Difference between revisions of "Higher-Order Functions Module"
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| Line 3: | Line 3: | ||
=Conventions= | =Conventions= | ||
| − | All functions in this module are assigned to the | + | All functions in this module are assigned to the {{Code|http://basex.org/modules/hof}} namespace, which is statically bound to the {{Code|hof}} prefix.<br/> |
=Functions= | =Functions= | ||
| Line 11: | Line 11: | ||
|- | |- | ||
| width='90' | '''Signatures''' | | width='90' | '''Signatures''' | ||
| − | | | + | |{{Func|hof:id|$expr as item()*|item()*}} |
|- | |- | ||
| '''Summary''' | | '''Summary''' | ||
| Line 18: | Line 18: | ||
| '''Examples''' | | '''Examples''' | ||
| | | | ||
| − | * | + | * {{Code|hof:id(1 to 5)}} returns {{Code|1 2 3 4 5}} |
* With higher-order functions: | * With higher-order functions: | ||
<pre class="brush:xquery"> | <pre class="brush:xquery"> | ||
| Line 41: | Line 41: | ||
|- | |- | ||
| width='90' | '''Signatures''' | | width='90' | '''Signatures''' | ||
| − | | | + | |{{Func|hof:const|$expr as item()*, $ignored as item()*|item()*}} |
|- | |- | ||
| '''Summary''' | | '''Summary''' | ||
| Line 48: | Line 48: | ||
| '''Examples''' | | '''Examples''' | ||
| | | | ||
| − | * | + | * {{Code|hof:const(42, 1337)}} returns {{Code|42}}. |
* With higher-order functions: | * With higher-order functions: | ||
<pre class="brush:xquery"> | <pre class="brush:xquery"> | ||
| Line 61: | Line 61: | ||
) | ) | ||
</pre> | </pre> | ||
| − | * Another use-case: When inserting a key into a map, | + | * Another use-case: When inserting a key into a map, {{Code|$f}} descides how to combine the new value with a possibly existing old one. {{Code|hof:const}} here means ignoring the old value, so that's normal insertion. |
<pre class="brush:xquery"> | <pre class="brush:xquery"> | ||
let $insert-with := function($f, $map, $k, $v) { | let $insert-with := function($f, $map, $k, $v) { | ||
| Line 76: | Line 76: | ||
) | ) | ||
</pre> | </pre> | ||
| − | returns | + | returns {{Code|3 42}} |
|} | |} | ||
| Line 83: | Line 83: | ||
|- | |- | ||
| width='90' | '''Signatures''' | | width='90' | '''Signatures''' | ||
| − | | | + | |{{Func|hof:fold-left1|$f as function(item()*, item()) as item()*, $seq as item()+)|item()*}} |
|- | |- | ||
| '''Summary''' | | '''Summary''' | ||
| Line 90: | Line 90: | ||
| '''Examples''' | | '''Examples''' | ||
| | | | ||
| − | * | + | * {{Code|hof:fold-left1(function($a, $b) { $a + $b }, 1 to 10)}} returns {{Code|55}}. |
| − | * | + | * {{Code|hof:fold-left1(function($a, $b) { $a + $b }, ())}} throws {{Code|XPTY0004}}, because {{Code|$seq}} has to be non-empty. |
|} | |} | ||
| Line 98: | Line 98: | ||
|- | |- | ||
| width='90' | '''Signatures''' | | width='90' | '''Signatures''' | ||
| − | | | + | |{{Func|hof:until|$pred as function(item()*) as xs:boolean, $f as function(item()*) as item()*, $start as item()*|item()*}} |
|- | |- | ||
| '''Summary''' | | '''Summary''' | ||
| − | |Applies the function | + | |Applies the function {{Code|$f}} to the initial value {{Code|$start}} until the predicate {{Code|$pred}} applied to the result returns {{Code|true()}}. |
|- | |- | ||
| '''Examples''' | | '''Examples''' | ||
| | | | ||
| − | * | + | * {{Code|hof:until(function($x) { $x ge 1000 }, function($y) { 2 * $y }, 1)}} returns {{Code|1024}}. |
* Calculating the square-root of a number by iteratively improving an initial guess: | * Calculating the square-root of a number by iteratively improving an initial guess: | ||
<pre class="brush:xquery"> | <pre class="brush:xquery"> | ||
| Line 117: | Line 117: | ||
return $sqrt(25) | return $sqrt(25) | ||
</pre> | </pre> | ||
| − | returns | + | returns {{Code|5.000000000053722}}. |
|} | |} | ||
| Line 127: | Line 127: | ||
|- | |- | ||
| width='90' | '''Signatures''' | | width='90' | '''Signatures''' | ||
| − | | | + | |{{Func|hof:top-k-by|$seq as item()*, $sort-key as function(item()) as item(), $k as xs:integer)|item()*}} |
|- | |- | ||
| '''Summary''' | | '''Summary''' | ||
| − | |Returns the | + | |Returns the {{Code|$k}} items in {{Code|$seq}} that are greatest when sorted by the result of {{Code|$f}} applied to the item. The function is a much more efficient implementation of the following scheme: |
<pre class="brush:xquery"> | <pre class="brush:xquery"> | ||
( | ( | ||
| Line 141: | Line 141: | ||
| '''Examples''' | | '''Examples''' | ||
| | | | ||
| − | * | + | * {{Code|hof:top-k-by(1 to 1000, hof:id#1, 5)}} returns {{Code|1000 999 998 997 996}} |
