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This paper presents an approach to completing variable names when writing programs in implicitly typed functional languages. As a first step toward developing practical systems, we considered a simple case: up to the cursor position the program text is given completely. With this assumption we specify a variable completion problem for an implicitly typed core functional language with letpolymorphism and show an algorithm for solving the problem. Based on the algorithm we have implemented adoi:10.1007/s10990-013-9095-x fatcat:3o65l2abtvg43bxbtv2fpkoiwi