arity = arity_of_rep body_R
|
blanchet@33192
|
1340 |
in
|
blanchet@33192
|
1341 |
kk_project (to_rep (Func (Struct [a_R, b_R], body_R)) u1)
|
blanchet@34123
|
1342 |
(map KK.Num (index_seq a_arity b_arity @
|
blanchet@34123
|
1343 |
index_seq 0 a_arity @
|
blanchet@34123
|
1344 |
index_seq ab_arity body_arity))
|
blanchet@33192
|
1345 |
|> rel_expr_from_rel_expr kk R (Func (Struct [b_R, a_R], body_R))
|
blanchet@33192
|
1346 |
end
|
blanchet@33192
|
1347 |
| Op1 (Closure, _, R, u1) =>
|
blanchet@33192
|
1348 |
if is_opt_rep R then
|
blanchet@33192
|
1349 |
let
|
blanchet@33192
|
1350 |
val T1 = type_of u1
|
blanchet@33192
|
1351 |
val R' = rep_to_binary_rel_rep ofs T1 (unopt_rep (rep_of u1))
|
blanchet@33192
|
1352 |
val R'' = opt_rep ofs T1 R'
|
blanchet@33192
|
1353 |
in
|
blanchet@34121
|
1354 |
single_rel_rel_let kk
|
blanchet@33192
|
1355 |
(fn r =>
|
blanchet@33192
|
1356 |
let
|
blanchet@33192
|
1357 |
val true_r = kk_closure (kk_join r true_atom)
|
blanchet@33192
|
1358 |
val full_r = full_rel_for_rep R'
|
blanchet@33192
|
1359 |
val false_r = kk_difference full_r
|
blanchet@33192
|
1360 |
(kk_closure (kk_difference full_r
|
blanchet@33192
|
1361 |
(kk_join r false_atom)))
|
blanchet@33192
|
1362 |
in
|
blanchet@33192
|
1363 |
rel_expr_from_rel_expr kk R R''
|
blanchet@33192
|
1364 |
(kk_union (kk_product true_r true_atom)
|
blanchet@33192
|
1365 |
(kk_product false_r false_atom))
|
blanchet@33192
|
1366 |
end) (to_rep R'' u1)
|
blanchet@33192
|
1367 |
end
|
blanchet@33192
|
1368 |
else
|
blanchet@33192
|
1369 |
let val R' = rep_to_binary_rel_rep ofs (type_of u1) (rep_of u1) in
|
blanchet@33192
|
1370 |
rel_expr_from_rel_expr kk R R' (kk_closure (to_rep R' u1))
|
blanchet@33192
|
1371 |
end
|
blanchet@33192
|
1372 |
| Op1 (SingletonSet, _, Func (R1, Opt _), Cst (Unrep, _, _)) =>
|
blanchet@33192
|
1373 |
(if R1 = Unit then I else kk_product (full_rel_for_rep R1)) false_atom
|
blanchet@33192
|
1374 |
| Op1 (SingletonSet, _, R, u1) =>
|
blanchet@33192
|
1375 |
(case R of
|
blanchet@33192
|
1376 |
Func (R1, Formula Neut) => to_rep R1 u1
|
blanchet@33192
|
1377 |
| Func (Unit, Opt R) => to_guard [u1] R true_atom
|
blanchet@33192
|
1378 |
| Func (R1, R2 as Opt _) =>
|
blanchet@34121
|
1379 |
single_rel_rel_let kk
|
blanchet@33192
|
1380 |
(fn r => kk_rel_if (kk_no r) (empty_rel_for_rep R)
|
blanchet@33192
|
1381 |
(rel_expr_to_func kk R1 bool_atom_R
|
blanchet@33192
|
1382 |
(Func (R1, Formula Neut)) r))
|
blanchet@33192
|
1383 |
(to_opt R1 u1)
|
blanchet@33224
|
1384 |
| _ => raise NUT ("Nitpick_Kodkod.to_r (SingletonSet)", [u]))
|
blanchet@33192
|
1385 |
| Op1 (Tha, T, R, u1) =>
|
blanchet@33192
|
1386 |
if is_opt_rep R then
|
blanchet@33192
|
1387 |
kk_join (to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1) true_atom
|
blanchet@33192
|
1388 |
else
|
blanchet@33192
|
1389 |
to_rep (Func (R, Formula Neut)) u1
|
blanchet@33192
|
1390 |
| Op1 (First, T, R, u1) => to_nth_pair_sel 0 T R u1
|
blanchet@33192
|
1391 |
| Op1 (Second, T, R, u1) => to_nth_pair_sel 1 T R u1
|
blanchet@33192
|
1392 |
| Op1 (Cast, _, R, u1) =>
|
blanchet@33192
|
1393 |
((case rep_of u1 of
|
blanchet@33192
|
1394 |
Formula _ =>
|
blanchet@33192
|
1395 |
(case unopt_rep R of
|
blanchet@33192
|
1396 |
Atom (2, j0) => atom_from_formula kk j0 (to_f u1)
|
blanchet@33192
|
1397 |
| _ => raise SAME ())
|
blanchet@33192
|
1398 |
| _ => raise SAME ())
|
blanchet@33192
|
1399 |
handle SAME () => rel_expr_from_rel_expr kk R (rep_of u1) (to_r u1))
|
blanchet@33192
|
1400 |
| Op2 (All, T, R as Opt _, u1, u2) =>
|
blanchet@33192
|
1401 |
to_r (Op1 (Not, T, R,
|
blanchet@33192
|
1402 |
Op2 (Exist, T, R, u1, Op1 (Not, T, rep_of u2, u2))))
|
blanchet@33192
|
1403 |
| Op2 (Exist, T, Opt _, u1, u2) =>
|
blanchet@33192
|
1404 |
let val rs1 = untuple to_decl u1 in
|
blanchet@33192
|
1405 |
if not (is_opt_rep (rep_of u2)) then
|
blanchet@34123
|
1406 |
kk_rel_if (kk_exist rs1 (to_f u2)) true_atom KK.None
|
blanchet@33192
|
1407 |
else
|
blanchet@33192
|
1408 |
let val r2 = to_r u2 in
|
blanchet@33192
|
1409 |
kk_union (kk_rel_if (kk_exist rs1 (kk_rel_eq r2 true_atom))
|
blanchet@34123
|
1410 |
true_atom KK.None)
|
blanchet@33192
|
1411 |
(kk_rel_if (kk_all rs1 (kk_rel_eq r2 false_atom))