| − | * | + | * {{Code|hof:top-k-by(1 to 1000, function($x) { -$x }, 3)}} returns {{Code|1 2 3}} |
| − | * | + | * {{Code|hof:top-k-by(<x a='1' b='2' c='3'/>/@*, xs:integer#1, 2)/node-name()}} returns {{Code|c b}} |
|} | |} | ||
| Line 153: | Line 153: | ||
|- | |- | ||
| width='90' | '''Signatures''' | | width='90' | '''Signatures''' | ||
| − | | | + | |{{Func|hof:top-k-with|$seq as item()*, $lt as function(item(), item()) as xs:boolean, $k as xs:integer)|item()*}} |
|- | |- | ||
| '''Summary''' | | '''Summary''' | ||
| − | |Returns the | + | |Returns the {{Code|$k}} items in {{Code|$seq}} that are greatest when sorted in the order of the ''less-than'' predicate {{Code|$lt}}. The function is a general version of {{Code|hof:top-k-by($seq, $sort-key, $k)}}. |
|- | |- | ||
| '''Examples''' | | '''Examples''' | ||
| | | | ||
| − | * | + | * {{Code|hof:top-k-with(1 to 1000, function($a, $b) { $a lt $b }, 5)}} returns {{Code|1000 999 998 997 996}} |
| − | * | + | * {{Code|hof:top-k-with(-5 to 5, function($a, $b) { abs($a) gt abs($b) }, 5)}} returns {{Code|0 1 -1 2 -2}} |
|} | |} | ||
Revision as of 16:05, 26 May 2012
This XQuery Module adds some useful higher-order functions, additional to the Higher-Order Functions provided by the official specification.
Contents
Conventions
All functions in this module are assigned to the http://basex.org/modules/hof namespace, which is statically bound to the hof prefix.
Functions
hof:id
| Signatures | hof:id($expr as item()*) as item()*
|
| Summary | Returns its argument unchanged. This function isn't useful on its own, but can be used as argument to other higher-order functions. |
| Examples |
let $sort-by := function($f, $seq) {
for $x in $seq
order by $f($x)
return $x
}
let $sort := $sort-by(hof:id#1, ?),
$reverse-sort := $sort-by(function($x) { -$x }, ?)
return (
$sort((1, 5, 3, 2, 4)),
'|',
$reverse-sort((1, 5, 3, 2, 4))
)
returns: |
hof:const
| Signatures | hof:const($expr as item()*, $ignored as item()*) as item()*
|
| Summary | Returns its first argument unchanged and irgores the second. This function isn't useful on its own, but can be used as argument to other higher-order functions, e.g. when a function combining two values is expected and one only wants to retain the left one. |
| Examples |
let $zip-sum := function($f, $seq1, $seq2) {
sum(map-pairs($f, $seq1, $seq2))
}
let $sum-all := $zip-sum(function($a, $b) { $a + $b }, ?, ?),
$sum-left := $zip-sum(hof:const#2, ?, ?)
return (
$sum-all((1, 1, 1, 1, 1), 1 to 5),
$sum-left((1, 1, 1, 1, 1), 1 to 5)
)
let $insert-with := function($f, $map, $k, $v) {
let $old := $map($k),
$new := if($old) then $f($v, $old) else $v
return map:new(($map, map{ $k := $new }))
}
let $map := map{ 'foo' := 1 }
let $add := $insert-with(function($a, $b) {$a + $b}, ?, ?, ?),
$insert := $insert-with(hof:const#2, ?, ?, ?)
return (
$add($map, 'foo', 2)('foo'),
$insert($map, 'foo', 42)('foo')
)
returns |
hof:fold-left1
| Signatures | hof:fold-left1($f as function(item()*, item()) as item()*, $seq as item()+)) as item()*
|
| Summary | Works the same as fn:fold-left($f, $seed, $seq), but doesn't need a seed, because the sequence must be non-empty. |
| Examples |
|
hof:until
| Signatures | hof:until($pred as function(item()*) as xs:boolean, $f as function(item()*) as item()*, $start as item()*) as item()*
|
| Summary | Applies the function $f to the initial value $start until the predicate $pred applied to the result returns true().
|
| Examples |
let $sqrt := function($x as xs:double) as xs:double {
hof:until(
function($res) { abs($res * $res - $x) < 0.00001 },
function($guess) { ($guess + $x div $guess) div 2 },
$x
)
}
return $sqrt(25)
returns |
hof:top-k-by
| Signatures | hof:top-k-by($seq as item()*, $sort-key as function(item()) as item(), $k as xs:integer)) as item()*
|
| Summary | Returns the $k items in $seq that are greatest when sorted by the result of $f applied to the item. The function is a much more efficient implementation of the following scheme:
( for $x in $seq order by $sort-key($x) descending return $x )[position() <= $k] |
| Examples |
|
hof:top-k-with
| Signatures | hof:top-k-with($seq as item()*, $lt as function(item(), item()) as xs:boolean, $k as xs:integer)) as item()*
|
| Summary | Returns the $k items in $seq that are greatest when sorted in the order of the less-than predicate $lt. The function is a general version of hof:top-k-by($seq, $sort-key, $k).
|
| Examples |
|
Changelog
Version 7.2
- Added: hof:top-k-by, hof:top-k-with
- Removed: hof:iterate
Version 7.0
- module added
