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
Phonological rule most general way possible. Thus, the intervocalic alveolar flapping described above can be formalized as The rule given above for intervocalic alveolar flapping describes what sound is changed, what the sound changes to, and where the change happens (in other words, what the "environment" is that triggers the change). The illustration below presents the same rule, with each of its parts labelled and described. Taken together and read from left to right, this notation of the rule for intervocalic alveolar flapping states that any alveolar stop consonant (/t/ or /d/) becomes a tap ([ɾ]) in the environment where it is