Assigning different numbers to variables in a term - prolog

Question

I'm trying to create a predicate, which will generate all possible evalutions of a compound term with numbers, e.g. assign_distinct_values([A-B], E). should yield 99 results.
However, I can't find the nondeterminism in my current effort:
assign_distinct_values(E, A) :-
term_variables(E, V),
assign_distinct_values(E, V, [0,1,2,3,4,5,6,7,8,9], A).
assign_distinct_values(E, [], [], E).
assign_distinct_values(E, [], _, E).
assign_distinct_values(E, V, N, A) :-
select(Num, N, N2),
select(Var, V, V2),
Var is Num,
assign_distinct_values(E, V2, N2, A).
which generates a symmetrical result with duplicates like:
1-0
0-1
0-1
1-0

Answer 1

First consider using a more meaningful naming convention: I recommend appending an "s" to the names of variables that denote lists, and numbering them more systematically (starting from 0), and using a more declarative and meaningful predicate name:
with_distinct_integers(E0, E) :-
term_variables(E0, Vs),
with_distinct_integers(E0, Vs, [0,1,2,3,4,5,6,7,8,9], E).
with_distinct_integers(E, [], [], E).
with_distinct_integers(E, [], _, E).
with_distinct_integers(E0, Vs0, Ns0, E) :-
select(Num, Ns0, Ns),
select(Var, Vs0, Vs),
Var is Num,
with_distinct_integers(E0, Vs, Ns, E).
Focusing on with_distinct_integers/4 now. You see that the first clause is subsumed by the second, so you can omit the first clause without losing solutions. The variable Var is only used to unify it with Num, so you can use a single variable right away:
with_distinct_integers(E, [], _, E).
with_distinct_integers(E0, Vs0, Ns0, E) :-
select(Num, Ns0, Ns),
select(Num, Vs0, Vs),
with_distinct_integers(E0, Vs, Ns, E).
You still find unintended duplicate solutions with this simplified version, and I leave it as an easy exercise to find out what causes this:
?- with_distinct_integers(X-Y, [X,Y], [0,1], A).
..., A = 0-1 ;
..., A = 1-0 ;
..., A = 1-0 ;
..., A = 0-1 ;
false.
Hint: Just reason declaratively over the simplified definition. Continuing with the simplification: Why pass around the original term when you already have everything you need, i.e., its variables, available? Consider:
with_distinct_integers(E) :-
term_variables(E, Vs),
numlist(0, 9, Ns),
with_distinct_integers(Vs, Ns).
with_distinct_integers([], _).
with_distinct_integers([V|Vs], Ns0) :-
select(V, Ns0, Ns),
with_distinct_integers(Vs, Ns).
Example query, counting all solutions:
?- findall(., with_distinct_integers([X-Y]), Ls), length(Ls, L).
Ls = ['.', '.', '.', '.', '.', '.', '.', '.', '.'|...],
L = 90.
Surprise on the side: there are only 90 solutions, not 99.
Also consider using finite domain constraints, which are relations over integers that let you easily formulate such tasks:
:- use_module(library(clpfd)).
with_distinct_integers(E) :-
term_variables(E, Vs),
Vs ins 0..9,
all_different(Vs),
label(Vs).
Example query:
?- with_distinct_integers(X-Y).
X = 0,
Y = 1 ;
X = 0,
Y = 2 ;
X = 0,
Y = 3 .

Answer 2

L being the list of values and E, A the output variables
assign_distinct_values(E, A, L) :-
member(E,L),
delete(L,E,L1),
member(A,L1).
using prolog predicates is quite quicker. member(X,L) checks if X is in L, if so, we create a new list L1 not containing X with delete(L,X,L1) and check again for a second member the same way.
Another version :
assign_distinct_values(E, A) :-
L = [0,1,2,3,4,5,6,7,8,9],
member(E,L),
delete(L,E,L1),
member(A,L1).
Does it work ? I don't have prolog installed on my machine.
Regards