|
blanchet@34123
|
1412 |
false_atom KK.None)
|
blanchet@33192
|
1413 |
end
|
blanchet@33192
|
1414 |
end
|
blanchet@33192
|
1415 |
| Op2 (Or, _, _, u1, u2) =>
|
blanchet@33192
|
1416 |
if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) true_atom (to_r u1)
|
blanchet@33192
|
1417 |
else kk_rel_if (to_f u1) true_atom (to_r u2)
|
blanchet@33192
|
1418 |
| Op2 (And, _, _, u1, u2) =>
|
blanchet@33192
|
1419 |
if is_opt_rep (rep_of u1) then kk_rel_if (to_f u2) (to_r u1) false_atom
|
blanchet@33192
|
1420 |
else kk_rel_if (to_f u1) (to_r u2) false_atom
|
blanchet@33192
|
1421 |
| Op2 (Less, _, _, u1, u2) =>
|
blanchet@34121
|
1422 |
(case type_of u1 of
|
blanchet@34121
|
1423 |
@{typ nat} =>
|
blanchet@34121
|
1424 |
if is_Cst Unrep u1 then to_compare_with_unrep u2 false_atom
|
blanchet@34121
|
1425 |
else if is_Cst Unrep u2 then to_compare_with_unrep u1 true_atom
|
blanchet@34121
|
1426 |
else kk_nat_less (to_integer u1) (to_integer u2)
|
blanchet@34121
|
1427 |
| @{typ int} => kk_int_less (to_integer u1) (to_integer u2)
|
blanchet@34121
|
1428 |
| _ => double_rel_rel_let kk
|
blanchet@34121
|
1429 |
(fn r1 => fn r2 =>
|
blanchet@34121
|
1430 |
kk_rel_if
|
blanchet@34121
|
1431 |
(fold kk_and (map_filter (fn (u, r) =>
|
blanchet@34121
|
1432 |
if is_opt_rep (rep_of u) then SOME (kk_some r)
|
blanchet@34123
|
1433 |
else NONE) [(u1, r1), (u2, r2)]) KK.True)
|
blanchet@34123
|
1434 |
(atom_from_formula kk bool_j0 (KK.LT (pairself
|
blanchet@34121
|
1435 |
(int_expr_from_atom kk (type_of u1)) (r1, r2))))
|
blanchet@34123
|
1436 |
KK.None)
|
blanchet@34121
|
1437 |
(to_r u1) (to_r u2))
|
blanchet@33192
|
1438 |
| Op2 (The, T, R, u1, u2) =>
|
blanchet@33192
|
1439 |
if is_opt_rep R then
|
blanchet@33192
|
1440 |
let val r1 = to_opt (Func (unopt_rep R, bool_atom_R)) u1 in
|
blanchet@33192
|
1441 |
kk_rel_if (kk_one (kk_join r1 true_atom)) (kk_join r1 true_atom)
|
blanchet@33192
|
1442 |
(kk_rel_if (kk_or (kk_some (kk_join r1 true_atom))
|
blanchet@33192
|
1443 |
(kk_subset (full_rel_for_rep R)
|
blanchet@33192
|
1444 |
(kk_join r1 false_atom)))
|
blanchet@33892
|
1445 |
(to_rep R u2) (empty_rel_for_rep R))
|
blanchet@33192
|
1446 |
end
|
blanchet@33192
|
1447 |
else
|
blanchet@33192
|
1448 |
let val r1 = to_rep (Func (R, Formula Neut)) u1 in
|
blanchet@33192
|
1449 |
kk_rel_if (kk_one r1) r1 (to_rep R u2)
|
blanchet@33192
|
1450 |
end
|
blanchet@33192
|
1451 |
| Op2 (Eps, T, R, u1, u2) =>
|
blanchet@33192
|
1452 |
if is_opt_rep (rep_of u1) then
|
blanchet@33192
|
1453 |
let
|
blanchet@33192
|
1454 |
val r1 = to_rep (Func (unopt_rep R, Opt bool_atom_R)) u1
|
blanchet@33192
|
1455 |
val r2 = to_rep R u2
|
blanchet@33192
|
1456 |
in
|
blanchet@33192
|
1457 |
kk_union (kk_rel_if (kk_one (kk_join r1 true_atom))
|
blanchet@33892
|
1458 |
(kk_join r1 true_atom) (empty_rel_for_rep R))
|
blanchet@33192
|
1459 |
(kk_rel_if (kk_or (kk_subset r2 (kk_join r1 true_atom))
|
blanchet@33192
|
1460 |
(kk_subset (full_rel_for_rep R)
|
blanchet@33192
|
1461 |
(kk_join r1 false_atom)))
|
blanchet@33892
|
1462 |
r2 (empty_rel_for_rep R))
|
blanchet@33192
|
1463 |
end
|
blanchet@33192
|
1464 |
else
|
blanchet@33192
|
1465 |
let
|
blanchet@33192
|
1466 |
val r1 = to_rep (Func (unopt_rep R, Formula Neut)) u1
|
blanchet@33192
|
1467 |
val r2 = to_rep R u2
|
blanchet@33192
|
1468 |
in
|
blanchet@33892
|
1469 |
kk_union (kk_rel_if (kk_one r1) r1 (empty_rel_for_rep R))
|
blanchet@33192
|
1470 |
(kk_rel_if (kk_or (kk_no r1) (kk_subset r2 r1))
|
blanchet@33892
|
1471 |
r2 (empty_rel_for_rep R))
|
blanchet@33192
|
1472 |
end
|
blanchet@33192
|
1473 |
| Op2 (Triad, T, Opt (Atom (2, j0)), u1, u2) =>
|
blanchet@33192
|
1474 |
let
|
blanchet@33192
|
1475 |
val f1 = to_f u1
|
blanchet@33192
|
1476 |
val f2 = to_f u2
|
blanchet@33192
|
1477 |
in
|
blanchet@33192
|
1478 |
if f1 = f2 then
|
blanchet@33192
|
1479 |
atom_from_formula kk j0 f1
|
blanchet@33192
|
1480 |
else
|
blanchet@34123
|
1481 |
kk_union (kk_rel_if f1 true_atom KK.None)
|
blanchet@34123
|
1482 |
(kk_rel_if f2 KK.None false_atom)
|
blanchet@33192
|
1483 |
end
|
blanchet@33192
|
1484 |
| Op2 (Union, _, R, u1, u2) =>
|
blanchet@33192
|
1485 |
to_set_op kk_or kk_or3 kk_union kk_union kk_intersect false R u1 u2
