Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A program transformation is any operation that takes a program and generates another program. It is often important that the derived program be semantically equivalent to the original, relative to a particular formal semantics. Other program transformations may generate programs that semantically differ from the original in predictable ways. A generalisation of semantic equivalence is the notion of program refinement: one program is a refinement of another if it terminates on all the initial states for which the original program terminates, and for each such state it is guaranteed to terminate in a possible final state for the original program. In other words, a refinement of a program is more defined and more deterministic than the original program. If two programs are refinements of each other, then the programs are equivalent.

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