We describe an implementation in Carpenter's typed feature formalism, ALE, of a discourse grammar of the kind proposed by Scha, Polanyi, et al. We examine their method for resolving parallelism-dependent anaphora and show that there is a coherent feature-structural rendition of this type of grammar which uses the operations of prwrity union and generalization. We describe an augmentation of the ALE system to encompass these operations and we show that an appropriate choice of definition for priority union gives the desired multiple output for examples of vP-ellipsis which exhibit a strict/sloppy ambiguity. 1 Discourse Grammar Working broadly within the sign-based paradigm exemplified by HPSG (Pollard and Sag in press) we have been exploring computational issues for a discourse level grammar by using the ALE system (Carpenter 1993) to implement a discourse grammar. Our central model of a discourse grammar is the Linguistic Discourse Model (LDM) most often associated with Scha, Pol...