I'm looking for creative uses of monads to learn from. I've read somewhere that monads have been used for example in AI, but being a monad newbie, I fail to see how.
Please include a link to the source code and sample usages. No standard monads please.
Phil Wadler has written many papers on monads, but the one to read first is a lot of fun and will be accessible to any programmer; it's called The essence of functional programming. The paper includes source code and sample usages.
A personal favorite of mine is the probability monad; if you can find Sungwoo Park's PhD thesis, it has a number of interesting example codes from robotics.
There's also LogicT (backtracking monad transformer with fair operations and pruning).
It has good value to AI Search algorithms because of its constructs for fair disjunctions, for example, easily enabling computations that succeed an infinite number of times to be combined (interleaved).
It's usage is described in the ICFP'05 paper Backtracking, Interleaving, and Terminating Monad Transformers
you can find interesting and advanced monads in the blog A Neighborhood of Infinity. I can note the Vector Space Monad, and its use for rational tangles description. Unfortunately,I don't think I understand this well enough to explain it here.
One of my favorite monads is Martin Escardo's search monad. It can be found on hackage in infinite-search package.
It is the monad of "search functions" for a set of elements of type a, namely (a -> Bool) -> Maybe a (finding an element in the set matching a given predicate).
Read series of articles on monads used to model probability and probabilistic processes here : http://www.randomhacks.net/articles/2007/03/03/smart-classification-with-haskell (follow links to prev/next parts)
Harpy, a package for run-time generation of x86 machine code, uses a code generation monad. From the description:
This is a combined reader-state-exception monad which handles all the details of handling code buffers, emitting binary data, relocation etc.
All the code generation functions in module Harpy.X86CodeGen live in this monad and use its error reporting facilities as well as the internal state maintained by the monad.
The library user can pass a user environment and user state through the monad. This state is independent from the internal state and may be used by higher-level code generation libraries to maintain their own state across code generation operations.
I found this a particularly interesting example because I think that this pattern is not uncommon: I'd invented something quite similar myself for generating a set of internal messages for my application based on messages received from a (stock) market data feed. It turns out to be an extremely comfortable way to have a framework keep track of various "global" things whilst composing simple operations that in and of themselves keep no state.
I took one step further his idea of having a user state (which I call a "substate") that could also be passed through the monad: I have a mechanism for switching out and restoring state during the monad run:
-- | Given a generator that uses different substate type, convert it
-- to a generator that runs with our substate type. As well as the
-- other-substate-type generator, the caller must provide an initial
-- substate for that generator and a function taking the final substate
-- of the generator and producing a new substate of our type. This
-- preserves all other (non-substate) parts of the master state touched
-- by the generator.
--
mgConvertSubstate :: MsgGen msg st' a -> st' -> (st' -> st) -> MsgGen msg st a
This is used for subgroups of combinators that had their own state needed for a short period. These run with just their state, not knowing anything about the state of the generator that invoked it (which helps make things more modular), and yet this preserves any non-user-specific state, such as the current list of messages generated and the current set of warnings or errors, as well as the control flow (i.e., allowing total aborts to flow upwards).
I'd like to list a couple of monads not yet mentioned in other answers.
The Omega monad can be used to productively traverse infinite lists of results. Compare:
>>> take 10 $ liftM2 (,) [0..] [0..]
[(0,0),(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9)]
>>> take 10 $ runOmega $ liftM2 (,) (each' [0..]) (each' [0..])
[(0,0),(0,1),(1,0),(0,2),(1,1),(2,0),(0,3),(1,2),(2,1),(3,0)]
With a bit more advanced WeightedSearch monad it is also possible to assign weights to computations so that results of computations with lower weights would appear first in the output.
A useful These data type forms a Monad similar to Either, but able to accumulate errors rather. The package also defines MonadChronicle class as well as ChronicleT monad transformer based on These.
