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