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In this document, we propose a description, via a Haskell implementation, ofa generalization of the notion of regular expression allowing us to group thedefinitions and the methods of (tree or word) automata constructions over onegeneric structure, based on enriched category theory tools. We first recallseveral methods of conversion from expressions to automata, enlightening thesimilarities between the words and trees cases. We then produce an originalstudy of the power of enriched category theory applied 1) to automata andexpressions implementation, and 2) to the study of associated algorithms, usingadvanced concepts of functional programming, while simultaneously constructinga Haskell implementation of notions of enriched category theory and associatedautomata. More precisely, the Haskell implementation and the algebraicdefinition of the generic automaton structure are based on the following ideas:  - enriched categories, enriched functors, enriched monads, etc. can beimplemented in Haskell;  - Type level programming can be used to properly encode function arity;  - monoids (word structure) and operads (tree structure) can be encoded asmonoid objects;  - tree and word automata can be represented by the same algebraic structure,via enriched categories.  This generalization leads to surprising remarks. As an example, someclassical algorithms (determinization, completion, conversion from alternatingto deterministic automaton) can be regrouped in only one function. We will thendefine a notion of generalized expressions based on the notion of monoidaltensor product.  Haskell sources are available at:http://ludovicmignot.free.fr/HDR/src-HDR.zip

A unified implementation of automata and expression structures, and of the associated algorithms using enriched categories