Anonymous recursion

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

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

This is usually the case when directly calling the current function would waste too many resources (stack space, execution time), cause 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 a quite some disadvantages:

  • You have to think up a name, which then pollutes the namespace
  • A 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.

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.

Contents

[edit] 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;

[edit] 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
}

[edit] 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)

[edit] 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

[edit] Bracmat

[edit] 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

[edit] 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

[edit] C

Using scoped function fib_i inside fib, with GCC:

#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

[edit] 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 actual_fib
{
double operator()(double n)
{
if(n < 2)
{
return n;
}
else
{
return (*this)(n-1) + (*this)(n-2);
}
}
};
 
return actual_fib()(n);
}
}

[edit] 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);
}
 

[edit] 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

[edit] 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)
 

[edit] Common Lisp

[edit] 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))

[edit] 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.

[edit] 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))))))

[edit] D

int fib(int arg) pure @nogc {
assert(arg >= 0);
 
return function int (int n) pure nothrow @nogc {
auto self = __traits(parent, {});
return (n < 2) ? n : self(n - 1) + self(n - 2);
}(arg);
}
 
void main() {
import std.stdio;
 
39.fib.writeln;
}
Output:
63245986

[edit] 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.

[edit] Déjà Vu

[edit] 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

[edit] 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.

[edit] 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
 

[edit] 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)

[edit] Elena

#define system.
 
#symbol fibo = (:n)
[
n < 0
 ? [ #throw InvalidArgumentException new:"Must be non negative". ].
 
^ { eval:n [ ^ (n > 1) ? [ ($self:(n - 2)) + ($self:(n - 1)) ] ! [ n ]. ] }:n.
].
 
#symbol program =
[
control forrange &int:-1 &int:10 &do: (&int:i)
[
console << "fib(" << i << ")=".
 
console writeLine:(fibo:i) | if &InvalidArgumentError: e
[
console writeLine:"invalid".
].
].
 
console readChar.
].

[edit] 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 ).
 
 

[edit] 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]

[edit] 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...

[edit] 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.

[edit] 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)

[edit] 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 . ;

[edit] 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

[edit] Go

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 f(func(a1, a2, a3 int) int {
return x(x)(a1, a2, a3)
})
}(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

[edit] 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

[edit] 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]

[edit] 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.

[edit] 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.

[edit] 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);
}
}

[edit] JavaScript

function fibo(n) {
if (n < 0)
throw "Argument cannot be negative";
else
return (function(n) {
if (n < 2)
return 1;
else
return 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";
else
return (function fib(n) {
if (n < 2)
return 1;
else
return fib(n-1) + fib(n-2);
})(n);
}

[edit] jq

As is the case, for example, with Julia, jq allows you to define an inner/nested function (here, aux) that is only defined within the surrounding function fib scope. Thus using such auxiliary functions does not cause name space pollution.

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 ;

[edit] 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

[edit] K

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

Examples:

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

[edit] 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

[edit] 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})

[edit] 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.

[edit] Mathematica

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}

[edit] 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)}
}
}
}

[edit] Nimrod

# Using scoped function fibI inside fib
proc fib(x): int =
proc fibI(n): int =
if n < 2: n else: fibI(n-2) + fibI(n-1)
if x < 0:
raise newException(EInvalidValue, "Invalid argument")
return fibI(x)
 
for i in 0..4:
echo fib(i)
 
# fibI(10) # undeclared identifier 'fibI'

Output:

0
1
1
2
3

[edit] 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;
}

[edit] 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

[edit] 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
 
 

[edit] PARI/GP

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)
};

[edit] Perl

Translation of: PicoLisp

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

sub recur (&@) {
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);
}

[edit] 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

[edit] Perl 6

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 Perl 6 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.

[edit] PHP

Don't know if this counts, but...

<?php
function fib($n) {
if ($n < 0)
throw new Exception('Negative numbers not allowed');
else if ($n < 2)
return 1;
else {
$f = __FUNCTION__;
return $f($n-1) + $f($n-2);
}
}
echo fib(8), "\n";
?>

However, __FUNCTION__ won't work for anonymous functions created with create_function() or closures in PHP 5.3+.

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";
?>

[edit] 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'.

[edit] 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}.

[edit] 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).

[edit] 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 )
 

[edit] 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)))
 

[edit] 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)
}

[edit] 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

[edit] REXX

[Modeled after the Fortran example.]

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

/*REXX program to show anonymous recursion  (of a function/subroutine). */
numeric digits 1e6 /*in case the user goes kaa-razy.*/
 
do j=0 to word(arg(1) 12, 1) /*use argument or the default: 12*/
say 'fibonacci('j") =" fib(j) /*show Fibonacci sequence: 0──►x */
end /*j*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────subroutines─────────────────────────*/
fib: procedure; if arg(1)>=0 then return .(arg(1))
say "***error!*** argument can't be negative."; exit
.:procedure; arg _; if _<2 then return _; return .(_-1)+.(_-2)

output when using the default input ( 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

[edit] 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.

[edit] 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.

[edit] 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'.

[edit] 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.

[edit] 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'.

[edit] 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))

[edit] 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)

[edit] 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

[edit] Sidef

__FUNC__ refers to the current function.

{ |i|
func (n) {
if (n < 0) { return };
n < 2 ? n
 : (__FUNC__(n-2) + __FUNC__(n-1));
}(i).to_s.say;
} * 10;

__BLOCK__ refers to the current block.

{ |i|
{ |n|
if (n < 0) { return };
n < 2 ? n
 : (__BLOCK__(n-2) + __BLOCK__(n-1));
}(i).to_s.say;
} * 10;

[edit] 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

[edit] 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

[edit] Swift

With internal named recursive closure
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))

[edit] 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
}

[edit] 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
@(do
(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)

[edit] 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

[edit] 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 (f,a) where a is the original argument, and f 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.

[edit] 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.

[edit] 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

[edit] 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
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