Difference between revisions of "Higher-Order Functions"
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=Function Items= | =Function Items= | ||
− | Probably the most important new feature in XQuery 3.0 are ''function items'', i. e., items that act as functions, but can also be passed to and from other functions and expressions. This feature makes functions ''first-class citizens'' of the language. | + | Probably the most important new feature in XQuery 3.0 are ''function items'', i. e., items that act as functions, but can also be passed to and from other functions and expressions. This feature makes functions ''first-class citizens'' of the language. The [[XQuery_3.0#Function_Items|XQuery 3.0]] page goes into details on how function items can be obtained. |
− | |||
− | The [[XQuery_3.0#Function_Items|XQuery 3.0]] page goes into details on how function items can be obtained. | ||
== Function Types == | == Function Types == | ||
− | Like every XQuery item, function items have a ''sequence type''. It can be | + | Like every XQuery item, function items have a ''sequence type''. It can be used to specify the ''arity'' (number of arguments the function takes) and the argument and result types. |
− | used to specify the ''arity'' (number of arguments the function takes) and | ||
− | the argument and result types. | ||
− | The most general function type is <code>function(*)</code>. It's the type of all | + | The most general function type is <code>function(*)</code>. It's the type of all function items. The following query for example goes through a list of XQuery items and, if it is a function item, prints its arity: |
− | function items. The following query for example goes through a list of XQuery | ||
− | items and, if it is a function item, prints its arity: | ||
− | <pre | + | <pre lang='xquery'> |
for $item in (1, 'foo', fn:concat#3, function($a) { 42 * $a }) | for $item in (1, 'foo', fn:concat#3, function($a) { 42 * $a }) | ||
where $item instance of function(*) | where $item instance of function(*) | ||
Line 24: | Line 18: | ||
''Result:'' <code>3 1</code> | ''Result:'' <code>3 1</code> | ||
− | The notation for specifying argument and return types is quite intuitive, as it | + | The notation for specifying argument and return types is quite intuitive, as it closely resembles the function declaration. The XQuery function |
− | closely resembles the function declaration. The XQuery function | ||
− | <pre | + | <pre lang='xquery'> |
declare function local:char-at( | declare function local:char-at( | ||
− | $str as xs:string, | + | $str as xs:string, |
− | $pos as xs:integer | + | $pos as xs:integer |
) as xs:string { | ) as xs:string { | ||
fn:substring($str, $pos, 1) | fn:substring($str, $pos, 1) | ||
Line 36: | Line 29: | ||
</pre> | </pre> | ||
− | for example has the type <code>function(xs:string, xs:integer) as xs:string</code>. It isn't possible to specify only the argument and not the result | + | for example has the type <code>function(xs:string, xs:integer) as xs:string</code>. It isn't possible to specify only the argument and not the result type or the other way round. A good place-holder to use when no restriction is wanted is <code>item()*</code>, as it matches any XQuery value. |
− | type or the other way round. A good place-holder to use when no restriction | ||
− | is wanted is <code>item()*</code>, as it matches any XQuery value. | ||
Function types can also be nested. As an example we take <code>local:on-sequences</code>, which takes a function defined on single items and makes it work on sequences as well: | Function types can also be nested. As an example we take <code>local:on-sequences</code>, which takes a function defined on single items and makes it work on sequences as well: | ||
