A page in this context refers to a unit of physical storage (probably on a hard disk), of the order of <math>2^{10}</math> to <math>2^{15}</math> bytes.
Shadow paging is a copy-on-write[?] technique for avoiding in-place updates of pages. Instead, when a page is to be modified, a shadow page is allocated. Since the shadow page has no references (from other pages on disk), it can be modified liberally, without concern consistency constraints, etc. When the page is ready to become durable, all pages that referred to the original are updated to refer to the new replacement page instead. Because the page is "activated" only when it is ready, it is atomic.
If the referring pages must also be updated via shadow paging, this procedure may recurse many times, becoming quite costly. One solution, employed by the WAFL file system (Write Anywhere File Layout) is to be lazy about making pages durable (i.e. write-behind caching). This increases performance significantly by avoiding many writes on hotspots high up in the referential hierarchy (eg: a file system superblock) at the cost of high commit latency.
Write ahead logging is a more popular solution that uses in-place updates.
Shadow paging is similar to the old master-new master batch processing technique used in mainframe database systems. In these systems, the output of each batch run (possibly a day's work) was written to two separate disks (or cards!). One was kept for backup, and the other was used as the starting point for the next day's work.
Shadow paging is also similar to purely functional data structures[?], in that in-place updates are avoided.
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