feat: add basic API for halting of TMs #675
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callesonne
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Sep 30, 2025
FormalConjectures/ForMathlib/Computability/TuringMachine/BusyBeavers.lean
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callesonne
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Oct 21, 2025
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This is mainly proofs so looks good to me, but I didn't review the original PR adding these files so can I ask: is the option in def step (M : Machine Γ Λ) : Cfg Γ Λ → Option (Cfg Γ Λ) really necessary? Couldn't you send ⟨none, t⟩ to ⟨none, t⟩ again? Instead of sending it to none. This is so that it could take values in Cfg Γ Λ which I feel would make some case work later easier. But I am not super familiar with Turing machines.
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| def neverHalts : Machine Γ Λ := fun l s => | ||
| match l, s with | ||
| | .S, .A => some (Λ.T, Stmt.write default Dir.right) | ||
| | .T, .A => some (Λ.S, Stmt.write default Dir.right) | ||
| | .S, .B => some (Λ.T, Stmt.write default Dir.left) | ||
| | .T, .B => some (Λ.T, Stmt.write default Dir.left) |
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I'm slightly confused why we are putting definitions in a test file? Is it because this is not going into Mathlib eventually?
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