> On Feb 19, 2017, at 14:40, Matthias Felleisen <matth...@ccs.neu.edu> wrote:
>> On Feb 18, 2017, at 11:12 PM, 'John Clements' via Racket Users 
>> <racket-users@googlegroups.com> wrote:
>> (cc:ak)
>> Okay, this sounds just crushingly obvious now that I say it, but honestly, I 
>> don’t think it’s occurred to me: 
>> One reason that equality is such a nightmare in Java and Python (which turns 
>> out to be JUST AS BAD), is that those of us that actually want to write unit 
>> test cases want *intensional* equality, not extensional equality—but not 
>> pointer-based equality.
>> I just came across a nice example while working on code for first-year 
>> students (thanks, Aaron!).
>> Specifically, imagine an “array” class that contains a backing array and a 
>> length, where the backing array might be arbitrarily longer than the length:
>> (struct arr (vec len))
>> So, for instance, an array with two elements in it might be represented as 
>> either
>> (arr (vector “apple" “horse” #f #f #f) 2)
>> or as
>> (arr (vector “apple” “horse” #f) 2)
>> —they both represent the array of length 2 that has “apple” as the first 
>> element, and “horse” as the second.
>> If I’m providing this library to be used by others, I probably want 
>> extensional equality; I don’t want users of my library to be able to 
>> distinguish between the two. However, if I’m writing unit tests for my 
>> library, I definitely *do* want to be able to distinguish between the two, 
>> for instance in checking the behavior of arrays that fill up and need to be 
>> resized. Moreover, pointer-based equality—the == of Java, and the `is` of 
>> Python (IIUC)—is also largely useless for unit tests.
>> It’s probably not terribly controversial to suggest that neither Python nor 
>> Java were designed with unit testing in mind. Accordingly, I shouldn’t be 
>> surprised to discover that they don’t provide a natural notion of equality 
>> that fits well with unit tests.
>> So, I have three questions:
>> 1) Is there an existing term for what I would call “functional extensional 
>> equality”—that is, Racket’s ‘equal?’ ?
>> 2) Does what I wrote make sense?
>> 3) Has this been written down somewhere else, as part of a larger work?
> John, 
> what you point out is that extensional equality depends on the point of view. 
> In your specific example, ‘arr’ from inside the module — specifically for 
> non-exported functions — equal? must take into account the full vector. For a 
> client module, equality is a notion of projection (elimination of array 
> fields). In particular, I would expect your module to declare the structure 
> opaque so that equal? does not inspect the full array. Additionally, I would 
> expect you to export a function called arr-equal? so that clients can 
> determine whether two instances are extensionally equal from their 
> perspective (which is apparently needed in your context). 
> If you were in a typed functional world, I’d use a sealed structure for the 
> module or at least an existential type so that the outside world cannot 
> inspect arr’s vec filed. This shows that equality is a type-dependent notion 
> — just as Reynolds said it. 
> In a typed OO world such as Java, you’d override .equal, which is public and 
> thus accessible. But for internal, private comparisons, you’d have to step 
> outside of Java’s equality predicate and use a method that inspects the full 
> vec field. Here this is relatively easy because you are dealing with just two 
> slots. 
> In any case, I doubt equal? helps you here. Did I misunderstand anything? 

No, I don’t think you missed anything, but from the standpoint of those 
teaching early classes in either Java or Python (a standpoint that I understand 
you are generally and mercifully not compelled to adopt), it seems that there’s 
a missing piece in unit testing frameworks: namely, the default check-expect 
form in these languages should not be one that refers to the notion of 
outside-of-module-extensional equality, but rather one that refers to 
inside-of-module-extensional equality, as check-expect does. I’d be tempted to 
call this notion of equality “testing equality,” but I’ve been called out 
before on my barbarous neologisms. (Not sure this one would be considered 
barbarous, at any rate.) Additionally, students should probably not be required 
to implement this notion of equality by hand. Sounds like a nice three-page 
position paper, probably not good enough for ITICSE, maybe SIGSCE (sigh).


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