Man or boy test

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Task
Man or boy test
You are encouraged to solve this task according to the task description, using any language you may know.

Background: The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not.

I have written the following simple routine, which may separate the 'man-compilers' from the 'boy-compilers'
Donald Knuth

Task: Imitate Knuth's example in Algol 60 in another language, as far as possible.

Details: Local variables of routines are often kept in activation records (also call frames). In many languages, these records are kept on a call stack. In Algol (and e.g. in Smalltalk), they are allocated on a heap instead. Hence it is possible to pass references to routines that still can use and update variables from their call environment, even if the routine where those variables are declared already returned. This difference in implementations is sometimes called the Funarg Problem.

In Knuth's example, each call to A allocates an activation record for the variable A. When B is called from A, any access to k now refers to this activation record. Now B in turn calls A, but passes itself as an argument. This argument remains bound to the activation record. This call to A also "shifts" the variables xi by one place, so eventually the argument B (still bound to its particular activation record) will appear as x4 or x5 in a call to A. If this happens when the expression x4 + x5 is evaluated, then this will again call B, which in turn will update k in the activation record it was originally bound to. As this activation record is shared with other instances of calls to A and B, it will influence the whole computation.

So all the example does is to set up a convoluted calling structure, where updates to k can influence the behavior in completely different parts of the call tree.

Knuth used this to test the correctness of the compiler, but one can of course also use it to test that other languages can emulate the Algol behavior correctly. If the handling of activation records is correct, the computed value will be −67.

Performance and Memory: Man or Boy is intense and can be pushed to challenge any machine. Memory (both stack and heap) not CPU time is the constraining resource as the recursion creates a proliferation activation records which will quickly exhaust memory and present itself through a stack error. Each language may have ways of adjusting the amount of memory or increasing the recursion depth. Optionally, show how you would make such adjustments.

The table below shows the result, call depths, and total calls for a range of k:

k 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
A 1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1,446 -3,250 -7,244 -16,065 -35,601 -78,985 -175,416 -389,695 -865,609 -1,922,362 -4,268,854 -9,479,595 -21,051,458 -46,750,171 -103,821,058 -230,560,902 -512,016,658
A called 1 2 3 4 8 18 38 80 167 347 722 1,509 3,168 6,673 14,091 29,825 63,287 134,652 287,264 614,442 1,317,533 2,831,900 6,100,852 13,172,239 28,499,827            
A depth 1 2 3 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608            
B called 0 1 2 3 7 17 37 79 166 346 721 1,508 3,167 6,672 14,090 29,824 63,286 134,651 287,263 614,441 1,317,532 2,831,899 6,100,851 13,172,238 28,499,826            
B depth 0 1 2 3 7 15 31 63 127 255 511 1,023 2,047 4,095 8,191 16,383 32,767 65,535 131,071 262,143 524,287 1,048,575 2,097,151 4,194,303 8,388,607            

Contents

[edit] Ada

Ada 2005 supports access to subprograms which is used in the implementation below:

Works with: Ada version 2005, 2012
with Ada.Text_IO;  use Ada.Text_IO;
 
procedure Man_Or_Boy is
function Zero return Integer is begin return 0; end Zero;
function One return Integer is begin return 1; end One;
function Neg return Integer is begin return -1; end Neg;
 
function A
( K : Integer;
X1, X2, X3, X4, X5 : access function return Integer
) return Integer is
M : Integer := K; -- K is read-only in Ada. Here is a mutable copy of
function B return Integer is
begin
M := M - 1;
return A (M, B'Access, X1, X2, X3, X4);
end B;
begin
if M <= 0 then
return X4.all + X5.all;
else
return B;
end if;
end A;
begin
Put_Line
( Integer'Image
( A
( 10,
One'Access, -- Returns 1
Neg'Access, -- Returns -1
Neg'Access, -- Returns -1
One'Access, -- Returns 1
Zero'Access -- Returns 0
) ) );
end Man_Or_Boy;

Ada 2012 supports expression functions and conditional expressions which are used in the implementation below:

Works with: Ada version 2012
with Ada.Text_IO;  use Ada.Text_IO;
 
procedure Man_Or_Boy is
function Zero return Integer is (0);
function One return Integer is (1);
function Neg return Integer is (-1);
 
function A
(K : Integer;
X1, X2, X3, X4, X5 : access function return Integer)
return Integer is
M : Integer := K; -- K is read-only in Ada. Here is a mutable copy of
function B return Integer is
begin
M := M - 1;
return A (M, B'Access, X1, X2, X3, X4);
end B;
begin
return (if M <= 0 then X4.all + X5.all else B);
end A;
begin
Put_Line
(Integer'Image
(A (K => 10,
X1 => One'Access,
X2 => Neg'Access,
X3 => Neg'Access,
X4 => One'Access,
X5 => Zero'Access)));
end Man_Or_Boy;

Sample output:

 -67

[edit] Aime

integer
F(list l)
{
return l[1];
}
 
integer
eval(list l)
{
return call(l[0], l);
}
 
integer A(list);
 
integer
B(list l)
{
integer x;
 
x = l[1];
x -= 1;
l_r_integer(l, 1, x);
 
return A(l_assemble(B, x, l, l[-5], l[-4], l[-3], l[-2]));
}
 
integer
A(list l)
{
integer x;
 
if (l_q_integer(l, 1) < 1) {
x = eval(l[-2]) + eval(l[-1]);
} else {
x = B(l);
}
 
return x;
}
 
integer
main(void)
{
list f1, f0, fn1;
 
l_append(f1, F);
l_append(f1, 1);
 
l_append(f0, F);
l_append(f0, 0);
 
l_append(fn1, F);
l_append(fn1, -1);
 
o_integer(A(l_assemble(B, 10, f1, fn1, fn1, f1, f0)));
o_byte('\n');
 
return 0;
}

Output:

 -67

[edit] ALGOL 60 - Knuth's example

begin
  real procedure A (k, x1, x2, x3, x4, x5);
  value k; integer k;
  begin
    real procedure B;
    begin k:= k - 1;
          B:= A := A (k, B, x1, x2, x3, x4);
    end;
    if k <= 0 then A:= x4 + x5 else B;
  end;
  outreal (A (10, 1, -1, -1, 1, 0));
end;

This creates a tree of B call frames that refer to each other and to the containing A call frames, each of which has its own copy of k that changes every time the associated B is called. Trying to work it through on paper is probably fruitless, but the correct answer is −67, despite the fact that in the original paper Knuth postulated it to be −121.

