Having assertions inside definitions in SMT - z3

Question

I want to capture the assertion inside fac.
int f( x )
{
if( x == 1) return 1;
else{
assert( x > 0 );
return 2;
}
}
int g (x)
{ assert( x > 5 );
return f(x-1) + f(x-2);
}
I want an smt2 code for this.
I can do this by striping the argument and making it global with unique name (also rename inside f), then do this 3 times each with a different name for function. Like below :
( declare-const x1 Int )
(define-fun f1 () Int
( ite ( x1 > 0) 1 2 )
)
(assert (> x1 0))
( declare-const x2 Int )
(define-fun f2 () Int
( ite ( x2 > 0) 1 2 )
)
(assert (> x2 0))
( declare-const x3 Int )
(define-fun g1 () Int
( + f1 f2 )
)
(assert (> x3 5))
I don't want to this. Is there any other way to do this without repeating ?
EDIT
My purpose is to find values violating the asserts.

Answer 1

As far as I know, it is not possible to embed assertions within function definitions.
What I would try to do is to separate the expected behavior, the input assumptions and the output guarantees (if any).
Example:
(define-fun f ((x Int)) Int
(ite (= x 1) 1 2)
)
(define-fun f-helper ((x Int)) Bool
(< 0 x)
)
(define-fun g ((x Int)) Int
(+ (f (- x 1)) (f (- x 2)))
)
(define-fun g-helper ((x Int)) Bool
(and (< 5 x)
(f-helper (- x 1))
(f-helper (- x 2))
)
)
(declare-const x Int)
(declare-const y Int)
(assert (and (= y (g x))
(g-helper x)
))
(check-sat)
(get-model)
In this example we use f to model the behavior of the original function f, and f-helper to model the assumptions of f. The output, using the online Z3 tool, is as follows:
sat
(model
(define-fun x () Int
6)
(define-fun y () Int
4)
)
I would conclude saying that this approach could become tricky as soon as f and g are used inside both positive and negative contexts.. in this case one should pay extra attention that the polarity of the assertions is correct wrt. the expected result.