− | <pre | + | <pre lang='xquery'> |
declare function local:on-sequences( | declare function local:on-sequences( | ||
$fun as function(item()) as item()* | $fun as function(item()) as item()* | ||
Line 49: | Line 40: | ||
}; | }; | ||
</pre> | </pre> | ||
− | We | + | |
+ | We willl see later how <code>fn:for-each(...)</code> works. The type of <code>local:on-sequences(...)</code> on the other hand is easily constructed, if a bit long: | ||
<code>function(function(item()) as item()*) as function(item()*) as item()*</code>. | <code>function(function(item()) as item()*) as function(item()*) as item()*</code>. | ||
Line 57: | Line 49: | ||
A ''higher-order function'' is a function that takes other functions as arguments and/or returns them as results. <code>fn:for-each</code> and <code>local:on-sequences</code> from the last chapter are nice examples. | A ''higher-order function'' is a function that takes other functions as arguments and/or returns them as results. <code>fn:for-each</code> and <code>local:on-sequences</code> from the last chapter are nice examples. | ||
− | With the help of higher-order functions, one can extract common patterns of | + | With the help of higher-order functions, one can extract common patterns of ''behavior'' and abstract them into a library function. |
− | '' | ||
== Sequences == | == Sequences == | ||
− | Some usage patterns on sequences are so common that the higher-order functions | + | Some usage patterns on sequences are so common that the higher-order functions describing them are in the XQuery standard libraries. They are listed here, together with their possible XQuery implementation and some motivating examples. |
− | describing them are in the XQuery standard libraries. They are listed here, together | ||
− | with their possible XQuery implementation and some motivating examples. | ||
===fn:for-each=== | ===fn:for-each=== | ||
{| | {| | ||
− | |- | + | |- valign="top" |
− | | width='120' | ''' | + | | width='120' | '''Signature''' |
− | | | + | |<pre>fn:for-each( |
− | |- | + | $input as item()*, |
+ | $action as function(item()) as item()* | ||
+ | ) as item()*</pre> | ||
+ | |- valign="top" | ||
| '''Summary''' | | '''Summary''' | ||
− | |Applies the | + | |Applies the specified <code>$action</code> to every item of <code>$input</code> and returns all results as a single sequence. |
− | |- | + | |- valign="top" |
| '''Examples''' | | '''Examples''' | ||
| | | | ||
<ul><li>Square all numbers from 1 to 10: | <ul><li>Square all numbers from 1 to 10: | ||
− | + | <pre lang='xquery'> | |
fn:for-each(1 to 10, math:pow(?, 2)) | fn:for-each(1 to 10, math:pow(?, 2)) | ||
</pre> | </pre> | ||
Line 85: | Line 77: | ||
</li> | </li> | ||
<li>Apply a list of functions to a string: | <li>Apply a list of functions to a string: | ||
− | <pre | + | <pre lang='xquery'> |
let $fs := ( | let $fs := ( | ||
fn:upper-case#1, | fn:upper-case#1, | ||
Line 96: | Line 88: | ||
</li> | </li> | ||
<li>Process each item of a sequence with the arrow operator: | <li>Process each item of a sequence with the arrow operator: | ||
− | <pre | + | <pre lang='xquery'> |
("one", "two", "three") => fn:for-each(fn:upper-case(?)) | ("one", "two", "three") => fn:for-each(fn:upper-case(?)) | ||
</pre> | </pre> | ||
''Result:'' <code>ONE TWO THREE</code> | ''Result:'' <code>ONE TWO THREE</code> | ||
</li></ul> | </li></ul> | ||
− | |- | + | |- valign="top" |
| '''XQuery 1.0''' | | '''XQuery 1.0''' | ||
|At the core, for-each is nothing else than a simple FLWOR expression: | |At the core, for-each is nothing else than a simple FLWOR expression: | ||
