On Mon, 5 Jan 2009 09:08:37 -0200, "Rafael Gustavo da Cunha Pereira
Pinto"
Hello everyone
I am a very eclectic person when it comes to computer languages, and I found this monad tutorial for OCaml programmers:
http://enfranchisedmind.com/blog/2007/08/06/a-monad-tutorial-for-ocaml/
I found it to be very interesting, since it shows those "warm, fuzzy things" implemented in another functional language with very clear explanations of what he is doing in each step.
Best regards, and a happy 2k9 for you all!
Rafael
From the aforementioned monad tutorial for O'Caml programmers:
A ‘newbie’, in Haskell, is someone who hasn’t yet implemented a compiler. They’ve only written a monad tutorial. -Pseudonymn
Fascinating.
Forget category theory. Forget space suits and free will and all the other bad analogies floating around about Monads. Monads are first and foremost a design pattern, as in the Gang of Four “Design Patterns” book.
An interesting perspective. The focus on design patterns brings to mind the book How to Design Programs (see http://www.htdp.org/), by Felleisen, Findler, Flatt, and Krishnamurthi, on Scheme, and the recent dialect of Typed Scheme (see http://www.ccs.neu.edu/home/samth/typed-scheme/), as well as the language Qi (see http://www.lambdassociates.org/whatsnew.htm). There is a somewhat similar tutorial on monads using Qi (see "Programming Kung Fu Qi: Monads in Qi" at http://programmingkungfuqi.blogspot.com/2007/02/monads-in-qi.html). For reference, I shall use the Haskell-based monad tutorial "All About Monads" (see http://www.haskell.org/all_about_monads/html/index.html) as a base for one of the Haskell versions of the examples. Most of my descriptions of the Haskell version will be borrowed from the descriptions contained in the section there entitled "Meet the Monads" (see http://www.haskell.org/all_about_monads/html/meet.html). Let's compare the Haskell version with the O'Caml version and a hypothetical pure Scheme version: Haskell version of monad rules (borrowed from the Qi-based tutorial (not the Haskell one)):
class Monad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b
O'Caml version of monad rules (borrowed from the O'Caml-based tutorial):
module type MonadRequirements = sig type ‘a t val bind : ‘a t -> (’a -> ‘b t) -> ‘b t val return : ‘a -> ‘a t end;;
Hypothetical pure Scheme version of monad rules (borrowed from the Qi-based tutorial):
(pipe (lift x) f) = (f x) (pipe m lift) = m (pipe (pipe m f) g) = (pipe m (lambda (x) (pipe (f x) g))
The Haskell version is the most concise. The "return" and "(>>=)" ("bind") operations in Haskell correspond to the "return" and "bind" operations in the O'Caml version, and to the "lift" and "pipe" operations in the hypothetical pure Scheme version. In the Haskell version, "m" is the type constructor, "return" is an operation that creates a value of the monad type "m a," while "(>>=)" (a.k.a. "bind") is an operation that combines a value of that type "m a" with a computation that produces values of that type to produce a new computation for values of that type "(a -> m b) -> m b." Superficially, so far, the three versions seem fairly equivalent to me. Now for examples of list monads: Haskell version (adapted from combining the Haskell-based and the Qi-based tutorials):
instance Monad [ ] where l >>= f = concatMap f l [] >>= f = [] return x = [x]
Your O'Caml version (borrowed from the O'Caml-based tutorial):
module ListMonad = struct type ‘a t = ‘a list;;
let bind lst f = List.concat (List.map f lst);;
let return x = [ x ];; end;;
Qi version (borrowed from the Qi-based tutorial):
(define bind [] _ -> [] [X | Xs] F -> (append (F X) (bind Xs F)))
(define return X -> [X] )
Here we start to see some differences. In the Haskell version, "return" simply creates a singleton list ("[x]"), while "(>>=)" (i.e., "bind") either returns a blank list "[]" in the case of a blank list, or otherwise creates a new list containing the results of applying the function to all of the values in the original list "concatMap f l." In the O'Caml version, notice the "List.concat" operation. After the List.map operation, we are left with not a "‘a list", but instead with a "‘a list list", so this is necessary to obtain the correct type "‘a list." Otherwise, the reasoning is similar. In the Qi version, we have split the monad into two functions: "bind" and "return." Splitting a large function into a smaller functions is typical Scheme style. Here, "return" simply pattern-matches an element into a list containing that element, while "bind" either pattern-matches