sbv-0.9.5: Symbolic Bit Vectors: Prove bit-precise program properties using SMT solvers.

Portabilityportable
Stabilityexperimental
Maintainererkokl@gmail.com

Data.SBV.Examples.Uninterpreted.AUF

Description

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.

Synopsis

Documentation

type A = SFunArray Word32 Word32Source

The array type, takes symbolic 32-bit unsigned indexes and stores 32-bit unsigned symbolic values

f :: SWord32 -> SWord64Source

Uninterpreted function in the theorem

thm :: SWord32 -> SWord32 -> A -> SWord32 -> SBoolSource

Correctness theorem. We state it for all values of x, y, and the array a. We also take an arbitrary initializer for the array.

proveThm :: IO ()Source

Prints Q.E.D. when run, as expected