Anonymous recursion: Difference between revisions

;Task:

If possible, demonstrate this by writing the recursive version of the fibonacci function   (see [[Fibonacci sequence]])   which checks for a negative argument before doing the actual recursion.

<br><br>

 

=={{header|11l}}==

{{trans|C++}}

F f(Int n) -> Int

I n < 2

 

L(i) 0..20

{{out}}

<pre>

 

Better would be to use type Natural instead of Integer, which lets Ada do the magic of checking the valid range.

function Actual_Fib (N: in Integer) return Integer is

begin

return Actual_Fib (X);

end if;

 

=={{header|ALGOL 68}}==

{{Trans|Ada}}

IF x < 0

THEN

actual fibonacci( x )

FI;

 

=={{header|APL}}==

though they are not quite first-class objects (you can't have an array of functions for example).

 

⍵<0:⎕SIGNAL 11 ⍝ DOMAIN ERROR if argument < 0

{ ⍝ Inner (anonymous) function

(∇⍵-1)+∇⍵-2 ⍝ ∇ = anonymous recursive call

}⍵ ⍝ Call function in place

 

 

=={{header|AppleScript}}==

-- For the sake of the task, a needlessly anonymous local script object containing a needlessly recursive handler.

-- The script could easily (and ideally should) be assigned to a local variable.

 

fibonacci(15) --> {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610}

 

 

Or, as the recursion of an anonymous declarative function, enabled by the Y combinator:

 

on run

set my text item delimiters to dlm

s

{{Out}}

<pre>missing value, missing value, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34

55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765</pre>

 

=={{header|AutoHotkey}}==

nold1 := 1

nold2 := 0

}

Return t

 

=={{header|AutoIt}}==

ConsoleWrite(Fibonacci(10) & @CRLF) ; ## USAGE EXAMPLE

ConsoleWrite(Fibonacci(20) & @CRLF) ; ## USAGE EXAMPLE

 

EndFunc

{{out}}

<pre>

=={{header|Axiom}}==

Using the Aldor compiler in Axiom/Fricas:

Z ==> Integer;

fib(x:Z):Z == {

f(n:Z,v1:Z,v2:Z):Z == if n<2 then v2 else f(n-1,v2,v1+v2);

f(x,1,1);

Z ==> Integer

TestPackage : with

f : Reference((Z,Z,Z) -> Z) := ref((n, v1, v2) +-> 0)

f() := (n, v1, v2) +-> if n<2 then v2 else f()(n-1,v2,v1+v2)

 

 

DEF FN fib(x) = FIB(x)

'--- using an alias

'fib(9)

 

{{trans|AutoIt}}

print Fibonacci(30)

print Fibonacci(-10)

return Fibonacci(num - 1) + Fibonacci(num - 2)

end If

{{out}}

<pre>6765

55</pre>

 

 

{{works with|BBC BASIC for Windows}}

This works by finding a pointer to the 'anonymous' function and calling it indirectly:

END

DEF FNfib(n%) IF n%<0 THEN ERROR 100, "Must not be negative"

LOCAL P% : P% = !384 + LEN$!384 + 4 : REM Function pointer

{{out}}

<pre>

55

</pre>

 

=={{header|Bracmat}}==

===lambda 'light'===

The first solution uses macro substitution. In an expression headed by an apostrophe operator with an empty lhs all subexpressions headed by a dollar operator with empty lhs are replaced by the values that the rhs are bound to, without otherwise evaluating the expression. Example: if <code>(x=7) & (y=4)</code> then <code>'($x+3+$y)</code> becomes <code>=7+3+4</code>. Notice that the solution below utilises no other names than <code>arg</code>, the keyword that always denotes a function's argument. The test for negative or non-numeric arguments is outside the recursive part. The function fails if given negative input.

=

. !arg:#:~<0

$ 30

)

Answer:

<pre>832040</pre>

===pure lambda calculus===

(See http://en.wikipedia.org/wiki/Lambda_calculus). The following solution works almost the same way as the previous solution, but uses lambda calculus

' ( x

. $x:#:~<0

)

$ 30

Answer:

<pre>832040</pre>

 

The following code calls an anonymous recursive Fibonacci function on each number of the range 0-9.

(𝕩<2)◶⟨+´𝕊¨,𝕏⟩𝕩-1‿2

 

[https://mlochbaum.github.io/BQN/try.html#code=ewogICjwnZWpPDIp4pe24p+oK8K08J2VisKoLPCdlY/in6nwnZWpLTHigL8yCn3CqOKGlTEw Try It!]

 

Recursion can also be performed using an internal name defined by a header such as <code>Fact:</code> or <code>Fact 𝕩:</code>. This header is visible inside the block but not outside of it, so from the outside the function is anonymous. The named form allows the outer function to be called within nested blocks, while <code>𝕊</code> can only refer to the immediately containing one.

(𝕩<2)◶⟨+´Fact¨,𝕏⟩𝕩-1‿2

 

=={{header|C}}==

Using scoped function fib_i inside fib, with GCC (required version 3.2 or higher):

 

long fib(long x)

 

return 0;

{{out}}

<pre>Bad argument: fib(-1)

 

Recursive functions can be defined within [https://gcc.gnu.org/onlinedocs/gcc/Statement-Exprs.html statement expressions]:

#include <stdio.h>

int main(){

}

 

 

=={{header|C sharp|C#}}==

The inner recursive function (delegate/lambda) has to be named.

static int Fib(int n)

{

return fib(n);

}

 

=={{header|C++}}==

In C++ (as of the 2003 version of the standard, possibly earlier), we can declare class within a function scope. By giving that class a public static member function, we can create a function whose symbol name is only known to the function in which the class was derived.

