This paper examines some ideas from Chomsky's (1995) Minimalist Program from the perspective of multimodal categorial grammar (e.g., Moortgat 1996 ). The use of features to drive derivations is seen to give rise automatically to chains, even though the deductive system itself ignores all syntactically inactive structure, including traces. Traces, chains, etc. appear when we examine the structure of the derivation using the Curry-Howard Morphism. In this sense, Curry-Howard proof terms correspond to T-markers, structures which both record the history of a transformational derivation (up to equivalence) and at the same time serve as a static analysis of the syntactic structure of a sentence. We use these tools to address problems both theory-internal, in particular the relation between derivational and representational characterizations of extraction phenomena, and theory-external, in particular the relationship between movement and chain formation on the one hand and hypothetical reasoning on the other hand as ways of accounting for properties of extraction phenomena.