[Haskell-cafe] Parsers are monadic?

[Dave Bayer]

On Jun 30, 2007, at 6:31 AM, Claus Reinke wrote:
> has anyone else had similar experiences with expressive limitations
> of monadic programming? things that one might be able to work
> around, but that don't feel as natural or simple as they should be?
> things that one hasn't been able to express at all (such as Swierstra
> & Duponcheel's static analysis of combinator parsers which
> inspired Hughes's proposal to use arrows)?

When you pretend you've never heard of monads or arrows, and write  
down the types what do you get?

When I finally overcame my resistance to monads, I only had to change  
names in my code to use the Maybe monad, the functions already had  
the right type. There's an inevitability to monads and arrows, and  
perhaps to what you're thinking, if it's a third species in a lazy  
list we're evaluating of such things.

--

Haskell does suffer from misrepresentation to outsiders. Even already  
familiar with ML and Ocaml, the "lazy, pure" approach read to me like  
a fetish, and monads seemed a tainted construct for if one absolutely  
must venture into the practical. The only reason I could see to learn  
Haskell was a sense that nevertheless comes through and probably puts  
some people off, that Haskell programmers are in the highest reading  
group. (Lisp programmers imagine that they are; one should learn  
both.) If one must suffer through the drudgery of using  a  
programming language, shouldn't it be a window to enlightenment that  
Aldous Huxley would admire? Haskell delivers, but I avoided monads to  
get the "pure" experience, when in fact Haskell is all about  
supporting functional idioms like monads.

The references cited in this thread are excellent. They certainly  
gave me more insight into the history of how Haskell evolved: Classes  
coming from Gofer precisely to make monads more elegant to use, and  
do notation a mutant form of monad comprehensions.

I went chasing references but couldn't substantiate this statement on  
page 11 of

	1996 Hutton, Meijer - Monadic parser combinators
	http://haskell.readscheme.org/servlets/cite.ss?pattern=hutton- 
parsers1996

> 	Indeed, the algebraic properties required of the monad operations  
> turn out to be precisely
> 	those required for the notation to make sense.

How do I reconcile this with the extension of do notation to support  
arrows?

If monads and arrows are two instances of something akin to "group  
theory" then the definition of a "group" is lurking within whatever  
this quote should have said...