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Ingy döt Net 2023-07-01 11:58:00 -04:00
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---
from: http://rosettacode.org/wiki/Anonymous_recursion
note: Recursion

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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), 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.
<br><br>

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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' )

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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;

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

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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;

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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}

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------------ 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

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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
]

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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
}

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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

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#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);
}

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)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)

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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

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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)

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{
(𝕩<2)+´𝕊¨,𝕏𝕩-12
}¨10

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0 1 1 2 3 5 8 13 21 34

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{Fact 𝕩:
(𝕩<2)+´Fact¨,𝕏𝕩-12
}¨10

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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)

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( (
=
. !arg:#:~<0
& ( (=.!arg$!arg)
$ (
=
.
' (
. !arg:<2
| (($arg)$($arg))$(!arg+-2)
+ (($arg)$($arg))$(!arg+-1)
)
)
)
$ !arg
)
$ 30
)

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

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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);
}
}

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#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);
}

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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);
}
}

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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);
}

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#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;
}

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#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;
}

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

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(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)))))

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# 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)

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

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(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))

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(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))))

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(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))))))

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(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))))))

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(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))))))

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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;
}

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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));
}

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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.

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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

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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))

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

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

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fix f = f (& fix f)

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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()
}

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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)

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-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 ).

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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)

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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)

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

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#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

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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 ) ;

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@ -0,0 +1,25 @@
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

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@ -0,0 +1,7 @@
: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, ] ;

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@ -0,0 +1,5 @@
( xt from :noname in the previous example )
variable pocket pocket !
: fib ( +n -- n' )
dup 0< abort" Negative numbers don't exist."
[ pocket @ compile, ] ;

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@ -0,0 +1,3 @@
: fib ( +n -- )
dup 0< abort" Negative numbers don't exist"
[: dup 2 < ?exit 1- dup MYSELF swap 1- MYSELF + ;] execute . ;

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@ -0,0 +1,18 @@
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

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@ -0,0 +1,42 @@
' 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

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@ -0,0 +1,45 @@
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)
})
})
}

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@ -0,0 +1,34 @@
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)
}
}
}

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@ -0,0 +1,4 @@
def fib = {
assert it > -1
{i -> i < 2 ? i : {j -> owner.call(j)}(i-1) + {k -> owner.call(k)}(i-2)}(it)
}

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@ -0,0 +1,9 @@
def fib0to20 = (0..20).collect(fib)
println fib0to20
try {
println fib(-25)
} catch (Throwable e) {
println "KABOOM!!"
println e.message
}

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@ -0,0 +1,7 @@
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)

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@ -0,0 +1,6 @@
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

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@ -0,0 +1,2 @@
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]

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@ -0,0 +1,23 @@
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]
_ -> []

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@ -0,0 +1,16 @@
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
190 LET FIB=0
200 CASE 1
210 LET FIB=1
220 CASE ELSE
230 LET FIB=FIB(K-1)+FIB(K-2)
240 END SELECT
250 END DEF

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@ -0,0 +1,24 @@
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

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@ -0,0 +1,9 @@
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

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@ -0,0 +1,7 @@
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)
)

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

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@ -0,0 +1,4 @@
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

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@ -0,0 +1 @@
basis ` ($: @: g) @. test

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@ -0,0 +1 @@
basis @: (g^:test^:_)

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@ -0,0 +1,10 @@
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);
}

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@ -0,0 +1,25 @@
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);
}
}

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@ -0,0 +1,7 @@
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);
}

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@ -0,0 +1,7 @@
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);
}

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@ -0,0 +1 @@
fib == [small] [] [pred dup pred] [+] binrec;

View file

@ -0,0 +1 @@
0 | recurse(. + 1)

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@ -0,0 +1,8 @@
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 ;

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@ -0,0 +1,7 @@
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

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

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

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@ -0,0 +1,4 @@
fib'!10
0 1 1 2 3 5 8 13 21 34
fib -1
"Error Negative Number"

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@ -0,0 +1,22 @@
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

View file

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

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@ -0,0 +1,11 @@
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()
}

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@ -0,0 +1,32 @@
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

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@ -0,0 +1,31 @@
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

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@ -0,0 +1,15 @@
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)
}

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@ -0,0 +1,12 @@
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

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@ -0,0 +1,2 @@
put fib(10)
-- 55

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@ -0,0 +1,7 @@
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)

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@ -0,0 +1,4 @@
return setmetatable({1,1},{__index = function(self, n)
self[n] = self[n-1] + self[n-2]
return self[n]
end})

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@ -0,0 +1,6 @@
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

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@ -0,0 +1,11 @@
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

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@ -0,0 +1,23 @@
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

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@ -0,0 +1,24 @@
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

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@ -0,0 +1,11 @@
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

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