{

if(n < 0)

return actual_fib::calc(n);

}

{{works with|C++11}}

using namespace std;

 

 

return actual_fib(n);

 

Using a local function object that calls itself using <code>this</code>:

 

{

if(n < 0)

return actual_fib(n);

}

 

=={{header|Clio}}==

Simple anonymous recursion to print from 9 to 0.

if n:

 

=={{header|Clojure}}==

The JVM as of now has no Tail call optimization so the default way of looping in Clojure uses anonymous recursion so not to be confusing.

(defn fib [n]

(when (neg? n)

v2

(recur (dec n) v2 (+ v1 v2)))))

Using an anonymous function

 

=={{header|CoffeeScript}}==

# function call itself.

fibonacci = (n) ->

recurse(n-2) + recurse(n-1)

recurse(n)

 

=={{header|Common Lisp}}==

This version uses the anaphoric <code>lambda</code> from [http://dunsmor.com/lisp/onlisp/onlisp_18.html Paul Graham's On Lisp].

 

`(labels ((self ,parms ,@body))

 

The Fibonacci function can then be defined as

 

(assert (>= n 0) nil "'~a' is a negative number" n)

(funcall

n

(+ (self (- n 1)) (self (- n 2)))))

 

===Using labels===

This puts a function in a local label. The function is not anonymous, but not only is it local, so that its name does not pollute the global namespace, but the name can be chosen to be identical to that of the surrounding function, so it is not a newly invented name

 

"Fibonacci sequence function."

(if (< number 0)

a

(fib (- n 1) b (+ a b)))))

Although name space polution isn't an issue, in recognition of the obvious convenience of anonymous recursive helpers, here is another solution: add the language feature for anonymously recursive blocks: the operator RECURSIVE, with a built-in local operator RECURSE to make recursive calls.

 

Here is <code>fib</code> rewritten to use RECURSIVE:

"Fibonacci sequence function."

(if (< number 0)

(if (= n 0)

a

Implementation of RECURSIVE:

(let ((hidden-name (gensym "RECURSIVE-")))

`(macrolet ((recurse (&rest args) `(,',hidden-name ,@args)))

(labels ((,hidden-name (,@(mapcar #'first parm-init-pairs)) ,@body))

RECURSIVE works by generating a local function with LABELS, but with a machine-generated unique name. Furthermore, it provides syntactic sugar so that the initial call to the recursive function takes place implicitly, and the initial values are specified using LET-like syntax. Of course, if RECURSIVE blocks are nested, each RECURSE refers to its own function. There is no way for an inner RECURSIVE to specify recursion to an other RECURSIVE. That is what names are for!

 

===Using the Y combinator===

 

(symbol-function '!!) (symbol-function 'apply))

 

(1 1)

(otherwise (+ (fib (- n 1))

 

=={{header|D}}==

assert(arg >= 0);

 

 

39.fib.writeln;

{{out}}

<pre>63245986</pre>

===With Anonymous Class===

In this version anonymous class is created, and by using opCall member function, the anonymous class object can take arguments and act like an anonymous function. The recursion is done by calling opCall inside itself.

 

int fib(in int n) pure nothrow {

void main() {

writeln(fib(39));

The output is the same.

 

This puts a function in a local method binding. The function is not anonymous, but the name fib1 is local and never pollutes the outside namespace.

 

define function fib (n)

when (n < 0)

fib1(n, 0, 1)

end

 

=={{header|Déjà Vu}}==

===With Y combinator===

labda y:

labda:

 

for j range 0 10:

===With <code>recurse</code>===

n 0 1

labda times back-2 back-1:

 

for j range 0 10:

 

Note that this method starts from 0, while the previous starts from 1.

 

=={{header|EchoLisp}}==

A '''named let''' provides a local lambda via a label.

(define (fib n)

(let _fib ((a 1) (b 1) (n n))

(<= n 1) a

(_fib b (+ a b) (1- n)))))

 

=={{header|Ela}}==

Using fix-point combinator:

Function 'fix' is defined in standard Prelude as follows:

 

=={{header|Elena}}==

 

fib(n)

{

}

 

public program()

{

{{out}}

<pre>

=={{header|Elixir}}==

With Y-Combinator:

fib = fn f -> (

fn x -> if x == 0, do: 0, else: (if x == 1, do: 1, else: f.(x - 1) + f.(x - 2)) end

 

IO.inspect y.(&(fib.(&1))).(40)

 

{{out}}

102334155

 

=={{header|Erlang}}==

Two solutions. First fib that use the module to hide its helper. The helper also is called fib so there is no naming problem. Then fib_internal which has the helper function inside itself.

 

-module( anonymous_recursion ).

-export( [fib/1, fib_internal/1] ).

fib( N, Next, Acc ) -> fib( N - 1, Acc+Next, Next ).

 

 

=={{header|F Sharp|F#}}==

 

The function 'fib2' is only visible inside the 'fib' function.

| n when n < 0 -> None

| n -> let rec fib2 = function

| 0 | 1 -> 1

| n -> fib2 (n-1) + fib2 (n-2)

'''Using a fixed point combinator:'''

 

let fib = function

| n when n < 0 -> None

{{out}}

Both functions have the same output.

 

=={{header|Factor}}==

 

To achieve anonymous recursion, this solution has a recursive quotation.

IN: rosettacode.fibonacci.ar

 

[ [ 2 - ] dip dup call ] 2bi +

] if

The name ''q'' in the stack effect has no significance; <code>call( x x -- x )</code> would still work.

 

=={{header|Falcon}}==

Falcon allows a function to refer to itself by use of the fself keyword which is always set to the currently executing function.

if x < 0

raise ParamError(description|"Negative argument invalid", extra|"Fibbonacci sequence is undefined for negative numbers")

catch in e

> e

{{out}}

<pre>

 

=={{header|FBSL}}==

 

FUNCTION Fibonacci(n)

PRINT Fibonacci(13.666)

 

'''Output:'''

Nuts!

