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sav08:proofs_and_induction [2008/02/20 22:24] vkuncak |
sav08:proofs_and_induction [2008/02/21 11:21] vkuncak |
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====== Informal Proofs and Mathematical Induction ====== | ====== Informal Proofs and Mathematical Induction ====== | ||
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===== Proof Rules ===== | ===== Proof Rules ===== | ||
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===== Using Proof Rules in Isabelle ===== | ===== Using Proof Rules in Isabelle ===== | ||
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+ | [[Isabelle theorem prover]] implements these rules. It names them: | ||
+ | * conjE, conjI, disjE, disjI1, disjI2, impE, impI, allE, allI, exE, exI | ||
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+ | The "E" (elimination) rules are for constructs on left-hand side, and "I" (introduction) rules are for constructs on right-hand side. | ||
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+ | More information: [[http://isabelle.in.tum.de/dist/Isabelle/doc/tutorial.pdf|Isabelle tutorial]], Chapter 5 "The Rules of the Game". | ||
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+ | Demo: Proving above example in Isabelle. | ||
===== Completeness for First-Order Logic ===== | ===== Completeness for First-Order Logic ===== | ||
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\] | \] | ||
- | Deriving one induction from another. | ||
==== Structural Induction ===== | ==== Structural Induction ===== | ||
* [[Calculus of Computation Textbook]], Chapter 4 (some example refer to previous chapters, if you do not understand them, ignore them for now) | * [[Calculus of Computation Textbook]], Chapter 4 (some example refer to previous chapters, if you do not understand them, ignore them for now) |