Alloy: define relation to only positive integers

Question

I have a model with this sig:

sig Thing {}
sig World {
    quantities: Thing ->one Int,
}

I want to define a constraint on the quantities relationship such that the quantity of each Thing must be a positive int.

I am total beginner with Alloy (and I have no theory background to draw on, am just a Python programmer). I followed through the tutorial but I did not see a recipe for what I want to do.

I know how to:

fact {
    all w: World | w.quantities <something>
}

...but I am not clear how to address members of the right-hand-side of the relationship when writing a fact.

I have defined it as a relationship (rather than having a quantity property on the Thing sig) because I understood from the tutorial that this was necessary in a dynamic model where I want to update the quantity of Things via predicates.

I tried defining a:

sig PositiveInt extends Int {}

...but this is not allowed.

Answer 1

updated This kind of subtyping works (imho) best with set enumeration:

 let PositiveInt = { i : Int | i > 0 }
 sig Thing {}
 sig World { quantities : Thing -> one PositiveInt }

┌──────────┬──────────┐
│this/World│quantities│
├──────────┼──────┬───┤
│World⁰    │Thing⁰│7  │
│          ├──────┼───┤
│          │Thing¹│6  │
│          ├──────┼───┤
│          │Thing²│4  │
└──────────┴──────┴───┘