an empty list "[]" following by anything "_" to an empty list "[]," or pattern-matches a list consisting of a car and a cdr "[X | Xs]," followed by a function "F," to "F" applied to "X," which is "(F X)," appended to a binding of the cdr of the list "Xs" to the function "F." It seems that studying the Qi version may shed some insight into the Haskell version by approaching it from a different perspective. This may also be true of the O'Caml version, but personally, I think that the splitting of the monad into separate functions for "bind" and "return" in the Qi version helps to differentiate it from the other two versions, and hence offers additional insight into the nature of the monad. It may also be said that the use of both "List.map" and "List.concat" in the O'Caml version offers similar insight. Now for a pet peeve that I have with one of the examples in the O'Caml monad tutorial:
module SerialMonad = struct type ‘a t = unit -> ‘a;; let serial_mutex = Mutex.create ();; let return x = (fun () -> x);; let bind m g = (fun () -> (g (m ())) ());; let access m = Mutex.lock serial_mutex; try let r = m () in Mutex.unlock serial_mutex; r with | e -> begin Mutex.unlock serial_mutex; raise e end end;;
This monad is basically identical to the previous FunMonad with the addition of the access function- which executes the process while holding the serial_mutex lock, which is always unlocked when the process completes (even if the process throws an exception). This forces all processes executing within a SerialMonad to be executed sequentially and serially (thus the name).
While a clear example, one problem that I have with this approach is that the emphasis on forcing "all processes executing within a SerialMonad to be executed sequentially and serially" reminds me of the Imperative Way. This brings to mind a posting by Paul Hudak on Haskell-Cafe, entitled "a regressive view of support for imperative programming in Haskell," dated "Wed Aug 8 14:20:39 EDT 2007" (see http://www.haskell.org/pipermail/haskell-cafe/2007-August/030178.html), in which he writes as follows:
In my opinion one of the key principles in the design of Haskell has been the insistence on purity. It is arguably what led the Haskell designers to "discover" the monadic solution to IO, and is more generally what inspired many researchers to "discover" purely functional solutions to many seemingly imperative problems. With references and mutable data structures and IO and who-knows-what-else to support the Imperative Way, this discovery process becomes stunted.
Well, you could argue, monad syntax is what really made Haskell become more accepted by the masses, and you may be right (although perhaps Simon's extraordinary performance at OSCOM is more of what we need). On the other hand, if we give imperative programmers the tools to do all the things they are used to doing in C++, then we will be depriving them of the joys of programming in the Functional Way. How many times have we seen responses to newbie posts along the lines of, "That's how you'd do it in C++, but in Haskell here's a better way...".
Although I greatly applaud alternative perspectives in learning Haskell, I am somewhat suspicious of the emphasis on a quasi-imperative approach. One of the factors that initially attracted me to Haskell in the first place was the emphasis on a functional style. In particular, purely functional code has a number of advantages, including easier reasoning about program behavior, easier formulation of proofs of correctness, and referential transparency. Together with referential transparency comes applicativity of formal methods of program analysis. All this is lost once the Functional Way is replaced by the Imperative Way. Here, the Qi-based monad tutorial seems to focus more on examples that use the functional approach, but perhaps this is just my opinion. Comparative programming languages can be a very interesting topic. If anybody knows of any alternative monad tutorials in other functional programming languages that could help to shed light on monads, please feel free to mention them in this thread. -- Benjamin L. Russell -- Benjamin L. Russell / DekuDekuplex at Yahoo dot com http://dekudekuplex.wordpress.com/ Translator/Interpreter / Mobile: +011 81 80-3603-6725 "Furuike ya, kawazu tobikomu mizu no oto." -- Matsuo Basho^ -- Benjamin L. Russell / DekuDekuplex at Yahoo dot com http://dekudekuplex.wordpress.com/ Translator/Interpreter / Mobile: +011 81 80-3603-6725 "Furuike ya, kawazu tobikomu mizu no oto." -- Matsuo Basho^