On Tue, Sep 10, 2013 at 1:14 PM, Bryan Vicknair <bryanvick@gmail.com> wrote:

This is scary though. This is the first leak I've found in the referential
transparency abstraction in Haskell (besides unsafePerformIO). And the problem
is, if I don't have referential transparency for 100% of pure functions, then I
have to be suspicious of every one.

It's not quite *that* bad. Floating point is a well known source of confusion, except to beginners; there are "why did it do this why is your language broken waaa" posts from people discovering floating point in every single programming language that supports them. You *cannot* 100% accurately store numbers that can have infinite precision in a limited address space. And the representation has its own issues, since computers work best in powers of 2 but we work in powers of 10; numbers that are finite in a decimal representation may be repeating infinite values in a normalized base 2 floating representation.

(There are types such as CReal which attempt to keep arbitrary precision. This breaks down as soon as you try to use them with transcendentals. There is no finite *and* 100% accurate representation of pi.)

Aside from this, the only other "leaks" you're likely to ever encounter (absent unsafePerformIO and friends) are other cases of physical hardware being less perfect than mathematical abstraction, which is to say running out of memory (by far the most common, but also the most amenable to modification/correction), hardware failures, memory bit-flips, etc. At some point, physical constraints are going to win because we can't run programs on abstract mathematical theories, we have to run them on (however abstracted) physical systems.

But practically, floating point is the main place where things go south; and yes, it's generally hated in the functional programming community: no matter what you do, real numbers are going to be a pain, and the standard compromise known as floating point is especially frustrating because its behavior can't be captured in a simple functional description. But floating point is what CPUs use and have specific support for.

brandon s allbery kf8nh sine nomine associates

allbery.b@gmail.com ballbery@sinenomine.net

unix, openafs, kerberos, infrastructure, xmonad http://sinenomine.net