[Haskell-cafe] Re: A question about "monad laws"

[Roman Leshchinskiy]

jerzy.karczmarczuk at info.unicaen.fr wrote:
> Trialog:
> Roman Leshchinskiy writes:
>> Richard A. O'Keefe wrote:
> 
>>> jerzy.karczmarczuk at info.unicaen.fr wrote:
>>>> Would you say that *no* typical floating-point software is reliable?
>>>
>>> With lots of hedging and clutching of protective amulets around the
>>> word "reliable", of course not.  What I *am* saying is that
>>> (a) it's exceptionally HARD to make reliable because although the 
>>> operations
>>>  are well defined and arguably reasonable they do NOT obey the laws that
>>>     school and university mathematics teach us to expect them to obey
>>
>> Ints do not obey those laws, either. It is not exceptionally hard to 
>> write reliable software using ints. You just have to check for 
>> exceptional conditions. That's also the case for floating point.
>> That said, I suspect that 90% of programs that use float and double 
>> would be much better off using something else. The only reason to use 
>> floating point is performance.
> 
> I have a bit different perspective...
> First, when I see the advice "use something else", I always ask "what",
> and I get an answer very, very rarely... Well? What do you propose?

For Haskell, Rational seems like a good choice. The fact that the 
standard requires defaulting to Double is quite unfortunate and 
inconsistent, IMO; the default should be Rational. Float and Double 
shouldn't even be in scope without an explicit import. There really is 
no good reason to use them unless you are writing a binding to existing 
libraries or really need the performance.

> Then, the problem is not always pathological, in the sense of "exceptional
> conditions". There are touchy points related to the stability of the
> algorithms for the solution of differential equations. There are doubtful
> random number generators in Monte-Carlo business. There are ill-conditioned
> matrices and screwed-up iterative definitions. Algorithms work, work, and
> ultimately explode or produce rubbish. The "laws" which get broken are
> "almost" respected for a long time, and then we have the Bald Man (Sorites)
> paradox...
> RAO'K very wisely says that people should avoid reinventing wheels, and
> they should use established packages, written by people who know.

Yes, I completely agree with that (even though my original email 
probably didn't sound as if I did). My point was that (a) most people 
don't need floating point and (b) those who do need it should learn how 
to use it.

> The problem *here* is that we would like to have something fabulous in
> Haskell - for example...

I think we mostly have it already.

Roman