While implementing a recursive function, it often happens that we must resort to a separate   helper function   to handle the actual recursion.

Task
Anonymous recursion
You are encouraged to solve this task according to the task description, using any language you may know.

This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), causing unwanted side-effects,   and/or the function doesn't have the right arguments and/or return values.

So we end up inventing some silly name like   foo2   or   foo_helper.   I have always found it painful to come up with a proper name, and see some disadvantages:

  •   You have to think up a name, which then pollutes the namespace
  •   Function is created which is called from nowhere else
  •   The program flow in the source code is interrupted

Some languages allow you to embed recursion directly in-place.   This might work via a label, a local gosub instruction, or some special keyword.

Anonymous recursion can also be accomplished using the   Y combinator.


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.

Related tasks



11l

Translation of: C++
F fib(n)
   F f(Int n) -> Int
      I n < 2
         R n
      R @f(n - 1) + @f(n - 2)
   R f(n)

L(i) 0..20
   print(fib(i), end' ‘ ’)
Output:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

Ada

In Ada you can define functions local to other functions/procedures. This makes it invisible to outside and prevents namespace pollution.

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

   function Fib (X: in Integer) return Integer is
      function Actual_Fib (N: in Integer) return Integer is
      begin
         if N < 2 then
            return N;
         else
            return Actual_Fib (N-1) + Actual_Fib (N-2);
         end if;
      end Actual_Fib;
   begin
      if X < 0 then
         raise Constraint_Error;
      else
         return Actual_Fib (X);
      end if;
   end Fib;

ALGOL 68

Translation of: Ada
PROC fibonacci = ( INT x )INT:
     IF x < 0
     THEN
         print( ( "negative parameter to fibonacci", newline ) );
         stop
     ELSE
         PROC actual fibonacci = ( INT n )INT:
             IF n < 2
             THEN
                 n
             ELSE
                 actual fibonacci( n - 1 ) + actual fibonacci( n - 2 )
             FI;
         actual fibonacci( x )
     FI;

APL

APL has the symbol which calls the current function recursively. Functions can be defined and then called in place without ever assigning them a name, though they are not quite first-class objects (you can't have an array of functions for example).

fib{               ⍝ Outer function
   <0:⎕SIGNAL 11   ⍝ DOMAIN ERROR if argument < 0
   {                ⍝ Inner (anonymous) function
      <2:⍵
      (∇⍵-1)+∇⍵-2   ⍝ ∇ = anonymous recursive call
   }               ⍝ Call function in place
}


AppleScript

on fibonacci(n) -- "Anonymous recursion" task.
    -- 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.
    script
        property one : 1
        property sequence : {}
 
        on f(n)
            if (n < 2) then
                set end of my sequence to 0
                if (n is 1) then set end of my sequence to one
            else
                f(n - 1)
                set end of my sequence to (item -2 of my sequence) + (end of my sequence)
            end if
        end f
    end script
 
    -- Don't insert any additional code here!
 
    -- Sort out whether the input's positive or negative and tell the object generated above to do the recursive business.
    tell result
        if (n < 0) then
            set its one to -1
            set n to -n
        end if
        f(n)
 
        return its sequence
    end tell
end fibonacci
 
fibonacci(15) --> {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610}
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:

------------ ANONYMOUS RECURSION WITH THE Y-COMBINATOR --------
on run
    
    --------------------- FIBONACCI EXAMPLE -------------------
    
    script
        on |λ|(f)
            script
                on |λ|(n)
                    if 0 > n then return missing value
                    if 0 = n then return 0
                    if 1 = n then return 1
                    (f's |λ|(n - 2)) + (f's |λ|(n - 1))
                end |λ|
            end script
        end |λ|
    end script
    
    unlines(map(showList, chunksOf(12, ¬
        map(|Y|(result), enumFromTo(-2, 20)))))
end run


------------------------ Y COMBINATOR ----------------------

on |Y|(f)
    script
        on |λ|(y)
            script
                on |λ|(x)
                    y's |λ|(y)'s |λ|(x)
                end |λ|
            end script
            
            f's |λ|(result)
        end |λ|
    end script
    
    result's |λ|(result)
end |Y|


----------- GENERIC FUNCTIONS FOR TEST AND DISPLAY ---------

-- chunksOf :: Int -> [a] -> [[a]]
on chunksOf(k, xs)
    script
        on go(ys)
            set ab to splitAt(k, ys)
            set a to item 1 of ab
            if {}  a then
                {a} & go(item 2 of ab)
            else
                a
            end if
        end go
    end script
    result's go(xs)
end chunksOf


-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
    if n < m then
        set d to -1
    else
        set d to 1
    end if
    set lst to {}
    repeat with i from m to n by d
        set end of lst to i
    end repeat
    return lst
end enumFromTo


-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
    set {dlm, my text item delimiters} to ¬
        {my text item delimiters, delim}
    set s to xs as text
    set my text item delimiters to dlm
    s
end intercalate


-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map


-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn


-- showList :: [a] -> String
on showList(xs)
    intercalate(", ", map(my str, xs))
end showList


-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
    if n > 0 and n < length of xs then
        if class of xs is text then
            {items 1 thru n of xs as text, ¬
                items (n + 1) thru -1 of xs as text}
        else
            {items 1 thru n of xs, items (n + 1) thru -1 of xs}
        end if
    else
        if n < 1 then
            {{}, xs}
        else
            {xs, {}}
        end if
    end if
end splitAt


-- str :: a -> String
on str(x)
    x as string
end str


-- unlines :: [String] -> String
on unlines(xs)
    -- A single string formed by the intercalation
    -- of a list of strings with the newline character.
    set {dlm, my text item delimiters} to ¬
        {my text item delimiters, linefeed}
    set s to xs as text
    set my text item delimiters to dlm
    s
end unlines
Output:
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

Arturo

Translation of: Nim
fib: function [x][
    ; Using scoped function fibI inside fib
    fibI: function [n][
        (n<2)? -> n -> add fibI n-2 fibI n-1
    ]
    if x < 0 -> panic "Invalid argument"
    return fibI x
]

loop 0..4 'x [
    print fib x
]
Output:
0
1
1
2
3

AutoHotkey

Fib(n) {
	nold1 := 1
	nold2 := 0
	If n < 0
	{
		MsgBox, Positive argument required!
		Return
	}
	Else If n = 0
		Return nold2
	Else If n = 1
		Return nold1
	Fib_Label:
	t := nold2+nold1
	If n > 2
	{
		n--
		nold2:=nold1
		nold1:=t
		GoSub Fib_Label
	}
	Return t
}

AutoIt

ConsoleWrite(Fibonacci(10) & @CRLF)						; ## USAGE EXAMPLE
ConsoleWrite(Fibonacci(20) & @CRLF)						; ## USAGE EXAMPLE
ConsoleWrite(Fibonacci(30))						        ; ## USAGE EXAMPLE

Func Fibonacci($number)

	If $number < 0 Then Return "Invalid argument" 				; No negative numbers

	If $number < 2 Then 							; If $number equals 0 or 1
		Return $number  						; then return that $number
	Else									; Else $number equals 2 or more
		Return Fibonacci($number - 1) + Fibonacci($number - 2) 		; FIBONACCI!
	EndIf

EndFunc
Output:
        55
        6765
        832040

Axiom

Using the Aldor compiler in Axiom/Fricas:

#include "axiom"
Z ==> Integer;
fib(x:Z):Z == {
	x <= 0 => error "argument outside of range";
	f(n:Z,v1:Z,v2:Z):Z == if n<2 then v2 else f(n-1,v2,v1+v2); 
	f(x,1,1);
}

The old Axiom compiler has scope issues with calling a local function recursively. One solution is to use the Reference (pointer) domain and initialise the local function with a dummy value:

)abbrev package TESTP TestPackage
Z ==> Integer
TestPackage : with
    fib : Z -> Z
  == add
    fib x ==
      x <= 0 => error "argument outside of range"
      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)
      f()(x,1,1)

BASIC

BaCon

DEF FN  fib(x) = FIB(x)

'============================
FUNCTION  FIB(int n) TYPE int
'============================
    
    IF n < 2 THEN
        PRINT n
       
    ELSE
        n1 = 0
        n2 = 1
        FOR i = 1 TO n 
            sum = n1 + n2
            n1 = n2
            n2 = sum
        NEXT 
        PRINT n1
    END IF  
END FUNCTION 

'--- less than 2
FIB(0)
FIB(1)

'--- greater than or equal to 2
FIB(2)
FIB(3)
FIB(4)
FIB(5)
FIB(6)
FIB(7)
FIB(8)
FIB(9)

'--- using an alias 
'fib(9)

BASIC256

Translation of: AutoIt
print Fibonacci(20)
print Fibonacci(30)
print Fibonacci(-10)
print Fibonacci(10)
end

function Fibonacci(num)
	if num < 0 then
		print "Invalid argument: ";
		return num
	end if

	if num < 2 then
		return num
	else
		return Fibonacci(num - 1) + Fibonacci(num - 2)
	end If
end function
Output:
6765
832040
Invalid argument: -10
55

Chipmunk Basic

Works with: Chipmunk Basic version 3.6.4
100 cls
110 sub fib(num)
120   if num < 0 then print "Invalid argument: "; : fib = num
130   if num < 2 then fib = num else fib = fib(num-1)+fib(num-2)
140 end sub
190 print fib(20)
200 print fib(30)
210 print fib(-10)
220 print fib(10)
230 end
Output:
Same as BASIC256 entry.

BBC BASIC

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

      PRINT FNfib(10)
      END
      
      DEF FNfib(n%) IF n%<0 THEN ERROR 100, "Must not be negative"
      LOCAL P% : P% = !384 + LEN$!384 + 4 : REM Function pointer
      (n%) IF n%<2 THEN = n% ELSE = FN(^P%)(n%-1) + FN(^P%)(n%-2)
Output:
        55

IS-BASIC

100 PROGRAM "Fibonacc.bas"
  110 FOR I=0 TO 10
  120   PRINT FIB(I);
  130 NEXT 
  140 DEF FIB(K)
  150   SELECT CASE K
  160   CASE IS<0
  170     PRINT "Negative parameter to Fibonacci.":STOP 
  180   CASE 0,1
  190     LET FIB=K
  200   CASE ELSE
  210     LET FIB=FIB(K-1)+FIB(K-2)
  220   END SELECT 
  230 END DEF

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 (x=7) & (y=4) then '($x+3+$y) becomes =7+3+4. Notice that the solution below utilises no other names than arg, 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
      &   ( (=.!arg$!arg)
          $ (
            =
              .
                ' (
                  .   !arg:<2
                    |   (($arg)$($arg))$(!arg+-2)
                      + (($arg)$($arg))$(!arg+-1)
                  )
            )
          )
        $ !arg
  )
$ 30
)

Answer:

832040

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
     .   $x:#:~<0
       &   ( /('(f.($f)$($f)))
           $ /(
              ' ( r
                . /(
                   ' ( n
                     .   $n:<2
                       |   (($r)$($r))$($n+-2)
                         + (($r)$($r))$($n+-1)
                     )
                   )
                )
              )
           )
         $ ($x)
     )
   )
$ 30
)

Answer:

832040

BQN

𝕊 is a useful symbol in BQN which references the function it is currently in. This can be used to perform anonymous recursion without the need of naming the function block.

