Question

This question is strongly related to this and this question.

The distinct function of Z3

(declare-const a S)
(declare-const b S)
(assert (distinct a b))

allows constraining sets of variables (here a and b) such that all variables in the set must take different values.

My question is: is it also possible to force a variable to take a unique value without explicitly referring to the set of variables from which it should be distinct? Something like

(declare-unique-const a S)
(declare-unique-const b S)
(declare-unique-const c S)

This would be nice in situations where you declare new variables in an iterative process, for example, during program verification.

If it is not possible, I guess one has to keep track of all distinct variables and use that set to emit appropriate distinct (newvar, oldvar1, ..., oldvarn)) constraints.

Answer 1

We can define an auxiliary fresh function f from S to Int, and assert

f(a_1) = 1
f(a_1) = 2
f(a_3) = 3
...
f(a_n) = n

Then, a_1, …, a_n must be different from each other.
If we want to say that b is also different from all a_is. We just assert

f(b) = n+1

In this approach, we only have to track the counter.