Massive generation of refutations via polynomials over Z/nZ #19
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eric-wieser
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Sep 27, 2024
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Hmm, the blueprint CI broke. I think I’ll wait for the overall discussion around file structure to settle before continueing here. Anyone is welcome to pick it up though. |
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dwrensha
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Sep 27, 2024
…into finite_poly_refutation
pitmonticone
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Sep 29, 2024
this extracts the “infrastructure” built in #19 into its own PR. In particular * The `Facts G [1,2] [3,4]` syntax to concisely and efficiently state that G satisfies Equation1 and Equation2, but not Equation3 and Equation4 There is also a crude `calculate_facts` command that takes a magma and an instance and a tactic and lists those for which the tactic succeeds. * The `decideFin!` tactic that is a bit like `decide` but simply believes that the statement is true, so that the check only happens by the kernel, and uses custom code to construct the `Decidable` instance for the kind of theorems we actually encounter, to avoid the (slow) type inference. * The `memoFinOp` elaborator that take a function `Fin n → Fin n → Fin n`, tabulates it, encodes this table in a single number and implements the lookup based on that. Presumably that's more compact and faster to evaluate by `decide` than other forms (array indexing, polynomials etc.)
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Should be merged after #110 only. |
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This PR adds a large number of automatically generated refutations by @carlini in https://github.com/carlini/equational_theories. All of them are magmas over Z/nZ with a polynomial of degree ≤2 as the operations.
For now, until we know better what to actually run, I excluded all magmas with 6 or more elements, just to keep this PR sizable.