Arithmetic algorithms for hereditarily binary natural numbers

In a typed functional language we specify a new tree-based number representation, hereditarily binary numbers, defined by applying recursively run-length encoding of bijective base-2 digits. Hereditarily binary numbers support arithmetic operations that are limited by the structural complexity of their operands, rather than their bitsizes. As a result, they enable new algorithms that, in the best case, collapse the complexity of arithmetic computations by super-exponential factors and in the worst case are within a constant factor of their traditional counterparts.

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