Extending monads with pattern matching
Tomas Petricek, Alan Mycroft and Don Syme
In Proceedings of Haskell Symposium 2011
Sequencing of effectful computations can be neatly captured using monads and elegantly written using
do notation. In practice such monads often allow additional ways of composing computations,
which have to be written explicitly using combinators.
We identify joinads, an abstract notion of computation that is stronger than monads and captures
many such ad-hoc extensions. In particular, joinads are monads with three additional operations:
one of type
m a -> m b -> m (a, b) captures various forms of parallel composition,
one of type
m a -> m a -> m a that is inspired by choice and one of type
m a -> m (m a)
that captures aliasing of computations. Algebraically, the first two operations form a
near-semiring with commutative multiplication.
docase notation that can be viewed as a monadic version of
case. Joinad laws
make it possible to prove various syntactic equivalences of programs written using
that are analogous to equivalences about
case. Examples of joinads that benefit from the notation
include speculative parallelism, waiting for a combination of user interface events, but also
encoding of validation rules using the intersection of parsers.
Paper and more information
- Download the paper (PDF)
- Download COQ script with some proofs
- See the original implementation (pre-processor and samples) at Github
- See GHC fork and GHC base fork for a proper implementation
- View talk slides from Haskell Symposium
Try Joinads is a web site, using the open-source release of F#, that implements the joinads extension for F#. It comes with an browser-based F# console where you can experiment with joinads and numerous tutorials that demonstrate the usfulness of joinads. Tutorials include asynchronous, parallel and concurrent programming as well as parsing.
- Visit the Try Joinads web site!
If you want to cite the paper, you can use the following BibTeX information, or get full details from the paper page on ACM.
1: 2: 3: 4: 5: 6: 7:
Published: Monday, 5 September 2011, 12:00 AM
Author: Tomas Petricek
Typos: Send me pull request!