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dekker.one
1/*%-----------------------------------------------------------------------------%
2% Domain encodings
3%-----------------------------------------------------------------------------%
4*/
5% Linear equality encoding
6
7 % Single variable: x = d <-> x_eq_d[d]
8predicate equality_encoding(var int: x, array[int] of var int: x_eq_d) =
9 x in index_set(x_eq_d)
10 /\
11 sum(d in dom(x))( x_eq_d[d] ) = 1
12 /\
13 sum(d in dom(x))( d * x_eq_d[d] ) = x
14 /\
15% my_trace( "eq_enc: \(x), index_set(pp)=" ++ show(index_set( x_eq_d )) ++ "\n" ) /\
16 if fPostprocessDomains then
17 equality_encoding__POST(x, x_eq_d)
18 else true endif
19 ;
20
21 % Two variables: x = d /\ y = e <-> x_eq_d[d] /\ y_eq_e[e] /\ xy_eq_de[d, e]
22predicate equality_encoding(var int: x, var int: y,
23 array[int] of var int: x_eq_d,
24 array[int] of var int: y_eq_e,
25 array[int, int] of var int: xy_eq_de
26 ) =
27 x in index_set(x_eq_d) /\
28 y in index_set(y_eq_e) /\
29 index_set(x_eq_d) == index_set_1of2(xy_eq_de) /\
30 index_set(y_eq_e) == index_set_2of2(xy_eq_de) /\
31 sum(d in dom(x), e in dom(y))( xy_eq_de[d, e] ) = 1
32 /\
33 forall(d in dom(x)) (sum(e in dom(y))( xy_eq_de[d, e] ) = x_eq_d[d])
34 /\
35 forall(e in dom(y)) (sum(d in dom(x))( xy_eq_de[d, e] ) = y_eq_e[e])
36 ;
37
38 % Array of variables: x[i] = d <-> x_eq_d[i,d]
39predicate equality_encoding(array[int] of var int: x,
40 array[int, int] of var int: x_eq_d) =
41 forall(i in index_set(x))(
42 x[i] in index_set_2of2(x_eq_d)
43 /\
44 sum(d in index_set_2of2(x_eq_d))( x_eq_d[i,d] ) = 1
45 /\
46 sum(d in index_set_2of2(x_eq_d))( d * x_eq_d[i,d] ) = x[i]
47 );
48
49function var int: eq_new_var(var int: x, int: i) ::promise_total =
50 if i in dom(x) then
51 let {
52 var 0..1: xi;
53 } in xi
54 else 0 endif;
55
56function array[int] of var int: eq_encode(var int: x) ::promise_total =
57 let {
58 array[int] of var int: y = array1d(lb(x)..ub(x),[eq_new_var(x,i) | i in lb(x)..ub(x)]);
59 constraint equality_encoding(x,y);
60% constraint
61% if card(dom(x))>0 then
62% my_trace(" eq_encode: dom(\(x)) = " ++ show(dom(x)) ++ ", card( dom(\(x)) ) = " ++ show(card(dom(x))) ++ "\n")
63% else true endif;
64 %% constraint assert(card(dom(x))>1, " eq_encode: card(dom(\(x))) == " ++ show(card(dom(x))));
65 } in y;
66
67function array[int] of int: eq_encode(int: x) ::promise_total =
68 array1d(lb(x)..ub(x),[ if i=x then 1 else 0 endif | i in lb(x)..ub(x)]);
69
70%%% The same for 2 variables:
71function var int: eq_new_var(var int: x, int: i, var int: y, int: j) ::promise_total =
72 if i in dom(x) /\ j in dom(y) then
73 let {
74 var 0..1: xi;
75 } in xi
76 else 0 endif;
77
78function array[int, int] of var int: eq_encode(var int: x, var int: y) ::promise_total =
79 let {
80 array[int] of var int: pX = eq_encode(x),
81 array[int] of var int: pY = eq_encode(y),
82 array[int, int] of var int: pp = array2d(index_set(pX), index_set(pY),
83 [eq_new_var(x,i,y,j) | i in index_set(pX), j in index_set(pY)]);
84 constraint equality_encoding(x, y, pX, pY, pp);
85 } in pp;
86
87function array[int, int] of int: eq_encode(int: x, int: y) ::promise_total =
88% let {
89% constraint if card(dom(x))*card(dom(y))>200 then
90% my_trace(" eq_encode: dom(\(x)) = " ++ show(dom(x)) ++ ", dom(\(y)) = " ++ show(dom(y)) ++ "\n")
91% else true endif;
92% } in
93 array2d(lb(x)..ub(x), lb(y)..ub(y),
94 [if i==x /\ j==y then 1 else 0 endif | i in lb(x)..ub(x), j in lb(y)..ub(y)]);
95
96function array[int,int] of var int: eq_encode(array[int] of var int: x) ::promise_total =
97 let {
98 array[index_set(x),lb_array(x)..ub_array(x)] of var int: y =
99 array2d(index_set(x),lb_array(x)..ub_array(x),
100 [ let {
101 array[int] of var int: xi = eq_encode(x[i])
102 } in if j in index_set(xi) then xi[j] else 0 endif
103 | i in index_set(x), j in lb_array(x)..ub_array(x)]
104 )
105 } in y;
106
107function array[int,int] of int: eq_encode(array[int] of int: x) ::promise_total =
108 array2d(index_set(x),lb_array(x)..ub_array(x),[ if j=x[i] then 1 else 0 endif | i in index_set(x), j in lb_array(x)..ub_array(x)]);
109
110%-----------------------------------------------------------------------------%
111%-----------------------------------------------------------------------------%