Question

I’m having some trouble using sorts in the SMTlib2 format. For example, I define an Interval as:

(declare-sort Pair 2)
(define-sort Interval () (Pair Int Int))

Now how can I return a new Interval from a function? e.g.:

(define-fun getInterval ((a Int) (b Int)) Interval
  (Interval a b))

This doesn’t work.
My question is: how can I construct and instantiate objects of a given sort, and how can I access their fields?

Right now I’m using 2 UFs that I created as field getters, but I still don’t know how to have a constructor:

(declare-fun L (Interval) Int)
(declare-fun H (Interval) Int)

Thanks,
Nuno

Answer 1

You should look into Record subsection, Datatypes section in Z3 SMT guide. Basically, you can create a record type with a constructor mk-pair and two selectors first and second for accessing its fields.

Here is an example^{rise4fun link}:

(set-option :macro-finder true)

(declare-datatypes (T1 T2) ((Pair (mk-pair (first T1) (second T2)))))

(define-sort Interval () (Pair Int Int))
(define-fun getInterval ((a Int) (b Int)) Interval
  (mk-pair a b))

(declare-const p1 Interval)
(declare-const p2 Interval)

;construct objects of a give sort
(assert (= p1 (getInterval 2 2)))

;accessing their fields
(assert (= (first p1) (second p2)))

(check-sat)
(get-model)