# Mutual recursion

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

Two functions are said to be mutually recursive if the first calls the second, and in turn the second calls the first.

Write two mutually recursive functions that compute members of the Hofstadter Female and Male sequences defined as:

\begin{align} F(0)&=1\ ;\ M(0)=0 \\ F(n)&=n-M(F(n-1)), \quad n>0 \\ M(n)&=n-F(M(n-1)), \quad n>0. \end{align}

(If a language does not allow for a solution using mutually recursive functions then state this rather than give a solution by other means).

## ACL2

(mutual-recursion (defun f (n)    (declare (xargs :mode :program))    (if (zp n)        1        (- n (m (f (1- n))))))  (defun m (n)    (declare (xargs :mode :program))    (if (zp n)        0        (- n (f (m (1- n)))))))

with Ada.Text_Io; use Ada.Text_Io; procedure Mutual_Recursion is   function M(N : Integer) return Integer;   function F(N : Integer) return Integer is   begin      if N = 0 then         return 1;      else         return N - M(F(N - 1));      end if;   end F;   function M(N : Integer) return Integer is   begin      if N = 0 then         return 0;      else         return N - F(M(N-1));      end if;   end M;begin   for I in 0..19 loop      Put_Line(Integer'Image(F(I)));   end loop;   New_Line;   for I in 0..19 loop      Put_Line(Integer'Image(M(I)));   end loop;end Mutual_recursion;

with Ada.Text_Io; use Ada.Text_Io;procedure Mutual_Recursion is   function M(N: Natural) return Natural;   function F(N: Natural) return Natural;    function M(N: Natural) return Natural is       (if N = 0 then 0 else N – F(M(N–1)));    function F(N: Natural) return Natural is       (if N =0 then 1 else N – M(F(N–1)));begin   for I in 0..19 loop      Put_Line(Integer'Image(F(I)));   end loop;   New_Line;   for I in 0..19 loop      Put_Line(Integer'Image(M(I)));   end loop; end Mutual_recursion;

## Aime

Translation of: C
integer F(integer n);integer M(integer n); integer F(integer n){    integer r;    if (n) {	r = n - M(F(n - 1));    } else {	r = 1;    }    return r;} integer M(integer n){    integer r;    if (n) {	r = n - F(M(n - 1));    } else {	r = 0;    }    return r;} integer main(void){    integer i;    i = 0;    while (i < 20) {	o_winteger(3, F(i));	i += 1;    }    o_byte('\n');    i = 0;    while (i < 20) {	o_winteger(3, M(i));	i += 1;    }    o_byte('\n');    return 0;}

## ALGOL 68

Translation of: C
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386
PROC (INT)INT m; # ONLY required for ELLA ALGOL 68RS - an official subset OF full ALGOL 68 # PROC f = (INT n)INT:  IF n = 0 THEN 1  ELSE n - m(f(n-1)) FI; m := (INT n)INT:  IF n = 0 THEN 0  ELSE n - f(m(n-1)) FI; main:(  FOR i FROM 0 TO 19 DO    print(whole(f(i),-3))  OD;  new line(stand out);  FOR i FROM 0 TO 19 DO    print(whole(m(i),-3))  OD;  new line(stand out))

Output:

  1  1  2  2  3  3  4  5  5  6  6  7  8  8  9  9 10 11 11 12
0  0  1  2  2  3  4  4  5  6  6  7  7  8  9  9 10 11 11 12


## AutoHotkey

Loop 20   i := A_Index-1, t .= "n" i "t   " M(i) "t     " F(i)MsgBox xtmaletfemalen%t% F(n) {   Return n ? n - M(F(n-1)) : 1} M(n) {   Return n ? n - F(M(n-1)) : 0}
Translation of: C

This one is an alternative to the above.

main()Return F(n){  If (n == 0)     Return 1  Else    Return n - M(F(n-1))} M(n){  If (n == 0)    Return 0  Else    Return n - F(M(n-1)) ;} main(){  i = 0  While, i < 20  {    male .= M(i) . "n"     female .= F(i) . "n"    i++  }  MsgBox % "male:n" . male  MsgBox % "female:n" . female}

## AWK

In AWK it is enough that both functions are defined somewhere. It matters not whether the BEGIN block is before or after the function definitions.

function F(n){  if ( n == 0 ) return 1;  return n - M(F(n-1))} function M(n){  if ( n == 0 ) return 0;  return n - F(M(n-1))} BEGIN {  for(i=0; i < 20; i++) {    printf "%3d ", F(i)  }  print ""  for(i=0; i < 20; i++) {    printf "%3d ", M(i)  }  print ""}

## BASIC

Works with: QBasic
DECLARE FUNCTION f! (n!)DECLARE FUNCTION m! (n!) FUNCTION f! (n!)    IF n = 0 THEN        f = 1    ELSE        f = m(f(n - 1))    END IFEND FUNCTION FUNCTION m! (n!)    IF n = 0 THEN        m = 0    ELSE        m = f(m(n - 1))    END IFEND FUNCTION

## BBC BASIC

      @% = 3 : REM Column width      PRINT "F sequence:"      FOR i% = 0 TO 20        PRINT FNf(i%) ;      NEXT      PRINT      PRINT "M sequence:"      FOR i% = 0 TO 20        PRINT FNm(i%) ;      NEXT      PRINT      END       DEF FNf(n%) IF n% = 0 THEN = 1 ELSE = n% - FNm(FNf(n% - 1))       DEF FNm(n%) IF n% = 0 THEN = 0 ELSE = n% - FNf(FNm(n% - 1))

Output:

F sequence:
1  1  2  2  3  3  4  5  5  6  6  7  8  8  9  9 10 11 11 12 13
M sequence:
0  0  1  2  2  3  4  4  5  6  6  7  7  8  9  9 10 11 11 12 12


## Bc

define f(n) {  if ( n == 0 ) return(1);  return(n - m(f(n-1)));} define m(n) {  if ( n == 0 ) return(0);  return(n - f(m(n-1)));}
Works with: GNU bc
Works with: OpenBSD bc

POSIX bc doesn't have the print statement.

