Documentation.SBV.Examples.Uninterpreted.AUF

Formalizes and proves the following theorem, about arithmetic, uninterpreted functions, and arrays. (For reference, see http://research.microsoft.com/en-us/um/redmond/projects/z3/fmcad06-slides.pdf slide number 24):

   x + 2 = y  implies  f (read (write (a, x, 3), y - 2)) = f (y - x + 1)

We interpret the types as follows (other interpretations certainly possible):

x

SWord32 (32-bit unsigned address)

y

SWord32 (32-bit unsigned address)

a

An array, indexed by 32-bit addresses, returning 32-bit unsigned integers

f

An uninterpreted function of type SWord32 -> SWord64

The function read and write are usual array operations.

Model using functional arrays

f :: SWord32 -> SWord64

Uninterpreted function in the theorem

thm :: SymArray a => SWord32 -> SWord32 -> a Word32 Word32 -> SBool

Correctness theorem. We state it for all values of x, y, and the given array a. Note that we're being generic in the type of array we're expecting.

proveSArray :: IO ThmResult

Prove it using SMT-Lib arrays.

>>> proveSArray
Q.E.D.

proveSFunArray :: IO ThmResult

Prove it using SBV's internal functional arrays.

>>> proveSFunArray
Q.E.D.