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

{
  (𝕩<2)+´𝕊¨,𝕏𝕩-12
}¨10
 0 1 1 2 3 5 8 13 21 34 

Try It!

Recursion can also be performed using an internal name defined by a header such as Fact: or Fact 𝕩:. 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 𝕊 can only refer to the immediately containing one.

{Fact 𝕩:
  (𝕩<2)+´Fact¨,𝕏𝕩-12
}¨10

C

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

#include <stdio.h>

long fib(long x)
{
        long fib_i(long n) { return n < 2 ? n : fib_i(n - 2) + fib_i(n - 1); };
        if (x < 0) {
                printf("Bad argument: fib(%ld)\n", x);
                return -1;
        }
        return fib_i(x);
}

long fib_i(long n) /* just to show the fib_i() inside fib() has no bearing outside it */
{
        printf("This is not the fib you are looking for\n");
        return -1;
}

int main()
{
        long x;
        for (x = -1; x < 4; x ++)
                printf("fib %ld = %ld\n", x, fib(x));

        printf("calling fib_i from outside fib:\n");
        fib_i(3);

        return 0;
}
Output:
Bad argument: fib(-1)
fib -1 = -1
fib 0 = 0
fib 1 = 1
fib 2 = 1
fib 3 = 2
calling fib_i from outside fib:
This is not the fib you are looking for

Recursive functions can be defined within statement expressions:

#include <stdio.h>
int main(){
    int n = 3;
    printf("%d",({
        int fib(int n){
            if (n <= 1)
              return n;
            return fib(n-1) + fib(n-2);
        }
        fib(n);
    }));
    return 0;
}

C#

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

static int Fib(int n)
{
    if (n < 0) throw new ArgumentException("Must be non negativ", "n");
 
    Func<int, int> fib = null; // Must be known, before we can assign recursively to it.
    fib = p => p > 1 ? fib(p - 2) + fib(p - 1) : p;
    return fib(n);
}

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.

double fib(double n)
{
  if(n < 0)
  {
    throw "Invalid argument passed to fib";
  }
  else
  {
    struct actual_fib
    {
        static double calc(double n)
        {
          if(n < 2)
          {
            return n;
          }
          else
          {
            return calc(n-1) + calc(n-2);
          }
        }
    };

    return actual_fib::calc(n);
  }
}
Works with: C++11
#include <functional>
using namespace std;

double fib(double n)
{
  if(n < 0)
    throw "Invalid argument";
  
  function<double(double)> actual_fib = [&](double n)
  {
    if(n < 2) return n;
    return actual_fib(n-1) + actual_fib(n-2);
  };

  return actual_fib(n);
}

Using a local function object that calls itself using this:

double fib(double n)
{
  if(n < 0)
  {
    throw "Invalid argument passed to fib";
  }
  else
  {
    struct
    {
      double operator()(double n)
      {
        if(n < 2)
        {
          return n;
        }
        else
        {
          return (*this)(n-1) + (*this)(n-2);
        }
      }
    } actual_fib;

    return actual_fib(n);
  }
}

Clio

Simple anonymous recursion to print from 9 to 0.

10 -> (@eager) fn n:
  if n:
    n - 1 -> print -> recall

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)
    (throw (new IllegalArgumentException "n should be > 0")))
  (loop [n n, v1 1, v2 1] 
    (if (< n 2)
      v2
      (recur (dec n) v2 (+ v1 v2)))))

Using an anonymous function

CoffeeScript

# This is a rather obscure technique to have an anonymous
# function call itself.
fibonacci = (n) ->
  throw "Argument cannot be negative" if n < 0
  do (n) ->
      return n if n <= 1
      arguments.callee(n-2) + arguments.callee(n-1)

# Since it's pretty lightweight to assign an anonymous
# function to a local variable, the idiom below might be
# more preferred.
fibonacci2 = (n) ->
  throw "Argument cannot be negative" if n < 0
  recurse = (n) ->
      return n if n <= 1
      recurse(n-2) + recurse(n-1)
  recurse(n)

Common Lisp

Using Anaphora

This version uses the anaphoric lambda from Paul Graham's On Lisp.

(defmacro alambda (parms &body body)
  `(labels ((self ,parms ,@body))
     #'self))

The Fibonacci function can then be defined as

(defun fib (n)
  (assert (>= n 0) nil "'~a' is a negative number" n)
  (funcall 
   (alambda (n)
     (if (>= 1 n)
	 n
	 (+ (self (- n 1)) (self (- n 2)))))
   n))

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

(defun fib (number)
  "Fibonacci sequence function."
  (if (< number 0)
      (error "Error. The number entered: ~A is negative" number)
      (labels ((fib (n a b)
                 (if (= n 0)
                     a
                     (fib (- n 1) b (+ a b)))))
        (fib number 0 1))))

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 fib rewritten to use RECURSIVE:

(defun fib (number)
  "Fibonacci sequence function."
  (if (< number 0)
      (error "Error. The number entered: ~A is negative" number)
      (recursive ((n number) (a 0) (b 1))
         (if (= n 0)
            a
            (recurse (- n 1) b (+ a b))))))

Implementation of RECURSIVE:

(defmacro recursive ((&rest parm-init-pairs) &body body)
  (let ((hidden-name (gensym "RECURSIVE-")))
    `(macrolet ((recurse (&rest args) `(,',hidden-name ,@args)))
       (labels ((,hidden-name (,@(mapcar #'first parm-init-pairs)) ,@body))
         (,hidden-name ,@(mapcar #'second parm-init-pairs))))))

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!

Exercises for reader:

  1. In the original fib, the recursive local function can obtain a reference to itself using #'fib. This would allow it to, for instance, (apply #'fib list-of-args). Add a way for RECURSIVE blocks to obtain a reference to themselves.
  2. Add support for &optional and &rest parameters. Optional: also &key and &aux.
  3. Add LOOPBACK operator whose syntax resembles RECURSE, but which simply assigns the variables and performs a branch back to the top rather than a recursive call.
  4. Tail recursion optimization is compiler-dependent in Lisp. Modify RECURSIVE so that it walks the expressions and identifies tail-recursive RECURSE calls, rewriting these to use looping code. Be careful that unevaluated literal lists which resemble RECURSE calls are not rewritten, and that RECURSE calls belonging to any nested RECURSIVE invocation are not accidentally treated.

Using the Y combinator

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

(defmacro ? (args &body body)
  `(lambda ,args ,@body))

(defstruct combinator
  (name     nil :type symbol)
  (function nil :type function))

(defmethod print-object ((combinator combinator) stream)
  (print-unreadable-object (combinator stream :type t)
    (format stream "~A" (combinator-name combinator))))

(defconstant +y-combinator+
  (make-combinator
   :name     'y-combinator
   :function (? (f) (! (? (g) (! g g))
                       (? (g) (! f (? (&rest a)
                                     (!! (! g g) a))))))))

(defconstant +z-combinator+
  (make-combinator
   :name     'z-combinator
   :function (? (f) (! (? (g) (! f (? (x) (! (! g g) x))))
                       (? (g) (! f (? (x) (! (! g g) x))))))))

(defparameter *default-combinator* +y-combinator+)

(defmacro with-y-combinator (&body body)
  `(let ((*default-combinator* +y-combinator+))
     ,@body))

(defmacro with-z-combinator (&body body)
  `(let ((*default-combinator* +z-combinator+))
     ,@body))

(defun x-call (x-function &rest args)
  (apply (funcall (combinator-function *default-combinator*) x-function) args))

(defmacro x-function ((name &rest args) &body body)
  `(lambda (,name)
     (lambda ,args
       (macrolet ((,name (&rest args)
                    `(funcall ,',name ,@args)))
         ,@body))))

(defmacro x-defun (name args &body body)
  `(defun ,name ,args
     (x-call (x-function (,name ,@args) ,@body) ,@args)))

;;;; examples

(x-defun factorial (n)
  (if (zerop n)
      1 
      (* n (factorial (1- n)))))

(x-defun fib (n)
  (case n
    (0 0)
    (1 1)
    (otherwise (+ (fib (- n 1))
                  (fib (- n 2))))))

D

int fib(in uint arg) pure nothrow @safe @nogc {
    assert(arg >= 0);

    return function uint(in uint n) pure nothrow @safe @nogc {
        static immutable self = &__traits(parent, {});
        return (n < 2) ? n : self(n - 1) + self(n - 2);
    }(arg);
}

void main() {
    import std.stdio;

    39.fib.writeln;
}
Output:
63245986

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.

import std.stdio;

int fib(in int n) pure nothrow {
    assert(n >= 0);

    return (new class {
        static int opCall(in int m) pure nothrow {
            if (m < 2)
                return m;
            else
                return opCall(m - 1) + opCall(m - 2);
        }
    })(n);
}

void main() {
    writeln(fib(39));
}

The output is the same.

Dylan

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)
    error("Can't take fibonacci of negative integer: %d\n", n)
  end;
  local method fib1 (n, a, b)
    if (n = 0)
      a
    else
      fib1(n - 1, b, a + b)
    end
  end;
  fib1(n, 0, 1)
end

Déjà Vu

With Y combinator

Y f:
	labda y:
		labda:
			f y @y
	call dup

labda fib n:
	if <= n 1:
		1
	else:
		fib - n 1
		fib - n 2
		+
Y
set :fibo

for j range 0 10:
	!print fibo j

With recurse

fibo-2 n:
	n 0 1
	labda times back-2 back-1:
		if = times 0:
			back-2
		elseif = times 1:
			back-1
		elseif = times 2:
			+ back-1 back-2
		else:
			recurse -- times back-1 + back-1 back-2
	call

for j range 0 10:
	!print fibo-2 j

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

Delphi

program AnonymousRecursion;

{$APPTYPE CONSOLE}

uses
  SysUtils;

function Fib(X: Integer): integer;

	function DoFib(N: Integer): Integer;
	begin
	if N < 2 then Result:=N
	else Result:=DoFib(N-1) + DoFib(N-2);
	end;

begin
if X < 0 then raise Exception.Create('Argument < 0')
else Result:=DoFib(X);
end;


var I: integer;

begin
for I:=-1 to 15 do
	begin
	try
	WriteLn(I:3,' - ',Fib(I):3);
	except WriteLn(I,' - Error'); end;
	end;
WriteLn('Hit Any Key');
ReadLn;
end.
Output:
 -1 - -1 - Error
  0 -   0
  1 -   1
  2 -   1
  3 -   2
  4 -   3
  5 -   5
  6 -   8
  7 -  13
  8 -  21
  9 -  34
 10 -  55
 11 -  89
 12 - 144
 13 - 233
 14 - 377
 15 - 610
Hit Any Key

EchoLisp

A named let provides a local lambda via a label.