Recursion is always anonymous in Forth, allowing it to be used in anonymous functions. However, definitions can't be defined during a definition (there are no 'local functions'), and the data stack can't be portably used to get data into a definition being defined.

{{works with|SwiftForth}} - and any Forth in which colon-sys consumes zero cells on the data stack.

dup 2 < ?exit

1- dup recurse swap 1- recurse + ; ( xt )

: fib ( +n -- n' )

dup 0< abort" Negative numbers don't exist."

Portability is achieved with a once-off variable (or any temporary-use space with a constant address - i.e., not PAD):

variable pocket pocket !

: fib ( +n -- n' )

dup 0< abort" Negative numbers don't exist."

Currently, most Forths have started to support embedded definitions (shown here for iForth):

dup 0< abort" Negative numbers don't exist"

 

=={{header|Fortran}}==

Since a hidden named function instead of an anonymous one seems to be ok with implementors, here is the Fortran version:

integer, intent(in) :: n

if (n < 0 ) then

end if

end function purefib

 

=={{header|FreeBASIC}}==

 

However, for compatibility with old QB code, gosub can be used if one specifies the 'fblite', 'qb' or 'deprecated dialects:

 

#Lang "fblite"

Print

Print "Press any key to quit"

 

{{out}}

=={{header|Fōrmulæ}}==

 

 

 

 

=={{header|Go}}==

Y combinator solution. Go has no special support for anonymous recursion.

 

import "fmt"

})

})

{{out}}

<pre>

fib 40 = 102334155

fib undefined for negative numbers

</pre>

 

=={{header|Groovy}}==

Groovy does not explicitly support anonymous recursion. This solution is a kludgy trick that takes advantage of the "owner" scoping variable (reserved word) for closures.

assert it > -1

{i -> i < 2 ? i : {j -> owner.call(j)}(i-1) + {k -> owner.call(k)}(i-2)}(it)

Test:

println fib0to20

 

println "KABOOM!!"

println e.message

{{out}}

<pre>[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765]

 

We're defining a function 'real' which is only available from within the fib function.

fib n

| n < 0 = Nothing

where real 0 = 1

real 1 = 1

 

'''Anonymous function:'''

 

This uses the 'fix' function to find the fixed point of the anonymous function.

 

fib :: Integer -> Maybe Integer

fib n

| n < 0 = Nothing

{{out}}

Both functions provide the same output when run in GHCI.

 

Or, without imports (inlining an anonymous fix)

 

fib n

| n < 0 = Nothing

case m of

Just x -> [x]

{{Out}}

<pre>[1,1,2,3,5,8,13,21,34,55,89]</pre>

 

This example does accomplish the goals of hiding the procedure inside ''fib'' so that the type and value checking is outside the recursion. It also does not require an identifier to reference the inner procedure; but, it requires a local variable to remember our return point. Also, each recursion will result in the current co-expression being refreshed, essentially copied, placing a heavy demand on co-expression resources.

every write("fib(",a := numeric(!A),")=",fib(a))

end

A := if type(A) == "list" then A[1]

return (@A, A) # prime and return

Some of the code requires some explaining:

* The double curly brace syntax after ''makeProc'' serves two different purposes, the outer set is used in the call to create a co-expression. The inner one binds all the expressions together as a single unit.

 

For reference, here is the non-cached version:

local source, i

if type(n) == "integer" & n >= 0 then

((i-1)@makeProc(^&current) + (i-2)@makeProc(^&current)) @ source

}}

The performance of this second version is 'truly impressive'. And I mean that in a really bad way. By way of example, using default memory settings on a current laptop, a simple recursive non-cached ''fib'' out distanced the non-cached ''fib'' above by a factor of 20,000. And a simple recursive cached version out distanced the cached version above by a factor of 2,000.

 

=={{header|Io}}==

The most natural way to solve this task is to use a nested function whose scope is limited to the helper function.

if(x < 0, Exception raise("Negative argument not allowed!"))

fib2 := method(n,

)

fib2(x floor)

 

=={{header|J}}==

Copied directly from the [[Fibonacci_sequence#J|fibonacci sequence]] task, which in turn copied from one of several implementations in an [[j:Essays/Fibonacci_Sequence|essay]] on the J Wiki:

Note that this is an identity function for arguments less than 1 (and 1 (and 5)).

 

'''Examples:'''

144

fibN i.31

(This implementation is doubly recursive except that results are cached across function calls.)

 

Note also http://www.jsoftware.com/pipermail/general/2003-August/015571.html which points out that the form

 

 

Of course, that won't work here, because we are adding two recursively obtained results where tail recursion requires that the recursive result is the final result.

 

=={{header|Java}}==

Creates an anonymous inner class to do the dirty work. While it does keep the recursive function out of the namespace of the class, it does seem to violate the spirit of the task in that the function is still named.

 

if (n < 0)

throw new IllegalArgumentException("n can not be a negative number");

}

}.fibInner(n);

 

Another way is to use the Java Y combinator implementation (the following uses the Java 8 version for better readability).

Note that the fib method below is practically the same as that of the version above, with less fibInner.

 

 

@FunctionalInterface

).apply(m);

}

 

=={{header|JavaScript}}==

if (n < 0) { throw "Argument cannot be negative"; }

 

return (function(n) {

})(n);

Note that <code>arguments.callee</code> will not be available in ES5 Strict mode. Instead, you are expected to "name" function (the name is only visible inside function however).

if (n < 0) { throw "Argument cannot be negative"; }

 

return (function fib(n) {

})(n);

 

=={{header|Joy}}==

This definition is taken from "Recursion Theory and Joy" by Manfred von Thun.

