Do you know online courses with Haskell for Theory of Computation?
This is another not-an-answer that might provide some useful resources. The last is probably the best, but not Haskell related
The two old standards for such a course are:

Introduction to Automata Theory, Languages, and Computation, by Hopcroft, Motwani, and Ullman. Earlier editions were just Hopcroft and Ullman.

Introduction to the Theory of Computation by Sipser.


I don't have the second book, and don't know if it includes any programming exercises, but there might be something in Scheme, knowing Sipser. Amazon's &quot;Look Inside&quot; doesn't seem to work for Sipser.
Two additional books, both very old and hard to get but very highly recommended if you can find them - both short and straightforward with clear explanations are

First Course in Formal Language Theory (Computer science texts)
by V. J. Rayward-Smith, and

First Course in Computability (Computer Science Texts)
by V. J. Rayward-Smith


The final suggestion is a software system with an associated text.
JFlap was created by Susan Rodger and her colleagues at Duke to form the basis of such a course. Students can easily create all sorts of finite automata. The book they wrote to go with this is JFap: An interactive Formal Languages and Automata Package, Rodger and Finley.
Wikipedia has an overview of JFlap.
Note that JFlap writes automata descriptions in XML which should be easy to parse in any language. All of the automata mentioned in the JFLap tutorial are available for download.
I was part of the NSF evaluation of this system and it is really excellent.