− | <pre | + | <pre lang='xquery'> |
declare function local:for-each( | declare function local:for-each( | ||
$seq as item()*, | $seq as item()*, | ||
Line 118: | Line 110: | ||
{| | {| | ||
− | |- | + | |- valign="top" |
− | | width='120' | ''' | + | | width='120' | '''Signature''' |
− | | | + | |<pre>fn:filter( |
− | |- | + | $input as item()*, |
+ | $predicate as function(item()) as xs:boolean | ||
+ | ) as item()*</pre> | ||
+ | |- valign="top" | ||
| '''Summary''' | | '''Summary''' | ||
− | |Applies the boolean | + | |Applies the boolean <code>$predicate</code> to all elements of the sequence <code>$input</code>, returning those for which it returns <code>true()</code>. |
− | |- | + | |- valign="top" |
| '''Examples''' | | '''Examples''' | ||
|<ul><li>All even integers until 10: | |<ul><li>All even integers until 10: | ||
− | <pre | + | <pre lang='xquery'> |
fn:filter(1 to 10, function($x) { $x mod 2 eq 0 }) | fn:filter(1 to 10, function($x) { $x mod 2 eq 0 }) | ||
</pre> | </pre> | ||
Line 133: | Line 128: | ||
</li> | </li> | ||
<li>Strings that start with an upper-case letter: | <li>Strings that start with an upper-case letter: | ||
− | <pre | + | <pre lang='xquery'> |
let $first-upper := function($str) { | let $first-upper := function($str) { | ||
let $first := fn:substring($str, 1, 1) | let $first := fn:substring($str, 1, 1) | ||
Line 143: | Line 138: | ||
</li> | </li> | ||
<li>Inefficient prime number generator: | <li>Inefficient prime number generator: | ||
− | <pre | + | <pre lang='xquery'> |
let $is-prime := function($x) { | let $is-prime := function($x) { | ||
$x gt 1 and (every $y in 2 to ($x - 1) satisfies $x mod $y ne 0) | $x gt 1 and (every $y in 2 to ($x - 1) satisfies $x mod $y ne 0) | ||
Line 151: | Line 146: | ||
''Result:'' <code>2 3 5 7 11 13 17 19</code> | ''Result:'' <code>2 3 5 7 11 13 17 19</code> | ||
</li></ul> | </li></ul> | ||
− | |- | + | |- valign="top" |
| '''Note''' | | '''Note''' | ||
|<code>fn:filter</code> can be easily implemented with <code>fn:for-each</code>: | |<code>fn:filter</code> can be easily implemented with <code>fn:for-each</code>: | ||
− | <pre | + | <pre lang='xquery'> |
declare function local:filter($seq, $pred) { | declare function local:filter($seq, $pred) { | ||
for-each( | for-each( | ||
Line 164: | Line 159: | ||
}; | }; | ||
</pre> | </pre> | ||
− | |- | + | |- valign="top" |
| '''XQuery 1.0''' | | '''XQuery 1.0''' | ||
|At the core, for-each is nothing else than a filter expression: | |At the core, for-each is nothing else than a filter expression: | ||
− | <pre | + | <pre lang='xquery'> |
declare function local:filter( | declare function local:filter( | ||
$seq as item()*, | $seq as item()*, | ||
Line 180: | Line 175: | ||
{| | {| | ||
− | |- | + | |- valign="top" |
− | | width='120' | ''' | + | | width='120' | '''Signature''' |
− | | | + | |<pre>fn:for-each-pair( |
− | |- | + | $input1 as item()*, |
+ | $input2 as item()*, | ||
+ | $action as function(item(), item()) as item()* | ||
+ | ) as item()*</pre> | ||
+ | |- valign="top" | ||
| '''Summary''' | | '''Summary''' | ||
− | | | + | |Applies the specified {{Code|$action}} to the successive pairs of items of <code>$input1</code> and <code>$input2</code>. Evaluation is stopped if one sequence yields no more items. |
− | |- | + | |- valign="top" |
| '''Examples''' | | '''Examples''' | ||
|<ul><li>Adding one to the numbers at odd positions: | |<ul><li>Adding one to the numbers at odd positions: | ||
− | <pre | + | <pre lang='xquery'> |
fn:for-each-pair( | fn:for-each-pair( | ||
