Question

I read in the alloy website that a signature defines a set. Given this definition, I was trying to understand the below alloy code:

enum dooroptype { unlocked, locked, opened}
enum enginetype {on,off}
enum motortype { ismoving, still}
enum key_location { in_car, faralone}

abstract sig state{
  inside,far, near : set Person,
  car_action : motortype,
  engine : enginetype,
  key_position : (Person + key_location),
  door : dooroptype
}

If a signature actually defines a set, then why do we have so many parameters in the signature definiton as a set is a unary relation? If I am wrong, how does one interpret this definition.

Answer 1

I’m taking my first steps in Alloy, but I’ll try to answer. This is what you have in the above code:

1. dooroptype = set (unary relation) with exactly 3 atoms.
2. enginetype = set (unary relation) with exactly 2 atoms.
3. motortype = set (unary relation) with exactly 2 atoms.
4. key_location = set (unary relation) with exactly 2 atoms.
5. state = set (unary relation) with 0 or more atoms.
6. inside, far and near = binary relations defined as state -> set Person
7. car_action = binary relation defined as state -> one motortype
8. engine = binary relation defined as state -> one enginetype
9. key_position = a union of two binary relations state -> Person and state -> key_location (but with multiplicity that constrains each state to appear at most once, so a state can be associated with either a Person or a key_location, but not with both)
10. door = binary relation defined as state -> dooroptype

In short, everything defined above is a relation, some are unary, some are binary. The binary relations inside, far and near are defined with set multiplicity, while all the others are defined with a multiplicity of one.

In other words, a signature is a set, and relations are defined inside the signatures, but are visible globally.