(define (fib n)
(let _fib ((a 1) (b 1) (n n))
		(if
		(<= n 1) a
		(_fib b (+ a b) (1- n)))))

Ela

Using fix-point combinator:

fib n | n < 0 = fail "Negative n"
      | else = fix (\f n -> if n < 2 then n else f (n - 1) + f (n - 2)) n

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

fix f = f (& fix f)

Elena

ELENA 6.x:

import extensions;

fib(n)
{
   if (n < 0)
      { InvalidArgumentException.raise() };
        
   ^ (n) {
      if (n > 1)
      { 
         ^ this self(n - 2) + (this self(n - 1))
      }
      else
      { 
         ^ n 
      }
   }(n)
}

public program()
{
   for (int i := -1; i <= 10; i += 1) 
   {
      console.print("fib(",i,")=");
      try
      {
         console.printLine(fib(i))
      }
      catch(Exception e)
      {
         console.printLine("invalid")
      }
   };
    
   console.readChar()
}
Output:
fib(-1)=invalid
fib(0)=0
fib(1)=1
fib(2)=1
fib(3)=2
fib(4)=3
fib(5)=5
fib(6)=8
fib(7)=13
fib(8)=21
fib(9)=34
fib(10)=55

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
	) 
end

y = fn x -> (
    fn f -> f.(f) 
  end).(
    fn g -> x.(fn z ->(g.(g)).(z) end) 
  end)
end

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

102334155

EMal

fun fibonacci = int by int n
  if n < 0 do
    logLine("Invalid argument: " + n) # logs on standard error
	return -1 ^| it should be better to raise an error,
	           | but the task is about recursive functions
	           |^
  end
  fun actualFibonacci = int by int n
    return when(n < 2, n, actualFibonacci(n - 1) + actualFibonacci(n - 2))
  end
  return actualFibonacci(n)
end
writeLine("F(0)   = " + fibonacci(0))
writeLine("F(20)  = " + fibonacci(20))
writeLine("F(-10) = " + fibonacci(-10))
writeLine("F(30)  = " + fibonacci(30))
writeLine("F(10)  = " + fibonacci(10))
Output:
F(0)   = 0
F(20)  = 6765
Invalid argument: -10
F(-10) = -1
F(30)  = 832040
F(10)  = 55

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 ) when N >= 0 ->
	fib( N, 1, 0 ).

fib_internal( N ) when N >= 0 ->
	Fun = fun (_F, 0, _Next, Acc ) -> Acc;
		(F, N, Next, Acc) -> F( F, N - 1, Acc+Next, Next )
		end,
	Fun( Fun, N, 1, 0 ).


fib( 0, _Next, Acc ) -> Acc;
fib( N, Next, Acc ) -> fib( N - 1, Acc+Next, Next ).

F#

Using a nested function:

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

let fib = function
    | n when n < 0 -> None
    | n -> let rec fib2 = function
               | 0 | 1 -> 1
               | n -> fib2 (n-1) + fib2 (n-2)
            in Some (fib2 n)

Using a fixed point combinator:

let rec fix f x = f (fix f) x

let fib = function
    | n when n < 0 -> None
    | n -> Some (fix (fun f -> (function | 0 | 1 -> 1 | n -> f (n-1) + f (n-2))) n)
Output:

Both functions have the same output.

[-1..5] |> List.map fib |> printfn "%A"
[null; Some 1; Some 1; Some 2; Some 3; Some 5; Some 8]

Factor

One would never use anonymous recursion. The better way defines a private word, like fib2, and recurse by name. This private word would pollute the namespace of one source file.

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

USING: kernel math ;
IN: rosettacode.fibonacci.ar

: fib ( n -- m )
    dup 0 < [ "fib of negative" throw ] when
    [
        ! If n < 2, then drop q, else find q(n - 1) + q(n - 2).
        [ dup 2 < ] dip swap [ drop ] [
            [ [ 1 - ] dip dup call ]
            [ [ 2 - ] dip dup call ] 2bi +
        ] if
    ] dup call( n q -- m ) ;

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

The recursive quotation has 2 significant disadvantages:

  1. To enable the recursion, a reference to the quotation stays on the stack. This q impedes access to other things on the stack. This solution must use dip and swap to move q out of the way. To simplify the code, one might move q to a local variable, but then the recursion would not be anonymous.
  2. Factor cannot infer the stack effect of a recursive quotation. The last line must have call( n q -- m ) instead of plain call; but call( n q -- m ) defers the stack effect check until runtime. So if the quotation has a wrong stack effect, the compiler would miss the error; only a run of fib would detect the error.

Falcon

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

function fib(x)
   if x < 0
      raise ParamError(description|"Negative argument invalid", extra|"Fibbonacci sequence is undefined for negative numbers")
   else
      return (function(y)
         if y == 0
            return 0
         elif y == 1
            return 1
         else
            return fself(y-1) + fself(y-2)
         end
      end)(x)  
   end
end
 
   
try 
>fib(2)
>fib(3)
>fib(4)
>fib(-1)
catch in e
> e
end
Output:
1
2
3
ParamError SS0000 at falcon.core.ParamError._init:(PC:ext.c): Negative argument invalid (Fibbonacci sequence is undefined for negative numbers)
  Traceback:
   falcon.core.ParamError._init:0(PC:ext.c)
   "/home/uDTVwo/prog.fam" prog.fib:3(PC:56)
   "/home/uDTVwo/prog.fam" prog.__main__:22(PC:132)

FBSL

#APPTYPE CONSOLE

FUNCTION Fibonacci(n)
	IF n < 0 THEN
		RETURN "Nuts!"
	ELSE
		RETURN Fib(n)
	END IF
	FUNCTION Fib(m)
		IF m < 2 THEN
			Fib = m
		ELSE
			Fib = Fib(m - 1) + Fib(m - 2)
		END IF
	END FUNCTION
END FUNCTION

PRINT Fibonacci(-1.5)
PRINT Fibonacci(1.5)
PRINT Fibonacci(13.666)

PAUSE

Output:

Nuts!
1.5
484.082

Press any key to continue...

Forth

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.

:noname ( n -- n' )
  dup 2 < ?exit
  1- dup recurse swap 1- recurse + ; ( xt )

: fib ( +n -- n' )
  dup 0< abort" Negative numbers don't exist."
  [ ( xt from the :NONAME above ) compile, ] ;

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

( xt from :noname in the previous example )
variable pocket  pocket !
: fib ( +n -- n' )
  dup 0< abort" Negative numbers don't exist."
  [ pocket @ compile, ] ;

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

: fib ( +n -- )  
	dup 0< abort" Negative numbers don't exist"  
	[: dup 2 < ?exit  1- dup MYSELF swap 1- MYSELF + ;] execute . ;

Fortran

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

integer function fib(n)
  integer, intent(in) :: n
  if (n < 0 ) then
    write (*,*) 'Bad argument: fib(',n,')'
    stop
  else
    fib = purefib(n)
  end if
contains
  recursive pure integer function purefib(n) result(f)
    integer, intent(in) :: n
    if (n < 2 ) then
      f = n
    else
      f = purefib(n-1) + purefib(n-2)
    end if
  end function purefib
end function fib

FreeBASIC

FreeBASIC does not support nested functions, lambda expressions, functions inside nested types or even (in the default dialect) gosub.

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

' FB 1.05.0 Win64

#Lang "fblite"

Option Gosub  '' enables Gosub to be used

' Using gosub to simulate a nested function
Function fib(n As UInteger) As UInteger
  Gosub nestedFib
  Exit Function

  nestedFib:
  fib = IIf(n < 2, n, fib(n - 1) + fib(n - 2))
  Return
End Function

' This function simulates (rather messily) gosub by using 2 gotos and would therefore work
' even in the default dialect 
Function fib2(n As UInteger) As UInteger
  Goto nestedFib

  exitFib:
  Exit Function

  nestedFib:
  fib2 = IIf(n < 2, n, fib2(n - 1) + fib2(n - 2))
  Goto exitFib
End Function

For i As Integer = 1 To 12
  Print fib(i); " ";
Next

Print

For j As Integer = 1 To 12
  Print fib2(j); " ";
Next

Print
Print "Press any key to quit"
Sleep
Output:
1 1 2 3 5 8 13 21 34 55 89 144
1 1 2 3 5 8 13 21 34 55 89 144

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution.

It consists in having a local function inside the main function, so it is neither visible nor available outside. The local function is defined after the validation, so if the input is invalid, neither the definition nor its invocation is performed.

 

Test cases

 

 

Go

Y combinator

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

package main

import "fmt"

func main() {
    for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 40, -1} {
        f, ok := arFib(n)
        if ok {
            fmt.Printf("fib %d = %d\n", n, f)
        } else {
            fmt.Println("fib undefined for negative numbers")
        }
    }
}

func arFib(n int) (int, bool) {
    switch {
    case n < 0:
        return 0, false
    case n < 2:
        return n, true
    }
    return yc(func(recurse fn) fn {
        return func(left, term1, term2 int) int {
            if left == 0 {
                return term1+term2
            }
            return recurse(left-1, term1+term2, term1)
        }
    })(n-2, 1, 0), true
}

type fn func(int, int, int) int
type ff func(fn) fn
type fx func(fx) fn

func yc(f ff) fn {
    return func(x fx) fn {
        return x(x)
    }(func(x fx) fn {
        return f(func(a1, a2, a3 int) int {
            return x(x)(a1, a2, a3)
        })
    })
}
Output:
fib 0 = 0
fib 1 = 1
fib 2 = 1
fib 3 = 2
fib 4 = 3
fib 5 = 5
fib 10 = 55
fib 40 = 102334155
fib undefined for negative numbers

Closure

package main

import (
	"errors"
	"fmt"
)

func fib(n int) (result int, err error) {
	var fib func(int) int // Must be declared first so it can be called in the closure
	fib = func(n int) int {
		if n < 2 {
			return n
		}
		return fib(n-1) + fib(n-2)
	}

	if n < 0 {
		err = errors.New("negative n is forbidden")
		return
	}

	result = fib(n)
	return
}

func main() {
	for i := -1; i <= 10; i++ {
		if result, err := fib(i); err != nil {
			fmt.Printf("fib(%d) returned error: %s\n", i, err)
		} else {
			fmt.Printf("fib(%d) = %d\n", i, result)
		}
	}
}
Output:
fib(-1) returned error: negative n is forbidden
fib(0) = 0
fib(1) = 1
fib(2) = 1
fib(3) = 2
fib(4) = 3
fib(5) = 5
fib(6) = 8
fib(7) = 13
fib(8) = 21
fib(9) = 34
fib(10) = 55

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.

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

Test:

def fib0to20 = (0..20).collect(fib)
println fib0to20

try {
    println fib(-25)
} catch (Throwable e) {
    println "KABOOM!!"
    println e.message
}
Output:
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765]
KABOOM!!
assert it > -1
       |  |
       |  false
       -25

Haskell

Haskell has two ways to use anonymous recursion. Both methods hide the 'anonymous' function from the containing module, however the first method is actually using a named function.

Named function:

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

fib :: Integer -> Maybe Integer
fib n
  | n < 0 = Nothing
  | otherwise = Just $ real n
              where real 0 = 1
                    real 1 = 1
                    real n = real (n-1) + real (n-2)

Anonymous function:

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

import Data.Function (fix)

fib :: Integer -> Maybe Integer
fib n 
  | n < 0 = Nothing
  | otherwise = Just $ fix (\f -> (\n -> if n > 1 then f (n-1) + f (n-2) else 1)) n
Output:

Both functions provide the same output when run in GHCI.

ghci> map fib [-4..10]
[Nothing,Nothing,Nothing,Nothing,Just 1,Just 1,Just 2,Just 3,Just 5,Just 8,Just 13,Just 21,Just 34,Just 55,Just 89]

Or, without imports (inlining an anonymous fix)

fib :: Integer -> Maybe Integer
fib n
  | n < 0 = Nothing
  | otherwise =
    Just $
    (\f ->
        let x = f x
        in x)
      (\f n ->
          if n > 1
            then f (n - 1) + f (n - 2)
            else 1)
      n

-- TEST ----------------------------------------------------------------------
main :: IO ()
main =
  print $
  fib <$> [-4 .. 10] >>=
  \m ->
     case m of
       Just x -> [x]
       _ -> []
Output:
[1,1,2,3,5,8,13,21,34,55,89]

Icon and Unicon

The following solution works in both languages. A cache is used to improve performance.