 

=={{header|jq}}==

The "recurse" filter supports a type of anonymous recursion, e.g. to generate a stream of integers starting at 0:

 

Also, as is the case for example with Julia, jq allows you to define an inner/nested function (in the follow example, <code>aux</code>) that is only defined within the scope of the surrounding function (here <code>fib</code>). It is thus invisible outside the function:

def aux: if . == 0 then 0

elif . == 1 then 1

if n < 0 then error("negative arguments not allowed")

else n | aux

 

=={{header|Julia}}==

Julia allows you to define an inner/nested function (here, <code>aux</code>) that is only defined within the surrounding function <code>fib</code> scope.

if n < 0

throw(ArgumentError("negative arguments not allowed"))

aux(m) = m < 2 ? one(m) : aux(m-1) + aux(m-2)

aux(n)

 

=={{header|K}}==

'''Examples:'''

0 1 1 2 3 5 8 13 21 34

fib -1

 

=={{header|Klingphix}}==

 

25 fib ?

msec ?

 

=={{header|Klong}}==

fib::{:[x<0;"error: negative":|x<2;x;.f(x-1)+.f(x-2)]}

 

=={{header|Kotlin}}==

{{trans|Dylan}}

require(n >= 0)

}

 

for (i in 0..20) print("${fib(i)} ")

println()

 

{{out}}

 

=={{header|Lambdatalk}}==

{def fibo {lambda {:n}

{lambda {:f :n :a :b}

{if {< :n 0}

else {if {< :n 1}

then :a

 

2) testing:

{fibo 8} -> 34

{fibo 1000} -> 7.0330367711422765e+208

-> 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946

We could also avoid any name and write an IIFE

{{lambda {:n}

{lambda {:f :n :a :b}

{if {< :n 0}

else {if {< :n 1}

then :a

8}

-> 34

 

 

=={{header|Lingo}}==

Lingo does not support anonymous functions. But what comes close: you can create and instantiate an "anonymous class":

if n<0 then return _player.alert("negative arguments not allowed")

 

 

return aux.fib(n)

 

 

=={{header|LOLCODE}}==

{{trans|C}}

 

HOW IZ I fib YR x

I IZ fib_i YR 3 MKAY

 

 

=={{header|Lua}}==

Using a [[Y combinator]].

 

return Y(function(fibs)

return n < 2 and 1 or fibs(n - 1) + fibs(n - 2)

end

using a metatable (also achieves memoization)

self[n] = self[n-1] + self[n-2]

return self[n]

 

=={{header|M2000 Interpreter}}==

We can use a function in string. We can named it so the error say about "Fibonacci"

To exclude first check for negative we have to declare a function in anonymous function, which may have a name (a local name)

A$={{ Module "Fibonacci" : Read X :If X<0 then {Error {X<0}} Else Fib=Lambda (x)->if(x>1->fib(x-1)+fib(x-2), x) : =fib(x)}}

Try Ok {

If Error or Not Ok Then Print Error$

Print Function(A$, 12)=144 ' true

 

For recursion we can use Lambda() or Lambda$() (for functions which return string) and not name of function so we can use it in a referenced function. Here in k() if we have the fib() we get an error, but with lambda(), interpreter use current function's name.

 

Function fib(x) {

If x<0 then Error "argument outside of range"

CheckIt &Fib()

Print fib(-2) ' error

 

Using lambda function

 

fib=lambda -> {

fib1=lambda (x)->If(x>1->lambda(x-1)+lambda(x-2), x)

Inventory Alfa = "key1":=Z

Print Alfa("key1")(12)=144

 

Using a Group (object in M2000) like a function

 

 

Class Something {

\\ this class is a global function

Print Alfa("Key2")(12)=144

Print Eval(Alfa("100"),12)=144, Eval(Alfa(100),12)=144

 

=={{header|Maple}}==

In Maple, the keyword thisproc refers to the currently executing procedure (closure), which need not be named. The following defines a procedure Fib, which uses a recursive, anonymous (unnamed) procedure to implement the Fibonacci sequence. For better efficiency, we use Maple's facility for automatic memoisation ("option remember").

Fib := proc( n :: nonnegint )

proc( k )

end( n )

end proc:

For example:

> seq( Fib( i ), i = 0 .. 10 );

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Error, invalid input: Fib expects its 1st argument, n, to be of type

nonnegint, but received -1

The check for a negative argument could be put either on the outer Fib procedure, or the anonymous inner procedure (or both). As it wasn't completely clear what was intended, I put it on Fib, which results in a slightly better error message in that it does not reveal how the procedure was actually implemented.

 

=={{header|Mathematica}} / {{header|Wolfram Language}}==

An anonymous reference to a function from within itself is named #0, arguments to that function are named #1,#2..#n, n being the position of the argument. The first argument may also be referenced as a # without a following number, the list of all arguments is referenced with ##. Anonymous functions are also known as [http://reference.wolfram.com/mathematica/tutorial/PureFunctions.html pure functions] in Mathematica.

fib := If[check[#],Throw["Negative Argument"],If[#<=1,1,#0[#-2]+#0[#-1]]&[#]]&

fib /@ Range[0,10]

 

Making sure that the check is only performed once.

fib /@ Range[0,4]

0

4

 

=={{header|MATLAB}}==

Not anonymous exactly, but using a nested function solves all the problems stated in the task description.

* does not need a new name, can reuse the parent name

* a nested function can be defined in the place where it is needed

function v = fibonacci(n)

assert(n >= 0)

end

end

 

=={{header|Nemerle}}==

* inner function not expected to be called from anywhere else

* nesting maintains program flow in source code

using System.Console;

 

}

}

 

=={{header|Nim}}==

proc fib(x: int): int =

proc fibI(n: int): int =

echo fib(i)

 

Output:

<pre>0

=={{header|Objective-C}}==

This shows how a method (not regular function) can recursively call itself without explicitly putting its name in the code.