/* GNU bc */for(i=0; i < 19; i++) {  print f(i); print " ";}print "\n";for(i=0; i < 19; i++) {  print m(i); print " ";}print "\n";

## Bracmat

 (F=.!arg:0&1|!arg+-1*M$(F$(!arg+-1))); (M=.!arg:0&0|!arg+-1*F$(M$(!arg+-1)));  -1:?n&whl'(!n+1:~>20:?n&put$(F$!n " "))&put$\n 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 -1:?n&whl'(!n+1:~>20:?n&put$(M$!n " "))&put$\n 0  0  1  2  2  3  4  4  5  6  6  7  7  8  9  9  10  11  11  12  12

## Brat

female = null #yes, this is necessary male = { n |  true? n == 0    { 0 }    { n - female male(n - 1) }} female = { n |  true? n == 0    { 1 }    { n - male female(n - 1 ) }} p 0.to(20).map! { n | female n }p 0.to(20).map! { n | male n }

## C

To let C see functions that will be used, it is enough to declare them. Normally this is done in a header file; in this example we do it directly in the code. If we do not declare them explicitly, they get an implicit declaration (if implicit declaration matches the use, everything's fine; but it is better however to write an explicit declaration)

#include <stdio.h>#include <stdlib.h> /* let us declare our functions; indeed here we need   really only M declaration, so that F can "see" it   and the compiler won't complain with a warning */int F(const int n);int M(const int n); int F(const int n){  return (n == 0) ? 1 : n - M(F(n - 1));} int M(const int n){  return (n == 0) ? 0 : n - F(M(n - 1));} int main(void){  int i;  for (i = 0; i < 20; i++)    printf("%2d ", F(i));  printf("\n");  for (i = 0; i < 20; i++)    printf("%2d ", M(i));  printf("\n");  return EXIT_SUCCESS;}

## C++

C++ has prior declaration rules similar to those stated above for C, if we would use two functions. Instead here we define M and F as static (class) methods of a class, and specify the bodies inline in the declaration of the class. Inlined methods in the class can still call other methods or access fields in the class, no matter what order they are declared in, without any additional pre-declaration. This is possible because all the possible methods and fields are declared somewhere in the class declaration, which is known the first time the class declaration is parsed.

#include <iostream>#include <vector>#include <iterator> class Hofstadter{public:  static int F(int n) {    if ( n == 0 ) return 1;    return n - M(F(n-1));  }  static int M(int n) {    if ( n == 0 ) return 0;    return n - F(M(n-1));  }}; using namespace std; int main(){  int i;  vector<int> ra, rb;   for(i=0; i < 20; i++) {    ra.push_back(Hofstadter::F(i));    rb.push_back(Hofstadter::M(i));  }  copy(ra.begin(), ra.end(),       ostream_iterator<int>(cout, " "));  cout << endl;  copy(rb.begin(), rb.end(),       ostream_iterator<int>(cout, " "));  cout << endl;  return 0;}

The following version shows better what's going on and why we seemingly didn't need pre-declaration (like C) when "encapsulating" the functions as static (class) methods.

This version is equivalent to the above but does not inline the definition of the methods into the definition of the class. Here the method declarations in the class definition serves as the "pre-declaration" for the methods, as in C.

class Hofstadter{public:  static int F(int n);  static int M(int n);}; int Hofstadter::F(int n){  if ( n == 0 ) return 1;  return n - M(F(n-1));} int Hofstadter::M(int n){  if ( n == 0 ) return 0;  return n - F(M(n-1));}

## C#

namespace RosettaCode {    class Hofstadter {        static public int F(int n) {            int result = 1;            if (n > 0) {                result = n - M(F(n-1));            }             return result;        }         static public int M(int n) {            int result = 0;            if (n > 0) {                result = n - F(M(n - 1));            }             return result;        }    }}

## Clojure

(declare F) ; forward reference  (defn M [n]  (if (zero? n)    0    (- n (F (M (dec n)))))) (defn F [n]  (if (zero? n)    1    (- n (M (F (dec n))))))

## CoffeeScript

 F = (n) ->  if n is 0 then 1 else n - M F n - 1 M = (n) ->  if n is 0 then 0 else n - F M n - 1 console.log [0...20].map Fconsole.log [0...20].map M

output

 > coffee mutual_recurse.coffee [ 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12 ][ 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12 ]

## Common Lisp

(defun m (n)    (if (zerop n)        0        (- n (f (m (- n 1)))))) (defun f (n)    (if (zerop n)        1        (- n (m (f (- n 1))))))

