semanticpreservation

Semantic preservation is a property of a program transformation whereby the transformed program maintains the same externally observable behavior as the original. In compiler design and programming language theory, a transformation is semantically preserving if, for every valid input program, the transformed version exhibits the same results and interactions with its environment.

Observable behavior typically includes outputs, termination status, exceptions, and memory or I/O effects defined by the language’s semantics. In languages with non-determinism or concurrency, preservation is often framed in terms of contextual or observational equivalence: no context can distinguish the original from the transformed program.

Common examples of semantics-preserving transformations include constant folding and dead code elimination, provided the expressions involved have no side effects. Renaming variables, reordering independent statements, and inlining functions can also be semantics-preserving under the right assumptions about side effects and evaluation order.

Proving semantic preservation usually relies on formal methods. One approach is to relate source and transformed programs via operational, denotational, or axiomatic semantics and establish a simulation or bisimulation between their execution. Contextual equivalence is another key concept: the transformed program must behave identically in all program contexts. Real-world compilers (for example, CompCert) are designed with proofs of semantic preservation to ensure correctness of optimizations.

Limitations and caveats include languages with undefined behavior, memory models, or concurrency, where timing and resource usage may change even if functional behavior remains intact. Semantic preservation focuses on correctness of observable behavior rather than performance characteristics.