 

@interface AnonymousRecursion : NSObject { }

}

return 0;

 

;With internal named recursive block:

{{works with|Mac OS X|10.6+}}

 

int fib(int n) {

}

return 0;

 

When ARC is disabled, the above should be:

 

int fib(int n) {

}

return 0;

 

=={{header|OCaml}}==

 

We're defining a function 'real' which is only available from within the fib function.

let rec real = function

0 -> 1

None

else

 

'''Anonymous function:'''

 

This uses the 'fix' function to find the fixed point of the anonymous function.

 

let fib n =

None

else

{{out}}

<pre># fib 8;;

=={{header|Ol}}==

This uses named let to create a local function (loop) that only exists inside of function fibonacci.

(define (fibonacci n)

(if (> 0 n)

(print

(map fibonacci '(1 2 3 4 5 6 7 8 9 10)))

{{out}}

<pre>'(1 1 2 3 5 8 13 21 34 55)</pre>

=={{header|OxygenBasic}}==

An inner function keeps the name-space clean:

function fiboRatio() as double

function fibo( double i, j ) as double

print fiboRatio

 

=={{header|PARI/GP}}==

This version uses a Y combinator to get a self-reference.

my(F=(k,f)->if(k<2,k,f(k-1,f)+f(k-2,f)));

if(n<0,(-1)^(n+1),1)*F(abs(n),F)

 

{{works with|PARI/GP|2.8.1+}}

This version gets a self-reference from <code>self()</code>.

my(F=k->my(f=self());if(k<2,k,f(k-1)+f(k-2)));

if(n<0,(-1)^(n+1),1)*F(abs(n))

 

=={{header|Perl}}==

{{trans|PicoLisp}}

<code>recur</code> isn't built into Perl, but it's easy to implement.

my $f = shift;

local *recurse = $f;

$m < 3 ? 1 : recurse($m - 1) + recurse($m - 2);

} $n;

Although for this task, it would be fine to use a lexical variable (closure) to hold an anonymous sub reference, we can also just push it onto the args stack and use it from there:

my ($n) = @_;

die "negative arg $n" if $n < 0;

}

 

One can also use <code>caller</code> to get the name of the current subroutine as a string, then call the sub with that string. But this won't work if the current subroutine is anonymous: <code>caller</code> will just return <code>'__ANON__'</code> for the name of the subroutine. Thus, the below program must check the sign of the argument every call, failing the task. Note that under stricture, the line <code>no strict 'refs';</code> is needed to permit using a string as a subroutine.

my $n = shift;

$n < 0 and die 'Negative argument';

no strict 'refs';

$n < 3 ? 1 : (caller(0))[3]->($n - 1) + (caller(0))[3]->($n - 2);

===Perl 5.16 and __SUB__===

Perl 5.16 introduced __SUB__ which refers to the current subroutine.

say sub {

my $n = shift;

$n < 2 ? $n : __SUB__->($n-2) + __SUB__->($n-1)

 

=={{header|Phix}}==

===using classes===

With proof that the private fib_i() does not pollute the outer namespace.

<span style="color: #008080;">without</span> <span style="color: #008080;">js</span> <span style="color: #000080;font-style:italic;">-- (no class yet)</span>

<span style="color: #008080;">class</span> <span style="color: #000000;">Fib</span>

<span style="color: #000080;font-style:italic;">--?f.fib_i(10) -- illegal</span>

<span style="color: #0000FF;">?</span><span style="color: #000000;">fib_i</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>

{{out}}

<pre>

Obviously the inner function does not have to and in fact is not allowed to have a name itself, but it needs to be stored in something with a name before it can be called,

and in being anonymous, in order to effect recursion it must be passed to itself, repeatedly and not really anonymous at all anymore.

<span style="color: #008080;">without</span> <span style="color: #008080;">js</span> <span style="color: #000080;font-style:italic;">-- (no lambda yet)</span>

<span style="color: #008080;">function</span> <span style="color: #000000;">erm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>

<span style="color: #0000FF;">?</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>

{{out}}

<pre>

In this solution, the function is always called using <code>call_user_func()</code> rather than using function call syntax directly. Inside the function, we get the function itself (without having to refer to the function by name) by relying on the fact that this function must have been passed as the first argument to <code>call_user_func()</code> one call up on the call stack. We can then use <code>debug_backtrace()</code> to get this out.

{{works with|PHP|5.3+}}

function fib($n) {

if ($n < 0)

}

echo fib(8), "\n";

 

;With internal named recursive function:

{{works with|PHP|5.3+}}

function fib($n) {

if ($n < 0)

}

echo fib(8), "\n";

 

;With a function object that can call itself using <code>$this</code>:

{{works with|PHP|5.3+}}

class fib_helper {

function __invoke($n) {

}

echo fib(8), "\n";

 

=={{header|PicoLisp}}==

(if (lt0 N)

(quit "Illegal argument" N) )

(if (> 2 N)

1

Explanation: The above uses the '[http://software-lab.de/doc/refR.html#recur recur]' / '[http://software-lab.de/doc/refR.html#recurse recurse]' function pair, which is defined as a standard language extensions as

Note how 'recur' dynamically defines the function 'recurse' at runtime, by binding the rest of the expression (i.e. the body of the 'recur' statement) to the symbol 'recurse'.

 

{{libheader|initlib}}

Postscript can make use of the higher order combinators to provide recursion.

/pfact {

{1} {*} primrec}.

