Alloy Analyzer: Quantifiers and Set Products - alloy

Question

I have encountered the following issue in Alloy. Consider the toy code which tries to capture even labeled entities (V1 is for State and V2 is for ProductStateSet):
enum State {s1, s2, s3, s4, s5, s6}
enum DummySet {b,c}
let ProductStateSet = DummySet->State
pred evenV1 (state: State){
(state = s2) or (state=s4) or (state=s6)
}
pred evensetV1 (stateset: State) {
all state: stateset | evenV1[state]
}
assert a2V1 {
evensetV1[(s2 + s4)]
}
pred evenV2 (state: ProductStateSet){
(state = b->s2) or (state=b->s4) or (state=b->s6)
}
assert a1V2 {
evenV2[b->s2]
}
pred evensetV2 (stateset: ProductStateSet) {
all state: stateset | evenV2[state]
}
assert a2V2 {
evensetV2[ (b->s2) + (b->s4) ]
}
The assertion a2V1 is true, but a2V2 is false, when I would have expected them to be the same. Why is this so, and what is the proper way to use quantifiers when dealing with set products?
If I change "evenset" to have "some" rather than "all", no issues with evensetV1, but for evensetV2 I get:
pred evensetV2 (stateset: ProductStateSet) {
some state: stateset | evenV2[state]
}
assert a2V2 {
evensetV2[ (b->s2) + (b->s4) ]
}
Executing "Check a2V2"
Solver=sat4j Bitwidth=4 MaxSeq=4 SkolemDepth=1 Symmetry=20
Generating CNF...
.
Analysis cannot be performed since it requires higher-order
quantification that could not be skolemized.
Another question for this example regarding set comprehension: I can write an assertion like:
assert a3V1{
#{state: State | evenV1[state]} > 2
}
Is there a way to print out the set elements, that is, can I print out the below set?
{state: State | evenV1[state]}
Thanks!

Answer 1

Regarding your first question:
EDITED (first answer was wrong)
Running the assertion gives 2 counter examples.
One is expected, in the sense that none -> none is not considered in the evenV2 predicate. But the other (see below) doesn't make sense for me.
My only logical explanation is that the quantification variable "state" of evenSetV2 is badly interpreted when given in parameter of evenV2 even though it seems somehow farfetched ...
I think whenever possible, one should avoid quantification and prefer more straightforward set operations. Implementing the predicate and assertion as follows solves the problem (you don't even need to differentiate between the singleton and the set approach anymore):
pred evenV2 ( state: ProductStateSet){
DummySet.state in (s2+s4+s6)
}
assert a2V2 {
evenV2[ (b->s4)+ (b->s6)]
}
END EDIT
For the second question, the Alloy evaluator is your friend.