## D

import std.stdio, std.algorithm, std.range; int male(in int n) pure nothrow {    return n ? n - male(n - 1).female : 0;} int female(in int n) pure nothrow {    return n ? n - female(n - 1).male : 1;} void main() {    20.iota.map!female.writeln;    20.iota.map!male.writeln;}
Output:
[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12]
[0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]

## Déjà Vu

F n:	if n:		- n M F -- n	else:		1 M n:	if n:		- n F M -- n	else:		0 for i range 0 10:	!.( M i F i )
Output:
0 1
0 1
1 2
2 2
2 3
3 3
4 4
4 5
5 5
6 6
6 6 

## Dart

int M(int n) => n==0?1:n-F(M(n-1));int F(int n) => n==0?0:n-M(F(n-1)); main() {  String f="",m="";  for(int i=0;i<20;i++) {    m+="${M(i)} "; f+="${F(i)} ";  }  print("M: $m"); print("F:$f");}

## Delphi

 unit Hofstadter; interface type  THofstadterFemaleMaleSequences = class  public    class function F(n: Integer): Integer;    class function M(n: Integer): Integer;  end; implementation class function THofstadterFemaleMaleSequences.F(n: Integer): Integer;begin  Result:= 1;  if (n > 0) then    Result:= n - M(F(n-1));end; class function THofstadterFemaleMaleSequences.M(n: Integer): Integer;begin  Result:= 0;  if (n > 0) then    Result:= n - F(M(n - 1));end; end.

## E

In E, nouns (variable names) always refer to preceding definitions, so to have mutual recursion, either one must be forward-declared or we must use a recursive def construct. Either one of these is syntactic sugar for first binding the noun to an E promise (a reference with an undetermined target), then resolving the promise to the value.

Recursive def:

def [F, M] := [  fn n { if (n <=> 0) { 1 } else { n - M(F(n - 1)) } },  fn n { if (n <=> 0) { 0 } else { n - F(M(n - 1)) } },]

Forward declaration:

def Mdef  F(n) { return if (n <=> 0) { 1 } else { n - M(F(n - 1)) } }bind M(n) { return if (n <=> 0) { 0 } else { n - F(M(n - 1)) } }

def M binds M to a promise, and stashes the resolver for that promise where bind can get to it. When def F... is executed, the function F closes over the promise which is the value of M. bind M... uses the resolver to resolve M to the provided definition. The recursive def operates similarly, except that it constructs promises for every variable on the left side ([F, M]), executes the right side ([fn ..., fn ...]) and collects the values, then resolves each promise to its corresponding value.

But you don't have to worry about that to use it.

## Erlang

-module(mutrec).-export([mutrec/0, f/1, m/1]). f(0) -> 1;f(N) -> N - m(f(N-1)). m(0) -> 0;m(N) -> N - f(m(N-1)). mutrec() -> lists:map(fun(X) -> io:format("~w ", [f(X)]) end, lists:seq(0,19)),	    io:format("~n", []),	    lists:map(fun(X) -> io:format("~w ", [m(X)]) end, lists:seq(0,19)),	    io:format("~n", []).

## Euphoria

integer idM, idF function F(integer n)    if n = 0 then        return 1    else        return n - call_func(idM,{F(n-1)})    end ifend function idF = routine_id("F") function M(integer n)    if n = 0 then        return 0    else        return n - call_func(idF,{M(n-1)})    end ifend function idM = routine_id("M")

## F#

let rec f n =    match n with    | 0 -> 1    | _ -> n - (m (f (n-1)))and m n =    match n with    | 0 -> 0    | _ -> n - (f (m (n-1)))

Like OCaml, the let rec f .. and m ... construct indicates that the functions call themselves (rec) and each other (and).

## Factor

In Factor, if you need a word before it's defined, you have to DEFER: it.

DEFER: F: M ( n -- n' ) dup 0 = [ dup 1 - M F - ] unless ;: F ( n -- n' ) dup 0 = [ drop 1 ] [ dup 1 - F M - ] if ;

## Mathematica

Without caching:

f[0]:=1m[0]:=0f[n_]:=n-m[f[n-1]]m[n_]:=n-f[m[n-1]]

With caching:

f[0]:=1m[0]:=0f[n_]:=f[n]=n-m[f[n-1]]m[n_]:=m[n]=n-f[m[n-1]]

Example finding f(1) to f(30) and m(1) to m(30):

m /@ Range[30] f /@ Range[30]

gives back:

{0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12,12,13,14,14,15,16,16,17,17,18,19}{1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12,13,13,14,14,15,16,16,17,17,18,19}

## MATLAB

female.m:

function Fn = female(n)     if n == 0        Fn = 1;        return    end     Fn = n - male(female(n-1));end

male.m:

function Mn = male(n)     if n == 0        Mn = 0;        return    end     Mn = n - female(male(n-1));end

Sample Output:

>> n = (0:10);>> arrayfun(@female,n) ans =      1     1     2     2     3     3     4     5     5     6     6 >> arrayfun(@male,n) ans =      0     0     1     2     2     3     4     4     5     6     6

## Maxima

f[0]: 1$m[0]: 0$f[n] := n - m[f[n - 1]]$m[n] := n - f[m[n - 1]]$ makelist(f[i], i, 0, 10);[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6] makelist(m[i], i, 0, 10);[0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6] remarray(m, f)$f(n) := if n = 0 then 1 else n - m(f(n - 1))$m(n) := if n = 0 then 0 else n - f(m(n - 1))$makelist(f(i), i, 0, 10);[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6] makelist(m(i), i, 0, 10);[0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6] remfunction(f, m)$

## Mercury

 :- module mutual_recursion.:- interface. :- import_module io.:- pred main(io::di, io::uo) is det. :- implementation.:- import_module int, list. main(!IO) :-   io.write(list.map(f, 0..19), !IO), io.nl(!IO),   io.write(list.map(m, 0..19), !IO), io.nl(!IO). :- func f(int) = int. f(N) = ( if N = 0 then 1 else N - m(f(N - 1)) ). :- func m(int) = int. m(N) = ( if N = 0 then 0 else N - f(m(N - 1)) ).

