[Haskell-beginners] Haskell triangular loop (correct use of (++))

[Rein Henrichs]

I should also mention that many times when you think you want memoization
in Haskell, what you actually want is to restructure your computation to
take better advantage of laziness (and especially sharing).

On Mon, Apr 11, 2016 at 2:10 PM Rein Henrichs <rein.henrichs at gmail.com>
wrote:

> Compilers generally don't provide memoization optimizations because there
> isn't a single dominating strategy: it varies on a case-by-case basis. (For
> example, memoization of some functions can take advantage of structures
> with sub-linear indexing, but this can't be done generically.)
>
> When you can implement your own memoization yourself within the language
> with exactly the properties you desire (and a number of libraries have
> already done so for many common strategies ([1], [2], [3], [4])), there has
> been little motivation to add an implementation to GHC which is either
> inferior by way of its generality or extremely complex by way of its many
> special cases.
>
> [1]: https://hackage.haskell.org/package/MemoTrie
> [2]: https://hackage.haskell.org/package/memoize
> [3]: http://hackage.haskell.org/package/data-memocombinators
> [4]: https://hackage.haskell.org/package/representable-tries
>
> On Sun, Apr 10, 2016 at 10:06 PM Silent Leaf <silent.leaf0 at gmail.com>
> wrote:
>
>> I'm sorry to hear, no implicit memoization (but then is there an explicit
>> approach?). in a pure language, this seems hardly logical, considering the
>> functional "to one output always the same result" and the language's
>> propensity to use recursion that uses then previous values already
>> calculated. Really hope for an explicit memoization! and i don't mean a
>> manual one ^^ if that is even possible?
>>
>> Anyway, i just don't get your function f. you did get that in mine, xs
>> was the value of my comprehension list, aka [.s1..n] ++ [0]
>> From there, if I'm not wrong, your function creates a list of all
>> truncated lists, I supposed to be used with a call for the nth element?
>> True, it memorizes all needed things, and in theory only "drops" once per
>> element of the list.
>>
>> As for incorporating it, i'm thinking, local variable? ^^ the function
>> itself could be outside the comprehension list, in a let or where, or
>> completely out of everything, I don't really see the problem. then it's
>> just a matter of it being called onto xs inside the comprehension list,
>> like that:
>> result = [(x,y) | let xs = [1,2,3,0], let yss = f xs, (x,i) <- zip xs
>> [1,2..], y <- yss !! i, x /= y]
>> The remaining possible issue is the call to !!... dunno if that's costy
>> or not.
>>
>> The best way to go through the list I suppose would be by recursion... oh
>> wait, I'm writing as I'm thinking, and I'm thinking:
>> result = [(x,y) | let xs = [1,2,3,0], let yss = f xs, x <- xs, ys <- yss,
>> y <- ys, x /= y]
>> after all, why not use the invisible internal recursion? What do you
>> think?
>>
>> As for the number-instead-of-number-list, the crucial point i mentioned
>> was to determine the maximum number of digit (biggest power of ten
>> reached), and fill up the holes of the smaller numbers with zeroes, so your
>> examples would be:
>> [1,2,3] = 123 --maximum size of a number = 1, no need to fill up
>> [12,3] = 1203 --maximum size of a number = 2 digits, thus the hole beside
>> 3 gets filled with a zero, just like on good old digital watches ^^
>> Do you think extraction of clusters of digits from numbers would be
>> advantageous, efficiently speaking?
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