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sav07_homework_2 [2007/03/28 14:43] vkuncak |
sav07_homework_2 [2007/03/29 22:21] vkuncak |
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====== Homework 2 ====== | ====== Homework 2 ====== | ||
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For in depth understanding you can also read references in there, in particular the relevant Wilfrid Hodges model theory book sections. | For in depth understanding you can also read references in there, in particular the relevant Wilfrid Hodges model theory book sections. | ||
- | + | **Hint**: You should be able to reduce the problem to reasoning about conjunctions and generate a disjunction over total orders over terms of form v+c. Alternatively, you may be able to use some ideas of [[http://citeseer.ist.psu.edu/71579.html|Fourier-Motzkin elimination]], but it is not necessary for this problem to have an efficient algorithm, only an algorithm that works in principle. | |
==== Verification condition generator ==== | ==== Verification condition generator ==== | ||
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| havoc(v,...,v) | | havoc(v,...,v) | ||
| S ; S | | S ; S | ||
- | | while (F) { S } | + | | while [inv F] (F) { S } |
| if (F) { S } else { S } | | if (F) { S } else { S } | ||
T ::= T+T | T-T | K*T | v | T ::= T+T | T-T | K*T | v | ||
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This notation corresponds to a fragment of the language of the [[wk>Isabelle theorem prover]], as well as the [[Jahob system]]. | This notation corresponds to a fragment of the language of the [[wk>Isabelle theorem prover]], as well as the [[Jahob system]]. | ||
+ | |||
+ | The notation for while loop indicates that all loops have supplied loop invariants. | ||
You do not need to build a parser for programs and formulas for this exercise, but it may make the testing of your implementation easier. | You do not need to build a parser for programs and formulas for this exercise, but it may make the testing of your implementation easier. | ||
- | 2. Given a statement S, compute wp(S,true) and pretty print it as a string conforming to the above grammar. Test your program on | + | To make sure that you correctly avoid accidental variable capture, one of the many tests for your program should be the following 4 line sequence of commands: |
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+ | x = 0; | ||
+ | y = x + 3; | ||
+ | havoc(x); | ||
+ | assert (y=3); | ||
+ | |||
+ | 2. Given a statement S, compute wp(S,true) using the part 1, and pretty print it as a string conforming to the above grammar. Test your program on | ||
* two input programs that generate valid formulas | * two input programs that generate valid formulas | ||
* two input programs that generate invalid formulas | * two input programs that generate invalid formulas | ||
Try using the [[wk>Isabelle theorem prover]] or formDecider in the [[Jahob system]] to prove the validity of the printed formulas and describe your experience. | Try using the [[wk>Isabelle theorem prover]] or formDecider in the [[Jahob system]] to prove the validity of the printed formulas and describe your experience. | ||