fn:for-each(1 to 10, function($x) { $x mod 2 }), | fn:for-each(1 to 10, function($x) { $x mod 2 }), | ||
Line 199: | Line 198: | ||
</li> | </li> | ||
<li>Line numbering: | <li>Line numbering: | ||
− | <pre | + | <pre lang='xquery'> |
let $number-words := function($str) { | let $number-words := function($str) { | ||
fn:string-join( | fn:string-join( | ||
Line 213: | Line 212: | ||
</pre> | </pre> | ||
''Result:'' | ''Result:'' | ||
− | <pre | + | <pre lang='xquery'> |
1: how | 1: how | ||
2: are | 2: are | ||
Line 220: | Line 219: | ||
</li> | </li> | ||
<li>Checking if a sequence is sorted: | <li>Checking if a sequence is sorted: | ||
− | <pre | + | <pre lang='xquery'> |
let $is-sorted := function($seq) { | let $is-sorted := function($seq) { | ||
every $b in | every $b in | ||
fn:for-each-pair( | fn:for-each-pair( | ||
$seq, | $seq, | ||
− | + | tail($seq), | |
function($a, $b) { $a le $b } | function($a, $b) { $a le $b } | ||
) | ) | ||
Line 236: | Line 235: | ||
</pre> | </pre> | ||
''Result:'' <code>true false</code></li></ul> | ''Result:'' <code>true false</code></li></ul> | ||
− | |- | + | |- valign="top" |
| '''XQuery 1.0''' | | '''XQuery 1.0''' | ||
− | |<pre | + | |<pre lang='xquery'> |
declare function local:for-each-pair( | declare function local:for-each-pair( | ||
$seq1 as item()*, | $seq1 as item()*, | ||
Line 252: | Line 251: | ||
== Folds == | == Folds == | ||
− | A ''fold'', also called ''reduce'' or ''accumulate'' in other languages, is a very | + | A ''fold'', also called ''reduce'' or ''accumulate'' in other languages, is a very basic higher-order function on sequences. It starts from a seed value and incrementally builds up a result, consuming one element from the sequence at a time and combining it with the aggregate of a user-defined function. |
− | basic higher-order function on sequences. It starts from a seed value and incrementally | ||
− | builds up a result, consuming one element from the sequence at a time and combining it with | ||
− | the aggregate of a user-defined function. | ||
− | Folds are one solution to the problem of not having ''state'' in functional programs. | + | Folds are one solution to the problem of not having ''state'' in functional programs. Solving a problem in ''imperative'' programming languages often means repeatedly updating the value of variables, which isn't allowed in functional languages. |
− | Solving a problem in ''imperative'' programming languages often means repeatedly updating | ||
− | the value of variables, which isn't allowed in functional languages. | ||
Calculating the ''product'' of a sequence of integers for example is easy in <code>Java</code>: | Calculating the ''product'' of a sequence of integers for example is easy in <code>Java</code>: | ||
− | <pre | + | |
+ | <pre lang="java"> | ||
public int product(int[] seq) { | public int product(int[] seq) { | ||
int result = 1; | int result = 1; | ||
Line 271: | Line 266: | ||
} | } | ||
</pre> | </pre> | ||
+ | |||
Nice and efficient implementations using folds will be given below. | Nice and efficient implementations using folds will be given below. | ||
− | The ''linear'' folds on sequences come in two | + | The ''linear'' folds on sequences come in two flavors. They differ in the direction in which they traverse the sequence: |
===fn:fold-left=== | ===fn:fold-left=== | ||
{| | {| | ||
− | |- | + | |- valign="top" |
− | | width='120' | ''' | + | | width='120' | '''Signature''' |
− | | | + | |<pre>fn:fold-left( |
− | |- | + | $input as item()*, |
+ | $zero as item()*, | ||
+ | $action as function(item()*, item()) as item()* | ||
+ | ) as item()*</pre> | ||
+ | |- valign="top" | ||
| '''Summary''' | | '''Summary''' | ||