This example is more a case of can it even be done, and just because we CAN do something - doesn't mean we should do it. The use of co-expressions for this purpose was probably never intended by the language designers and is more than a little bit intensive and definitely NOT recommended.

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.

procedure main(A)
   every write("fib(",a := numeric(!A),")=",fib(a))
end
 
procedure fib(n)
   local  source, i
   static cache
   initial {
      cache := table()
      cache[0] := 0
      cache[1] := 1
      }
   if type(n) == "integer" & n >= 0 then
      return n @ makeProc {{
         i := @(source := &source)                                          # 1
         /cache[i] := ((i-1)@makeProc(^&current)+(i-2)@makeProc(^&current)) # 2
         cache[i] @ source                                                  # 3
         }}
end

procedure makeProc(A)
   A := if type(A) == "list" then A[1]
   return (@A, A)                    # prime and return
end

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.
  • At #1 we remember where we came from and receive n from our caller
  • At #2 we transmit the new parameters to refreshed copies of the current co-expression setup to act as a normal procedure and cache the result.
  • At #3 we transmit the result back to our caller.
  • The procedure makeProc consumes the the first transmission to the co-expression which is ignored. Essentially this primes the co-expression to behave like a regular procedure.

For reference, here is the non-cached version:

procedure fib(n)
   local  source, i
   if type(n) == "integer" & n >= 0 then
      return n @ makeProc {{
         i := @(source := &source)
         if i = (0|1) then i@source
         ((i-1)@makeProc(^&current) + (i-2)@makeProc(^&current)) @ source
         }}
end

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.

Io

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

fib := method(x,
    if(x < 0, Exception raise("Negative argument not allowed!"))
    fib2 := method(n,
        if(n < 2, n, fib2(n-1) + fib2(n-2))
    )
    fib2(x floor)
)

J

Copied directly from the fibonacci sequence task, which in turn copied from one of several implementations in an essay on the J Wiki:

   fibN=: (-&2 +&$: -&1)^:(1&<) M."0

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

Examples:

   fibN 12
144
   fibN  i.31
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040

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

$: is an anonymous reference to the largest containing verb in the sentence.


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

basis ` ($: @: g) @. test

which is an anonymous form matches the "tail recursion" pattern is not automatically transformed to satisfy the classic "tail recursion optimization". That optimization would be implemented as transforming this particular example of recursion to the non-recursive

basis @: (g^:test^:_)

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.


See also Y combinator but note that that approach is less efficient (has higher costs).

Also, note that J's "implicit mapping" is primitive recursive (as is arithmetic in general), and thus in some contexts a "more efficient approach to recursion".

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.

public static long fib(int n) {
    if (n < 0)
        throw new IllegalArgumentException("n can not be a negative number");

    return new Object() {
        private long fibInner(int n) {
            return (n < 2) ? n : (fibInner(n - 1) + fibInner(n - 2));
        }
    }.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.

import java.util.function.Function;

@FunctionalInterface
interface SelfApplicable<OUTPUT> {
    OUTPUT apply(SelfApplicable<OUTPUT> input);
}

class Utils {
    public static <INPUT, OUTPUT> SelfApplicable<Function<Function<Function<INPUT, OUTPUT>, Function<INPUT, OUTPUT>>, Function<INPUT, OUTPUT>>> y() {
        return y -> f -> x -> f.apply(y.apply(y).apply(f)).apply(x);
    }

    public static <INPUT, OUTPUT> Function<Function<Function<INPUT, OUTPUT>, Function<INPUT, OUTPUT>>, Function<INPUT, OUTPUT>> fix() {
        return Utils.<INPUT, OUTPUT>y().apply(Utils.<INPUT, OUTPUT>y());
    }

    public static long fib(int m) {
        if (m < 0)
            throw new IllegalArgumentException("n can not be a negative number");

        return Utils.<Integer, Long>fix().apply(
                f -> n -> (n < 2) ? n : (f.apply(n - 1) + f.apply(n - 2))
        ).apply(m);
    }
}

JavaScript

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

  return (function(n) {
    return (n < 2) ? n : arguments.callee(n-1) + arguments.callee(n-2);
  })(n);
}

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

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

  return (function fib(n) {
    return (n < 2) ? n : fib(n-1) + fib(n-2);
  })(n);
}

Joy

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

fib == [small] [] [pred dup pred] [+] binrec;

jq

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

0 | recurse(. + 1)

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

def fib(n):
  def aux: if   . == 0 then 0
           elif . == 1 then 1
           else (. - 1 | aux) + (. - 2 | aux)
           end;
  if n < 0 then error("negative arguments not allowed")
  else n | aux
  end ;

Julia

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

function fib(n)
    if n < 0
        throw(ArgumentError("negative arguments not allowed"))
    end
    aux(m) = m < 2 ? one(m) : aux(m-1) + aux(m-2)
    aux(n)
end

K

Works with: Kona
fib: {:[x<0; "Error Negative Number"; {:[x<2;x;_f[x-2]+_f[x-1]]}x]}
Works with: ngn/k

:

fib: {:[x<0; "Error Negative Number"; {:[x<2;x;o[x-2]+o[x-1]]}x]}

Examples:

  fib'!10
0 1 1 2 3 5 8 13 21 34
  fib -1
"Error Negative Number"

Klingphix

include ..\Utilitys.tlhy

  
:fib %f !f
    %fr
    [ %n !n
        $n 2 <
        ( [$n]
          [$n 1 - $fr eval $n 2 - $fr eval +] )
        if
    ] !fr 
        
    $f 0 <
    ( ["Error: number is negative"]
      [$f true $fr if] )
    if
;


25 fib ?
msec ?
"End " input

Klong

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

Kotlin

Translation of: Dylan
fun fib(n: Int): Int {
   require(n >= 0)
   fun fib(k: Int, a: Int, b: Int): Int =
       if (k == 0) a else fib(k - 1, b, a + b)
   return fib(n, 0, 1)
}

fun main(args: Array<String>) {
    for (i in 0..20) print("${fib(i)} ")
    println()
}
Output:
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765

Lambdatalk

1) defining a quasi-recursive function combined with a simple Ω-combinator:
{def fibo {lambda {:n}
 {{{lambda {:f} {:f :f}} 
  {lambda {:f :n :a :b}
   {if {< :n 0}
    then the number must be positive! 
    else {if {<  :n 1}
    then :a
    else {:f :f {- :n 1} {+ :a :b} :a}}}}} :n 1 0}}}
-> fibo

2) testing:
{fibo -1} -> the number must be positive!
{fibo 0} -> 1
{fibo 8} -> 34
{fibo 1000} -> 7.0330367711422765e+208
{S.map fibo {S.serie 1 20}}
-> 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} {:f :f}} 
  {lambda {:f :n :a :b}
   {if {< :n 0}
    then the number must be positive! 
    else {if {<  :n 1}
    then :a
    else {:f :f {- :n 1} {+ :a :b} :a}}}}} :n 1 0}}
 8}
-> 34

Lang

fp.fib = ($n) -> {
	if($n < 0) {
		throw fn.withErrorMessage($LANG_ERROR_INVALID_ARGUMENTS, n must be >= 0)
	}
	
	fp.innerFib = ($n) -> {
		if($n < 2) {
			return $n
		}
		
		return parser.op(fp.innerFib($n - 1) + fp.innerFib($n - 2))
	}
	
	return fp.innerFib($n)
}

Lingo

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

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

  -- create instance of unnamed class in memory only (does not pollute namespace)
  m = new(#script)
  r = RETURN
  m.scriptText = "on fib (me,n)"&r&"if n<2 then return n"&r&"return me.fib(n-1)+me.fib(n-2)"&r&"end"
  aux = m.script.new()
  m.erase()

  return aux.fib(n)
end
put fib(10)
-- 55

LOLCODE

Translation of: C
HAI 1.3

HOW IZ I fib YR x
    DIFFRINT x AN BIGGR OF x AN 0, O RLY?
        YA RLY, FOUND YR "ERROR"
    OIC

    HOW IZ I fib_i YR n
        DIFFRINT n AN BIGGR OF n AN 2, O RLY?
            YA RLY, FOUND YR n
        OIC

        FOUND YR SUM OF...
        I IZ fib_i YR DIFF OF n AN 2 MKAY AN...
        I IZ fib_i YR DIFF OF n AN 1 MKAY
    IF U SAY SO

    FOUND YR I IZ fib_i YR x MKAY
IF U SAY SO

HOW IZ I fib_i YR n
    VISIBLE "SRY U CANT HAS FIBS DIS TIEM"
IF U SAY SO

IM IN YR fibber UPPIN YR i TIL BOTH SAEM i AN 5
    I HAS A i ITZ DIFF OF i AN 1
    VISIBLE "fib(:{i}) = " I IZ fib YR i MKAY
IM OUTTA YR fibber

I IZ fib_i YR 3 MKAY

KTHXBYE

Lua

Using a Y combinator.

local function Y(x) return (function (f) return f(f) end)(function(y) return x(function(z) return y(y)(z) end) end) end

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

using a metatable (also achieves memoization)

return setmetatable({1,1},{__index = function(self, n)
  self[n] = self[n-1] + self[n-2]
  return self[n]
end})

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$={{ Module "Fibonacci" : Read X  :If X<0 then {Error {X<0}} Else  Fib=Lambda (x)->if(x>1->fib(x-1)+fib(x-2), x) : =fib(x)}}
Try Ok {
      Print Function(A$, -12)
}
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"
      If x<2 then =x : exit
      Def fib1(x)=If(x>1->lambda(x-1)+lambda(x-2), x)
      =fib1(x)
}
Module CheckIt (&k()) {
      Print k(12)
}
CheckIt &Fib()
Print fib(-2)  ' error

Using lambda function

fib=lambda -> {
       fib1=lambda (x)->If(x>1->lambda(x-1)+lambda(x-2), x)
      =lambda fib1 (x) -> {
            If x<0 then Error "argument outside of range"
            If x<2 then =x : exit
            =fib1(x)
      }
}()  ' using () execute this lambda so fib get the returned lambda
Module  CheckIt (&k()) {
      Print k(12)
}
CheckIt &Fib()
Try {
      Print fib(-2)
}
Print Error$
Z=Fib
Print Z(12)
Dim a(10)
a(3)=Z
Print a(3)(12)=144
Inventory Alfa = "key1":=Z
Print Alfa("key1")(12)=144

Using a Group (object in M2000) like a function

A Group may have a name like k (which hold a unique group), or can be unnamed like item in A(4), or can be pointed by a variable (or an array item) (we can use many pointers for the same group)


Class Something {
\\ this class is a global function 
\\ return a group with a value with one parameter
private:
      \\ we can use lambda(), but here we use .fib1() as This.fib1()
       fib1=lambda (x)->If(x>1->.fib1(x-1)+.fib1(x-2), x)      
public:
      Value (x) {
            If x<0 then Error "argument outside of range"
            If x<2 then =x : exit
            =This.fib1(x)            \\ we can omit This using .fib1(x)
      }
}
K=Something()     ' K is a static group here
Print k(12)=144
Dim a(10)
a(4)=Group(K)
Print a(4)(12)=144
pk->Something()   ' pk is a pointer to group (object in M2000)
\\ pointers need Eval to process arguments
Print Eval(pk, 12)=144
Inventory Alfa = "Key2":=Group(k), 10*10:=pk
Print Alfa("Key2")(12)=144
Print Eval(Alfa("100"),12)=144, Eval(Alfa(100),12)=144

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 )
                option  remember; # automatically memoise
                if k = 0 then
                        0
                elif k = 1 then
                        1
                else
                        # Recurse, anonymously
                        thisproc( k - 1 ) + thisproc( k - 2 )
                end
        end( n )
end proc:

For example:

> seq( Fib( i ), i = 0 .. 10 );
                  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

> Fib( -1 );
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.

