Understanding developmental and evolutionary aspects of the language faculty requires comparing adult languages users' abilities with those of non-verbal subjects, such as babies and non-human animals. Classically, comparative work in this area has relied on the rich theoretical frameworks developed by linguists in the generative grammar tradition. However, the great variety of generative theories and the fact that they are models of language specifically makes it difficult to know what to test in animals and children lacking the expressive abilities of normal, mature adults. We suggest that this problem can be mitigated by tapping equally rich, but more formal mathematical approaches to language.