|
blanchet@33192
|
1486 |
| Op2 (SetDifference, _, R, u1, u2) =>
|
blanchet@33192
|
1487 |
to_set_op kk_notimplies kk_notimplies3 kk_difference kk_intersect
|
blanchet@33192
|
1488 |
kk_union true R u1 u2
|
blanchet@33192
|
1489 |
| Op2 (Intersect, _, R, u1, u2) =>
|
blanchet@33192
|
1490 |
to_set_op kk_and kk_and3 kk_intersect kk_intersect kk_union false R
|
blanchet@33192
|
1491 |
u1 u2
|
blanchet@33192
|
1492 |
| Op2 (Composition, _, R, u1, u2) =>
|
blanchet@33192
|
1493 |
let
|
blanchet@33863
|
1494 |
val (a_T, b_T) = HOLogic.dest_prodT (domain_type (type_of u1))
|
blanchet@33863
|
1495 |
val (_, c_T) = HOLogic.dest_prodT (domain_type (type_of u2))
|
blanchet@33863
|
1496 |
val ab_k = card_of_domain_from_rep 2 (rep_of u1)
|
blanchet@33863
|
1497 |
val bc_k = card_of_domain_from_rep 2 (rep_of u2)
|
blanchet@33192
|
1498 |
val ac_k = card_of_domain_from_rep 2 R
|
blanchet@33192
|
1499 |
val a_k = exact_root 2 (ac_k * ab_k div bc_k)
|
blanchet@33192
|
1500 |
val b_k = exact_root 2 (ab_k * bc_k div ac_k)
|
blanchet@33192
|
1501 |
val c_k = exact_root 2 (bc_k * ac_k div ab_k)
|
blanchet@33192
|
1502 |
val a_R = Atom (a_k, offset_of_type ofs a_T)
|
blanchet@33192
|
1503 |
val b_R = Atom (b_k, offset_of_type ofs b_T)
|
blanchet@33192
|
1504 |
val c_R = Atom (c_k, offset_of_type ofs c_T)
|
blanchet@33192
|
1505 |
val body_R = body_rep R
|
blanchet@33192
|
1506 |
in
|
blanchet@33192
|
1507 |
(case body_R of
|
blanchet@33192
|
1508 |
Formula Neut =>
|
blanchet@33863
|
1509 |
kk_join (to_rep (Func (Struct [a_R, b_R], Formula Neut)) u1)
|
blanchet@33863
|
1510 |
(to_rep (Func (Struct [b_R, c_R], Formula Neut)) u2)
|
blanchet@33192
|
1511 |
| Opt (Atom (2, _)) =>
|
blanchet@33192
|
1512 |
let
|
blanchet@33886
|
1513 |
(* FIXME: merge with similar code above *)
|
blanchet@34123
|
1514 |
(* rep -> rep -> nut -> KK.rel_expr *)
|
blanchet@33886
|
1515 |
fun must R1 R2 u =
|
blanchet@33886
|
1516 |
kk_join (to_rep (Func (Struct [R1, R2], body_R)) u) true_atom
|
blanchet@33886
|
1517 |
fun may R1 R2 u =
|
blanchet@33886
|
1518 |
kk_difference
|
blanchet@33886
|
1519 |
(full_rel_for_rep (Struct [R1, R2]))
|
blanchet@33886
|
1520 |
(kk_join (to_rep (Func (Struct [R1, R2], body_R)) u)
|
blanchet@33886
|
1521 |
false_atom)
|
blanchet@33886
|
1522 |
in
|
blanchet@33886
|
1523 |
kk_union
|
blanchet@33886
|
1524 |
(kk_product (kk_join (must a_R b_R u1) (must b_R c_R u2))
|
blanchet@33886
|
1525 |
true_atom)
|
blanchet@33886
|
1526 |
(kk_product (kk_difference
|
blanchet@33886
|
1527 |
(full_rel_for_rep (Struct [a_R, c_R]))
|
blanchet@33886
|
1528 |
(kk_join (may a_R b_R u1) (may b_R c_R u2)))
|
blanchet@33886
|
1529 |
false_atom)
|
blanchet@33886
|
1530 |
end
|
blanchet@33224
|
1531 |
| _ => raise NUT ("Nitpick_Kodkod.to_r (Composition)", [u]))
|
blanchet@33192
|
1532 |
|> rel_expr_from_rel_expr kk R (Func (Struct [a_R, c_R], body_R))
|
blanchet@33192
|
1533 |
end
|
blanchet@33192
|
1534 |
| Op2 (Product, T, R, u1, u2) =>
|
blanchet@33192
|
1535 |
let
|
blanchet@33192
|
1536 |
val (a_T, b_T) = HOLogic.dest_prodT (domain_type T)
|
blanchet@33192
|
1537 |
val a_k = card_of_domain_from_rep 2 (rep_of u1)
|
blanchet@33192
|
1538 |
val b_k = card_of_domain_from_rep 2 (rep_of u2)
|
blanchet@33192
|
1539 |
val a_R = Atom (a_k, offset_of_type ofs a_T)
|
blanchet@33192
|
1540 |
val b_R = Atom (b_k, offset_of_type ofs b_T)
|
blanchet@33192
|
1541 |
val body_R = body_rep R
|
blanchet@33192
|
1542 |
in
|
blanchet@33192
|
1543 |
(case body_R of
|
blanchet@33192
|
1544 |
Formula Neut =>
|
blanchet@33192
|
1545 |
kk_product (to_rep (Func (a_R, Formula Neut)) u1)
|
blanchet@33192
|
1546 |
(to_rep (Func (b_R, Formula Neut)) u2)
|
blanchet@33192
|
1547 |
| Opt (Atom (2, _)) =>
|
blanchet@33192
|
1548 |
let
|
blanchet@34123
|
1549 |
(* KK.rel_expr -> rep -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1550 |
fun do_nut r R u = kk_join (to_rep (Func (R, body_R)) u) r
|
blanchet@34123
|
1551 |
(* KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
1552 |
fun do_term r =
|
blanchet@33192
|
1553 |
kk_product (kk_product (do_nut r a_R u1) (do_nut r b_R u2)) r
|
blanchet@33192
|
1554 |
in kk_union (do_term true_atom) (do_term false_atom) end
|
blanchet@33224