Mathematica / 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 pure functions in Mathematica.

check := #<0&
fib := If[check[#],Throw["Negative Argument"],If[#<=1,1,#0[#-2]+#0[#-1]]&[#]]&
fib /@ Range[0,10]

{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89}

Making sure that the check is only performed once.

check := (Print[#];#<0)&
fib /@ Range[0,4]
0
1
2
3
4

{1, 1, 2, 3, 5}

MATLAB

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

  • does not exist outside of parent function
  • 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)
v = fibonacci(n,0,1);

    % nested function
    function a = fibonacci(n,a,b)
        if n ~= 0
            a = fibonacci(n-1,b,a+b);
        end
    end
end

Nemerle

Not anonymous exactly, but using inner function solves all problems stated in task description.

  • name is basically the same as outer function and doesn't pollute the namespace
  • inner function not expected to be called from anywhere else
  • nesting maintains program flow in source code
using System;
using System.Console;

module Fib
{
    Fib(n : long) : long
    {
        def fib(m : long)
        {
            |0 => 1
            |1 => 1
            |_ => fib(m - 1) + fib(m - 2)
        }
        
        match(n)
        {
            |n when (n < 0) => throw ArgumentException("Fib() not defined on negative numbers")
            |_ => fib(n)
        }
    }
    
    Main() : void
    {
        foreach (i in [-2 .. 10])
        {
            try {WriteLine("{0}", Fib(i));}
            catch {|e is ArgumentException => WriteLine(e.Message)}
        }
    }
}

Nim

# Using scoped function fibI inside fib
proc fib(x: int): int =
  proc fibI(n: int): int =
    if n < 2: n else: fibI(n-2) + fibI(n-1)
  if x < 0:
    raise newException(ValueError, "Invalid argument")
  return fibI(x)

for i in 0..4:
  echo fib(i)

# fibI(10) # undeclared identifier 'fibI'

Output:

0
1
1
2
3

Objective-C

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

#import <Foundation/Foundation.h>

@interface AnonymousRecursion : NSObject { }
- (NSNumber *)fibonacci:(NSNumber *)n;
@end

@implementation AnonymousRecursion
- (NSNumber *)fibonacci:(NSNumber *)n {
  int i = [n intValue];
  if (i < 0)
    @throw [NSException exceptionWithName:NSInvalidArgumentException
                                 reason:@"fibonacci: no negative numbers"
                               userInfo:nil];
  int result;
  if (i < 2)
    result = 1;
  else
    result = [[self performSelector:_cmd withObject:@(i-1)] intValue]
           + [[self performSelector:_cmd withObject:@(i-2)] intValue];
  return @(result);
}
@end

int main (int argc, const char *argv[]) {
  @autoreleasepool {
  
    AnonymousRecursion *dummy = [[AnonymousRecursion alloc] init];
    NSLog(@"%@", [dummy fibonacci:@8]);

  }
  return 0;
}
With internal named recursive block
Works with: Mac OS X version 10.6+
#import <Foundation/Foundation.h>

int fib(int n) {
    if (n < 0)
        @throw [NSException exceptionWithName:NSInvalidArgumentException
                                 reason:@"fib: no negative numbers"
                               userInfo:nil];
    int (^f)(int);
    __block __weak int (^weak_f)(int); // block cannot capture strong reference to itself
    weak_f = f = ^(int n) {
        if (n < 2)
            return 1;
        else
            return weak_f(n-1) + weak_f(n-2);
    };
    return f(n);
}

int main (int argc, const char *argv[]) {
  @autoreleasepool {
  
    NSLog(@"%d", fib(8));

  }
  return 0;
}

When ARC is disabled, the above should be:

#import <Foundation/Foundation.h>

int fib(int n) {
    if (n < 0)
        @throw [NSException exceptionWithName:NSInvalidArgumentException
                                 reason:@"fib: no negative numbers"
                               userInfo:nil];
    __block int (^f)(int);
    f = ^(int n) {
        if (n < 2)
            return 1;
        else
            return f(n-1) + f(n-2);
    };
    return f(n);
}

int main (int argc, const char *argv[]) {
  @autoreleasepool {
  
    NSLog(@"%d", fib(8));

  }
  return 0;
}

OCaml

Translation of: Haskell

OCaml has two ways to use anonymous recursion. Both methods hide the 'anonymous' function from the containing module, however the first method is actually using a named function.

Named function:

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

let fib n =
  let rec real = function
      0 -> 1
    | 1 -> 1
    | n -> real (n-1) + real (n-2)
  in
  if n < 0 then
    None
  else
    Some (real n)

Anonymous function:

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

let rec fix f x = f (fix f) x

let fib n =
  if n < 0 then
    None
  else
    Some (fix (fun f -> fun n -> if n <= 1 then 1 else f (n-1) + f (n-2)) n)
Output:
# fib 8;;
- : int option = Some 34

Ol

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

(define (fibonacci n)
   (if (> 0 n)
      "error: negative argument."
      (let loop ((a 1) (b 0) (count n))
         (if (= count 0)
            b
            (loop (+ a b) a (- count 1))))))

(print
   (map fibonacci '(1 2 3 4 5 6 7 8 9 10)))
Output:
'(1 1 2 3 5 8 13 21 34 55)

OxygenBasic

An inner function keeps the name-space clean:

function fiboRatio() as double
    function fibo( double i, j ) as double
        if j > 2e12 then return j / i
        return fibo j, i + j
    end function
    return fibo 1, 1 
end function

print fiboRatio

PARI/GP

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

Fib(n)={
  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 version 2.8.1+

This version gets a self-reference from self().

Fib(n)={
  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))
};

Pascal

program AnonymousRecursion;

function Fib(X: Integer): integer;

	function DoFib(N: Integer): Integer;
	begin
	if N < 2 then DoFib:=N
	else DoFib:=DoFib(N-1) + DoFib(N-2);
	end;

begin
if X < 0 then Fib:=X
else Fib:=DoFib(X);
end;


var I,V: integer;

begin
for I:=-1 to 15 do
	begin
	V:=Fib(I);
	Write(I:3,' - ',V:3);
	if V<0 then Write(' - Error');
	WriteLn;
	end;
WriteLn('Hit Any Key');
ReadLn;
end.
Output:
 -1 - -1 - Error
  0 -   0
  1 -   1
  2 -   1
  3 -   2
  4 -   3
  5 -   5
  6 -   8
  7 -  13
  8 -  21
  9 -  34
 10 -  55
 11 -  89
 12 - 144
 13 - 233
 14 - 377
 15 - 610
Hit Any Key

PascalABC.NET

function Fib(n: integer): integer;
begin
  if n <= 0 then
    raise new System.ArgumentOutOfRangeException('Must be > 0','n');
  var fibHelper: (integer,integer,integer) -> integer;
  fibHelper := (n,a,b) -> n = 1 ? a : fibHelper(n-1, b, a + b);
  Result := fibHelper(n,1,1);
end;

begin
  for var i:=1 to 10 do
    Fib(i).Print;
end.

or

function Fib(n: integer): integer;
  function fibHelper(n,a,b: integer): integer := 
    n = 1 ? a : fibHelper(n-1, b, a + b);
begin
  if n <= 0 then
    raise new System.ArgumentOutOfRangeException('Must be > 0','n');
  Result := fibHelper(n,1,1);
end;

begin
  for var i:=1 to 10 do
    Fib(i).Print;
end.
Output:
1 1 2 3 5 8 13 21 34 55 

Perl

Translation of: PicoLisp

recur isn't built into Perl, but it's easy to implement.

sub recur :prototype(&@) {
    my $f = shift;
    local *recurse = $f;
    $f->(@_);
}

sub fibo {
    my $n = shift;
    $n < 0 and die 'Negative argument';
    recur {
        my $m = shift;
        $m < 3 ? 1 : recurse($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:

sub fib {
	my ($n) = @_;
	die "negative arg $n" if $n < 0;
	# put anon sub on stack and do a magic goto to it
	@_ = ($n, sub {
		my ($n, $f) = @_;
		# anon sub recurs with the sub ref on stack
		$n < 2 ? $n : $f->($n - 1, $f) + $f->($n - 2, $f)
	});
	goto $_[1];
}

print(fib($_), " ") for (0 .. 10);

One can also use caller 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: caller will just return '__ANON__' 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 no strict 'refs'; is needed to permit using a string as a subroutine.

sub fibo {
    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.

use v5.16;
say sub {
  my $n = shift;
  $n < 2 ? $n : __SUB__->($n-2) + __SUB__->($n-1)
}->($_) for 0..10

Phix

Library: Phix/Class

using classes

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

without js -- (no class yet)
class Fib
    private function fib_i(integer n)
        return iff(n<2?n:this.fib_i(n-1)+this.fib_i(n-2))
    end function
    public function fib(integer n)
        if n<0 then throw("constraint error") end if
        return this.fib_i(n)
    end function
end class
Fib f = new()

function fib_i(integer i)
    return sprintf("this is not the fib_i(%d) you are looking for\n",i)
end function

?f.fib(10)
--?f.fib_i(10)  -- illegal
?fib_i(10)
Output:
55
"this is not the fib_i(10) you are looking for\n"

using a lambda expression

Make of this what you will...
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.

without js -- (no lambda yet)
function erm(integer n, f)
    return f(n,f)
end function

function fib(integer n)
    if n<0 then throw("constraint error") end if
    return erm(n,function(integer n,f) return iff(n<2?n:f(n-1,f)+f(n-2,f)) end function)
end function

?fib(10)
Output:
55

PHP

In this solution, the function is always called using call_user_func() 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 call_user_func() one call up on the call stack. We can then use debug_backtrace() to get this out.

