Structural rule A famous structural rule is known as cut. Considerable effort is spent by proof theorists in showing that cut rules are superfluous in various logics. More precisely, what is shown is that cut is only (in a sense) a tool for abbreviating proofs, and does not add to the theorems that can be proved. The successful 'removal' of cut rules, known as "cut elimination", is directly related to the philosophy of "computation as normalization" (see Curry–Howard correspondence); it often gives a good indication of the complexity of deciding a given logic. Structural rule In proof theory, a structural rule is
As-if rule As-if rule The standard for the C++ programming language allows compilers for this language to apply any optimizing transformation to a program during compilation, provided that such optimizations make no change in the "observable behavior" of the program, as specified in the standard; this mostly means that any actions the program performs on its environment occur in the specified order. This rule is commonly referred to as the as-if rule. The rule has three main exceptions. The first is that programs exhibiting undefined behavior are exempt; since the observable behavior is not well-defined anyway, "any" transformation is valid. The other