|
1555 |
| _ => raise NUT ("Nitpick_Kodkod.to_r (Product)", [u]))
|
blanchet@33192
|
1556 |
|> rel_expr_from_rel_expr kk R (Func (Struct [a_R, b_R], body_R))
|
blanchet@33192
|
1557 |
end
|
blanchet@33192
|
1558 |
| Op2 (Image, T, R, u1, u2) =>
|
blanchet@33192
|
1559 |
(case (rep_of u1, rep_of u2) of
|
blanchet@33192
|
1560 |
(Func (R11, R12), Func (R21, Formula Neut)) =>
|
blanchet@33192
|
1561 |
if R21 = R11 andalso is_lone_rep R12 then
|
blanchet@33192
|
1562 |
let
|
blanchet@34123
|
1563 |
(* KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
1564 |
fun big_join r = kk_n_fold_join kk false R21 R12 r (to_r u1)
|
blanchet@33192
|
1565 |
val core_r = big_join (to_r u2)
|
blanchet@33192
|
1566 |
val core_R = Func (R12, Formula Neut)
|
blanchet@33192
|
1567 |
in
|
blanchet@33192
|
1568 |
if is_opt_rep R12 then
|
blanchet@33192
|
1569 |
let
|
blanchet@33192
|
1570 |
val schema = atom_schema_of_rep R21
|
blanchet@33192
|
1571 |
val decls = decls_for_atom_schema ~1 schema
|
blanchet@33192
|
1572 |
val vars = unary_var_seq ~1 (length decls)
|
blanchet@33192
|
1573 |
val f = kk_some (big_join (fold1 kk_product vars))
|
blanchet@33192
|
1574 |
in
|
blanchet@33192
|
1575 |
kk_rel_if (kk_all decls f)
|
blanchet@33192
|
1576 |
(rel_expr_from_rel_expr kk R core_R core_r)
|
blanchet@33192
|
1577 |
(rel_expr_from_rel_expr kk R (opt_rep ofs T core_R)
|
blanchet@33192
|
1578 |
(kk_product core_r true_atom))
|
blanchet@33192
|
1579 |
end
|
blanchet@33192
|
1580 |
else
|
blanchet@33192
|
1581 |
rel_expr_from_rel_expr kk R core_R core_r
|
blanchet@33192
|
1582 |
end
|
blanchet@33192
|
1583 |
else
|
blanchet@33224
|
1584 |
raise NUT ("Nitpick_Kodkod.to_r (Image)", [u1, u2])
|
blanchet@33224
|
1585 |
| _ => raise NUT ("Nitpick_Kodkod.to_r (Image)", [u1, u2]))
|
blanchet@33192
|
1586 |
| Op2 (Apply, @{typ nat}, _,
|
blanchet@33192
|
1587 |
Op2 (Apply, _, _, Cst (Subtract, _, _), u1), u2) =>
|
blanchet@33192
|
1588 |
if is_Cst Unrep u2 andalso not (is_opt_rep (rep_of u1)) then
|
blanchet@34123
|
1589 |
KK.Atom (offset_of_type ofs nat_T)
|
blanchet@33192
|
1590 |
else
|
blanchet@34123
|
1591 |
fold kk_join (map to_integer [u1, u2]) (KK.Rel nat_subtract_rel)
|
blanchet@33192
|
1592 |
| Op2 (Apply, _, R, u1, u2) =>
|
blanchet@34923
|
1593 |
if is_Cst Unrep u2 andalso is_set_type (type_of u1) andalso
|
blanchet@34923
|
1594 |
is_FreeName u1 then
|
blanchet@33192
|
1595 |
false_atom
|
blanchet@33192
|
1596 |
else
|
blanchet@33192
|
1597 |
to_apply R u1 u2
|
blanchet@33192
|
1598 |
| Op2 (Lambda, T, R as Opt (Atom (1, j0)), u1, u2) =>
|
blanchet@34123
|
1599 |
to_guard [u1, u2] R (KK.Atom j0)
|
blanchet@33192
|
1600 |
| Op2 (Lambda, T, Func (_, Formula Neut), u1, u2) =>
|
blanchet@33192
|
1601 |
kk_comprehension (untuple to_decl u1) (to_f u2)
|
blanchet@33192
|
1602 |
| Op2 (Lambda, T, Func (_, R2), u1, u2) =>
|
blanchet@33192
|
1603 |
let
|
blanchet@33192
|
1604 |
val dom_decls = untuple to_decl u1
|
blanchet@33192
|
1605 |
val ran_schema = atom_schema_of_rep R2
|
blanchet@33192
|
1606 |
val ran_decls = decls_for_atom_schema ~1 ran_schema
|
blanchet@33192
|
1607 |
val ran_vars = unary_var_seq ~1 (length ran_decls)
|
blanchet@33192
|
1608 |
in
|
blanchet@33192
|
1609 |
kk_comprehension (dom_decls @ ran_decls)
|
blanchet@33192
|
1610 |
(kk_subset (fold1 kk_product ran_vars)
|
blanchet@33192
|
1611 |
(to_rep R2 u2))
|
blanchet@33192
|
1612 |
end
|
blanchet@33192
|
1613 |
| Op3 (Let, _, R, u1, u2, u3) =>
|
blanchet@33192
|
1614 |
kk_rel_let [to_expr_assign u1 u2] (to_rep R u3)
|
blanchet@33192
|
1615 |
| Op3 (If, _, R, u1, u2, u3) =>
|
blanchet@33192
|
1616 |
if is_opt_rep (rep_of u1) then
|
blanchet@34121
|
1617 |
tripl_rel_rel_let kk
|
blanchet@33192
|
1618 |
(fn r1 => fn r2 => fn r3 =>
|
blanchet@33192
|
1619 |
let val empty_r = empty_rel_for_rep R in
|
blanchet@33192
|
1620 |
fold1 kk_union
|
blanchet@33192
|
1621 |
[kk_rel_if (kk_rel_eq r1 true_atom) r2 empty_r,
|
blanchet@33192
|
1622 |
kk_rel_if (kk_rel_eq r1 false_atom) r3 empty_r,
|
blanchet@33192
|
1623 |
kk_rel_if (kk_rel_eq r2 r3)
|
blanchet@33192
|
1624 |
(if inline_rel_expr r2 then r2 else r3) empty_r]
|
blanchet@33192
|
1625 |
end)
|
blanchet@33192
|
1626 |
(to_r u1) (to_rep R u2) (to_rep R u3)
