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XQuery 3.0 higher order functions helper library

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# library module: http://snelson.org.uk/functions/functional
  
# functional.xq

A library of useful functionality for working with XQuery 3.0 higher order  functions. Includes a number of functions from the standard Haskell prelude,  as well as functions to perform currying, function composition, and  Y-combination.

Author:  John Snelson  
Version:  0.9

## Table of Contents

* Functions: [id\#1](#func_id_1), [incr\#1](#func_incr_1), [flip\#1](#func_flip_1), [iterate\#2](#func_iterate_2), [repeat\#1](#func_repeat_1), [take\#2](#func_take_2), [until\#3](#func_until_3), [ref\#1](#func_ref_1), [deref\#1](#func_deref_1), [curry\#1](#func_curry_1), [Y\#1](#func_Y_1), [compose\#1](#func_compose_1), [compose\#2](#func_compose_2), [compose\#3](#func_compose_3), [compose\#4](#func_compose_4), [compose\#5](#func_compose_5), [compose\#6](#func_compose_6), [compose\#7](#func_compose_7), [compose\#8](#func_compose_8), [compose\#9](#func_compose_9), [compose\#10](#func_compose_10)

## Functions

### <a name="func_id_1"/> id\#1
```xquery
id($a
)
```
 Returns the argument

#### Params

* $a

### <a name="func_incr_1"/> incr\#1
```xquery
incr($a
)
```
 Adds one to the argument

#### Params

* $a

### <a name="func_flip_1"/> flip\#1
```xquery
flip(
  $f as function(item()*,item()*) as item()*
) as  function(item()*,item()*) as item()*
```
 Reverses the order of the arguments in the function passed as an argument

#### Params

* $f as  function(item()\*,item()\*) as item()\*

#### Returns
*  function(item()\*,item()\*) as item()\*

### <a name="func_iterate_2"/> iterate\#2
```xquery
iterate($f, $a
)
```
  Returns an infinite sequence of ($a, $f($a), $f($f($a)), ...).  Only really useful on an implementation that supports lazy evaluation

#### Params

* $f

* $a

### <a name="func_repeat_1"/> repeat\#1
```xquery
repeat($a
)
```
  Returns an infinite sequence of the argument sequence repeated.  Only really useful on an implementation that supports lazy evaluation

#### Params

* $a

### <a name="func_take_2"/> take\#2
```xquery
take($n, $l
)
```
  Returns the first $n items from the sequence $l

#### Params

* $n: the number of items to return

* $l: the sequence to return items from

### <a name="func_until_3"/> until\#3
```xquery
until($p, $f, $a
)
```
  Tests the predicate $p($a), returning $a if true, or until($p, $f, $f($a)) otherwise.

#### Params

* $p: the predicate function

* $f: the function to iteratively apply

* $a: the initial starting value

### <a name="func_ref_1"/> ref\#1
```xquery
ref($arg as item()*
) as  function() as item()*
```
 Wrap a sequence as a function item

#### Params

* $arg as  item()\*

#### Returns
*  function() as item()\*

### <a name="func_deref_1"/> deref\#1
```xquery
deref($arg as function() as item()*
) as  item()*
```
 Unwrap a sequence from a function item

#### Params

* $arg as  function() as item()\*

#### Returns
*  item()\*

### <a name="func_curry_1"/> curry\#1
```xquery
curry($f as function(*)
) as  function(item()*) as item()*
```
  Curries a function (up to arity 10). Takes a function that accepts  a number of arguments, and returns a function that accepts the first argument,  then returns a new function to accept the second, and so on.

#### Params

* $f as  function(\*): The function to curry.

#### Returns
*  function(item()\*) as item()\*: The curried version of the function.

#### Errors
 If $f has an arity greater than 10 or less than 1.

### <a name="func_Y_1"/> Y\#1
```xquery
Y($f as function(*)
) as  function(*)
```
  Y combinator for a function (up to arity 10). Partially applies a function as  the first argument to itself, so that it can call itself recursively using the  value. Returns the partially applied function. ie:

```xquery
  Y(function($f,$a) { if($a gt 0) then ($a, $f($a - 1)) else $a })(10)  
```

#### Params

* $f as  function(\*): The function to partially apply to itself.

#### Returns
*  function(\*): The partially applied function.

#### Errors
 If $f has an arity greater than 10 or less than 1.

### <a name="func_compose_1"/> compose\#1
```xquery
compose($functions as function(*)+
) as  function(*)
```
  Compose a sequence of functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments. ie:

```xquery
  compose((fn:count#1, fn:filter#2))  
```

#### Params

* $functions as  function(\*)+: The sequence of functions to compose

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_2"/> compose\#2
```xquery
compose($f1 as function(*), $f2 as function(*)
) as  function(*)
```
  Compose two functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments. ie:

```xquery
  compose(fn:count#1, fn:filter#2)  
```

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_3"/> compose\#3
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*)
) as  function(*)
```
  Compose three functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_4"/> compose\#4
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*)
) as  function(*)
```
  Compose four functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_5"/> compose\#5
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*), $f5 as function(*)
) as  function(*)
```
  Compose five functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

* $f5 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_6"/> compose\#6
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*), $f5 as function(*),
  $f6 as function(*)
) as  function(*)
```
  Compose six functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

* $f5 as  function(\*)

* $f6 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_7"/> compose\#7
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*), $f5 as function(*),
  $f6 as function(*), $f7 as function(*)
) as  function(*)
```
  Compose seven functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

* $f5 as  function(\*)

* $f6 as  function(\*)

* $f7 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_8"/> compose\#8
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*), $f5 as function(*),
  $f6 as function(*), $f7 as function(*), $f8 as function(*)
) as  function(*)
```
  Compose eight functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

* $f5 as  function(\*)

* $f6 as  function(\*)

* $f7 as  function(\*)

* $f8 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_9"/> compose\#9
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*), $f5 as function(*),
  $f6 as function(*), $f7 as function(*), $f8 as function(*), $f9 as function(*)
) as  function(*)
```
  Compose nine functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

* $f5 as  function(\*)

* $f6 as  function(\*)

* $f7 as  function(\*)

* $f8 as  function(\*)

* $f9 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

### <a name="func_compose_10"/> compose\#10
```xquery
compose($f1 as function(*), $f2 as function(*), $f3 as function(*), $f4 as function(*), $f5 as function(*),
  $f6 as function(*), $f7 as function(*), $f8 as function(*), $f9 as function(*), $f10 as function(*)
) as  function(*)
```
  Compose ten functions into a single function. All the functions   except the last one must have an arity of 1. The last function may accept  between 0 and 10 arguments.

#### Params

* $f1 as  function(\*)

* $f2 as  function(\*)

* $f3 as  function(\*)

* $f4 as  function(\*)

* $f5 as  function(\*)

* $f6 as  function(\*)

* $f7 as  function(\*)

* $f8 as  function(\*)

* $f9 as  function(\*)

* $f10 as  function(\*)

#### Returns
*  function(\*): The composed function.

#### Errors
 If the last function has an arity greater than 10.

*Generated by [xquerydoc](https://github.com/xquery/xquerydoc)*

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