Stone, ZacharyOperations which take in tuples of syntactic objects and assign them output syntactic objects are used to formalize the generative component of most formal grammars in the minimalist tradition. However, these models do not usually include information which relates the structure of the input and output objects explicitly. We develop a very general formal model of grammars which includes this structural change data, and also allows for richer dependency structures such as feature geometry and feature-sharing. Importantly, syntactic operations involving phrasal attachment selection, agreement, licensing, head-adjunction, etc. can all be captured as special kinds of structural changes, and hence we can analyze them using a uniform technique. Using this data, we give a rich theory of isomorphisms, equivalences, and substructures of syntactic objects, structural changes, derivations, rules, grammars, and languages. We show that many of these notions, while useful, are technically difficult or impossible to state in prior models. It is immediately possible to define grammatical notions like projection, agreement, selection, etc. structurally in a manner preserved under equivalences of various sorts. We use the richer structure of syntactic objects to give a novel characterization of c-command naturally arising from this structure. We use the richer structure of rules to give a general theory of structural analyses and generating structural changes. Our theory of structural analyses makes it possible to extract from productions what structure is targeted by a rule and what conditions a rule can apply in, regardless of the underlying structure of syntactic objects or the kinds of phrasal and featural manipulations performed, where other formal models have difficulty incorporating such structure-sensitive rules. This knowledge of structural changes also makes it possible to extend rules to new objects straightforwardly. Our theory of structural changes allows us to deconstruct them into component parts and show relationships between operations which are missed by models lacking this data. Finally, we extend the model to a copying theory of movement. We implement a traditional model of copying ‘online’, where copies and chains are formed throughout the course of the derivation (while still admitting a feature calculus in the objects themselves). Part of what allows for this is having a robust theory of substructures of derived objects and how they are related throughout a derivation. We show consequences for checking features in chains and feature-sharing.enDissertationLinguisticsagreementcategory theoryformal grammarsminimalist grammarsphrase structuresyntax