Since Stalnaker 1974, Heim 1983, and Karttunen 1974, satisfaction of presuppositions in a particular local context has been taken to be a prominent factor determining whether or not certain parts of discourse are felicitous. Consider the following ever-elusive data.

(1) Hi! Mary has a wetsuit! I hope Mary brings her wetsuit!    (Perfectly acceptable)

(2) I hope Mary brings her wetsuit! Hi! Mary has a wetsuit!    (Surprisingly unacceptable)

Recently, monads have been used in semantic theorizing to help explain certain grammatical relations between expressions that appear to display a left-to-right bias: this bias has been argued to appear in the domains of scope (Barker & Shan, 2014; Charlow, 2015), binding and anaphora (Charlow, 2015; Bumford, 2016), as well as others. As far as I know, monadic grammars have not been used to treat the left-to-right bias in the determination of contexts for presupposition-satisfaction, illustrated by data like (1) and (2). I therefore provide an update to the proof-theoretic account of presupposition failure presented earlier in the year that allows it to track discourse updates which my alter the local context, changing the content of presuppositions. Because of the left-to-right bias of the formalism, discourse-updates may only occur left-to-right. I then give the proof-theoretic account a model-theoretic interpretation using a variant of the State.Set monad introduced in Charlow 2015. This is work in progress, and feedback is much appreciated!