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Theories of morphology have been classified as Item-and-Arrangement (in which both roots and affixes are treated as morphemes), or Item-and-Process (in which roots are morphemes, but affixes are rules). I will show that in reality, a description using affixes-as-morphemes (Item-and-Arrangement morphology) can be mapped into a single representation.
A different classification of morphological theories is based on whether all allomorphs are listed in the lexicon, or whether phonologically conditioned allomorphs are derived from a single listed form. I show that in reality, derivational theories incorporate a device (allomorphy rules) which can do virtually the same work as listing the phonologically conditioned allomorphs. In fact, it is possible to mechanically map a description with multiple listed allomorphs into a description with single underlying forms and allomorphy rules.