monadic composition instead of monad transformers

Mon, 07 May 2012 09:28:29 +0000

As we probably all know, monads are handy programming constructs that let us express different "execution environments" and operations therein in a uniform way. Every monad gives the programmer some kind of an environment where it is possible perform arbitrary computations in the ordinary way, while the monad controls the workings of the environment and usually provides some additional services specific to that environment. For instance, the ''state monad'' provides an environment with two additional services, storing a value for later reference and querying the stored value. The monad takes care of threading this stored value through the whole computation, including recursive calls, etc. Any kind of effect that could be achieved through "side effects" (violations of functional purity) can be modelled as services in a monad that is specifically designed to be able to provide those services.

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Monadic parsers are a prime ~~example.~~ example of monadic composition. A parser is a function that takes an "input stream" (a string, for instance), and returns a value (the result of parsing the beginning of the input stream) and an updated input stream, with the already parsed content removed. {{{ parseInt "300 square meters" ==> (300, " square meters") }}} The input stream can be seen as a state which is inspected by various parsing operations (for finding out the result of parsing) and updated (by dropping elements from the beginning). It must be threaded (with updates and all) through the whole parsing computation, so it is useful to use the state monad to handle the input stream.

But, it also happens that parsers are functions that can ''fail'' under invalid input. For instance, the result of parseInt "you suck" should probably not be any trash integer but rather a value denoting failure. So a parser is also ~~and~~ an instance of the so called ''exception monad'', a monad whose sole service is to give a possibility to abort the computation and return nothing. (The exception monad can also provide some service to perform "alternative computations", trying out another computation in case the first one fails.) {{{ parseInt "300 square meters" ==> Just (300, " square meters") parseInt "you suck" ==> Nothing }}} (People who know the related literature will yell at me for introducing the exception monad, instead of the indeterminism monad, here. Let it be just for the sake of demonstration, right?)

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The downside, of course, is that you can't use the services provided by the existing monads but you'll have to write wrapper services for ~~those~~ the services, in addition to the definitions of bind (>>=) and return.

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