DeepFrozen is a guard and auditor for the property that a reference is transitively immutable: the authority granted by that reference does not include any observable side effects.
Most E implementations provide the DeepFrozen guard, but the DeepFrozen auditor has as yet only been implemented in E-on-CL, as it is the only implementation yet providing the guard-based auditing facility.
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EventuallyDeepFrozen is a variant of the DeepFrozen auditor provided by E-on-CL. Instead of requiring at audit time that the object audited is shown to be immutable, the object is written to be selectively transparent to the DeepFrozen system. Then when the DeepFrozen guard is applied to the object, it recursively examines the object's internal references (through the transparency), just as it would for an ordinary Transparent object, to determine if the object is now DeepFrozen.