Double Applicative Functors
Writing easily readable parser code is a classic application of monads in functional programming. For simpler cases, the Applicative and Alternative type classes in Haskell can be used for this purpose instead of the more powerful Monad and MonadPlus classes. Counterparts of all parsing expression grammar constructs except lookaheads are expressible via the Applicative and Alternative class methods. Yet their error handling capabilities are unsatisfactory even for simple applications. This paper proposes double applicative functors for increasing the flexibility of error handling without full monadic power, along with an extended set of operations, and studies relationships between mathematical laws that these operations are assumed to fulfill. Many properties of these operations are generalizations of semantic equivalences previously known for parsing expression grammars.
KeywordsApplicative functors Monads Parsing Error handling
The work was partially supported by the Estonian Research Council under R&D project No. IUT2-1.
The author thanks Tarmo Uustalu for fruitful discussions and also the anonymous reviewers for valuable feedback.
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