Dear Richard,
that would be nice. Your answers certainly made me curious about your
Smalltalk. :-D
Regarding strict supremum/infimum, I think that transducers do not lend
themselves naturally to the complete problem. How did you solve it in your
library?
Out of curiosity, I came up with the following non-optimized hybrid solution.
As I do not have an image at hand right now, I did not test the code snippets
yet. Lets assume the following class hierarchy:
Collection <- SortedCollection <- SplayTree
Collection>>strictSupremumOf: x
"Answer the least upper Bound that is strictly greater than x"
^self minimum <~ self greaterThan: x
Collection>>minimum
"Compute the minimum element of a sequence in the order of the receiver"
^[:min :b | min ifNotNil: [:a | a min: b]] init: nil
Collection>>greaterThan: x
"Answer a sequence of elements > x in the order of the receiver"
^[:y | y > x] filter <~ self
SortedCollection>>minimum
"The first element of a sorted sequence is the minimum"
^[:min :b | Stop return: b] init: nil
SortedCollection>>greaterThan: x
"Take advantage of binary search"
index := self indexOf: x.
"1. x not found"
index = 0 ifTrue: [^#()].
"2. x found, skip to first y ~= x"
^[:i | self at: i] map
<~ [:i | (self at: i) = x] dropWhileTrue
<~ ((index + 1) to: self size)
SplayTree>>greaterThan: x
"Take advantage of the splay operation"
top := (self splay: x) value.
"1. x found, elements > x at right child"
top = x ifTrue: [^root rightChild].
"2. x not found, elements > x at root"
top > x ifTrue: [^root].
"3. x not found, no elements > x"
^SplayTree empty.
Note, #map, #filter and #dropWhileTrue are (optional) shorthands to create
respective transducers. All collections are expected to implement
#inject:into:. The strict infimum can be computed analogously if we can reverse
the order in #lessThan: efficiently.
Kind regards,
Steffen
Richard O'Keefe schrieb am Dienstag, 25. April 2023 04:11:47 (+02:00):
There is a much newer version. I've made some minor corrections today.
I really must put it up on github.
Let me get back to you about that.
On Sat, 22 Apr 2023 at 18:57, Bernhard Pieber <bernh...@pieber.com> wrote:
Hi Richard,
I really liked your concise description about what is the point of using an
object-oriented language. It made my day.
I searched the Web for your Smalltalk library and found this link:
http://www.cs.otago.ac.nz/staffpriv/ok/astc-1711.tar.gz
Is there a newer version available somewhere?
Cheers,
Bernhard
Am 22.04.2023 um 00:51 schrieb Richard O'Keefe <rao...@gmail.com>:
I'm sorry, it appears that I failed to explain the question
well enough. I thought I'd explained earlier.
successor: target
^(self select: [:each | target < each]) min
is trivial. What's wrong with it is that it allocates
an intermediate collection and takes two passes.
FIXING that is is also trivial.
successor: target
^(self virtualSelect: [:each | target < each]) min
^^^^^^^
This does allocate something, but it's just a few words,
and a single traversal is one.
In other languages/contexts we'd be talking about
loop fusion/listless transformation/deforestation.
It is my understanding that using Transducers would
get me *this* level of improvement.
The problem is that this is still a linear-time
algorithm. If you take advantage of the order in
a SortedCollection or SortedSet,it can take logarithmic
time. When SortedSet is implemented as a splay tree
-- as it is in my library -- iterating over all its
elements using #successor: is amortised CONSTANT time
per element. So we need THREE algorithms:
- worst case O(n) select+min
- worst case O(lg n) binary search
- amortised O(1) splaying
and we want the algorithm selection to be
A U T O M A T I C.
That's the point of using an object-oriented language.
I say what I want done and the receiver decides how to
do it. Anything where I have to write different
calling code depending on the structure of the receiver
doesn't count as a solution.
Now we come to the heart of the problem.
