[Haskell-cafe] naturally, length :: a -> Int

[Ben Franksen]

Am 04.03.21 um 14:17 schrieb Olaf Klinke:
>> Am 03.03.21 um 16:17 schrieb Olaf Klinke:
>>> I like the idea that Johannes Waldmann and Jaro Reinders brought up: 
>>> Why is length :: Foldable a => a -> Int so convenient? Short answer:
>>> Because of "affine" things like `availableSpace - length xs'.
>>>
>>> There are indeed two types involved here, as the foundation package
>>> points out: relative offsets (like a tangent space?) and absolute
>>> counts. Think of NominalDiffTime versus UTCTime, or the two
>>> interpretations of vectors as points/movements in space. 
>>>
>>> In this light one could regard the current length as 
>>> "the relative offset of the end of the list" which can readily be
>>> subtracted from another relative offset. In mathematical terms: Int the
>>> free group over the monoid of cardinal lengths.
>>
>> Hm, interesting point.
>>
>> If we do embrace that viewpoint, then I'd say we should go all the way
>> and interpret indices modulo (non-negative) structure size! This makes
>> (safe) indexing total (for non-empty structures) and allows things like
>> xs !! (-1) == last xs as in Perl and some other languages. Unsafe
>> indexing (as in the vector package) could remain as is for performance
>> critical code.
>>
>> Cheers
>> Ben
> 
> I like Haskell particularly for not being like Matlab, where virtually
> any well-bracketed indexing syntax does produce a result, but not
> necessarily what you intended or expected.

Okay, so you expect the result of

  list !! (-1)
  vector ! (-1)

to be bottom a.k.a. "error: index out of range".

Whether a non-result like that corresponds closer to what you expected
or intended depends pretty much on your expectations and intentions.
Indexing modulo size/length is well-defined, logically sound, easy to
understand and remember, and therefore (IMHO) very practical. Of course
YMMV.

> Besides, for some structures
> length is expensive but index is not so much, so I wonder whether one
> can modulo-index into a lazy container without evaluating its entire
> spine.

One cannot, naturally, index into a list with a negative index or with
one that is greater than or equal to the length w/o evaluating its
entire spine. So what? If you write

  "abc" !! 3

this will throw an error nowadays, but only after traversing the full
spine. Now you may argue that

  [0..] !! (-1)

at least crashes immediately, whereas with my proposal it would first
eat up all your memory. Okay, not so nice. However, note that replacing
Int with Word for size/length/indexing has exactly the same
disadvantage, e.g. with

  [0..] !! (0 - 1)

Cheers
Ben