improve documentation of Serial method about smallcheck

[UnkindPartition]

I tried to clarify this in 97d5d12.

Is this what you meant? You emphasized "all values", but I don't see why it has to be so. You could write a reduced generator for a large testing space. Can you explain what you mean by consN not working correctly?

[jwaldmann]

Thanks for following up on this.

I guess the underlying issue is that the specification of the consN functions is left implicit. Example: why is "instance ... where series d = [d]" not a good generator for natural numbers? Note that with Test.SmallCheck.smallCheck, it behaves as a complete enumeration. But the cons2 of two such generators will not produce all pairs, as I was expecting, but only identical pairs.

More formally, I was expecting that the following holds:

Specification: if consN is applied to "complete" generators, the result will be a complete generator (for the product type)

(and a similar statement for the instances (Serial a, Serial b) => Serial (a,b) etc)

where I was assuming the definition of "complete" is "enumeration (with possible repetitions)":

Definition-1 (wrong): a generator (a Serial instance) is called "complete" for a set S, if for each element x in S, there is some d in Int such that x is contained in series d.

but the above example shows that this is not correct, and the truth is more like:

Definition-2: a generator (a Serial instance) is called "complete" for a set S, if the sequence [ series 0, series 1, ...]
is monotonically increasing (w.r.t. inclusion of the underlying sets) and its limit (supremum, union) is S.

Well, since hackage has source links, it's maybe easier to look at the (one-line) implementation of consN. But on the other hand, testing is about separating specification from implementation, so ...

[UnkindPartition]

I see. It seems to me that the main confusion was that "series d" should return only values of depth exactly d rather than up to d. But your point about unspecified behaviour of consN is also valid.

I tried to address those in 23d018b and 0340f53.
Please let me know what you think.

[jwaldmann]

Yes, I like it.