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, incr#1, flip#1, iterate#2, repeat#1, take#2, until#3, ref#1, deref#1, curry#1, Y#1, compose#1, compose#2, compose#3, compose#4, compose#5, compose#6, compose#7, compose#8, compose#9, compose#10

Functions

id#1

id($a
)

Returns the argument

Params

• $a

incr#1

incr($a
)

Adds one to the argument

Params

• $a

flip#1

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()*

iterate#2

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

repeat#1

repeat($a
)

Returns an infinite sequence of the argument sequence repeated. Only really useful on an implementation that supports lazy evaluation

Params

• $a

take#2

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

until#3

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

ref#1

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

Wrap a sequence as a function item

Params

• $arg as item()*

Returns

• function() as item()*

deref#1

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

Unwrap a sequence from a function item

Params

• $arg as function() as item()*

Returns

• item()*

curry#1

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.

Y#1

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:

  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.

compose#1

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:

  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.

compose#2

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:

  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.

compose#3

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.

compose#4

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.

compose#5

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.

compose#6

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.

compose#7

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.

compose#8

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.

compose#9

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.

compose#10

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.

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