− | |The ''left fold'' traverses the | + | |The ''left fold'' traverses the {{Code|$input}} from the left. |
− | The query <code>fn:fold-left(1 to 5, 0, $f)</code> for example would be evaluated as: | + | The query <code>fn:fold-left(1 to 5, 0, $f)</code>, for example, would be evaluated as: |
− | <pre | + | <pre lang='xquery'> |
$f($f($f($f($f(0, 1), 2), 3), 4), 5) | $f($f($f($f($f(0, 1), 2), 3), 4), 5) | ||
</pre> | </pre> | ||
− | |- | + | |- valign="top" |
| '''Examples''' | | '''Examples''' | ||
|<ul><li>Product of a sequence of integers: | |<ul><li>Product of a sequence of integers: | ||
− | <pre | + | <pre lang='xquery'> |
fn:fold-left(1 to 5, 1, | fn:fold-left(1 to 5, 1, | ||
function($result, $curr) { $result * $curr } | function($result, $curr) { $result * $curr } | ||
Line 299: | Line 299: | ||
</li> | </li> | ||
<li>Illustrating the evaluation order: | <li>Illustrating the evaluation order: | ||
− | <pre | + | <pre lang='xquery'> |
fn:fold-left(1 to 5, '$seed', | fn:fold-left(1 to 5, '$seed', | ||
concat('$f(', ?, ', ', ?, ')') | concat('$f(', ?, ', ', ?, ')') | ||
Line 307: | Line 307: | ||
</li> | </li> | ||
<li>Building a decimal number from digits: | <li>Building a decimal number from digits: | ||
− | <pre | + | <pre lang='xquery'> |
let $from-digits := fold-left(?, 0, | let $from-digits := fold-left(?, 0, | ||
function($n, $d) { 10 * $n + $d } | function($n, $d) { 10 * $n + $d } | ||
Line 318: | Line 318: | ||
''Result:'' <code>12345 42</code> | ''Result:'' <code>12345 42</code> | ||
</li></ul> | </li></ul> | ||
− | |- | + | |- valign="top" |
| '''XQuery 1.0''' | | '''XQuery 1.0''' | ||
|As folds are more general than ''FLWOR'' expressions, the implementation isn't as concise as the former ones: | |As folds are more general than ''FLWOR'' expressions, the implementation isn't as concise as the former ones: | ||
− | <pre | + | <pre lang='xquery'> |
declare function local:fold-left( | declare function local:fold-left( | ||
− | $ | + | $input as item()*, |
− | $ | + | $zero as item()*, |
− | $ | + | $action as function(item()*, item()) as item()* |
) as item()* { | ) as item()* { | ||
− | if(empty($ | + | if(empty($input)) then $zero |
else local:fold-left( | else local:fold-left( | ||
− | + | tail($input), | |
− | $ | + | $action($zero, head($input)), |
− | $ | + | $action |
) | ) | ||
}; | }; | ||
Line 340: | Line 340: | ||
{| | {| | ||
− | |- | + | |- valign="top" |
− | | width='120' | ''' | + | | width='120' | '''Signature''' |
− | | | + | |<pre>fn:fold-right( |
− | |- | + | $input as item()*, |
+ | $zero as item()*, | ||
+ | $action as function(item(), item()*) as item()* | ||
+ | ) as item()*</pre> | ||
+ | |- valign="top" | ||
| '''Summary''' | | '''Summary''' | ||
− | |The ''right fold'' | + | |The ''right fold'' traverses the {{Code|$input}} from the right. |
− | The query <code>fn:fold-right(1 to 5, 0, $f)</code> for example would be evaluated as: | + | The query <code>fn:fold-right(1 to 5, 0, $f)</code>, for example, would be evaluated as: |
− | <pre | + | <pre lang='xquery'> |
$f(1, $f(2, $f(3, $f(4, $f(5, 0))))) | $f(1, $f(2, $f(3, $f(4, $f(5, 0))))) | ||
</pre> | </pre> | ||
− | |- | + | |- valign="top" |
| '''Examples''' | | '''Examples''' | ||
|<ul><li>Product of a sequence of integers: | |<ul><li>Product of a sequence of integers: | ||
− | <pre | + | <pre lang='xquery'> |
fn:fold-right(1 to 5, 1, | fn:fold-right(1 to 5, 1, | ||
function($curr, $result) { $result * $curr } | function($curr, $result) { $result * $curr } | ||
Line 361: | Line 365: | ||
</li> | </li> | ||
<li>Illustrating the evaluation order: | <li>Illustrating the evaluation order: | ||
