adamtopaz/equational_dataset

This dataset was generated using (a fork of) T. Tao's equational theories project.

The file implications.jsonl was generated using the command lake exe extract_implications --jsonl --closure > implications.jsonl. The file tokenized_equations.jsonl was generated using the command lake exe tokenized_data equations > tokenized_equations.jsonl. The file random_tokenized_equations.jsonl was generated using the command lake exe tokenized_data lake exe tokenized_data generate xyzwuvrst 10000000 1 10 > random_tokenized_equations.jsonl.

From there, the set of equations in implications.jsonl was collected, shuffled, and split into two subsets of (essentially) equal size, say A and B. The file train_impl.json contains only those implications whose lhs and rhs equations are both contained in A.

Similarly, the collection of implications whose lhs and rhs are both contained in B was computed, call it S. The set S was shuffled, and also split into two subsets of (essentially) equal size, say U and V. The file val_impl.json contains those implications appearing in U, and the file test_impl.json contains those implications appearing in V.

The magma expressions appearing in the equations in tokenized_equations.jsonl and random_tokenized_equations.jsonl are tokenized using prefix notation. For example, the magma expression (x * y) * z is tokenized as ["mul", "mul", "x", "y", "z"] while x * (y * z) is tokenized as ["mul", "x", "mul", "y", "z"].