Works with: PHP version 5.3+
<?php
function fib($n) {
    if ($n < 0)
        throw new Exception('Negative numbers not allowed');
    $f = function($n) { // This function must be called using call_user_func() only
        if ($n < 2)
            return 1;
        else {
            $g = debug_backtrace()[1]['args'][0];
            return call_user_func($g, $n-1) + call_user_func($g, $n-2);
        }
    };
    return call_user_func($f, $n);
}
echo fib(8), "\n";
?>
With internal named recursive function
Works with: PHP version 5.3+
<?php
function fib($n) {
    if ($n < 0)
        throw new Exception('Negative numbers not allowed');
    $f = function($n) use (&$f) {
        if ($n < 2)
            return 1;
        else
            return $f($n-1) + $f($n-2);
    };
    return $f($n);
}
echo fib(8), "\n";
?>
With a function object that can call itself using $this
Works with: PHP version 5.3+
<?php
class fib_helper {
    function __invoke($n) {
        if ($n < 2)
            return 1;
        else
            return $this($n-1) + $this($n-2);
    }
}

function fib($n) {
    if ($n < 0)
        throw new Exception('Negative numbers not allowed');
    $f = new fib_helper();
    return $f($n);
}
echo fib(8), "\n";
?>

PicoLisp

(de fibo (N)
   (if (lt0 N)
      (quit "Illegal argument" N) )
   (recur (N)
      (if (> 2 N)
         1
         (+ (recurse (dec N)) (recurse (- N 2))) ) ) )

Explanation: The above uses the 'recur' / 'recurse' function pair, which is defined as a standard language extensions as

(de recur recurse
   (run (cdr recurse)) )

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'.

PostScript

Library: initlib

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

% primitive recursion
/pfact {
  {1} {*} primrec}.

%linear recursion
/lfact {
   {dup 0 eq}
   {pop 1}
   {dup pred} 
   {*}
   linrec}.

% general recursion
/gfact {
    {0 eq}
    {succ}
    {dup pred}
    {i *}
    genrec}.

% binary recursion
/fib {
    {2 lt} {} {pred dup pred} {+} binrec}.

Prolog

Works with SWI-Prolog and module lambda, written by Ulrich Neumerkel 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.

:- use_module(lambda).

fib(N, _F) :-
	N < 0, !,
	write('fib is undefined for negative numbers.'), nl.

fib(N, F) :-
    % code of Fibonacci
    PF     = \Nb^R^Rr1^(Nb < 2 ->
			  R = Nb
                        ;
			  N1 is Nb - 1,
			  N2 is Nb - 2,
			  call(Rr1,N1,R1,Rr1),
			  call(Rr1,N2,R2,Rr1),
			  R is R1 + R2
			),

    % The Y combinator.

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

    call(Pred,N,F).

Python

>>> Y = lambda f: (lambda x: x(x))(lambda y: f(lambda *args: y(y)(*args)))
>>> 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) ]
[None, None, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

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

>>>from functools import partial
>>> 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) ]
[None, None, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

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

>>> from functools import partial
>>> 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) ]
[None, None, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

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

>>> from inspect import currentframe
>>> from types import FunctionType
>>> def myself (*args, **kw):
...    caller_frame = currentframe(1)
...    code = caller_frame.f_code
...    return FunctionType(code, caller_frame.f_globals)(*args, **kw)
...
>>> 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]


QBasic

Works with: QBasic
Translation of: BASIC256
DECLARE FUNCTION Fibonacci! (num!)

PRINT Fibonacci(20)
PRINT Fibonacci(30)
PRINT Fibonacci(-10)
PRINT Fibonacci(10)
END

FUNCTION Fibonacci (num)
  IF num < 0 THEN
    PRINT "Invalid argument: ";
    Fibonacci = num
  END IF

  IF num < 2 THEN
    Fibonacci = num
  ELSE
    Fibonacci = Fibonacci(num - 1) + Fibonacci(num - 2)
  END IF
END FUNCTION
Output:
Igual que la entrada de BASIC256.


Qi

Use of anonymous recursive functions is not common in Qi. The philosophy of Qi seems to be that using a "silly name" like "foo2" or "foo_helper" makes the code clearer than using anonymous recursive functions.

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

(define fib
  N -> (let A (/. A N
                  (if (< N 2)
                      N
                      (+ (A A (- N 2))
                         (A A (- N 1)))))
         (A A N)))

Quackery

Quackery can do anonymous recursion via the word recurse.

[ dup 0 < iff
  $ "negative argument passed to fibonacci"
  fail
  [ dup  2 < if done
    dup  1 - recurse
    swap 2 - recurse + ] ]         is fibonacci ( n --> n )

recurse causes the current nest (i.e. the on that starts [ dup and ends + ] to be evaluated recursively. This means that if, for example, the first recursive call was inside one or more nested nests, it would not work as desired. So the first instance of recurse in:

( *** faulty code *** )
[ dup 0 < iff
  $ "negative argument passed to fibonacci"
  fail
  [ dup 2 < if done
    [ [ [ [ [ [ 
      [ dup 1 - recurse ]
    ] ] ] ] ] ] 
    swap 2 - recurse + ] ]        is fibonacci (  n --> n )

would cause the nest [ dup 1 - recurse ]to be evaluated, and the program would go into a tailspin, recursively evaluating that nest until the return stack overflowed.

This limitation can be overcome with the understanding that recursion can be factored out into two ideas, i.e. self-reference and evaluation. The self-reference word in Quackery is this, which puts a pointer to the current nest on the data stack (usually just called "the stack") and the evaluation word is do, which takes an item from the stack and evaluates it. So this do is equivalent to recurse.

The final example fixes the previous example by using this and do to put the pointer to the current nest on the stack at the correct level of nesting and evaluate it within the nested nests. See also Even or Odd#Quackery: With Anonymous Mutual recursion.

[ dup 0 < iff
  $ "negative argument passed to fibonacci"
  fail
  [ dup 2 < if done
    this 
    [ [ [ [ [ [ 
      [ dip [ dup 1 - ] do ]
    ] ] ] ] ] ] 
    swap 2 - recurse + ] ]        is fibonacci ( n --> n )

Quackery also provides named recursion with forward and resolves, so this is usually not necessary but can be useful in unusual circumstances.

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.

fib2 <- function(n) {
  (n >= 0) || stop("bad argument")
  ( function(n) if (n <= 1) 1 else Recall(n-1)+Recall(n-2) )(n)
}

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
 
;; Natural -> Natural
;; Calculate factorial
(define (fact n)
  (define (fact-helper n acc)
    (if (= n 0)
        acc
        (fact-helper (sub1 n) (* n acc))))
  (unless (exact-nonnegative-integer? n)
    (raise-argument-error 'fact "natural" n))
  (fact-helper n 1))
 
;; Unit tests, works in v5.3 and newer
(module+ test
  (require rackunit)
  (check-equal? (fact 0) 1)
  (check-equal? (fact 5) 120))

This calculates the slightly more complex Fibonacci funciton:

#lang racket
;; Natural -> Natural
;; Calculate fibonacci
(define (fibb n)
  (define (fibb-helper n fibb_n-1 fibb_n-2)
    (if (= 1 n)
        fibb_n-1
        (fibb-helper (sub1 n) (+ fibb_n-1 fibb_n-2) fibb_n-1)))
  (unless (exact-nonnegative-integer? n)
    (raise-argument-error 'fibb "natural" n))
  (if (zero? n) 0 (fibb-helper n 1 0)))

;; Unit tests, works in v5.3 and newer
(module+ test
  (require rackunit)
  (check-exn exn:fail? (lambda () (fibb -2)))  
  (check-equal?
   (for/list ([i (in-range 21)]) (fibb i))
   '(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)
(define Z
  (λ (f)
    ((λ (x) (f (λ (g) ((x x) g))))
     (λ (x) (f (λ (g) ((x x) g)))))))

(define fibonacci
  (Z (λ (fibo)
       (λ (n)
         (if (<= n 2)
             1
             (+ (fibo (- n 1))
                (fibo (- n 2))))))))
> (fibonacci -2)
1
> (fibonacci 5)
5
> (fibonacci 10)
55

Raku

(formerly Perl 6)

Works with: Rakudo version 2015.12

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:

sub fib($n) {
    die "Naughty fib" if $n < 0;
    return {
        $_ < 2
            ?? $_
            !!  &?BLOCK($_-1) + &?BLOCK($_-2);
    }($n);
}

say fib(10);

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.

constant @fib = 0, 1, *+* ... *;
say @fib[10];

Here the closure, *+*, is just a quick way to write a lambda, -> $a, $b { $a + $b }. 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.

At this point someone may complain that the solution is doesn't fit the specified task because the sequence operator doesn't do the check for negative. True, but the sequence operator is not the whole of the solution; this check is supplied by the subscripting operator itself when you ask for @fib[-1]. Instead of scattering all kinds of arbitrary boundary conditions throughout your functions, the sequence operator maps them quite naturally to the boundary of definedness at the start of a list.

REBOL

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

REXX

[Modeled after the Fortran example.]

Since a hidden named function (instead of an anonymous function) seems to be OK with the implementers, here are the REXX versions.

simplistic

/*REXX program to show anonymous recursion  (of a function or subroutine).              */
numeric digits 1e6                               /*in case the user goes ka-razy with X.*/
parse arg x .                                    /*obtain the optional argument from CL.*/
if x=='' | x==","  then x= 12                    /*Not specified?  Then use the default.*/
w= length(x)                                     /*W:  used for formatting the output.  */
                   do j=0  for x+1               /*use the  argument  as an upper limit.*/
                   say 'fibonacci('right(j, w)") ="   fib(j)
                   end  /*j*/                    /* [↑] show Fibonacci sequence: 0 ──► X*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
fib: procedure; parse arg z;  if z>=0  then return .(z)
                              say "***error***  argument can't be negative.";   exit
.:   procedure; parse arg #;  if #<2  then return #;              return .(#-1)  +  .(#-2)
output   when using the input of:     12
fibonacci( 0) = 0
fibonacci( 1) = 1
fibonacci( 2) = 1
fibonacci( 3) = 2
fibonacci( 4) = 3
fibonacci( 5) = 5
fibonacci( 6) = 8
fibonacci( 7) = 13
fibonacci( 8) = 21
fibonacci( 9) = 34
fibonacci(10) = 55
fibonacci(11) = 89
fibonacci(12) = 144

memoization

Since the above REXX version is   very   slow for larger numbers, the following version was added that incorporates memoization.  
It's many orders of magnitude faster for larger values.

/*REXX program to show anonymous recursion of a function or subroutine with memoization.*/
numeric digits 1e6                               /*in case the user goes ka-razy with X.*/
parse arg x .                                    /*obtain the optional argument from CL.*/
if x=='' | x==","  then x= 12                    /*Not specified?  Then use the default.*/
@.= .;     @.0= 0;      @.1= 1                   /*used to implement memoization for FIB*/
w= length(x)                                     /*W:  used for formatting the output.  */
                   do j=0  for x+1               /*use the  argument  as an upper limit.*/
                   say 'fibonacci('right(j, w)") ="   fib(j)
                   end  /*j*/                    /* [↑] show Fibonacci sequence: 0 ──► X*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
fib: procedure expose @.; arg z;  if z>=0  then return .(z)
                          say "***error***  argument can't be negative.";   exit
.: procedure expose @.; arg #; if @.#\==.  then return @.#;  @.#=.(#-1)+.(#-2); return @.#
output   is identical to the 1st REXX version.



