# module LO = Monad.List.T(Monad.Option);;
# module OL = Monad.Option.P(Monad.List);; (* we use the `.P` transformer to hoist List's ++ operation *)
- # OL.(run (mzero ++ mid 20 >>= fun i -> mid (i+10)));;
+ # OL.(run (mzero ++ mid 20 >>= fun x -> mid (x+10) ));;
- : int OL.result = [Some 30]
When List is on the inside, the failed results just got dropped and the computation proceeds without them.
- # LO.(run (hoist Monad.Option.mzero ++ mid 20 >>= fun i -> mid (i+10)));;
+ # LO.(run (hoist Monad.Option.mzero ++ mid 20 >>= fun x -> mid (x+10) ));;
- : int LO.result = None
On the other hand, when Option is on the inside, as in LO, failures (which we again represent by `mzero`s from the Option monad, not the List monad's own `mzero`; but here since it's the inner monad we need to `hoist Monad.Option.mzero`) abort the whole computation. (If you instead used the List monad's `mzero`, it'd be ignored by `++` and you'd end with just `Some [30]`.)
-This is fun. Notice the difference it makes whether the second `++` is native to the outer `Monad.List`, or whether it's the inner `Monad.List`'s `++` hoisted into the outer wrapper:
+This is fun. Here is a List around a List. Notice the difference it makes whether the second `++` is native to the outer `Monad.List`, or whether it's the inner `Monad.List`'s `++` hoisted into the outer wrapper:
# module LL = Monad.List.T(Monad.List);;
# LL.(run(mid 1 ++ mid 2 >>= fun x -> mid x ++ mid (10*x) ));;
- : int LL.result = \[[1; 10; 2; 20]]
- # LL.(run(mid 1 ++ mid 2 >>= fun x -> hoist Monad.List.(mid x ++ mid (10*x) )));;
+ # LL.(run(mid 1 ++ mid 2 >>= fun x -> hoist Monad.List.(mid x ++ mid (10*x)) ));;
- : int LL.result = [[1; 2]; [1; 20]; [10; 2]; [10; 20]]
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Further Reading
---------------
-* This is excellent, everyone should read: [Monad Transformers Step by Step](http://www.grabmueller.de/martin/www/pub/Transformers.pdf)
+* This is excellent, everyone should read: [Monad Transformers Step by Step](http://www.cs.virginia.edu/~wh5a/personal/Transformers.pdf)
+<!-- also http://web.archive.org/web/20140711174905/http://www.grabmueller.de/martin/www/pub/Transformers.pdf -->
* Read Part III of [All About Monads](http://web.archive.org/web/20071106232016/haskell.org/all_about_monads/html/introIII.html). This link is to an archived version, the main link to haskell.org seems to be broken. Some but not all of this site has been [absorbed into the Haskell wikibook](http://en.wikibooks.org/wiki/Haskell/Monad_transformers).