| 1. | The above example also illustrates the use of an inductive loop invariant.
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| 2. | Loop invariants are used to monitor specific properties of a loop during successive iterations.
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| 3. | The technique of abstract interpretation can be used to detect loop invariant of given code automatically.
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| 4. | The boolean formula " I " in this rule is known as the loop invariant.
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| 5. | Traditional optimizations such as common subexpression elimination and loop invariant hoisting often focus on eliminating redundant computation.
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| 6. | Loop invariants are essentially constants within a loop, but their value may change outside of the loop.
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| 7. | This implies that when a loop terminates correctly, both the exit condition and the loop invariant are satisfied.
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| 8. | Hence, loop invariants and variants are provided by human users, or are inferred by some abstract interpretation procedure.
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| 9. | A loop invariant is an assertion which must be true before the first loop iteration and remain true after each iteration.
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| 10. | When loops are nested, an induction variable in the outer loop can be a loop invariant in the inner loop.
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