Illustration. The interaction principles of LG provide a particularly direct way of capturing phenomena that depend on infixation rather than concatenation.  The derivations below (using monotonicity, and (dual) residuation steps) show how the same pieces of information (the same premises) can be used either to introduce an implication B\C on the left of the turnstile, or a coimplication B ⊘ C on the right.  The first option leads to a rule of Application — the central composition operation of standard Lambek calculus. The second option leads to a Co-Application variant.  Although these two rules are derived from the same premises, there is an important difference between them.  When the implication B\C composes with its argument, it must stay external to X.  In the case of the coimplication, when X is some product of factors A1,…,An, the conditions for the interaction principles are met.  This means that the coimplication B ⊘ C will be able to descend into the phrase X and associate with any of the constituent parts Ai into a formula (B ⊘ C) ⦸ Ai.