|
blanchet@33192
|
1627 |
else
|
blanchet@33192
|
1628 |
kk_rel_if (to_f u1) (to_rep R u2) (to_rep R u3)
|
blanchet@33192
|
1629 |
| Tuple (_, R, us) =>
|
blanchet@33192
|
1630 |
(case unopt_rep R of
|
blanchet@33192
|
1631 |
Struct Rs => to_product Rs us
|
blanchet@33192
|
1632 |
| Vect (k, R) => to_product (replicate k R) us
|
blanchet@33192
|
1633 |
| Atom (1, j0) =>
|
blanchet@33192
|
1634 |
(case filter (not_equal Unit o rep_of) us of
|
blanchet@34123
|
1635 |
[] => KK.Atom j0
|
blanchet@34123
|
1636 |
| us' => kk_rel_if (kk_some (fold1 kk_product (map to_r us')))
|
blanchet@34123
|
1637 |
(KK.Atom j0) KK.None)
|
blanchet@33224
|
1638 |
| _ => raise NUT ("Nitpick_Kodkod.to_r (Tuple)", [u]))
|
blanchet@33192
|
1639 |
| Construct ([u'], _, _, []) => to_r u'
|
blanchet@34288
|
1640 |
| Construct (discr_u :: sel_us, T, R, arg_us) =>
|
blanchet@33192
|
1641 |
let
|
blanchet@33192
|
1642 |
val set_rs =
|
blanchet@33192
|
1643 |
map2 (fn sel_u => fn arg_u =>
|
blanchet@33192
|
1644 |
let
|
blanchet@33192
|
1645 |
val (R1, R2) = dest_Func (rep_of sel_u)
|
blanchet@33192
|
1646 |
val sel_r = to_r sel_u
|
blanchet@33192
|
1647 |
val arg_r = to_opt R2 arg_u
|
blanchet@33192
|
1648 |
in
|
blanchet@33192
|
1649 |
if is_one_rep R2 then
|
blanchet@33192
|
1650 |
kk_n_fold_join kk true R2 R1 arg_r
|
blanchet@33192
|
1651 |
(kk_project sel_r (flip_nums (arity_of_rep R2)))
|
blanchet@33192
|
1652 |
else
|
blanchet@34288
|
1653 |
kk_comprehension [KK.DeclOne ((1, ~1), to_r discr_u)]
|
blanchet@34123
|
1654 |
(kk_rel_eq (kk_join (KK.Var (1, ~1)) sel_r) arg_r)
|
blanchet@33192
|
1655 |
end) sel_us arg_us
|
blanchet@33192
|
1656 |
in fold1 kk_intersect set_rs end
|
blanchet@34123
|
1657 |
| BoundRel (x, _, _, _) => KK.Var x
|
blanchet@34123
|
1658 |
| FreeRel (x, _, _, _) => KK.Rel x
|
blanchet@34123
|
1659 |
| RelReg (j, _, R) => KK.RelReg (arity_of_rep R, j)
|
blanchet@33224
|
1660 |
| u => raise NUT ("Nitpick_Kodkod.to_r", [u])
|
blanchet@34123
|
1661 |
(* nut -> KK.decl *)
|
blanchet@33192
|
1662 |
and to_decl (BoundRel (x, _, R, _)) =
|
blanchet@34123
|
1663 |
KK.DeclOne (x, KK.AtomSeq (the_single (atom_schema_of_rep R)))
|
blanchet@33224
|
1664 |
| to_decl u = raise NUT ("Nitpick_Kodkod.to_decl", [u])
|
blanchet@34123
|
1665 |
(* nut -> KK.expr_assign *)
|
blanchet@33192
|
1666 |
and to_expr_assign (FormulaReg (j, _, R)) u =
|
blanchet@34123
|
1667 |
KK.AssignFormulaReg (j, to_f u)
|
blanchet@33192
|
1668 |
| to_expr_assign (RelReg (j, _, R)) u =
|
blanchet@34123
|
1669 |
KK.AssignRelReg ((arity_of_rep R, j), to_r u)
|
blanchet@33224
|
1670 |
| to_expr_assign u1 _ = raise NUT ("Nitpick_Kodkod.to_expr_assign", [u1])
|
blanchet@34123
|
1671 |
(* int * int -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1672 |
and to_atom (x as (k, j0)) u =
|
blanchet@33192
|
1673 |
case rep_of u of
|
blanchet@33192
|
1674 |
Formula _ => atom_from_formula kk j0 (to_f u)
|
blanchet@34123
|
1675 |
| Unit => if k = 1 then KK.Atom j0
|
blanchet@33224
|
1676 |
else raise NUT ("Nitpick_Kodkod.to_atom", [u])
|
blanchet@33192
|
1677 |
| R => atom_from_rel_expr kk x R (to_r u)
|
blanchet@34123
|
1678 |
(* rep list -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1679 |
and to_struct Rs u =
|
blanchet@33192
|
1680 |
case rep_of u of
|
blanchet@33192
|
1681 |
Unit => full_rel_for_rep (Struct Rs)
|
blanchet@33192
|
1682 |
| R' => struct_from_rel_expr kk Rs R' (to_r u)
|
blanchet@34123
|
1683 |
(* int -> rep -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1684 |
and to_vect k R u =
|
blanchet@33192
|
1685 |
case rep_of u of
|
blanchet@33192
|
1686 |
Unit => full_rel_for_rep (Vect (k, R))
|
blanchet@33192
|
1687 |
| R' => vect_from_rel_expr kk k R R' (to_r u)
|
blanchet@34123
|
1688 |
(* rep -> rep -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1689 |
and to_func R1 R2 u =
|
blanchet@33192
|
1690 |
case rep_of u of
|
blanchet@33192
|
1691 |
Unit => full_rel_for_rep (Func (R1, R2))
|
blanchet@33192
|
1692 |
| R' => rel_expr_to_func kk R1 R2 R' (to_r u)
|
blanchet@34123
|
1693 |
(* rep -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1694 |
and to_opt R u =
|
blanchet@33192
|
1695 |
let val old_R = rep_of u in
|
blanchet@33192
|
1696 |
