Array-based programming languages have shown significant promise for improving performance of column-based in-memory database systems, allowing elegant representation of query execution plans that are also amenable to standard compiler optimization techniques. Use of loop fusion, however, is not straightforward, due to the complexity of built-in functions for implementing complex database operators. In this work, we apply a compiler approach to optimize SQL query execution plans that are expressed in an array-based intermediate representation. We analyze this code to determine shape properties of the data being processed, and use a subsequent optimization phase to fuse multiple database operators into single, compound operations, reducing the need for separate computation and storage of intermediate values. Experimental results on a range of TPC-H queries show that our fusion technique is effective in generating efficient code, improving query time over a baseline system.