− | <pre | + | <pre lang='xquery'> |
fn:fold-right(1 to 5, '$seed', | fn:fold-right(1 to 5, '$seed', | ||
concat('$f(', ?, ', ', ?, ')') | concat('$f(', ?, ', ', ?, ')') | ||
Line 369: | Line 373: | ||
</li> | </li> | ||
<li>Reversing a sequence of items: | <li>Reversing a sequence of items: | ||
− | <pre | + | <pre lang='xquery'> |
let $reverse := fn:fold-right(?, (), | let $reverse := fn:fold-right(?, (), | ||
function($item, $rev) { | function($item, $rev) { | ||
Line 379: | Line 383: | ||
''Result:'' <code>10 9 8 7 6 5 4 3 2 1</code> | ''Result:'' <code>10 9 8 7 6 5 4 3 2 1</code> | ||
</li></ul> | </li></ul> | ||
− | |- | + | |- valign="top" |
| '''XQuery 1.0''' | | '''XQuery 1.0''' | ||
− | |<pre | + | |<pre lang='xquery'> |
declare function local:fold-right( | declare function local:fold-right( | ||
− | $ | + | $input as item()*, |
− | $ | + | $zero as item()*, |
− | $ | + | $action as function(item(), item()*) as item()* |
) as item()* { | ) as item()* { | ||
− | if(empty($ | + | if(empty($input)) then $zero |
− | else $ | + | else $action( |
− | + | head($input), | |
− | local:fold-right(tail($ | + | local:fold-right(tail($input), $zero, $action) |
) | ) | ||
}; | }; |
Latest revision as of 18:39, 1 December 2023
This page present some higher-order functions of the XQuery specification. The BaseX-specific Higher-Order Functions Module contains some additional useful functions.
Contents
Function Items[edit]
Probably the most important new feature in XQuery 3.0 are function items, i. e., items that act as functions, but can also be passed to and from other functions and expressions. This feature makes functions first-class citizens of the language. The XQuery 3.0 page goes into details on how function items can be obtained.
Function Types[edit]
Like every XQuery item, function items have a sequence type. It can be used to specify the arity (number of arguments the function takes) and the argument and result types.
The most general function type is function(*)
. It's the type of all function items. The following query for example goes through a list of XQuery items and, if it is a function item, prints its arity:
for $item in (1, 'foo', fn:concat#3, function($a) { 42 * $a })
where $item instance of function(*)
return fn:function-arity($item)
Result: 3 1
The notation for specifying argument and return types is quite intuitive, as it closely resembles the function declaration. The XQuery function
declare function local:char-at(
$str as xs:string,
$pos as xs:integer
) as xs:string {
fn:substring($str, $pos, 1)
};
for example has the type function(xs:string, xs:integer) as xs:string
. It isn't possible to specify only the argument and not the result type or the other way round. A good place-holder to use when no restriction is wanted is item()*
, as it matches any XQuery value.
Function types can also be nested. As an example we take local:on-sequences
, which takes a function defined on single items and makes it work on sequences as well:
declare function local:on-sequences(
$fun as function(item()) as item()*
) as function(item()*) as item()* {
fn:for-each($fun, ?)
};
We willl see later how fn:for-each(...)
works. The type of local:on-sequences(...)
on the other hand is easily constructed, if a bit long:
function(function(item()) as item()*) as function(item()*) as item()*
.
Higher-Order Functions[edit]
A higher-order function is a function that takes other functions as arguments and/or returns them as results. fn:for-each
and local:on-sequences
from the last chapter are nice examples.
With the help of higher-order functions, one can extract common patterns of behavior and abstract them into a library function.