if is_opt_rep old_R then
|
blanchet@33192
|
1697 |
rel_expr_from_rel_expr kk (Opt R) old_R (to_r u)
|
blanchet@33192
|
1698 |
else
|
blanchet@33192
|
1699 |
to_rep R u
|
blanchet@33192
|
1700 |
end
|
blanchet@34123
|
1701 |
(* rep -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1702 |
and to_rep (Atom x) u = to_atom x u
|
blanchet@33192
|
1703 |
| to_rep (Struct Rs) u = to_struct Rs u
|
blanchet@33192
|
1704 |
| to_rep (Vect (k, R)) u = to_vect k R u
|
blanchet@33192
|
1705 |
| to_rep (Func (R1, R2)) u = to_func R1 R2 u
|
blanchet@33192
|
1706 |
| to_rep (Opt R) u = to_opt R u
|
blanchet@33224
|
1707 |
| to_rep R _ = raise REP ("Nitpick_Kodkod.to_rep", [R])
|
blanchet@34123
|
1708 |
(* nut -> KK.rel_expr *)
|
blanchet@33192
|
1709 |
and to_integer u = to_opt (one_rep ofs (type_of u) (rep_of u)) u
|
blanchet@34123
|
1710 |
(* nut list -> rep -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
1711 |
and to_guard guard_us R r =
|
blanchet@33192
|
1712 |
let
|
blanchet@33192
|
1713 |
val unpacked_rs = unpack_joins r
|
blanchet@33192
|
1714 |
val plain_guard_rs =
|
blanchet@33192
|
1715 |
map to_r (filter (is_Opt o rep_of) guard_us)
|
blanchet@33192
|
1716 |
|> filter_out (member (op =) unpacked_rs)
|
blanchet@33192
|
1717 |
val func_guard_us =
|
blanchet@33192
|
1718 |
filter ((is_Func andf is_opt_rep) o rep_of) guard_us
|
blanchet@33192
|
1719 |
val func_guard_rs = map to_r func_guard_us
|
blanchet@33192
|
1720 |
val guard_fs =
|
blanchet@33192
|
1721 |
map kk_no plain_guard_rs @
|
blanchet@33192
|
1722 |
map2 (kk_not oo kk_n_ary_function kk)
|
blanchet@33192
|
1723 |
(map (unopt_rep o rep_of) func_guard_us) func_guard_rs
|
blanchet@33192
|
1724 |
in
|
blanchet@33192
|
1725 |
if null guard_fs then
|
blanchet@33192
|
1726 |
r
|
blanchet@33192
|
1727 |
else
|
blanchet@33192
|
1728 |
kk_rel_if (fold1 kk_or guard_fs) (empty_rel_for_rep R) r
|
blanchet@33192
|
1729 |
end
|
blanchet@34123
|
1730 |
(* rep -> rep -> KK.rel_expr -> int -> KK.rel_expr *)
|
blanchet@33192
|
1731 |
and to_project new_R old_R r j0 =
|
blanchet@33192
|
1732 |
rel_expr_from_rel_expr kk new_R old_R
|
blanchet@33192
|
1733 |
(kk_project_seq r j0 (arity_of_rep old_R))
|
blanchet@34123
|
1734 |
(* rep list -> nut list -> KK.rel_expr *)
|
blanchet@33192
|
1735 |
and to_product Rs us =
|
blanchet@33192
|
1736 |
case map (uncurry to_opt) (filter (not_equal Unit o fst) (Rs ~~ us)) of
|
blanchet@33224
|
1737 |
[] => raise REP ("Nitpick_Kodkod.to_product", Rs)
|
blanchet@33192
|
1738 |
| rs => fold1 kk_product rs
|
blanchet@34123
|
1739 |
(* int -> typ -> rep -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1740 |
and to_nth_pair_sel n res_T res_R u =
|
blanchet@33192
|
1741 |
case u of
|
blanchet@33192
|
1742 |
Tuple (_, _, us) => to_rep res_R (nth us n)
|
blanchet@33192
|
1743 |
| _ => let
|
blanchet@33192
|
1744 |
val R = rep_of u
|
blanchet@33192
|
1745 |
val (a_T, b_T) = HOLogic.dest_prodT (type_of u)
|
blanchet@33192
|
1746 |
val Rs =
|
blanchet@33192
|
1747 |
case unopt_rep R of
|
blanchet@33192
|
1748 |
Struct (Rs as [_, _]) => Rs
|
blanchet@33192
|
1749 |
| _ =>
|
blanchet@33192
|
1750 |
let
|
blanchet@33192
|
1751 |
val res_card = card_of_rep res_R
|
blanchet@33192
|
1752 |
val other_card = card_of_rep R div res_card
|
blanchet@33192
|
1753 |
val (a_card, b_card) = (res_card, other_card)
|
blanchet@33192
|
1754 |
|> n = 1 ? swap
|
blanchet@33192
|
1755 |
in
|
blanchet@33192
|
1756 |
[Atom (a_card, offset_of_type ofs a_T),
|
blanchet@33192
|
1757 |
Atom (b_card, offset_of_type ofs b_T)]
|
blanchet@33192
|
1758 |
end
|
blanchet@33192
|
1759 |
val nth_R = nth Rs n
|
blanchet@33192
|
1760 |
val j0 = if n = 0 then 0 else arity_of_rep (hd Rs)
|
blanchet@33192
|
1761 |
in
|
blanchet@33192
|
1762 |
case arity_of_rep nth_R of
|
blanchet@33192
|
1763 |
0 => to_guard [u] res_R
|
blanchet@33192
|
1764 |
(to_rep res_R (Cst (Unity, res_T, Unit)))
|
blanchet@33192
|
1765 |
| arity => to_project res_R nth_R (to_rep (Opt (Struct Rs)) u) j0
|
blanchet@33192
|
1766 |
end
|
blanchet@34123
|
1767 |
(* (KK.formula -> KK.formula -> KK.formula)
|
blanchet@34123
|
1768 |
-> (KK.rel_expr -> KK.rel_expr -> KK.formula) -> nut -> nut
|
blanchet@34123
|
1769 |
-> KK.formula *)
|