## MMIX

	LOC	Data_Segment 	GREG	@NL	BYTE	#a,0	GREG	@buf	OCTA	0,0 t	IS	$128Ja IS$127 	LOC #1000 	GREG @// print 2 digits integer with trailing space to StdOut// reg $3 contains int to be printedbp IS$710H	GREG	#0000000000203020 prtInt	STO	0B,buf		% initialize buffer	LDA	bp,buf+7	% points after LSD 				% REPEAT1H	SUB	bp,bp,1		%  move buffer pointer	DIV	$3,$3,10		%  divmod (x,10)	GET	t,rR		%  get remainder	INCL	t,'0'		%  make char digit	STB	t,bp		%  store digit	PBNZ	$3,1B % UNTIL no more digits LDA$255,bp	TRAP	0,Fputs,StdOut	% print integer	GO	Ja,Ja,0		% 'return'// Female functionF	GET	$1,rJ % save return addr PBNZ$0,1F		% if N != 0 then F N 	INCL	$0,1 % F 0 = 1 PUT rJ,$1		% restore return addr	POP	1,0		% return 11H	SUBU	$3,$0,1		% N1 = N - 1	PUSHJ	$2,F % do F (N - 1) ADDU$3,$2,0 % place result in arg. reg. PUSHJ$2,M		% do M F ( N - 1)	PUT	rJ,$1 % restore ret addr SUBU$0,$0,$2	POP	1,0		% return N - M F ( N - 1 )// Male functionM	GET	$1,rJ PBNZ$0,1F	PUT	rJ,$1 POP 1,0 % return M 0 = 01H SUBU$3,$0,1 PUSHJ$2,M	ADDU	$3,$2,0	PUSHJ	$2,F PUT rJ,$1	SUBU	$0,$0,$2 POP 1,0$ return N - F M ( N - 1 )// do a female runMain	SET	$1,0 % for (i=0; i<25; i++){1H ADDU$4,$1,0 % PUSHJ$3,F		%  F (i)	GO	Ja,prtInt	%  print F (i)	INCL	$1,1 CMP t,$1,25	PBNZ	t,1B		% }	LDA	$255,NL TRAP 0,Fputs,StdOut// do a male run SET$1,0		% for (i=0; i<25; i++){1H	ADDU	$4,$1,0		%	PUSHJ	$3,M % M (i) GO Ja,prtInt % print M (i) INCL$1,1	CMP	t,$1,25 PBNZ t,1B % } LDA$255,NL	TRAP	0,Fputs,StdOut	TRAP	0,Halt,0

Output:

~/MIX/MMIX/Rosetta> mmix mutualrecurs1
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13 13 14 14 15
0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12 13 14 14 15


## Nemerle

using System;using System.Console; module Hofstadter{    F(n : int) : int    {        |0 => 1        |_ => n - M(F(n - 1))    }     M(n : int) : int    {        |0 => 0        |_ => n - F(M(n - 1))    }     Main() : void    {        foreach (n in [0 .. 20]) Write("{0} ", F(n));        WriteLine();        foreach (n in [0 .. 20]) Write("{0} ", M(n));    }}

## Objective-C

Objective-C has prior declaration rules similar to those stated above for C, for C-like types. In this example we show the use of a two class method; this works since we need an interface block that is like declaration of functions in C code.

#import <Foundation/Foundation.h> @interface Hofstadter : NSObject+ (int)M: (int)n;+ (int)F: (int)n;@end @implementation Hofstadter+ (int)M: (int)n{  if ( n == 0 ) return 0;  return n - [self F: [self M: (n-1)]];}+ (int)F: (int)n{  if ( n == 0 ) return 1;  return n - [self M: [self F: (n-1)]];}@end int main(){  int i;   for(i=0; i < 20; i++) {    printf("%3d ", [Hofstadter F: i]);  }  printf("\n");  for(i=0; i < 20; i++) {    printf("%3d ", [Hofstadter M: i]);  }  printf("\n");  return 0;}

## Objeck

Translation of: C
 class MutualRecursion {  function : Main(args : String[]) ~ Nil {    for(i := 0; i < 20; i+=1;) {      f(i)->PrintLine();    };    "---"->PrintLine();    for (i := 0; i < 20; i+=1;) {      m(i)->PrintLine();    };  }   function : f(n : Int) ~ Int {    return n = 0 ? 1 : n - m(f(n - 1));  }   function : m(n : Int) ~ Int {    return n = 0 ? 0 : n - f(m(n - 1));  }}

## OCaml

let rec f = function  | 0 -> 1  | n -> n - m(f(n-1))and m = function  | 0 -> 0  | n -> n - f(m(n-1));;

The let rec f ... and m ... construct indicates that the functions call themselves (rec) and each other (and).