Sequences[edit]
Some usage patterns on sequences are so common that the higher-order functions describing them are in the XQuery standard libraries. They are listed here, together with their possible XQuery implementation and some motivating examples.
fn:for-each[edit]
Signature | fn:for-each( $input as item()*, $action as function(item()) as item()* ) as item()* |
Summary | Applies the specified $action to every item of $input and returns all results as a single sequence.
|
Examples |
|
XQuery 1.0 | At the core, for-each is nothing else than a simple FLWOR expression:
declare function local:for-each(
$seq as item()*,
$fun as function(item()) as item()*
) as item()* {
for $s in $seq
return $fun($s)
};
|
fn:filter[edit]
Signature | fn:filter( $input as item()*, $predicate as function(item()) as xs:boolean ) as item()* |
Summary | Applies the boolean $predicate to all elements of the sequence $input , returning those for which it returns true() .
|
Examples |
|
Note | fn:filter can be easily implemented with fn:for-each :
declare function local:filter($seq, $pred) {
for-each(
$seq,
function($x) {
if($pred($x)) then $x else ()
}
)
};
|
XQuery 1.0 | At the core, for-each is nothing else than a filter expression:
declare function local:filter(
$seq as item()*,
$pred as function(item()) as xs:boolean
) as item()* {
$seq[$pred(.)]
};
|
fn:for-each-pair[edit]
Signature | fn:for-each-pair( $input1 as item()*, $input2 as item()*, $action as function(item(), item()) as item()* ) as item()* |
Summary | Applies the specified $action to the successive pairs of items of $input1 and $input2 . Evaluation is stopped if one sequence yields no more items.
|
Examples |
|
XQuery 1.0 | declare function local:for-each-pair(
$seq1 as item()*,
$seq2 as item()*,
$fun as function(item(), item()) as item()*
) as item()* {
for $pos in 1 to min((count($seq1), count($seq2)))
return $fun($seq1[$pos], $seq2[$pos])
};
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Folds[edit]
A fold, also called reduce or accumulate in other languages, is a very basic higher-order function on sequences. It starts from a seed value and incrementally builds up a result, consuming one element from the sequence at a time and combining it with the aggregate of a user-defined function.
Folds are one solution to the problem of not having state in functional programs. Solving a problem in imperative programming languages often means repeatedly updating the value of variables, which isn't allowed in functional languages.
Calculating the product of a sequence of integers for example is easy in Java
:
public int product(int[] seq) {
int result = 1;
for(int i : seq) {
result = result * i;
}
return result;
}
Nice and efficient implementations using folds will be given below.
The linear folds on sequences come in two flavors. They differ in the direction in which they traverse the sequence:
fn:fold-left[edit]
Signature | fn:fold-left( $input as item()*, $zero as item()*, $action as function(item()*, item()) as item()* ) as item()* |
Summary | The left fold traverses the $input from the left.
The query $f($f($f($f($f(0, 1), 2), 3), 4), 5)
|
Examples |
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XQuery 1.0 | As folds are more general than FLWOR expressions, the implementation isn't as concise as the former ones:
declare function local:fold-left(
$input as item()*,
$zero as item()*,
$action as function(item()*, item()) as item()*
) as item()* {
if(empty($input)) then $zero
else local:fold-left(
tail($input),
$action($zero, head($input)),
$action
)
};
|
fn:fold-right[edit]
Signature | fn:fold-right( $input as item()*, $zero as item()*, $action as function(item(), item()*) as item()* ) as item()* |
Summary | The right fold traverses the $input from the right.
The query $f(1, $f(2, $f(3, $f(4, $f(5, 0)))))
|
Examples |
|
XQuery 1.0 | declare function local:fold-right(
$input as item()*,
$zero as item()*,
$action as function(item(), item()*) as item()*
) as item()* {
if(empty($input)) then $zero
else $action(
head($input),
local:fold-right(tail($input), $zero, $action)
)
};
Note that the order of the arguments of |