blanchet@33192
|
1770 |
and to_set_bool_op connective set_oper u1 u2 =
|
blanchet@33192
|
1771 |
let
|
blanchet@33192
|
1772 |
val min_R = min_rep (rep_of u1) (rep_of u2)
|
blanchet@33192
|
1773 |
val r1 = to_rep min_R u1
|
blanchet@33192
|
1774 |
val r2 = to_rep min_R u2
|
blanchet@33192
|
1775 |
in
|
blanchet@33192
|
1776 |
case min_R of
|
blanchet@33192
|
1777 |
Vect (k, Atom _) => kk_vect_set_bool_op connective k r1 r2
|
blanchet@33192
|
1778 |
| Func (R1, Formula Neut) => set_oper r1 r2
|
blanchet@33192
|
1779 |
| Func (Unit, Atom (2, j0)) =>
|
blanchet@33192
|
1780 |
connective (formula_from_atom j0 r1) (formula_from_atom j0 r2)
|
blanchet@33192
|
1781 |
| Func (R1, Atom _) => set_oper (kk_join r1 true_atom)
|
blanchet@33192
|
1782 |
(kk_join r2 true_atom)
|
blanchet@33224
|
1783 |
| _ => raise REP ("Nitpick_Kodkod.to_set_bool_op", [min_R])
|
blanchet@33192
|
1784 |
end
|
blanchet@34123
|
1785 |
(* (KK.formula -> KK.formula -> KK.formula)
|
blanchet@34123
|
1786 |
-> (KK.rel_expr -> KK.rel_expr -> KK.rel_expr)
|
blanchet@34123
|
1787 |
-> (KK.rel_expr -> KK.rel_expr -> KK.formula)
|
blanchet@34123
|
1788 |
-> (KK.rel_expr -> KK.rel_expr -> KK.formula)
|
blanchet@34123
|
1789 |
-> (KK.rel_expr -> KK.rel_expr -> KK.formula) -> bool -> rep -> nut
|
blanchet@34123
|
1790 |
-> nut -> KK.rel_expr *)
|
blanchet@33192
|
1791 |
and to_set_op connective connective3 set_oper true_set_oper false_set_oper
|
blanchet@33192
|
1792 |
neg_second R u1 u2 =
|
blanchet@33192
|
1793 |
let
|
blanchet@33192
|
1794 |
val min_R = min_rep (rep_of u1) (rep_of u2)
|
blanchet@33192
|
1795 |
val r1 = to_rep min_R u1
|
blanchet@33192
|
1796 |
val r2 = to_rep min_R u2
|
blanchet@33192
|
1797 |
val unopt_R = unopt_rep R
|
blanchet@33192
|
1798 |
in
|
blanchet@33192
|
1799 |
rel_expr_from_rel_expr kk unopt_R (unopt_rep min_R)
|
blanchet@33192
|
1800 |
(case min_R of
|
blanchet@33192
|
1801 |
Opt (Vect (k, Atom _)) => kk_vect_set_op connective k r1 r2
|
blanchet@33192
|
1802 |
| Vect (k, Atom _) => kk_vect_set_op connective k r1 r2
|
blanchet@33192
|
1803 |
| Func (_, Formula Neut) => set_oper r1 r2
|
blanchet@33192
|
1804 |
| Func (Unit, _) => connective3 r1 r2
|
blanchet@33192
|
1805 |
| Func (R1, _) =>
|
blanchet@34121
|
1806 |
double_rel_rel_let kk
|
blanchet@33192
|
1807 |
(fn r1 => fn r2 =>
|
blanchet@33192
|
1808 |
kk_union
|
blanchet@33192
|
1809 |
(kk_product
|
blanchet@33192
|
1810 |
(true_set_oper (kk_join r1 true_atom)
|
blanchet@33192
|
1811 |
(kk_join r2 (atom_for_bool bool_j0
|
blanchet@33192
|
1812 |
(not neg_second))))
|
blanchet@33192
|
1813 |
true_atom)
|
blanchet@33192
|
1814 |
(kk_product
|
blanchet@33192
|
1815 |
(false_set_oper (kk_join r1 false_atom)
|
blanchet@33192
|
1816 |
(kk_join r2 (atom_for_bool bool_j0
|
blanchet@33192
|
1817 |
neg_second)))
|
blanchet@33192
|
1818 |
false_atom))
|
blanchet@33192
|
1819 |
r1 r2
|
blanchet@33224
|
1820 |
| _ => raise REP ("Nitpick_Kodkod.to_set_op", [min_R]))
|
blanchet@33192
|
1821 |
end
|
blanchet@34123
|
1822 |
(* typ -> rep -> (KK.int_expr -> KK.int_expr) -> KK.rel_expr *)
|
blanchet@34121
|
1823 |
and to_bit_word_unary_op T R oper =
|
blanchet@34121
|
1824 |
let
|
blanchet@34121
|
1825 |
val Ts = strip_type T ||> single |> op @
|
blanchet@34123
|
1826 |
(* int -> KK.int_expr *)
|
blanchet@34123
|
1827 |
fun int_arg j = int_expr_from_atom kk (nth Ts j) (KK.Var (1, j))
|
blanchet@34121
|
1828 |
in
|
blanchet@34121
|
1829 |
kk_comprehension (decls_for_atom_schema 0 (atom_schema_of_rep R))
|
blanchet@34123
|
1830 |
(KK.FormulaLet
|
blanchet@34123
|
1831 |
(map (fn j => KK.AssignIntReg (j, int_arg j)) (0 upto 1),
|
blanchet@34123
|
1832 |
KK.IntEq (KK.IntReg 1, oper (KK.IntReg 0))))
|
blanchet@34121
|
1833 |
end
|
blanchet@34123
|
1834 |
(* typ -> rep -> (KK.int_expr -> KK.int_expr -> KK.int_expr -> bool) option
|
blanchet@34123
|
1835 |
-> (KK.int_expr -> KK.int_expr -> KK.int_expr) option -> KK.rel_expr *)
|
blanchet@34121
|
1836 |
and to_bit_word_binary_op T R opt_guard opt_oper =
|
blanchet@34121
|
1837 |
let
|
blanchet@34121
|
1838 |
val Ts = strip_type T ||> single |> op @
|
blanchet@34123
|
1839 |
(* int -> KK.int_expr *)
|
blanchet@34123
|
1840 |
fun int_arg j = int_expr_from_atom kk (nth Ts j) (KK.Var (1, j))
