[Haskell-cafe] Explaining monads
ronguida at mindspring.com
Sun Aug 12 11:36:18 EDT 2007
Tillmann Rendel wrote:
> Ronald Guida wrote:
>> Here's a toy language, described by a regular expression:
>> I want to read characters, one at a time, and eventually decide to
>> "Accept" or "Reject" a string.
>> Let me try to understand my options.
>> * With a simple Arrow, I can create a fixed sequence of "read"
>> operations, and I can't act on the results (i.e. by choosing
>> whether or not to keep reading) at run-time.
> Nothing stops your Arrow-based RegExp-library from defining suitable
> combinators to implement choices in RegExp's without using
> ArrowChoice or ArrowApply. But if your Arrow-type is abstract, the
> users of your library can only use the combinators you provided, so
> you can safely assume they do only RegExp parsing, and optimize your
> Arrows in the runRegExp-function for the special case of
So it seems I was thinking too narrowly of arrows...
If I think of an arrow as defining a Domain Specific Embedded Language
(DSEL), then with a plain arrow, users can't embed Haskel inside the
> But if you decide to expose ArrowApply-functionality to the users of
> your RegExp-library, they are able to define arbitrary string
> matching on top of your RegExp library, so you can't do any
> optimizations because you never know what your users decided to do.
If I think of a monad (ArrowApply) as defining a Domain Specific
Embedded Language (DSEL), then users can embed anything they want
within the DSEL.
> From a software engineering point of view, the idea of
> Arrow-and-only-Arrow is to encode the whole computation in the
> internal structure of the arrow, independent of the interpreting
> language Haskell. This internal structure could be as expressible as
> Haskell. In contrast, ArrowApply and Monad use regular Haskell
> expressions for everything Haskell can do (like if-then-else,
> recursion, ...) and only encode special operations into the internal
> structure (like access to state, nondeterminism, ...).
> This distinction is reflected in the treatment of variables in
> arrow-based vs. monadic code. monadic code can use normal Haskell
> variables, arrow-based code has to keep the variables "inside" the
> arrow in some structure.
So if I want to explain arrows and monads as concisely as possible:
Arrows and monads are abstract data types used to construct Domain
Specific Embedded Languages (DSELs) within Haskel. A simple arrow
provides a closed DSEL. A monad is a special type of arrow that
creates an open DSEL by allowing users to embed arbitrary Haskel
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