The two senses of "invariant" are two of the most important concepts in programming and physics, respectively.

The programming sense is a predicate that stays the same as you go through a loop. See sorting example of invariant. Knowing your invariants is a good way to write bug free code.

In physics, invariants are closely tied to conservation properties. I.e. invariance under time and translation implies conservation of momentum.

In software engineering, a explicit logical statement that must evaluate to true at all externally observable times during the lifecycle of a method or component. (Compare with precondition and postcondition). "Externally observable" is an important qualifier, since the component's regular operation may require several steps, between which the invariant is not necessarily satisfied. In the design by contract paradigm, pioneered by the Eiffel language, invariants are embodied as formal assertions that are tested on the entry and exit of a method. Failure of an invariant can denote an error either by the "client" or the "supplier", and places no guarantees that the component still functions as designed.

In complex application software, an invariant represents a known consistent state of an object, or complex data structure of objects. In a database, for example, relational constraints must be maintained, often through transaction management. However, invariants have a role to play in much smaller components. They can be used to guard against possible corruption of an object, and calculations based on invariants may be moved out of iterative code during optimization.

Violations in invariants are often used as detection for race conditions in multithreading environments. Without a suitable synchronization mechanism, one thread of execution operates on the object while in a state where it should not be externally observable. The invariant, and hence the behavior of the object, cannot be guaranteed under these conditions.

In*va"ri*ant (?), n. Math.

An invariable quantity; specifically, a function of the coefficients of one or more forms, which remains unaltered, when these undergo suitable linear transformations.

J. J. Sylvester.

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