Copyright | (c) Levent Erkok |
---|---|

License | BSD3 |

Maintainer | erkokl@gmail.com |

Stability | experimental |

Safe Haskell | None |

Language | Haskell2010 |

Example inductive proof to show partial correctness of the for-loop based fibonacci algorithm:

i = 0 k = 1 m = 0 while i < n: m, k = k, m + k i++

We do the proof against an axiomatized fibonacci implementation using an uninterpreted function.

# System state

System state. We simply have two components, parameterized over the type so we can put in both concrete and symbolic values.

## Instances

fibCorrect :: IO (InductionResult (S Integer)) Source #

Encoding partial correctness of the sum algorithm. We have:

`>>>`

Q.E.D.`fibCorrect`

NB. In my experiments, I found that this proof is quite fragile due to the use of quantifiers: If you make a mistake in your algorithm or the coding, z3 pretty much spins forever without finding a counter-example. However, with the correct coding, the proof is almost instantaneous!