% binary recursion

/fib {

 

=={{header|Prolog}}==

Works with SWI-Prolog and module <b>lambda</b>, written by <b>Ulrich Neumerkel</b> found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl

The code is inspired from this page : http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/ISO-Hiord#Hiord (p 106). It uses the Y combinator.

 

fib(N, _F) :-

Pred = PF +\Nb2^F2^call(PF,Nb2,F2,PF),

 

 

=={{header|Python}}==

>>> fib = lambda f: lambda n: None if n < 0 else (0 if n == 0 else (1 if n == 1 else f(n-1) + f(n-2)))

>>> [ Y(fib)(i) for i in range(-2, 10) ]

 

Same thing as the above, but modified so that the function is uncurried:

>>> Y = lambda f: (lambda x: x(x))(lambda y: partial(f, lambda *args: y(y)(*args)))

>>> fib = lambda f, n: None if n < 0 else (0 if n == 0 else (1 if n == 1 else f(n-1) + f(n-2)))

>>> [ Y(fib)(i) for i in range(-2, 10) ]

 

A different approach: the function always receives itself as the first argument, and when recursing, makes sure to pass the called function as the first argument also

>>> Y = lambda f: partial(f, f)

>>> fib = lambda f, n: None if n < 0 else (0 if n == 0 else (1 if n == 1 else f(f, n-1) + f(f, n-2)))

>>> [ Y(fib)(i) for i in range(-2, 10) ]

 

An interesting approach using introspection (from http://metapython.blogspot.com/2010/11/recursive-lambda-functions.html)

>>> from inspect import currentframe

>>> from types import FunctionType

>>> print "factorial(5) =",

>>> print (lambda n:1 if n<=1 else n*myself(n-1)) ( 5 )

 

Another way of implementing the "Y" function is given in this post: https://stackoverflow.com/questions/481692/can-a-lambda-function-call-itself-recursively-in-python. The main problem to solve is that the function "fib" can't call itself. Therefore, the function "Y" is used to help "fib" call itself.

 

>>> Y = lambda f: lambda n: f(f,n)

>>> fib = lambda f, n: None if n < 0 else (0 if n == 0 else (1 if n == 1 else f(f,n-1) + f(f,n-2))) #same as the first three implementations

>>> [ Y(fib)(i) for i in range(-2, 10) ]

[None, None, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

 

All in one line:

>>> fib_func = (lambda f: lambda n: f(f,n))(lambda f, n: None if n < 0 else (0 if n == 0 else (1 if n == 1 else f(f,n-1) + f(f,n-2))))

>>> [ fib_func(i) for i in range(-2, 10) ]

[None, None, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

 

 

{{works with|QBasic}}

{{trans|BASIC256}}

 

PRINT Fibonacci(20)

Fibonacci = Fibonacci(num - 1) + Fibonacci(num - 2)

END IF

{{out}}

<pre>

However, it can be done, for instance like this:

 

(define fib

N -> (let A (/. A N

(A A (- N 1)))))

(A A N)))

 

=={{header|Quackery}}==

=={{header|R}}==

R provides Recall() as a wrapper which finds the calling function, with limitations; Recall will not work if passed to another function as an argument.

(n >= 0) || stop("bad argument")

( function(n) if (n <= 1) 1 else Recall(n-1)+Recall(n-2) )(n)

 

=={{header|Racket}}==

In Racket, local helper function definitions inside of a function are only visible locally and do not pollute the module or global scope.

 

#lang racket

(check-equal? (fact 0) 1)

(check-equal? (fact 5) 120))

 

This calculates the slightly more complex Fibonacci funciton:

#lang racket

;; Natural -> Natural

'(0 1 1 2 3 5 8 13 21 34 55 89 144 233

377 610 987 1597 2584 4181 6765)))

 

Also with the help of first-class functions in Racket, anonymous recursion can be implemented using fixed-points operators:

 

#lang racket

;; We use Z combinator (applicative order fixed-point operator)

(+ (fibo (- n 1))

(fibo (- n 2))))))))

 

<pre>

 

In addition to the methods in the [[Perl]] entry above, and the Y-combinator described in [[Y_combinator]], you may also refer to an anonymous block or function from the inside:

die "Naughty fib" if $n < 0;

return {

}

 

However, using any of these methods is insane, when Raku provides a sort of inside-out combinator that lets you define lazy infinite constants, where the demand for a particular value is divorced from dependencies on more primitive values. This operator, known as the sequence operator, does in a sense provide anonymous recursion to a closure that refers to more primitive values.

Here the closure, <tt>*+*</tt>, is just a quick way to write a lambda, <tt>-> $a, $b { $a + $b }</tt>. The sequence operator implicitly maps the two arguments to the -2nd and -1st elements of the sequence. So the sequence operator certainly applies an anonymous lambda, but whether it's recursion or not depends on whether you view a sequence as iteration or as simply a convenient way of memoizing a recursion. Either view is justifiable.

 

=={{header|REBOL}}==

 

fib: func [n /f][ do f: func [m] [ either m < 2 [m][(f m - 1) + f m - 2]] n]

 

=={{header|REXX}}==

to be OK with the implementers, here are the REXX versions.

===simplistic===

numeric digits 1e6 /*in case the user goes ka-razy with X.*/

parse arg x . /*obtain the optional argument from CL.*/

fib: procedure; parse arg z; if z>=0 then return .(z)

say "***error*** argument can't be negative."; exit

{{out|output|text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> 12 </tt>}}

<pre>

Since the above REXX version is &nbsp; ''very'' &nbsp; slow for larger numbers, the following version was added that incorporates memoization. &nbsp;

<br>It's many orders of magnitude faster for larger values.

numeric digits 1e6 /*in case the user goes ka-razy with X.*/

parse arg x . /*obtain the optional argument from CL.*/

fib: procedure expose @.; arg z; if z>=0 then return .(z)

say "***error*** argument can't be negative."; exit

{{out|output|text=&nbsp; is identical to the 1^st REXX version.}} <br><br>

 

=={{header|Ring}}==

# Project : Anonymous recursion

 

end

return t

Output:

<pre>

144

</pre>

 

=={{header|Ruby}}==

We can recurse a block of code, but we must provide the block with a reference to itself. The easiest solution is to use a local variable.