The binary search algorithm is NOT a special case
of the linear search algorithm. It is not made of
pieces that can be related to the parts of the linear
search algorithm.
The splaying algorithm is NOT a special case of the
linear search algorithm OR the binary search algorithm.
It is not made of pieces that can be related to their
parts.
So *IF* I want automatic selection of an appropriate
algorithm, then I have to rely on inheritance and
overriding, and in order to do that I have to have
a named method that *can* be overridden, and at that
point I'm no longer building a transducer out of
pluggable pieces.
So that's the point of this exercise.
How do we get
(a) composition of transducers out of pluggable parts
AND
(b) automatic selection of appropriate algorithms
On Fri, 21 Apr 2023 at 20:35, Steffen Märcker <merk...@web.de> wrote:
Hi Richard,
Now that's much clearer to me:
min{y | y in c . y > x} "strict supremum"
max{y | y in c . y < x} "strict infimum"
For the general case of a sequence (not sorted) of elements we can do
strictSupremumOf: x in: sequence
^(sequence transduce filter: [:y | y > x])
"virtual sequence"
inject: nil
into: [:min :b | min ifNotNil: [:a | a min: b]]
I just picked a variant of minimum that answers nil if no element is found.
Other variants would work, too.
The focus of transducers is on re-use and composition of processing steps. We
can break this up into steps if needed:
minimum := [:min :b | min ifNotNil: [:a | a min: b]] init: nil.
"reduction"
upperBounds := Filter predicate: [:y | y > x].
"transducer"
strictSup := minimum transduce: upperBounds.
"transformed reduction"
^strictSup reduce: sequence
We can also use a different notation similar to a data flow:
minimum <~ upperBounds <~ sequence
Of course, if we know how the sequence is sorted, we should use another
algorithm. Assuming an ascending order with no random access, we'd change
minimum to stop early:
minimum := [:min :b | Stop result: b].
Kind regards,
Steffen
Richard O'Keefe schrieb am Freitag, 21. April 2023 05:33:44 (+02:00):
successor of x in c = the smallest element of c that is larger than x
min {y | y in c . y > x}
predecessor of x in c = the largest element of c that is smaller than x
max {y | y in c . y < x}
On Thu, 20 Apr 2023 at 21:08, Steffen Märcker <merk...@web.de> wrote:
Dear Richard,
thanks for that additional piece. I'll put insert-<left/right> on my list of
possible variants. I think we come back to naming after the initial port is
done and everyone can play with it. Generally, I made the observation to better
be careful with names since it's too easy to alienate other or trigger wrong
assumptions.
New topic! (quote below)
Honestly, my knowledge of Haskell is rather limited and rusted. Hence, I am
having difficulties understanding what exactly these operations with a sequence
of elements. Can you give an example or some pseude/smalltalk code from your
use-case and library?
Kind regards
Changing the subject a wee bit, there's an operation family
in my library, and I wonder how it would fit into Transducers?
To avoid bias, here's a specification in Haskell (for lists,
because I haven't had any luck installing Data.Witherable).
uccessorBy, predecessorBy :: (a -> a -> Ordering) -> a -> [a] -> a
successor, predecessor :: Ord a => a -> [a] -> a
successor = successorBy compare
successorBy cmp x = minimumBy cmp . filter (\y -> cmp x y == LT)
predecessor = predecessorBy compare
predecessorBy cmp = successorBy (flip cmp)
The reason these operations exist is to pick neighbouring
elements in SortedCollections and SortedSets. But they make
*sense* for any Enumerable. So there are "generic"
definitions with orderrides for those two classes.
A filter + a reduce . Traditionally, a #select:thenFold:ifNone:
in order to avoid building an intermediate collection. That much
I see how to do with transducers. But you can't get the desired
override for #successor:[sortBlock:][ifNone:] by overriding
#select:thenFold:ifNone: in SortedCollection or SortedSet. So what
*should* one do?
--
Gesendet mit Vivaldi Mail. Laden Sie Vivaldi kostenlos unter vivaldi.com
herunter
