We explore the consequences of letting the incremental and integrative nature of language processing inform the design of competence grammar. What emerges is a view of grammar as a system of local monotonic constraints that provide a direct characterization of the signs (the form-meaning correspondences) of a given language. This "sign-based" conception of grammar has provided precise solutions to the key problems long thought to motivate movement-based analyses, has supported three decades of computational research developing large-scale grammar implementations, and is now beginning to play a role in computational psycholinguistics research that explores the use of underspecification in the incremental computation of partial meanings.