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 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.