[SOLVED] What pattern is suitable for expressing Null value in a SBV formula

What pattern is suitable for expressing Null value in a SBV formula

I am translating SQL predicate into Z3 language. SQL predicate expression is very close to expressions in Z3:

where x + y > 0
====
(declare-const x Int)
(declare-const y Int)
(assert (> (+ x y) 0)))

but I don't see how to represent Null values. In bare Z3 I can define datatype:

(declare-datatype
 NullableInt
 (
  (justInt (theInt Int))
  (nullInt)
  )
)

# where x is null or x > 10
(declare-const x NullableInt)
(assert (ite (= x nullInt) true (> (justInt x) 10)))

SBV doesn't have declare-datatype.

First option which comes to my head is to replace all x references with x + 1 then x = 0 could be treated as null

Solution

SBV has full support for optional values, modeling the Maybe datatype:

https://hackage.haskell.org/package/sbv-8.16/docs/Data-SBV-Maybe.html

So, I'd go by modeling it as you would in regular Haskell, i.e., via a Maybe Integer; or in SBV parlance, its symbolic equivalent SMaybe Integer. That should be a very direct correspondence. Here's an example use:

ghci> import Data.SBV
ghci> import qualified Data.SBV.Maybe as SM
ghci> sat $ \mi -> SM.maybe sTrue (.>= 10) mi
Satisfiable. Model:
  s0 = Nothing :: Maybe Integer
ghci> sat $ \mi -> SM.maybe sFalse (.>= 10) mi
Satisfiable. Model:
  s0 = Just 10 :: Maybe Integer