Re: What is the relationship between transforming, ma

Yes, in XPath the "!" operator corresponds to the flatMap operation of other
functional programming languages, not to the map operation, and you are quite
right to point out that I failed to make this distinction. A filter operation
can be expressed in terms of flatMap, but not in terms of a pure map operation
which is always one-to-one.

Michael Kay
Saxonica

> On 1 Sep 2021, at 03:03, Dimitre Novatchev dnovatchev@xxxxxxxxx
<xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx> wrote:
>
> Wikipedia:
> In mathematics <https://en.wikipedia.org/wiki/Mathematics>, a function[note
1] <https://en.wikipedia.org/wiki/Function_(mathematics)#cite_note-1> is a
binary relation <https://en.wikipedia.org/wiki/Binary_relation> between two
sets <https://en.wikipedia.org/wiki/Set_(mathematics)> that associates each
element of the first set to exactly one element of the second set. Typical
examples are functions from integers <https://en.wikipedia.org/wiki/Integer>
to integers, or from the real numbers
<https://en.wikipedia.org/wiki/Real_number> to real numbers.
>
> In computer science[edit
<https://en.wikipedia.org/w/index.php?title=Map_(mathematics)&action=edit&sec
tion=6>]
> In the communities surrounding programming languages
<https://en.wikipedia.org/wiki/Programming_language> that treat functions as
first-class citizens <https://en.wikipedia.org/wiki/First-class_citizen>, a
map <https://en.wikipedia.org/wiki/Map_(higher-order_function)> is often
referred to as the binary <https://en.wikipedia.org/wiki/Binary_function>
higher-order function <https://en.wikipedia.org/wiki/Higher-order_function>
that takes a function f and a list
<https://en.wikipedia.org/wiki/List_(abstract_data_type)> [v0, v1, ..., vn] as
arguments <https://en.wikipedia.org/wiki/Argument_of_a_function> and returns
[f(v0), f(v1), ..., f(vn)] (where n b	% 0).
>
>
> As we see from these definitions, filtering is not mapping, because the
result of filtering may have fewer items than the source upon which filtering
is applied. For me "mapping" is synonymous to "projection". Both are in a
sense "preserving" or "non-destructive". Filtering on the other hand is
generally destructive: the result-set of (2, 4, 6)[. mod 2 ] is the empty
sequence () .
>
> Unfortunately, XPath allows "functions"  that can return nothing (the empty
sequence) and this leads to the possibility to confuse mapping (strictly
defined) with filtering and other malformations. As mentioned in the 2nd
Wikipedia citation above, well-thought programming languages maintain the
important property of mapping that the number of items (or cardinality of) the
input is the same as the number of items (or cardinality of) the output.
>
> This is why I would prefer to work with XPath arrays, because even the empty
array is something, it is not the empty sequence. Thus if a function could
produce an empty array, but not the empty sequence, this function is still a
mapping, as the number of result items in the input and result sequences is
the same.
>
> Transformation (as in XSLT transformation) is synonymous to performing any
program on an input (including input which is the empty sequence). As some
people have proven, XSLT is Turing-complete, thus any program (Turing machine)
is a transformation.
>
>
>
> On Tue, Aug 31, 2021 at 10:58 AM Roger L Costello costello@xxxxxxxxx
<mailto:costello@xxxxxxxxx> <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx
<mailto:xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx>> wrote:
> Hi Folks,
>
> How do you define those terms? Are they synonymous? Is one a subset of
another?
>
> By "mapping" I mean populating XML instances of one data standard with data
from another data standard. For example, I am currently mapping a military air
navigation data standard to a civilian air navigation data standard.
>
> By "filtering" I mean performing actions on data such as redacting, fuzzing,
and zeroing. One could think of these actions as mapping: if I fuzz a lat/long
location, I am essentially mapping the location to another location.
>
> By "transforming" I mean all the kinds of things you can do with XSLT.
>
> Is filtering a subset of mapping? Is mapping a subset of transforming?
>
> /Roger
>
>
>
>
> --
> Cheers,
> Dimitre Novatchev
> ---------------------------------------
> Truly great madness cannot be achieved without significant intelligence.
> ---------------------------------------
> To invent, you need a good imagination and a pile of junk
> -------------------------------------
> Never fight an inanimate object
> -------------------------------------
> To avoid situations in which you might make mistakes may be the
> biggest mistake of all
> ------------------------------------
> Quality means doing it right when no one is looking.
> -------------------------------------
> You've achieved success in your field when you don't know whether what
you're doing is work or play
> -------------------------------------
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all patents, too? :)
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