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sav08:proving_correctness_of_some_small_examples [2010/02/22 12:16] vkuncak |
sav08:proving_correctness_of_some_small_examples [2015/04/21 17:30] |
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| - | ====== Proving Correctness of Some Small Examples ====== | ||
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| - | In this demo we go through several examples and prove them correct using the [[:Jahob system]]. | ||
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| - | ==== A Recursive Function ==== | ||
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| - | Consider the following recursive function: | ||
| - | |||
| - | <code> | ||
| - | private static int f(int x, int y) | ||
| - | { | ||
| - | if (y == 0) { | ||
| - | return 0; | ||
| - | } else { | ||
| - | if (y % 2 == 0) { | ||
| - | int z = f(x, y / 2); | ||
| - | return (2 * z); | ||
| - | } else { | ||
| - | return (x + f(x, y - 1)); | ||
| - | } | ||
| - | } | ||
| - | } | ||
| - | </code> | ||
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| - | * What does 'f' compute? | ||
| - | * How can we prove it? | ||
| - | * [[Proof of first lecture01 example]] | ||
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| - | === An Iterative Example === | ||
| - | |||
| - | <code> | ||
| - | private static int fi(int x, int y) | ||
| - | { | ||
| - | int r = 0; | ||
| - | int i = 0; | ||
| - | while | ||
| - | (i < y) { | ||
| - | i = i + 1; | ||
| - | r = r + x; | ||
| - | } | ||
| - | return r; | ||
| - | } | ||
| - | </code> | ||
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| - | * How can we prove it? | ||
| - | * [[Notion of inductive loop invariant]] | ||
| - | * What is and is not inductive loop invariant in this example | ||
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| - | === Transforming iterative version === | ||
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| - | * changing initial condition | ||
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| - | === Summary of these Small Examples === | ||
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| - | {{sav08:integerdemo.java.txt|Examples of Functions with Specifications}} | ||
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| - | === Some other Examples done in Jahob === | ||
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| - | * http://javaverification.org/ | ||
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| - | === Another System === | ||
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| - | * [[http://research.microsoft.com/en-us/projects/vcc|VCC: A Verifier for Concurrent C]] | ||