We propose a method for formulating CCG as a recursive composition in a continuous vector space.Recent CCG supertagging and parsing models generally demonstrate high performance, yet rely on black-box neural architectures to implicitly model phrase structure dependencies.Instead, we leverage the method of holographic embeddings (Nickel et al., 2016) as a compositional operator to explicitly model the dependencies between words and phrase structures in the embedding space.Experimental results revealed that holographic composition effectively improves the supertagging accuracy to achieve state-of-the-art parsing performance when using a C&C parser.The proposed span-based parsing algorithm using holographic composition achieves performance comparable to state-of-the-art neural parsing with Transformers.Furthermore, our model can semantically and syntactically infill text at the phrase level due to the decomposability of holographic composition.