## Octave

We don't need to pre-declare or specify in some other way a function that will be defined later; but both must be declared before their use.
(The code is written to handle vectors, as the testing part shows)

function r = F(n)  for i = 1:length(n)    if (n(i) == 0)      r(i) = 1;    else      r(i) = n(i) - M(F(n(i)-1));    endif  endforendfunction function r = M(n)  for i = 1:length(n)    if (n(i) == 0)      r(i) = 0;    else      r(i) = n(i) - F(M(n(i)-1));    endif  endforendfunction
# testingra = F([0:19]);rb = M([0:19]);disp(ra);disp(rb);

## Order

Since Order is powered by the C preprocessor, definitions follow the same rule as CPP macros: they can appear in any order relative to each other as long as all are defined before the ORDER_PP block that calls them.

#include <order/interpreter.h> #define ORDER_PP_DEF_8f                         \ORDER_PP_FN(8fn(8N,                             \                8if(8is_0(8N),                  \                    1,                          \                    8sub(8N, 8m(8f(8dec(8N))))))) #define ORDER_PP_DEF_8m                         \ORDER_PP_FN(8fn(8N,                             \                8if(8is_0(8N),                  \                    0,                          \                    8sub(8N, 8f(8m(8dec(8N))))))) //TestORDER_PP(8for_each_in_range(8fn(8N, 8print(8f(8N))), 0, 19))ORDER_PP(8for_each_in_range(8fn(8N, 8print(8m(8N))), 0, 19))

## Oz

declare  fun {F N}     if N == 0 then 1     elseif N > 0 then N - {M {F N-1}}     end  end   fun {M N}     if N == 0 then 0     elseif N > 0 then N - {F {M N-1}}     end  endin  {Show {Map {List.number 0 9 1} F}}  {Show {Map {List.number 0 9 1} M}}

## PARI/GP

F(n)=if(n,n-M(F(n-1)),1)M(n)=if(n,n-F(M(n-1)),0)

## Pascal

In Pascal we need to pre-declare functions/procedures; to do so, the forward statement is used.

Program MutualRecursion; {M definition comes after F which uses it}function M(n : Integer) : Integer; forward; function F(n : Integer) : Integer;begin   if n = 0 then      F := 1   else      F := n - M(F(n-1));end; function M(n : Integer) : Integer;begin   if n = 0 then      M := 0   else      M := n - F(M(n-1));end; var   i : Integer; begin    for i := 0 to 19 do begin      write(F(i) : 4)   end;   writeln;   for i := 0 to 19 do begin      write(M(i) : 4)   end;   writeln;end.

## PicoLisp

(de f (N)   (if (=0 N)      1      (- N (m (f (dec N)))) ) ) (de m (N)   (if (=0 N)      0      (- N (f (m (dec N)))) ) )

## PL/I

 test: procedure options (main); M: procedure (n) returns (fixed) recursive;    /* 8/1/2010 */   declare n fixed;   if n <= 0 then return (0);   else return ( n - F(M(n-1)) );end M; F: procedure (n) returns (fixed) recursive;   declare n fixed;   if n <= 0 then return (1);   else return ( n - M(F(n-1)) );end F;    declare i fixed;    do i = 1 to 15;      put skip list ( F(i), M(i) );   end;end test;

## PostScript

 /female{/n exch defn 0 eq{1}{n n 1 sub female male sub}ifelse}def /male{/n exch defn 0 eq{0}{n n 1 sub male female sub}ifelse}def
Library: initlib
 /F {{    {0 eq} {pop 1} is?    {0 gt} {dup 1 sub F M sub} is?} cond}. /M {{    {0 eq} {pop 0} is?    {0 gt} {dup 1 sub M F sub} is?} cond}.

## PowerShell

function F($n) { if ($n -eq 0) { return 1 }    return $n - (M (F ($n - 1)))} function M($n) { if ($n -eq 0) { return 0 }    return $n - (F (M ($n - 1)))}

## Prolog

female(0,1).female(N,F) :- N>0, 	       N1 is N-1, 	       female(N1,R),	       male(R, R1),	       F is N-R1. male(0,0).male(N,F) :- N>0, 	     N1 is N-1, 	     male(N1,R),	     female(R, R1),	     F is N-R1.
Works with: GNU Prolog
flist(S) :- for(X, 0, S), female(X, R), format('~d ', [R]), fail.mlist(S) :- for(X, 0, S), male(X, R), format('~d ', [R]), fail.

Testing

| ?- flist(19).
1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12

no
| ?- mlist(19).
0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12

## Pure

The Pure definitions very closely maps to the mathematical definitions.

