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Engineering composite materials and devices with desired topological properties is accelerating the development of topological physics and its applications. Approaches of realizing novel topological hybrids, including in-situ epitaxy growth, planar/layered superlattices, and assembled (artificial) atom/dot arrays, etc., endow the topological systems with a substantial degree of control and tunability. Here, we propose a framework for realizing a field-programmable topological array (FPTA) that enables the implementation of dynamically reconfigurable topological platforms. FPTA allows for the independent, simultaneous, and local programmability of the various platform properties, such as the electromagnetic field, the spin-orbit field, and the superconducting order parameter. To demonstrate the effectiveness of the FPTA in rendering the system topologically-nontrivial and implementing non-Abelian manipulations, we simulate their operation in various case-studies. Our framework provides a playground for unearthing novel topological phases using components of high feasibility and sets the guidelines for run-time dynamic reconfiguration which is crucial for high-performance topological electronic circuits and quantum computing.