Is it possible to cast a bitvector of one bit into a boolean variable in SMTLib2?

Question

I want to have a boolean variable that test if, e.g., the third bit of a bit vector is 0. The theory of bitvector allows to extract 1 bit as a bitvector, but not a boolean t

Answer 1

What you are doing is just fine; it's just that bit0 is a reserved name. Just call it something else. (mybit0 would work, or some other unreserved name.)

Answer 2

Create an equality between the extraction of the third bit and a bit-vector with value 1 (and one bit).

E.g,

(declare-const x (_ BitVec 5))
(assert (= #b1 ((_ extract 2 2) x)))
(check-sat)
(get-model)

produces

sat
(model
  (define-fun x () (_ BitVec 5)
    #b00100)
)