[Haskell-cafe] Comments from OCaml Hacker Brian Hurt

[Jeremy Shaw]

Hello,

Personally, I would like to see the laws more explicitly listed. Some
like:

-- The Monoid Laws:
-- 
-- 1. Associative: 
-- 
--    x `mappend` (y `mappend` z) == (x `mappend` y) `mappend` z
--
-- 2. Left Identity:
--
--  mempty `mappend` y == y
--
-- 3. Right identity:
--
--  x `mappend` mempty == x

(Actually, what I'd really like to see is the laws provided as
QuickCheck properties. I know there is a project doing this already.)

j.

At Fri, 16 Jan 2009 13:39:10 +0000,
Duncan Coutts wrote:
> 
> On Fri, 2009-01-16 at 14:16 +0100, david48 wrote:
> 
> > Upon reading this thread, I asked myself : what's a monoid ? I had no
> > idea. I read some posts, then google "haskell monoid".
> > 
> > The first link leads me to Data.Monoid which starts with
> > 
> > <<
> > Description
> > The Monoid class with various general-purpose instances.
> > 
> > Inspired by the paper /Functional Programming with Overloading and
> > Higher-Order Polymorphism/, Mark P Jones
> > (http://citeseer.ist.psu.edu/jones95functional.html) Advanced School
> > of Functional Programming, 1995.
> > >>
> 
> Ross just updated the documentation for the Monoid module. Here is how
> it reads now:
> 
> The module header now reads simply:
> 
>         A class for monoids (types with an associative binary operation
>         that has an identity) with various general-purpose instances.
> 
> Note, no links to papers.
> 
> And the Monoid class has:
> 
>         The class of monoids (types with an associative binary operation
>         that has an identity).  The method names refer to the monoid of
>         lists, but there are many other instances.
>         
>         Minimal complete definition: 'mempty' and 'mappend'.
>         
>         Some types can be viewed as a monoid in more than one way, e.g.
>         both addition and multiplication on numbers. In such cases we
>         often define @newtype at s and make those instances of 'Monoid',
>         e.g. 'Sum' and 'Product'.
>         
> If you or anyone else has further concrete suggestions / improvements
> then post them here now! :-)
> 
> 
> Duncan
> 
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