Stability | experimental |
---|---|

Maintainer | erkokl@gmail.com |

Safe Haskell | None |

Demonstrates function counter-examples

# Documentation

thmGood :: SWord8 -> SWord8 -> SWord8 -> SBoolSource

Asserts that `f x z == f (y+2) z`

whenever `x == y+2`

. Naturally correct:

`>>>`

Q.E.D.`prove thmGood`

thmBad :: SWord8 -> SWord8 -> SBoolSource

Asserts that `f`

is commutative; which is not necessarily true!
Indeed, the SMT solver returns a counter-example function that is
not commutative. (Note that we have to use Yices as Z3 function
counterexamples are not yet supported by sbv.) We have:

`>>>`

Falsifiable. Counter-example: x = 0 :: SWord8 y = 128 :: SWord8 -- uninterpreted: f f 128 0 = 32768 f _ _ = 0`proveWith yices $ forAll ["x", "y"] thmBad`

Note how the counterexample function `f`

returned by Yices violates commutativity;
thus providing evidence that the asserted theorem is not valid.