|
blanchet@34121
|
1841 |
in
|
blanchet@34121
|
1842 |
kk_comprehension (decls_for_atom_schema 0 (atom_schema_of_rep R))
|
blanchet@34123
|
1843 |
(KK.FormulaLet
|
blanchet@34123
|
1844 |
(map (fn j => KK.AssignIntReg (j, int_arg j)) (0 upto 2),
|
blanchet@34121
|
1845 |
fold1 kk_and
|
blanchet@34121
|
1846 |
((case opt_guard of
|
blanchet@34121
|
1847 |
NONE => []
|
blanchet@34121
|
1848 |
| SOME guard =>
|
blanchet@34123
|
1849 |
[guard (KK.IntReg 0) (KK.IntReg 1) (KK.IntReg 2)]) @
|
blanchet@34121
|
1850 |
(case opt_oper of
|
blanchet@34121
|
1851 |
NONE => []
|
blanchet@34121
|
1852 |
| SOME oper =>
|
blanchet@34123
|
1853 |
[KK.IntEq (KK.IntReg 2,
|
blanchet@34123
|
1854 |
oper (KK.IntReg 0) (KK.IntReg 1))]))))
|
blanchet@34121
|
1855 |
end
|
blanchet@34123
|
1856 |
(* rep -> rep -> KK.rel_expr -> nut -> KK.rel_expr *)
|
blanchet@33192
|
1857 |
and to_apply res_R func_u arg_u =
|
blanchet@33192
|
1858 |
case unopt_rep (rep_of func_u) of
|
blanchet@33192
|
1859 |
Unit =>
|
blanchet@33192
|
1860 |
let val j0 = offset_of_type ofs (type_of func_u) in
|
blanchet@33192
|
1861 |
to_guard [arg_u] res_R
|
blanchet@34123
|
1862 |
(rel_expr_from_rel_expr kk res_R (Atom (1, j0)) (KK.Atom j0))
|
blanchet@33192
|
1863 |
end
|
blanchet@33192
|
1864 |
| Atom (1, j0) =>
|
blanchet@33192
|
1865 |
to_guard [arg_u] res_R
|
blanchet@33192
|
1866 |
(rel_expr_from_rel_expr kk res_R (Atom (1, j0)) (to_r func_u))
|
blanchet@33192
|
1867 |
| Atom (k, j0) =>
|
blanchet@33192
|
1868 |
let
|
blanchet@33192
|
1869 |
val dom_card = card_of_rep (rep_of arg_u)
|
blanchet@33192
|
1870 |
val ran_R = Atom (exact_root dom_card k,
|
blanchet@33192
|
1871 |
offset_of_type ofs (range_type (type_of func_u)))
|
blanchet@33192
|
1872 |
in
|
blanchet@33192
|
1873 |
to_apply_vect dom_card ran_R res_R (to_vect dom_card ran_R func_u)
|
blanchet@33192
|
1874 |
arg_u
|
blanchet@33192
|
1875 |
end
|
blanchet@33192
|
1876 |
| Vect (1, R') =>
|
blanchet@33192
|
1877 |
to_guard [arg_u] res_R
|
blanchet@33192
|
1878 |
(rel_expr_from_rel_expr kk res_R R' (to_r func_u))
|
blanchet@33192
|
1879 |
| Vect (k, R') => to_apply_vect k R' res_R (to_r func_u) arg_u
|
blanchet@33192
|
1880 |
| Func (R, Formula Neut) =>
|
blanchet@33192
|
1881 |
to_guard [arg_u] res_R (rel_expr_from_formula kk res_R
|
blanchet@33192
|
1882 |
(kk_subset (to_opt R arg_u) (to_r func_u)))
|
blanchet@33192
|
1883 |
| Func (Unit, R2) =>
|
blanchet@33192
|
1884 |
to_guard [arg_u] res_R
|
blanchet@33192
|
1885 |
(rel_expr_from_rel_expr kk res_R R2 (to_r func_u))
|
blanchet@33192
|
1886 |
| Func (R1, R2) =>
|
blanchet@33192
|
1887 |
rel_expr_from_rel_expr kk res_R R2
|
blanchet@33192
|
1888 |
(kk_n_fold_join kk true R1 R2 (to_opt R1 arg_u) (to_r func_u))
|
blanchet@33192
|
1889 |
|> body_rep R2 = Formula Neut ? to_guard [arg_u] res_R
|
blanchet@33224
|
1890 |
| _ => raise NUT ("Nitpick_Kodkod.to_apply", [func_u])
|
blanchet@34123
|
1891 |
(* int -> rep -> rep -> KK.rel_expr -> nut *)
|
blanchet@33192
|
1892 |
and to_apply_vect k R' res_R func_r arg_u =
|
blanchet@33192
|
1893 |
let
|
blanchet@33192
|
1894 |
val arg_R = one_rep ofs (type_of arg_u) (unopt_rep (rep_of arg_u))
|
blanchet@33192
|
1895 |
val vect_r = vect_from_rel_expr kk k res_R (Vect (k, R')) func_r
|
blanchet@33192
|
1896 |
val vect_rs = unpack_vect_in_chunks kk (arity_of_rep res_R) k vect_r
|
blanchet@33192
|
1897 |
in
|
blanchet@33192
|
1898 |
kk_case_switch kk arg_R res_R (to_opt arg_R arg_u)
|
blanchet@33192
|
1899 |
(all_singletons_for_rep arg_R) vect_rs
|
blanchet@33192
|
1900 |
end
|
blanchet@34123
|
1901 |
(* bool -> nut -> KK.formula *)
|
blanchet@33192
|
1902 |
and to_could_be_unrep neg u =
|
blanchet@34123
|
1903 |
if neg andalso is_opt_rep (rep_of u) then kk_no (to_r u) else KK.False
|
blanchet@34123
|
1904 |
(* nut -> KK.rel_expr -> KK.rel_expr *)
|
blanchet@33192
|
1905 |
and to_compare_with_unrep u r =
|
blanchet@33892
|
1906 |
if is_opt_rep (rep_of u) then
|
blanchet@33892
|
1907 |
kk_rel_if (kk_some (to_r u)) r (empty_rel_for_rep (rep_of u))
|
blanchet@33892
|
1908 |
else
|
blanchet@33892
|
1909 |
r
|
blanchet@33192
|
1910 |
in to_f_with_polarity Pos u end
|
blanchet@33192
|
1911 |
|
blanchet@33192
|
1912 |
end;
|