This paper presents a syntax-based framework for gap resolution in analytic languages. CCG, reputable for dealing with deletion under coordination, is extended with a memory mechanism similar to the slot-and-filler mechanism, resulting in a wider coverage of syntactic gaps patterns. Though our grammar formalism is more expressive than the canonical CCG, its generative power is bounded by Partially Linear Indexed Grammar. Despite the spurious ambiguity originated from the memory mechanism, we also show that its probabilistic parsing is feasible by using the dual decomposition algorithm.