Prolog code:

    append([], X, X).
    append([X|R], L, [X|S]) :- append(R, L, S).

In long form:

    sub append {
        my ($a, $b, $ab) = @_;
        
        my ($x, $r, $l, $s);
        $_ = Logic::Variable->new for $x, $r, $l, $s;

        Logic::Basic::Alternation->new(
            Logic::Data::Unify->new(
                [$a, $b, $ab], 
                [[], $x, $x],
            ),

            Logic::Basic::Sequence->new(
                Logic::Data::Unify->new(
                    [ $a, $b, $ab ],
                    [ Logic::Data::Cons->new($x, $r),
                      $l,
                      Logic::Data::Cons->new($x, $s) ],
                ),
                Logic::Basic::Rule->new(sub {
                    append($r, $l, $s),
                }),
            ),
        );
    }