Ring

# Project : Anonymous recursion

t=0
for x = -2 to 12
     n = x
     recursion()
     if x > -1
        see t + nl
     ok
next
 
func recursion()
        nold1=1
        nold2=0
        if n < 0 
           see "positive argument required!" + nl
           return 
        ok
        if n=0
           t=nold2
           return t
        ok
        if n=1
           t=nold1
           return  t
        ok
        while n
                  t=nold2+nold1
                  if n>2
                     n=n-1
                     nold2=nold1
                     nold1=t
                     loop
                  ok
                  return t
        end
        return t

Output:

positive argument required!
positive argument required!
0
1
1
2
3
5
8
13
21
34
55
89
144

RPL

Hidden variable

The recursive part of the function is stored in a local variable, which is made accessible to all the recursive instances by starting its name with the character.

Works with: HP version 48G
≪ ≪ IF DUP 1 > THEN
        DUP 1 - ←fib EVAL 
        SWAP 2 - ←fib EVAL +
     END ≫ → ←fib
   ≪ IF DUP 0 < 
      THEN DROP "Negative value" DOERR
      ELSE ←fib EVAL END
≫ ≫ 'FIBAR' STO
-2 FIBAR
10 FIBAR
Output:
1: 55

Truly anonymous

Both the recursive block and the argument are pushed onto the stack, without any naming. This meets the requirements of the task perfectly and works on any RPL machine, but it is far from idiomatic and uses a lot of stack space.

Works with: HP version 28
IF DUP 0 < 
      THEN DROP "Negative value" 
      ELSEIF DUP 1 > THEN
            DUP2 1 - OVER EVAL 
            ROT ROT 2 - OVER EVAL +
         ELSE SWAP DROP END
      ≫
      SWAP OVER EVAL
      END
≫ 'FIBAR' STO

Ruby

Ruby has no keyword for anonymous recursion.

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

def fib(n)
  raise RangeError, "fib of negative" if n < 0
  (fib2 = proc { |m| m < 2 ? m : fib2[m - 1] + fib2[m - 2] })[n]
end
(-2..12).map { |i| fib i rescue :error }
=> [:error, :error, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]

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.

  • The fib() method has two local variables 'fib2' and 'n'.
  • The block has a local variable 'm' and closes on both 'fib2' and 'n'.

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.

def fib(n)
  raise RangeError, "fib of negative" if n < 0
  (fib2 = proc { |n| n < 2 ? n : fib2[n - 1] + fib2[n - 2] })[n]
end
# Ruby 1.9
(-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 }
=> [:error, :error, 0, 1, 0, -3, -8, -15, -24, -35, -48, -63, -80, -99, -120]

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 fib2[n - 1] changes the value of 'n', and fib2[n - 2] uses the wrong value of 'n', thus the wrong answer.

Ruby with Hash

def fib(n)
  raise RangeError, "fib of negative" if n < 0
  Hash.new { |fib2, m|
    fib2[m] = (m < 2 ? m : fib2[m - 1] + fib2[m - 2]) }[n]
end

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

  • The fib() method has one local variable 'n'.
  • The block has two local variables 'fib2' and 'm', and closes on 'n'.

Ruby with recur/recurse

Translation of: PicoLisp
Library: continuation
require 'continuation' unless defined? Continuation

module Kernel
  module_function

  def recur(*args, &block)
    cont = catch(:recur) { return block[*args] }
    cont[block]
  end

  def recurse(*args)
    block = callcc { |cont| throw(:recur, cont) }
    block[*args]
  end
end

def fib(n)
  raise RangeError, "fib of negative" if n < 0
  recur(n) { |m| m < 2 ? m : (recurse m - 1) + (recurse m - 2) }
end

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

To start, Kernel#recur calls the block once. From inside the block, Kernel#recurse calls the block again. To find the block, recurse() plays a trick. First, Kernel#callcc creates a Continuation. Second, throw(:recur, cont) unwinds the call stack until it finds a matching Kernel#catch(:recur), which returns our Continuation. Third, Kernel#recur uses our Continuation to continue the matching Kernel#callcc, which returns our recursive block.

Ruby with arguments.callee

Translation of: JavaScript
Library: continuation
require 'continuation' unless defined? Continuation

module Kernel
  module_function

  def function(&block)
    f = (proc do |*args|
           (class << args; self; end).class_eval do
             define_method(:callee) { f }
           end
           ret = nil
           cont = catch(:function) { ret = block.call(*args); nil }
           cont[args] if cont
           ret
         end)
  end

  def arguments
    callcc { |cont| throw(:function, cont) }
  end
end

def fib(n)
  raise RangeError, "fib of negative" if n < 0
  function { |m|
    if m < 2
      m
    else
      arguments.callee[m - 1] + arguments.callee[m - 2]
    end
  }[n]
end

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'.

Rust

fn fib(n: i64) -> Option<i64> {
    // A function declared inside another function does not pollute the outer namespace.
    fn actual_fib(n: i64) -> i64 {
        if n < 2 {
            n
        } else {
            actual_fib(n - 1) + actual_fib(n - 2)
        }
    }

    if n < 0 {
        None
    } else {
        Some(actual_fib(n))
    }
}

fn main() {
    println!("Fib(-1) = {:?}", fib(-1));
    println!("Fib(0) = {:?}", fib(0));
    println!("Fib(1) = {:?}", fib(1));
    println!("Fib(2) = {:?}", fib(2));
    println!("Fib(3) = {:?}", fib(3));
    println!("Fib(4) = {:?}", fib(4));
    println!("Fib(5) = {:?}", fib(5));
    println!("Fib(10) = {:?}", fib(10));
}

#[test]
fn test_fib() {
    assert_eq!(fib(0).unwrap(), 0);
    assert_eq!(fib(1).unwrap(), 1);
    assert_eq!(fib(2).unwrap(), 1);
    assert_eq!(fib(3).unwrap(), 2);
    assert_eq!(fib(4).unwrap(), 3);
    assert_eq!(fib(5).unwrap(), 5);
    assert_eq!(fib(10).unwrap(), 55);
}

#[test]
fn test_invalid_argument() {
    assert_eq!(fib(-1), None);
}

Scala

Using a Y-combinator:

def Y[A, B](f: (A ⇒ B) ⇒ (A ⇒ B)): A ⇒ B = f(Y(f))(_)
  
def fib(n: Int): Option[Int] =
  if (n < 0) None
  else Some(Y[Int, Int](f ⇒ i ⇒
    if (i < 2) 1
    else f(i - 1) + f(i - 2))(n))
      
-2 to 5 map (n ⇒ (n, fib(n))) foreach println
Output:
(-2,None)
(-1,None)
(0,Some(1))
(1,Some(1))
(2,Some(2))
(3,Some(3))
(4,Some(5))
(5,Some(8))

Scheme

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

(define (fibonacci n)
  (if (> 0 n)
      "Error: argument must not be negative."
      (let aux ((a 1) (b 0) (count n))
        (if (= count 0)
            b
            (aux (+ a b) a (- count 1))))))

(map fibonacci '(1 2 3 4 5 6 7 8 9 10))
Output:
'(1 1 2 3 5 8 13 21 34 55)

Seed7

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

$ include "seed7_05.s7i";

const func integer: fib (in integer: x) is func
  result
    var integer: fib is 0;
  local
    const func integer: fib1 (in integer: n) is func
      result
        var integer: fib1 is 0;
      begin
        if n < 2 then
          fib1 := n;
        else
          fib1 := fib1(n-2) + fib1(n-1);
        end if;
      end func;
  begin
    if x < 0 then
      raise RANGE_ERROR;
    else
      fib := fib1(x);
    end if;
  end func;

const proc: main is func
  local
    var integer: i is 0;
  begin
    for i range 0 to 4 do
      writeln(fib(i));
    end for;
  end func;
Output:
0
1
1
2
3

Sidef

__FUNC__ refers to the current function.

func fib(n) {
    return NaN if (n < 0)

    func (n) {
        n < 2 ? n
              : (__FUNC__(n-1) + __FUNC__(n-2))
    }(n)
}

__BLOCK__ refers to the current block.

func fib(n) {
    return NaN if (n < 0)

    {|n|
        n < 2 ? n
              : (__BLOCK__(n-1) + __BLOCK__(n-2))
    }(n)
}

Smalltalk

In Smalltalk, things are referred to by a name, so the following may not fully qualify as solutions.
Also: doing things like this is not considered "good style" (give things a good name to make the meaning obvious).

Notice, that none of the two solutions below pollutes any namespace; in (a), the variable introduced is strictly local to the method, in (b) not even a method-local is introduced (so maybe (b) does qualify, after all).

a) Use a funny local name (in this case: "_"). Here the closure is defined as "_", and then evaluated (by sending it a value: message).

myMethodComputingFib:arg
    |_|

    ^ (_ := [:n | n <= 1 
                    ifTrue:[n] 
                    ifFalse:[(_ value:(n - 1))+(_ value:(n - 2))]]
      ) value:arg.

b) Define it in a local scope to not infect the outer scopes.
Here, a separate closure is defined (and evaluated with value), in which fib is defined and evaluated with the argument. This is semantically equivalent to the named let solution of Scheme.

myMethodComputingFib2:arg
    ^ [
        |fib|

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

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.

Sparkling

As a function expression:

function(n, f) {
    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:

spn:1> function(n, f) { return f(n, f); }(10, function(n, f) { return n < 2 ? 1 : f(n - 1, f) + f(n - 2, f); })
= 89

Standard ML

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

fun fix f x = f (fix f) x

fun fib n =
    if n < 0 then raise Fail "Negative"
    else
        fix (fn fib =>
                (fn 0 => 0
                | 1 => 1
                | n => fib (n-1) + fib (n-2))) n

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

fun fib n =
    let
        fun fib 0 = 0
          | fib 1 = 1
          | fib n = fib (n-1) + fib (n-2)
    in
        if n < 0 then
            raise Fail "Negative"
        else
            fib n
    end

In this example the local function has the same name as the outer function. This is fine: the local definition shadows the outer definition, so the line "fib n" will refer to our helper function.

