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dekker.one
1predicate fzn_lex_lesseq_bool_reif(array[int] of var bool: x,
2 array[int] of var bool: y,
3 var bool: c) =
4 let { int: lx = min(index_set(x)),
5 int: ux = max(index_set(x)),
6 int: ly = min(index_set(y)),
7 int: uy = max(index_set(y)),
8 int: size = max(ux - lx, uy - ly),
9 array[0..size+1] of var bool: b }
10 % b[i] is true if the lexicographical order holds from position i on.
11 in
12 (c <-> b[0])
13 /\
14 forall(i in 0..size) (
15 ( b[i] -> ( x[lx + i] <= y[ly + i] ) ) /\
16 bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) <= 2
17 /\
18 ( b[i] -> ( x[lx + i] < y[ly + i] \/ b[i+1] ) ) /\
19 bool2int(b[i]) + (1-bool2int(x[lx + i])) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
20 /\ bool2int(b[i]) + bool2int(x[lx + i]) + bool2int(y[ly + i]) + (1-bool2int(b[i+1])) <= 3
21 /\ bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
22 )
23 /\ b[size+1] = (ux-lx <= uy-ly)
24% endif
25;
26
27predicate fzn_lex_lesseq_bool_imp(array[int] of var bool: x,
28 array[int] of var bool: y,
29 var bool: c) =
30 let { int: lx = min(index_set(x)),
31 int: ux = max(index_set(x)),
32 int: ly = min(index_set(y)),
33 int: uy = max(index_set(y)),
34 int: size = max(ux - lx, uy - ly),
35 array[0..size+1] of var bool: b }
36 % b[i] is true if the lexicographical order holds from position i on.
37 in
38 (c -> b[0])
39 /\
40 forall(i in 0..size) (
41 ( b[i] -> ( x[lx + i] <= y[ly + i] ) ) /\
42 bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) <= 2
43 /\
44 ( b[i] -> ( x[lx + i] < y[ly + i] \/ b[i+1] ) ) /\
45 bool2int(b[i]) + (1-bool2int(x[lx + i])) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
46 /\ bool2int(b[i]) + bool2int(x[lx + i]) + bool2int(y[ly + i]) + (1-bool2int(b[i+1])) <= 3
47 /\ bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
48 )
49 /\ b[size+1] = (ux-lx <= uy-ly)
50;