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official:goals [2012/04/25 15:57] paddy |
official:goals [2012/07/06 18:08] (current) paddy |
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| * More advanced example. | * More advanced example. | ||
| - | * Be able to define the algorithm and specify its correctness. | + | * Be able to define the algorithm and specify its correctness. |
| + | * Doing the proof at this point can be challenging. | ||
| + | * It highly depends on your definitions and your knowledge of the proof system. | ||
| + | * You should be able to do it at the end of the semester the latest. | ||
| ===== Sheet 3 ===== | ===== Sheet 3 ===== | ||
| Line 38: | Line 40: | ||
| * Be able to specify properties on such functions. | * Be able to specify properties on such functions. | ||
| * Be able to prove many of these properties with a simple proof pattern. | * Be able to prove many of these properties with a simple proof pattern. | ||
| - | * Next steps in finding missing lemmas from proofs which do not working yet. | + | * Next steps in finding missing lemmas from proofs which are not working yet. |
| ==== Exercise 2 ==== | ==== Exercise 2 ==== | ||
| Line 47: | Line 49: | ||
| ==== Exercise 3 ==== | ==== Exercise 3 ==== | ||
| - | * More exercise in writing functional programs and using datatypes. | + | * More exercise in writing, understanding and modifying functional programs and datatypes. |
| * Get familiar with proofs, proof commands and proof states in a very simple setting. | * Get familiar with proofs, proof commands and proof states in a very simple setting. | ||
| * In general, understand how provers work and how one could implement one. | * In general, understand how provers work and how one could implement one. | ||
| + | |||
| + | |||
| + | ===== Sheet 4 ===== | ||
| + | |||
| + | * Basic theory questions you should be able to answer about the HOL core, universes, models, conservative extensions, etc. | ||
| + | * Exercise 2 (d/e) More and more advanced questions where you can get more familiar with using Isabelle/HOL, proofs, finding and applying theorems, etc. | ||
| + | |||
| + | ===== Sheet 5 ===== | ||
| + | |||
| + | |||
| + | ==== Exercise 1 ==== | ||
| + | |||
| + | * Be able to apply methods to rules and do proofs. | ||
| + | * Get to know the different methods. | ||
| + | * Get to know more and more rules. | ||
| + | * Be able to do arbitrary proofs on propositional and predicate logic theorems. | ||
| + | |||
| + | ==== Exercise 2 ==== | ||
| + | |||
| + | * Get familiar with designing and defining both syntax and semantics of languages. | ||
| + | * First steps towards formulating and proving properties relating models, in this case two language semantics and a compiler. | ||
| + | |||
| + | ===== Sheet 6 ===== | ||
| + | |||
| + | * First steps in finding needed theorems from the library, using the Find Theorems function. | ||
| + | * First steps in using different induction schemes. | ||
| + | * First case study about specifying models, properties and proving their consistency. | ||
| + | |||
| + | ===== Sheet 7 ===== | ||
| + | |||
| + | * Two more complex case studies for specifying models, properties and proving their consistency. | ||
| + | * Be able to define advanced models. | ||
| + | * Be able to specify properties for such models. | ||
| + | * Be able to prove those properties with regard to the models. | ||
| + | |||
| + | * Understand and proof properties on paper about lattices and fixpoints. | ||
| + | * Be able to specify inductive sets on paper and understand their semantics. | ||
| + | |||
| + | ===== Sheet 8 ===== | ||
| + | |||
| + | * Get familiar with LTL. | ||
| + | * Be able to specify properties about transition systems in LTL. | ||
| + | * Be able to do proofs of LTL properties, using the semantics. | ||
| + | * Get to know one possible definition of traces and transition systems and how to use it for proofs. | ||
| + | * First steps in defining a calculus for an embedded logic in Isabelle/HOL and using the calculus to do proofs. | ||
| + | * Learn how the specification affects proofs and how changes in the specification can help the proofs. | ||
| + | |||
| + | ===== Sheet 9 ===== | ||
| + | |||
| + | * Understand the difference between different styles of semantics. | ||
| + | * Be able to prove properties about language semantics. | ||
| + | * Be able to do induction over inductive sets / predicates. | ||
| + | |||
| + | ===== Sheet 10 ===== | ||
| + | |||
| + | * Be able to do pen & paper proofs using the Hoare calculus. | ||
| + | * Be able to find simple loop invariants. | ||
| + | * Be able to translate proofs into the framework created in the lecture. | ||
official/goals.1335362222.txt.gz · Last modified: 2012/04/25 15:57 by paddy
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