Short-circuit Logic

[Steven D'Aprano]

On Fri, 31 May 2013 17:09:01 +1000, Chris Angelico wrote:

> On Fri, May 31, 2013 at 3:13 PM, Steven D'Aprano
> <steve+comp.lang.python at pearwood.info> wrote:
>> What makes you think that the commutative law is relevant here?
>>
>>
> Equality should be commutative. If a == b, then b == a. Also, it's
> generally understood that if a == c and b == c, then a == b, though
> there are more exceptions to that (especially in loosely-typed
> languages).

Who is talking about equality? Did I just pass through the Looking Glass 
into Wonderland again? *wink*

We're talking about *approximate equality*, which is not the same thing, 
despite the presence of the word "equality" in it. It is non-commutative, 
just like other comparisons like "less than" and "greater than or equal 
to". Nobody gets their knickers in a twist because the >= operator is non-
commutative.

Approximate equality is not just non-commutative, it's also intransitive. 
I'm reminded of a story about Ken Iverson, the creator of APL. Iverson 
was a strong proponent of what he called "tolerant equality", and APL 
defined the = operator as a relative approximate equal, rather than the 
more familiar exactly-equal operator most programming languages use.

    In an early talk Ken was explaining the advantages of tolerant
    comparison. A member of the audience asked incredulously, 
    “Surely you don’t mean that when A=B and B=C, A may not equal C?”
    Without skipping a beat, Ken replied, “Any carpenter knows that!”
    and went on to the next question. — Paul Berry

 
    The intransitivity of [tolerant] equality is well known in
    practical situations and can be easily demonstrated by sawing
    several pieces of wood of equal length. In one case, use the
    first piece to measure subsequent lengths; in the second case,
    use the last piece cut to measure the next. Compare the lengths
    of the two final pieces.
    — Richard Lathwell, APL Comparison Tolerance, APL76, 1976 


See also here:

http://www.jsoftware.com/papers/APLEvol.htm

(search for "fuzz" or "tolerance".



-- 
Steven