===Ruby with local variable===

raise RangeError, "fib of negative" if n < 0

(fib2 = proc { |m| m < 2 ? m : fib2[m - 1] + fib2[m - 2] })[n]

 

 

Here 'fib2' is a local variable of the fib() method. Only the fib() method, or a block inside the fib() method, can call this 'fib2'. The rest of this program cannot call this 'fib2', but it can use the name 'fib2' for other things.

 

'''Caution!''' The recursive block has a difference from Ruby 1.8 to Ruby 1.9. Here is the same method, except changing the block parameter from 'm' to 'n', so that block 'n' and method 'n' have the same name.

raise RangeError, "fib of negative" if n < 0

(fib2 = proc { |n| n < 2 ? n : fib2[n - 1] + fib2[n - 2] })[n]

(-2..12).map { |i| fib i rescue :error }

=> [:error, :error, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]

# Ruby 1.8

(-2..12).map { |i| fib i rescue :error }

Ruby 1.9 still shows the correct answer, but Ruby 1.8 shows the wrong answer. With Ruby 1.9, 'n' is still a local variable of the block. With Ruby 1.8, 'n' of the block closes on 'n' of the fib() method. All calls to the block share the 'n' of one call to the method. So <tt>fib2[n - 1]</tt> changes the value of 'n', and <tt>fib2[n - 2]</tt> uses the wrong value of 'n', thus the wrong answer.

===Ruby with Hash===

raise RangeError, "fib of negative" if n < 0

Hash.new { |fib2, m|

fib2[m] = (m < 2 ? m : fib2[m - 1] + fib2[m - 2]) }[n]

This uses a Hash to memoize the recursion. After <tt>fib2[m - 1]</tt> returns, <tt>fib2[m - 2]</tt> uses the value in the Hash, without redoing the calculations.

 

{{trans|PicoLisp}}

{{libheader|continuation}}

 

module Kernel

raise RangeError, "fib of negative" if n < 0

recur(n) { |m| m < 2 ? m : (recurse m - 1) + (recurse m - 2) }

 

Our recursive block now lives in the 'block' variable of the Kernel#recur method.

{{trans|JavaScript}}

{{libheader|continuation}}

 

module Kernel

end

}[n]

Our recursive block now lives in the 'block' variable of the Kernel#function method. Another block 'f' wraps our original block and sets up the 'arguments' array. Kernel#function returns this wrapper block. Kernel#arguments plays a trick to get the array of arguments from 'f'; this array has an extra singleton method #callee which returns 'f'.

 

=={{header|Rust}}==

// A function declared inside another function does not pollute the outer namespace.

fn actual_fib(n: i64) -> i64 {

fn test_invalid_argument() {

assert_eq!(fib(-1), None);

 

=={{header|Scala}}==

Using a Y-combinator:

def fib(n: Int): Option[Int] =

else f(i - 1) + f(i - 2))(n))

{{out}}

<pre>

=={{header|Scheme}}==

This uses named let to create a function (aux) that only exists inside of fibonacci:

(if (> 0 n)

"Error: argument must not be negative."

(aux (+ a b) a (- count 1))))))

 

{{out}}

<pre>'(1 1 2 3 5 8 13 21 34 55)</pre>

=={{header|Seed7}}==

Uses a local function to do the dirty work. The local function has a name, but it is not in the global namespace.

 

const func integer: fib (in integer: x) is func

writeln(fib(i));

end for;

 

{{out}}

=={{header|Sidef}}==

__FUNC__ refers to the current function.

return NaN if (n < 0)

 

: (__FUNC__(n-1) + __FUNC__(n-2))

}(n)

 

__BLOCK__ refers to the current block.

 

return NaN if (n < 0)

 

: (__BLOCK__(n-1) + __BLOCK__(n-2))

}(n)

 

=={{header|Smalltalk}}==

a) Use a funny local name (in this case: "_").

Here the closure is defined as "_", and then evaluated (by sending it a <tt>value:</tt> message).

myMethodComputingFib:arg

|_|

ifTrue:[n]

ifFalse:[(_ value:(n - 1))+(_ value:(n - 2))]]

b) Define it in a local scope to not infect the outer scopes.

<br>Here, a separate closure is defined (and evaluated with <tt>value</tt>), in which fib is defined and evaluated with the argument.

This is semantically equivalent to the named let solution of Scheme.

myMethodComputingFib2:arg

^ [

ifTrue:[1]

ifFalse:[(fib value:(n - 1))+(fun value:(n - 2))]] value:arg.

To completely make it anonymous, we could use reflection to get at the current executed block (via thisContext),

but that is too ugly and obfuscating to be shown here.

