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  1. Proceedings of the 2013 ACM SIGPLAN symposium on Haskell (Haskell '13)
  2. Understanding idiomatic traversals backwards and forwards
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An EDSL approach to high performance Haskell programming
Names for free: polymorphic views of names and binders
Understanding idiomatic traversals backwards and forwards
Adding structure to monoids: thus hopefully ending Haskell's string type confusion
Splittable pseudorandom number generators using cryptographic hashing
Extensible effects: an alternative to monad transformers
Maintaining verified software
Hasochism: the pleasure and pain of dependently typed haskell programming
Data flow fusion with series expressions in Haskell
The Intel labs Haskell research compiler
Monadic functional reactive programming
Mio: a high-performance multicore io manager for GHC
Causality of optimized Haskell: what is burning our cycles?

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Understanding idiomatic traversals backwards and forwards

Content Provider ACM Digital Library
Author Schrijvers, Tom Mehner, Stefan Gibbons, Jeremy Bird, Richard Voigtländer, Janis
Abstract We present new ways of reasoning about a particular class of effectful Haskell programs, namely those expressed as idiomatic traversals. Starting out with a specific problem about labelling and unlabelling binary trees, we extract a general inversion law, applicable to any monad, relating a traversal over the elements of an arbitrary traversable type to a traversal that goes in the opposite direction. This law can be invoked to show that, in a suitable sense, unlabelling is the inverse of labelling. The inversion law, as well as a number of other properties of idiomatic traversals, is a corollary of a more general theorem characterising traversable functors as finitary containers: an arbitrary traversable object can be decomposed uniquely into shape and contents, and traversal be understood in terms of those. Proof of the theorem involves the properties of traversal in a special idiom related to the free applicative functor.
Starting Page 25
Ending Page 36
Page Count 12
File Format PDF
ISBN 9781450323833
DOI 10.1145/2503778.2503781
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2013-09-23
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Monads Finitary containers Applicative functors Idioms Traversable functors
Content Type Text
Resource Type Article
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