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":

fun fib 0 = 0
  | fib 1 = 1
  | fib n = fib (n-1) + fib (n-2)

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

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|
	if(n >= 0) {
		if(n < 2) { n } { thisFunction.(n-1) + thisFunction.(n-2) }
	}
};
(0..20).collect(f)
)

Swift

With internal named recursive closure
Works with: Swift version 2.x
let fib: Int -> Int = {
  func f(n: Int) -> Int {
    assert(n >= 0, "fib: no negative numbers")
    return n < 2 ? 1 : f(n-1) + f(n-2)
  }
  return f
}()

print(fib(8))
Works with: Swift version 1.x
let fib: Int -> Int = {
  var f: (Int -> Int)!
  f = { n in
    assert(n >= 0, "fib: no negative numbers")
    return n < 2 ? 1 : f(n-1) + f(n-2)
  }
  return f
}()

println(fib(8))
Using Y combinator
struct RecursiveFunc<F> {
  let o : RecursiveFunc<F> -> F
}

func y<A, B>(f: (A -> B) -> A -> B) -> A -> B {
  let r = RecursiveFunc<A -> B> { w in f { w.o(w)($0) } }
  return r.o(r)
}

func fib(n: Int) -> Int {
  assert(n >= 0, "fib: no negative numbers")
  return y {f in {n in n < 2 ? 1 : f(n-1) + f(n-2)}} (n)
}

println(fib(8))

Tailspin

See the actual fibonacci solution Fibonacci_sequence#State_machine

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 apply command.

proc fib n {
    # sanity checks
    if {[incr n 0] < 0} {error "argument may not be negative"}
    apply {x {
	if {$x < 2} {return $x}
	# Extract the lambda term from the stack introspector for brevity
	set f [lindex [info level 0] 1]
	expr {[apply $f [incr x -1]] + [apply $f [incr x -1]]}
    }} $n
}

Demonstrating:

puts [fib 12]
Output:

}

144

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:

proc fib n {
    if {[incr n 0] < 0} {error "argument may not be negative"}
    apply {x {expr {
        $x < 2
          ? $x
          : [apply [lindex [info level 0] 1] [incr x -1]]
            + [apply [lindex [info level 0] 1] [incr x -1]]
    }}} $n
}

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

# Pick the lambda term out of the introspected caller's stack frame
proc tcl::mathfunc::recurse args {apply [lindex [info level -1] 1] {*}$args}
proc fib n {
    if {[incr n 0] < 0} {error "argument may not be negative"}
    apply {x {expr {
        $x < 2 ? $x : recurse([incr x -1]) + recurse([incr x -1])
    }}} $n
}


True BASIC

Translation of: BASIC256
Works with: QBasic
FUNCTION Fibonacci (num)
    IF num < 0 THEN
       PRINT "Invalid argument: ";
       LET Fibonacci = num
    END IF

    IF num < 2 THEN
       LET Fibonacci = num
    ELSE
       LET Fibonacci = Fibonacci(num - 1) + Fibonacci(num - 2)
    END IF
END FUNCTION

PRINT Fibonacci(20)
PRINT Fibonacci(30)
PRINT Fibonacci(-10)
PRINT Fibonacci(10)
END
Output:
Igual que la entrada de BASIC256.


TXR

For the Y combinator approach in TXR, see the Y combinator task.

The following easy transliteration of one of the Common Lisp solutions shows the conceptual and cultural compatibility between TXR Lisp macros and CL macros:

Translation of: Common_Lisp
(defmacro recursive ((. parm-init-pairs) . body)
  (let ((hidden-name (gensym "RECURSIVE-")))
    ^(macrolet ((recurse (. args) ^(,',hidden-name ,*args)))
       (labels ((,hidden-name (,*[mapcar first parm-init-pairs]) ,*body))
         (,hidden-name ,*[mapcar second parm-init-pairs])))))

(defun fib (number)
  (if (< number 0) 
    (error "Error. The number entered: ~a is negative" number)
    (recursive ((n number) (a 0) (b 1))
      (if (= n 0)
        a
        (recurse (- n 1) b (+ a b))))))

(put-line `fib(10) = @(fib 10)`)
(put-line `fib(-1) = @(fib -1)`))
Output:
$ txr anonymous-recursion.txr 
fib(10) = 55
txr: unhandled exception of type error:
txr: possibly triggered by anonymous-recursion.txr:9
txr: Error. The number entered: -1 is negative
Aborted (core dumped)

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.

fib() {
  if test 0 -gt "$1"; then
    echo "fib: fib of negative" 1>&2
    return 1
  else
    (
      fib2() {
        if test 2 -gt "$1"; then
          echo "$1"
        else
          echo $(( $(fib2 $(($1 - 1)) ) + $(fib2 $(($1 - 2)) ) ))
        fi
      }
      fib2 "$1"
    )
  fi
}
$ for i in -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12; do
>   fib $i
> done
fib: fib of negative
fib: fib of negative
0
1
1
2
3
5
8
13
21
34
55
89
144

Ursala

#import nat

fib =

~&izZB?(                    # test the sign bit of the argument
   <'fib of negative'>!%,   # throw an exception if it's negative
   {0,1}^?<a(               # test the argument to a recursively defined function
      ~&a,                  # if the argument was a member of {0,1}, return it
      sum^|W(               # otherwise return the sum of two recursive calls
         ~&,                # to the function thus defined
         predecessor^~(     # with the respective predecessors of
            ~&,             # the given argument
            predecessor)))) # and the predecessor thereof

Anonymous recursion is often achieved using the recursive conditional operator, ( _ )^?( _ , _ ), 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 ^?< 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.

The recursive conditional operator ^? differs from the ordinary conditional ? seen at the outermost level by arranging for its predicate and component functions to be given an input of the form   where   is the original argument, and   is a copy of the whole function. Code within the function body may then access itself anonymously according to all the usual language idioms pertaining to deconstruction of tuples, and call itself by any of several recursion combinators, such as the pairwise recursion form W seen above.

UTFool

Solution with anonymous class

···
http://rosettacode.org/wiki/Anonymous_recursion
···
⟦import java.util.function.UnaryOperator;⟧

■ AnonymousRecursion
  § static
    ▶ main
    • args⦂ String[]
      if 0 > Integer.valueOf args[0]
         System.out.println "negative argument"
      else
         System.out.println *UnaryOperator⟨Integer⟩° ■
           ▶ apply⦂ Integer
           • n⦂ Integer
             ⏎ n ≤ 1 ? n ! (apply n - 1) + (apply n - 2)
         °.apply Integer.valueOf args[0]

VBA

Sub Main()
Debug.Print F(-10)
Debug.Print F(10)
End Sub

Private Function F(N As Long) As Variant
    If N < 0 Then
        F = "Error. Negative argument"
    ElseIf N <= 1 Then
        F = N
    Else
        F = F(N - 1) + F(N - 2)
    End If
End Function
Output:
Error. Negative argument
 55

Wart

def (fib n)
  if (n >= 0)
    (transform n :thru (afn (n)
                         (if (n < 2)
                           n
                           (+ (self n-1)
                              (self n-2)))))

afn creates an anonymous function that can be recursed by calling self.

WDTE

let str => 'strings';

let fib n => switch n {
  < 0 => str.format 'Bad argument: {q}' n;
  default => n -> (@ memo s n => switch n {
    == 0 => 0; == 1 => 1;
    default => + (s (- n 1)) (s (- n 2));
  });
};

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

Wren

class Fibonacci {
    static compute(n) {
        var fib
        fib = Fn.new {|n|
            if (n < 2) return n
            return fib.call(n - 1) + fib.call(n - 2)
        }

        if (n < 0) return null
        return fib.call(n)
    }
}

System.print(Fibonacci.compute(36))
Output:
14930352

x86 Assembly

Works with: NASM
Works with: Linux

32 bit

Fakes the actual first call to the function that generates Fibonacci numbers. 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)
; Build:
;   nasm -felf32 fib.asm
;   ld -m elf32_i386 fib.o -o fib

global  _start
section .text

_start:
    mov ecx, 48         ; Initialize loop counter
.loop:
    mov ebx, 48         ; Calculate which Fn will be computed
    sub ebx, ecx        ; Takes into account the reversed nature
    push    ebx         ; Pass the parameter in on the stack
    push    .done       ; Emulate a call but "return" to end of loop
                        ; The return adress is manually set on the stack
; int fib (int n)
; Returns the n'th Fn
; fib(n) =  0                   if n <= 0
;           1                   if n == 1
;           fib(n-1) + fib(n-2) otherwise
.fib:
    push    ebp         ; Setup stack frame
    mov ebp, esp
    push    ebx         ; Save needed registers

    xor eax, eax
    mov ebx, [ebp + 8]  ; Get the parameter
    cmp ebx, 1          ; Test for base cases
    jl  .return
    mov eax, 1
    je  .return
    dec ebx             ; Calculate fib(n-1)
    push    ebx
    call    .fib
    mov [esp], eax      ; Save result on top of parameter in stack
    dec ebx             ; Calculate fib(n-2)
    push    ebx
    call    .fib
    add eax, [esp + 4]  ; Add the first to the second
    add esp, 8          ; Reset local stack
.return:
    pop ebx             ; Restore modified registers
    mov esp, ebp        ; Tear down stack frame and return
    pop ebp
    ret
.done:
    mov [esp], ecx      ; Save the counter between calls
    push    eax         ; Print the number
    call    print_num
    add esp, 4
    pop ecx             ; Restore the loop counter
    loop    .loop       ; Loop until 0

    mov eax, 0x01       ; sys_exit(int error)
    xor ebx, ebx        ; error = 0 (success)
    int 0x80            ; syscall

; void print_num (int n)
; Prints an integer and newline
print_num:
    push    ebp
    mov ebp, esp
    sub esp, 11         ; Save space for digits and newline

    lea ecx, [ebp - 1]  ; Save a pointer to after the buffer
    mov BYTE [ecx], 0x0A    ; Set the newline at the end
    mov eax, [ebp + 8]  ; Get the parameter
    mov ebx, DWORD 10   ; Divisor
.loop:
    dec ecx             ; Move pointer to next digit
    xor edx, edx
    div ebx             ; Extract one digit, quot in eax, rem in edx
    add dl, 0x30        ; Convert remainder to ascii
    mov [ecx], dl       ; Save the ascii form
    cmp eax, 0          ; Loop until all digits have been converted
    jg  .loop

    mov eax, 0x04       ; sys_write(int fd, char **buf, int len)
    mov ebx, 1          ; stdout
    mov edx, ebp        ; Calculate the length
    sub edx, ecx        ; address after newline - address of first digit
    int 0x80

    mov esp, ebp
    pop ebp
    ret

XPL0

In XPL0 you can nest functions/procedures inside other functions/procedures up to eight levels deep. This makes those nested functions invisible to the outside, thus preventing namespace pollution.

include c:\cxpl\codes;

func Fib(X);
int X;
        func ActualFib(N);
        int N;
        [if N<2 then return N
        else return ActualFib(N-1) + ActualFib(N-2);
        ]; \ActualFib;

[if X<0 then [Text(0, "Error "); return 0]
else return ActualFib(X);
]; \Fib;

[IntOut(0, Fib(8));  CrLf(0);
 IntOut(0, Fib(-2)); CrLf(0);
]
Output:
21
Error 0

Yabasic

Translation of: AutoIt
print Fibonacci(-10)
print Fibonacci(10)

 
sub Fibonacci(number)
 
    If number < 0 print "Invalid argument: "; : return number
 
    If number < 2 Then
        Return number
    Else
        Return Fibonacci(number - 1) + Fibonacci(number - 2)
    EndIf
 
end sub

zkl

fcn fib(n){
   if (n<0) throw(Exception.ValueError);
   fcn(n){
      if (n < 2) return(1);
      else       return(self.fcn(n-1) + self.fcn(n-2));
   }(n);
}
fib(8) .println();
fib(-8).println();
Output:
34
ValueError thrown

ZX Spectrum Basic

Translation of: AutoHotkey
10 INPUT "Enter a number: ";n
20 LET t=0
30 GO SUB 60
40 PRINT t
50 STOP 
60 LET nold1=1: LET nold2=0
70 IF n<0 THEN PRINT "Positive argument required!": RETURN 
80 IF n=0 THEN LET t=nold2: RETURN 
90 IF n=1 THEN LET t=nold1: RETURN 
100 LET t=nold2+nold1
110 IF n>2 THEN LET n=n-1: LET nold2=nold1: LET nold1=t: GO SUB 100
120 RETURN