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ctchou
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chenson2018,
fmontesi,
kim-em and
sorrachai
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September 14, 2026 03:53
eric-wieser
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Sep 14, 2026
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| class RightCongruence (α : Type*) extends eq : Setoid (List α) where | ||
| right_cov : CovariantClass _ _ (fun x y => y ++ x) eq |
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It might be worth copying Con and RingCon here; that is, skipping CovariantClass and writing these more directly as append_left and append_right.
Note that those also don't override toSetoid to eq, and instead add a FunLike instance.
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But wouldn't that require a Mul (List α) with ++ being the multiplication? My impression from the following Zulip thread is that that is not considered a good idea:
#Is there code for X? > List as a monoid
eric-wieser
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This PR develops yet another characterization of regular languages: a language is regular if and only if its syntactic monoid is finite. The syntactic monoid is the quotient of the free monoid by the Myhill congruence, which is a two-sided congruence on finite words that is finer than the Nerode congruence used in the Myhill-Nerode theorem.
As part of this PR, both left and two-sided congruences on finite words are defined and all congruences on finite words are moved from the namespace
Cslibto the more appropriate namespaceLanguage.