feat: prove that regular languages are closed under Kleene star #241
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Rebase on #239. |
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Rebase on #239 again. |
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Rebase on #239. |
chenson2018
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In this patch we prove that regular languages are closed under concatenation, by leveraging the results already proved about the infinite executions of the automata concatenation construction in `NA/Concat.lean`. In order to do so, we introduce the notion of a "total LTS", which means that the LTS has a next state for any given starting state and label, and a "LTS.totalize" construction that converts any LTS into a total LTS by adding a sink state and transitions from all states to the sink state. Then the notion of "total" and the "totalize" construction are generalized to NA. By "totalizing" NA's, we can extend any finite execution of a NA into an infinite execution and thus re-use the results already proved for infinite executions. The same technique can be applied to `NA/Loop.lean` to prove that regular languages are closed under the Kleene star; see PR #241.
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Jan 9, 2026
… the move to the new module system)
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My style comments have been addressed.
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@fmontesi, could you review this PR? Chris has approved it. Thanks! |
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This patch proves that regular languages are closed under Kleene star. The proof technique is similar to the one used in PR #239 and re-uses much of the infrastructure introduce in that PR.