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The work extends the computational model EULAG-MHD to include Hall magnetohydrodynamics (HMHD)---important to explore physical systems undergoing fast magnetic reconnection at the order of the ion inertial length scale. Examples include solar transients along with reconnections in magnetosphere, magnetotail and laboratory plasmas. The paper documents the results of two distinct sets of implicit large-eddy simulations in the presence and absence of the Hall forcing term, initiated with an unidirectional sinusoidal magnetic field. The HMHD simulation while benchmarking the code also emphasizes the complexity of three dimensional (3D) evolution over its two dimensional (2D) counterpart. The magnetic reconnections onset significantly earlier in HMHD. Importantly, the magnetic field generated by the Hall term breaks any inherent symmetry, ultimately making the evolution 3D. The resulting 3D reconnections develop magnetic flux ropes and magnetic flux tubes. Projected on the reconnection plane, the ropes and tubes appear as magnetic islands, which later break into secondary islands, and finally coalesce to generate an X-type neutral point. These findings are in agreement with the theory and contemporary simulations of HMHD, and thus verify our extension of the EULAG-MHD model. The second set explores the influence of the Hall forcing on generation and ascend of a magnetic flux rope from sheared magnetic arcades---a novel scenario instructive in understanding the coronal transients. The rope evolves through intermediate complex structures, ultimately breaking locally because of reconnections. Interestingly, the breakage occurs earlier in the presence of the Hall term, signifying faster dynamics leading to magnetic topology favorable for reconnections.