F 0 = 1;M 0 = 0;F n = n - M(F(n-1)) if n>0;M n = n - F(M(n-1)) if n>0;
> let females = map F (0..10); females;[1,1,2,2,3,3,4,5,5,6,6]> let males = map M (0..10); males;[0,0,1,2,2,3,4,4,5,6,6]

## PureBasic

Declare M(n) Procedure F(n)  If n = 0    ProcedureReturn 1  ElseIf n > 0    ProcedureReturn n - M(F(n - 1))  EndIf EndProcedure Procedure M(n)  If n = 0    ProcedureReturn 0  ElseIf n > 0    ProcedureReturn n - F(M(n - 1))  EndIf EndProcedure Define iIf OpenConsole()   For i = 0 To 19    Print(Str(F(i)))    If i = 19      Continue    EndIf    Print(", ")  Next   PrintN("")  For i = 0 To 19    Print(Str(M(i)))    If i = 19      Continue    EndIf    Print(", ")  Next    Print(#CRLF$+ #CRLF$ + "Press ENTER to exit")  Input()  CloseConsole()EndIf

Sample output:

1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12
0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12

## Python

Works with: Python version 3.0
.
Works with: Python version 2.6

def F(n): return 1 if n == 0 else n - M(F(n-1))def M(n): return 0 if n == 0 else n - F(M(n-1)) print ([ F(n) for n in range(20) ])print ([ M(n) for n in range(20) ])

Output:

[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12]
[0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]

In python there is no need to pre-declare M for it to be used in the definition of F. (However M must be defined before F calls it).

## R

F <- function(n) ifelse(n == 0, 1, n - M(F(n-1)))M <- function(n) ifelse(n == 0, 0, n - F(M(n-1)))
print.table(lapply(0:19, M))print.table(lapply(0:19, F))

## REBOL

rebol [    Title: "Mutual Recursion"    Date: 2009-12-14    Author: oofoe    URL: http://rosettacode.org/wiki/Mutual_Recursion	References: [http://en.wikipedia.org/wiki/Hofstadter_sequence#Hofstadter_Female_and_Male_sequences]] f: func [	"Female."	n [integer!] "Value."] [either 0 = n [1][n - m f n - 1]] m: func [	"Male."	n [integer!] "Value."] [either 0 = n [0][n - f m n - 1]] fs: []  ms: []  for i 0 19 1 [append fs f i  append ms m i]print ["F:" mold fs  crlf  "M:" mold ms]

Output:

F: [1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12]
M: [0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12]

## Racket

#lang racket(define (F n)  (if (>= 0 n)      1      (- n (M (F (sub1 n)))))) (define (M n)  (if (>= 0 n)      0      (- n (F (M (sub1 n))))))

## REXX

### vanilla

This version uses vertical formatting.

/*REXX program shows mutual recursion (via Hofstadter Male & Female seq)*/arg lim .;   if lim=='' then lim=40;     pad=left('',20)        do j=0 to lim;     jj=Jw(j);     ff=F(j);     mm=M(j)       say    pad    'F('jj") ="    Jw(ff)    pad    'M('jj") ="    Jw(mm)          end   /*j*/exit                                   /*stick a fork in it, we're done.*//*─────────────────────────────────────F, M, Jw  subroutines────────────*/F:  procedure;  arg n;   if n==0 then return 1;   return n-M(F(n-1))M:  procedure;  arg n;   if n==0 then return 0;   return n-F(M(n-1))Jw: return right(arg(1),length(lim))   /*right justifies # for nice look*/

output (using the default of 40):

                     F( 0) =  1                      M( 0) =  0
F( 1) =  1                      M( 1) =  0
F( 2) =  2                      M( 2) =  1
F( 3) =  2                      M( 3) =  2
F( 4) =  3                      M( 4) =  2
F( 5) =  3                      M( 5) =  3
F( 6) =  4                      M( 6) =  4
F( 7) =  5                      M( 7) =  4
F( 8) =  5                      M( 8) =  5
F( 9) =  6                      M( 9) =  6
F(10) =  6                      M(10) =  6
F(11) =  7                      M(11) =  7
F(12) =  8                      M(12) =  7
F(13) =  8                      M(13) =  8
F(14) =  9                      M(14) =  9
F(15) =  9                      M(15) =  9
F(16) = 10                      M(16) = 10
F(17) = 11                      M(17) = 11
F(18) = 11                      M(18) = 11
F(19) = 12                      M(19) = 12
F(20) = 13                      M(20) = 12
F(21) = 13                      M(21) = 13
F(22) = 14                      M(22) = 14
F(23) = 14                      M(23) = 14
F(24) = 15                      M(24) = 15
F(25) = 16                      M(25) = 16
F(26) = 16                      M(26) = 16
F(27) = 17                      M(27) = 17
F(28) = 17                      M(28) = 17
F(29) = 18                      M(29) = 18
F(30) = 19                      M(30) = 19
F(31) = 19                      M(31) = 19
F(32) = 20                      M(32) = 20
F(33) = 21                      M(33) = 20
F(34) = 21                      M(34) = 21
F(35) = 22                      M(35) = 22
F(36) = 22                      M(36) = 22
F(37) = 23                      M(37) = 23
F(38) = 24                      M(38) = 24
F(39) = 24                      M(39) = 24
F(40) = 25                      M(40) = 25


### with memoization

This version uses memoization as well as a horizontal output format.

The optimization due to memoization is faster by many orders of magnitude.

