Question

I need to reinitialized a real variable based on some some Boolean flag as follows.
Alongside changing the truth value of location_next I want to reinitialize x_next with another value. How can I do that?

location, location_next = Bools('location location_next')
x, x_next = Reals('x x_next')
...
location_next == If(And(Not(location), x_next >= 12),
                    True,
                    If(And(location, x_next <= 0), False, location))

Answer 1

The function If (in the Z3 API) can be also used to create non-Boolean expressions.
We must have that for every If(c, t1, t2), c has sort Boolean, and t1 and t2 have the same sort (type) S. In this case, If(c, t1, t2) is will produce a Z3 expression of sort S. Here is a small example:

x, y = Reals('x y')
print If(x > 0, x + 1, y - 1)

Here is a link with the example above: http://rise4fun.com/Z3Py/V4e

In the following example, we have a formula such that x_next is equal to x+1 when location is False and x >= 12, is equal to x-1 when location is True and x <= 0, and is equal to x otherwise.

x_next == If(And(Not(location), x >= 12),
             x+1,
             If(And(location, x <= 0), x-1, x))