=={{header|Sparkling}}==

As a function expression:

return f(n, f);

}(10, function(n, f) {

return n < 2 ? 1 : f(n - 1, f) + f(n - 2, f);

})

 

When typed into the REPL:

 

=={{header|Standard ML}}==

ML does not have a built-in construct for anonymous recursion, but you can easily write your own fix-point combinator:

 

fun fib n =

(fn 0 => 0

| 1 => 1

 

Instead of using a fix-point, the more common approach is to locally define a recursive function and call it once:

let

fun fib 0 = 0

else

fib n

 

In this example the local function has the same name as the outer function. This is fine: the local definition shadows

 

Another variation is possible. Instead, we could define the recursive "fib" at top-level, then shadow it with a non-recursive wrapper. To force the wrapper to be non-recursive, we use the "val" syntax instead of "fun":

| fib 1 = 1

| fib n = fib (n-1) + fib (n-2)

 

val fib = fn n => if n < 0 then raise Fail "Negative"

 

=={{header|SuperCollider}}==

SuperCollider has a keyword "thisFunction", which refers to the current function context. The example below uses this for anonymous recursion. One may think that "thisFunction" would refer to the second branch of the if statement, but because if statements are inlined, the function is the outer one.

 

(

f = { |n|

(0..20).collect(f)

)

 

=={{header|Swift}}==

;With internal named recursive closure:

{{works with|Swift|2.x}}

func f(n: Int) -> Int {

assert(n >= 0, "fib: no negative numbers")

}()

 

{{works with|Swift|1.x}}

var f: (Int -> Int)!

f = { n in

}()

 

 

;Using Y combinator:

let o : RecursiveFunc<F> -> F

}

}

 

 

=={{header|Tailspin}}==

=={{header|Tcl}}==

This solution uses Tcl 8.5's lambda terms, extracting the current term from the call stack using introspection (storing it in a local variable only for convenience, with that ''not'' in any way being the name of the lambda term; just what it is stored in, and only as a convenience that keeps the code shorter). The lambda terms are applied with the <code>apply</code> command.

# sanity checks

if {[incr n 0] < 0} {error "argument may not be negative"}

expr {[apply $f [incr x -1]] + [apply $f [incr x -1]]}

}} $n

Demonstrating:

{{out}}}

<pre>144</pre>

The code above can be written without even using a local variable to hold the lambda term, though this is generally less idiomatic because the code ends up longer and clumsier:

if {[incr n 0] < 0} {error "argument may not be negative"}

apply {x {expr {

+ [apply [lindex [info level 0] 1] [incr x -1]]

}}} $n

However, we can create a <code>recurse</code> function that makes this much more straight-forward:

proc tcl::mathfunc::recurse args {apply [lindex [info level -1] 1] {*}$args}

proc fib n {

$x < 2 ? $x : recurse([incr x -1]) + recurse([incr x -1])

}}} $n

 

 

{{trans|BASIC256}}

{{works with|QBasic}}

IF num < 0 THEN

PRINT "Invalid argument: ";

PRINT Fibonacci(-10)

PRINT Fibonacci(10)

{{out}}

<pre>

{{trans|Common_Lisp}}

 

(let ((hidden-name (gensym "RECURSIVE-")))

^(macrolet ((recurse (. args) ^(,',hidden-name ,*args)))

 

(put-line `fib(10) = @(fib 10)`)

 

{{out}}

=={{header|UNIX Shell}}==

The shell does not have anonymous functions. Every function must have a name. However, one can create a subshell such that some function, which has a name in the subshell, is effectively anonymous to the parent shell.

if test 0 -gt "$1"; then

echo "fib: fib of negative" 1>&2

)

fi

> fib $i

> done

55

89

 

=={{header|Ursala}}==

 

fib =

predecessor^~( # with the respective predecessors of

~&, # the given argument

Anonymous recursion is often achieved using the recursive conditional operator, <code>( _ )^?( _ , _ )</code>, which takes a predicate on the left and a pair of functions on the right, typically one for the base and one for the inductive case in a recursive definition. The form <code>^?<</code> can be used if the relevant predicate is given by membership of the argument in a constant set, in which case only the set needs to be specified rather than the whole predicate.

 

'''Solution with anonymous class'''

 

···

http://rosettacode.org/wiki/Anonymous_recursion

⏎ n ≤ 1 ? n ! (apply n - 1) + (apply n - 2)

°.apply Integer.valueOf args[0]

 

=={{header|VBA}}==

Sub Main()

Debug.Print F(-10)

F = F(N - 1) + F(N - 2)

End If

{{out}}

<pre>Error. Negative argument

 

=={{header|Wart}}==

if (n >= 0)

(transform n :thru (afn (n)

n

(+ (self n-1)

 

<code>afn</code> creates an anonymous function that can be recursed by calling <code>self</code>.

 

=={{header|WDTE}}==

 

let fib n => switch n {

default => + (s (- n 1)) (s (- n 2));

});

 

In WDTE, a lambda, defined in a block delineated by <code>(@)</code>, gets passed itself as its first argument, allowing for recursion.

 

=={{header|Wren}}==

static compute(n) {

var fib

}

 

 

{{out}}

The address of the instructions after the function get put on the stack and then execution continues into the actual function.

When the recursion is complete, instead of returning to the location of the call it goes to the end of the loop.

; Calculates and prints Fibonacci numbers (Fn)

; Prints numbers 1 - 47 (largest 32bit Fn that fits)

pop ebp

ret

 

=={{header|XPL0}}==

This makes those nested functions invisible to the outside, thus preventing namespace pollution.

 

 

func Fib(X);

[IntOut(0, Fib(8)); CrLf(0);

IntOut(0, Fib(-2)); CrLf(0);

 

{{out}}

=={{header|Yabasic}}==

{{trans|AutoIt}}

print Fibonacci(10)

 

EndIf

 

=={{header|zkl}}==

if (n<0) throw(Exception.ValueError);

fcn(n){

fib(8) .println();

fib(-8).println();

{{out}}

<pre>

=={{header|ZX Spectrum Basic}}==

{{trans|AutoHotkey}}

20 LET t=0

30 GO SUB 60

110 IF n>2 THEN LET n=n-1: LET nold2=nold1: LET nold1=t: GO SUB 100

120 RETURN

 

{{omit from|ACL2}}