/*REXX program shows mutual recursion (via Hofstadter Male & Female seq)*/arg lim .;if lim=='' then lim=99; hm.=; hm.0=0; hf.=; hf.0=1; Js=; Fs=; Ms=                 do j=0 to lim;                   ff=F(j);         mm=M(j)                         Js=Js jW(j);   Fs=Fs jw(ff);    Ms=Ms jW(mm)                end   /*j*/say 'Js=' Jssay 'Fs=' Fssay 'Ms=' Msexit                                   /*stick a fork in it, we're done.*//*─────────────────────────────────────F, M, Jw  subroutines────────────*/F:  procedure expose hm. hf.; arg n; if hf.n=='' then hf.n=n-M(F(n-1)); return hf.n M:  procedure expose hm. hf.; arg n; if hm.n=='' then hm.n=n-F(M(n-1)); return hm.nJw: return right(arg(1),length(lim))   /*right justifies # for nice look*/

output (using the default of 99):

Js=  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99
Fs=  1  1  2  2  3  3  4  5  5  6  6  7  8  8  9  9 10 11 11 12 13 13 14 14 15 16 16 17 17 18 19 19 20 21 21 22 22 23 24 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 34 34 35 35 36 37 37 38 38 39 40 40 41 42 42 43 43 44 45 45 46 46 47 48 48 49 50 50 51 51 52 53 53 54 55 55 56 56 57 58 58 59 59 60 61 61
Ms=  0  0  1  2  2  3  4  4  5  6  6  7  7  8  9  9 10 11 11 12 12 13 14 14 15 16 16 17 17 18 19 19 20 20 21 22 22 23 24 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 33 34 35 35 36 37 37 38 38 39 40 40 41 42 42 43 43 44 45 45 46 46 47 48 48 49 50 50 51 51 52 53 53 54 54 55 56 56 57 58 58 59 59 60 61 61


### with memoization, specific entry

This version is identical in function to the previous example, but it also can compute and
display a specific request (indicated by a negative number for the argument).

/*REXX program shows mutual recursion (via Hofstadter Male & Female seq)*//*If LIM is negative,  only show a single result for the abs(lim) entry.*/ parse arg lim .;     if lim=='' then lim=99;     aLim=abs(lim)parse var lim . hm. hf. Js Fs Ms;    hm.0=0;     hf.0=1                 do j=0 to Alim;               ff=F(j);           mm=M(j)                      Js=Js jW(j);     Fs=Fs jw(ff);      Ms=Ms jW(mm)                end if lim>0  then  say 'Js='  Js;    else  say  'J('aLim")="  word(Js,aLim+1)if lim>0  then  say 'Fs='  Fs;    else  say  'F('aLim")="  word(Fs,aLim+1)if lim>0  then  say 'Ms='  Ms;    else  say  'M('aLim")="  word(Ms,aLim+1)exit                                   /*stick a fork in it, we're done.*//*─────────────────────────────────────F, M, Jw  subroutines────────────*/F:  procedure expose hm. hf.; arg n; if hf.n=='' then hf.n=n-M(F(n-1)); return hf.nM:  procedure expose hm. hf.; arg n; if hm.n=='' then hm.n=n-F(M(n-1)); return hm.nJw: return right(arg(1),length(lim))   /*right justifies # for nice look*/

output using the input of: -70000

J(70000)= 70000
F(70000)= 43262
M(70000)= 43262


output using the input of a ¼ million: -250000

J(250000)= 250000
F(250000)= 154509
M(250000)= 154509


## Ruby

def F(n)  n == 0 ? 1 : n - M(F(n-1))enddef M(n)  n == 0 ? 0 : n - F(M(n-1))end p (Array.new(20) {|n| F(n) })p (Array.new(20) {|n| M(n) })

Output:

[1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12]
[0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12]

In ruby there is no need to pre-declare M for it to be used in the definition of F. (However M must be defined before F calls it).

## Run BASIC

print "F sequence:";for i = 0 to 20  print f(i);" ";next iprint :print "M sequence:";for i = 0 to 20  print m(i);" ";next iend function f(n) f = 1 if n <> 0 then f = n - m(f(n - 1))end function function m(n) m = 0 if n <> 0 then m = n - f(m(n - 1))end function

Output:

F sequence:1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12 13
M sequence:0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12 12

## Rust

fn f(n: int) -> int {    match n {        0 => 1,        _ => n - m(f(n - 1))    }} fn m(n: int) -> int {    match n {        0 => 0,        _ => n - f(m(n - 1))    }} fn main() {    for i in range(0, 20).map(f) {        print!("{} ", i);    }    println!("")     for i in range(0, 20).map(m) {        print!("{} ", i);    }    println!("")}

Output:

1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12
0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12

## Sather

class MAIN is   f(n:INT):INT    pre n >= 0  is    if n = 0 then return 1; end;    return n - m(f(n-1));  end;   m(n:INT):INT    pre n >= 0  is    if n = 0 then return 0; end;    return n - f(m(n-1));  end;   main is    loop i ::= 0.upto!(19);      #OUT + #FMT("%2d ", f(i));    end;    #OUT + "\n";    loop i ::= 0.upto!(19);      #OUT + #FMT("%2d ", m(i));    end;  end;end;

There's no need to pre-declare someway F or M.

## Scala

def F(n:Int):Int =  if (n == 0) 1 else n - M(F(n-1))def M(n:Int):Int =  if (n == 0) 0 else n - F(M(n-1)) println((0 until 20).map(F).mkString(", "))println((0 until 20).map(M).mkString(", "))

Output:

1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12
0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12

## Scheme

define declarations are automatically mutually recursive:

(define (F n)  (if (= n 0) 1      (- n (M (F (- n 1)))))) (define (M n)  (if (= n 0) 0      (- n (F (M (- n 1))))))

If you wanted to use a let-like construct to create local bindings, you would do the following. The define construct above is just a syntactic sugar for the following where the entire rest of the scope is used as the body.

(letrec ((F (lambda (n)              (if (= n 0) 1                  (- n (M (F (- n 1)))))))         (M (lambda (n)              (if (= n 0) 0                  (- n (F (M (- n 1))))))))  (F 19)) # evaluates to 12

The letrec indicates that the definitions can be recursive, and fact that we placed these two in the same letrec block makes them mutually recursive.

## Standard ML

fun f 0 = 1  | f n = n - m (f (n-1))and m 0 = 0  | m n = n - f (m (n-1));

The fun construct creates recursive functions, and the and allows a group of functions to call each other. The above is just a shortcut for the following:

val rec f = fn 0 => 1             | n => n - m (f (n-1))and m = fn 0 => 0         | n => n - f (m (n-1));

which indicates that the functions call themselves (rec) and each other (and).

## Tcl

proc m {n} {    if { $n == 0 } { expr 0; } else { expr {$n - [f [m [expr {$n-1}] ]]}; }}proc f {n} { if {$n == 0 } { expr 1; } else {	expr {$n - [m [f [expr {$n-1}] ]]};    }} for {set i 0} {$i < 20} {incr i} { puts -nonewline [f$i];    puts -nonewline " ";}puts ""for {set i 0} {$i < 20} {incr i} { puts -nonewline [m$i];    puts -nonewline " ";}puts ""

## TI-89 BASIC

Define F(n) = when(n=0, 1, n - M(F(n - 1)))Define M(n) = when(n=0, 0, n - F(M(n - 1)))

## Translation of: Racket

@(do   (defun f (n)     (if (>= 0 n)       1       (- n (m (f (- n 1))))))    (defun m (n)     (if (>= 0 n)       0       (- n (f (m (- n 1))))))    (each ((n (range 0 15)))     (format t "f(~s) = ~s; m(~s) = ~s\n" n (f n) n (m n))))

## Ursala

Forward declarations are not an issue in Ursala, which allows any definition to depend on any symbol declared within the same scope. However, cyclic dependences are not accepted unless the programmer explicitly accounts for their semantics. If the recurrence can be solved using a fixed point combinator, the compiler can be directed to use one by the #fix directive as shown, in this case with one of a family of functional fixed point combinators from a library. (There are easier ways to define these functions in Ursala than by mutual recursion, but fixed points are useful for other things as well.)

#import std#import nat#import sol #fix general_function_fixer 0 F = ~&?\1! difference^/~& M+ F+ predecessorM = ~&?\0! difference^/~& F+ M+ predecessor

This test program applies both functions to the first twenty natural numbers.

#cast %nLW test = ^(F*,M*) iota 20

output:

(
<1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12>,
<0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12>)

## x86 Assembly

Works with: nasm

Since all "labels" (symbols), if not local, can be seen by the whole code in the same source unit, we don't need special care to let the subroutine func_f call func_m. If the function would have been in another source unit, we should have declared it extern (the linker will resolve the symbol), as done for printf.
(It must be linked with the C standard library libc or similar and a startup code; lazyly a gcc mutrec.o works, being mutrec.o produced by e.g. nasm -f elf mutrec.asm)

	global	main	extern	printf 	section	.text func_f	mov	eax, [esp+4]	cmp	eax, 0	jz	f_ret	dec	eax	push	eax	call	func_f	mov	[esp+0], eax	call	func_m	add	esp, 4	mov	ebx, [esp+4]	sub	ebx, eax	mov	eax, ebx	retf_ret	mov	eax, 1	ret func_m	mov	eax, [esp+4]	cmp	eax, 0	jz	m_ret	dec	eax	push	eax	call	func_m	mov	[esp+0], eax	call	func_f	add	esp, 4	mov	ebx, [esp+4]	sub	ebx, eax	mov	eax, ebx	retm_ret	xor	eax, eax	ret main	mov	edx, func_f	call	output_res	mov	edx, func_m	call	output_res	ret output_res	xor	ecx, ecxloop0	push	ecx	call	edx         push    edx 	push	eax	push	form	call	printf	add	esp, 8 	pop     edx        pop     ecx 	inc	ecx	cmp	ecx, 20	jnz	loop0 	push	newline	call	printf	add	esp, 4 	ret  	section	.rodataform	db	'%d ',0newline	db	10,0 	end

## XPL0

code    ChOut=8, CrLf=9, IntOut=11; ffunc M; \forward-referenced function declaration func F(N);int N;return if N=0 then 1 else N - M(F(N-1)); func M(N);int N;return if N=0 then 0 else N - F(M(N-1)); int I;[for I:= 0 to 19 do [IntOut(0, F(I));  ChOut(0, ^ )];CrLf(0); for I:= 0 to 19 do [IntOut(0, M(I));  ChOut(0, ^ )];CrLf(0);]

Output:

1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10 11 11 12
0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 11 11 12


## zkl

zkl doesn't like referencing undefined objects so there is a bit of sleaze here.

fcn f(n,m){if(n==0)return(1); n-m(f(n-1,m),f)}fcn m(n,f){if(n==0)return(0); n-f(m(n-1,f),m)}[0..19].apply(f.fp1(m))[0..19].apply(m.fp1(f))
Output:
L(1,1,2,2,3,3,4,5,5,6,6,7,8,8,9,9,10,11,11,12)
L(0,0,1,2,2,3,4,4,5,6,6,7,7,8,9,9,10,11,11,12)