Note that Knuth's code states:

    if k <= 0 then A:= x4 + x5 else B;

which actually discards the result value from the call to B. Most of the translated examples below are equivalent to:

    A := (if k <= 0 then x4 + x5 else B);

and are therefore strictly incorrect, although in a correct 'man' compiler they do produce the expected result, because Knuth's version has already assigned to the return variable for A from within B, and it is in fact that assignment which is the true return value of the function:

          B:= A := A (k, B, x1, x2, x3, x4);

It is most likely that this was a deliberate attempt by Knuth to find yet another way to break 'boy' compilers, rather than merely being sloppy code.

[edit] ALGOL 68

Translation of: ALGOL 60
Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny

Charles H. Lindsey implemented this man boy test in ALGOL 68, and - as call by name is not necessary - the same algorithm can be implemented in many languages including Pascal and PL/I .

PROC a = (INT in k, PROC INT xl, x2, x3, x4, x5) INT:(
INT k := in k;
PROC b = INT: a(k-:=1, b, xl, x2, x3, x4);
( k<=0 | x4 + x5 | b )
);
 
test:(
printf(($gl$,a(10, INT:1, INT:-1, INT:-1, INT:1, INT:0)))
)

Output:

        -67

[edit] AppleScript

Works with: Smile

AppleScript's stack limit is around 500 frames, which is too low to run this example. It runs in the compatible Smile environment, however.

on a(k, x1, x2, x3, x4, x5)
script b
set k to k - 1
return a(k, b, x1, x2, x3, x4)
end script
if k ≤ 0 then
return (run x4) + (run x5)
else
return (run b)
end if
end a
 
on int(x)
script s
return x
end script
return s
end int
 
a(10, int(1), int(-1), int(-1), int(1), int(0))
 

Output:

-67

[edit] BBC BASIC

      HIMEM = PAGE + 200000000 : REM Increase recursion depth
 
FOR k% = 0 TO 20
PRINT FNA(k%, ^FN1(), ^FN_1(), ^FN_1(), ^FN1(), ^FN0())
NEXT
END
 
DEF FNA(k%, x1%, x2%, x3%, x4%, x5%)
IF k% <= 0 THEN = FN(x4%)(x4%) + FN(x5%)(x5%)
LOCAL b{}
DIM b{fn%, k%, x1%, x2%, x3%, x4%, x5%}
b.fn% = !^FNB()
b.k% = k%
b.x1% = x1%
b.x2% = x2%
b.x3% = x3%
b.x4% = x4%
b.x5% = x5%
DEF FNB(!(^b{}+4))
b.k% -= 1
= FNA(b.k%, b{}, b.x1%, b.x2%, b.x3%, b.x4%)
 
DEF FN0(d%) = 0
DEF FN1(d%) = 1
DEF FN_1(d%) = -1

Output:

         1
         0
        -2
         0
         1
         0
         1
        -1
       -10
       -30
       -67
      -138
      -291
      -642
     -1446
     -3250
     -7244
    -16065
    -35601
    -78985
   -175416

[edit] C

Even if closures are not available in a language, their effect can be simulated. This is what happens in the following C implementation:

/* man-or-boy.c */
#include <stdio.h>
#include <stdlib.h>
 
// --- thunks
typedef struct arg
{
int (*fn)(struct arg*);
int *k;
struct arg *x1, *x2, *x3, *x4, *x5;
} ARG;
 
// --- lambdas
int f_1 (ARG* _) { return -1; }
int f0 (ARG* _) { return 0; }
int f1 (ARG* _) { return 1; }
 
// --- helper
int eval(ARG* a) { return a->fn(a); }
#define MAKE_ARG(...) (&(ARG){__VA_ARGS__})
#define FUN(...) MAKE_ARG(B, &k, __VA_ARGS__)
 
int A(ARG*);
 
// --- functions
int B(ARG* a)
{
int k = *a->k -= 1;
return A(FUN(a, a->x1, a->x2, a->x3, a->x4));
}
 
int A(ARG* a)
{
return *a->k <= 0 ? eval(a->x4) + eval(a->x5) : B(a);
}
 
int main(int argc, char **argv)
{
int k = argc == 2 ? strtol(argv[1], 0, 0) : 10;
printf("%d\n", A(FUN(MAKE_ARG(f1), MAKE_ARG(f_1), MAKE_ARG(f_1),
MAKE_ARG(f1), MAKE_ARG(f0))));
return 0;
}

Two gcc extensions to the C language, nested functions and block sub-expressions, can be combined to create this elegant version:

Version: gcc version 4.1.2 20070925 (Red Hat 4.1.2-27)

#include <stdio.h>
#define INT(body) ({ int lambda(){ body; }; lambda; })
main(){
int a(int k, int xl(), int x2(), int x3(), int x4(), int x5()){
int b(){
return a(--k, b, xl, x2, x3, x4);
}
return k<=0 ? x4() + x5() : b();
}
printf(" %d\n",a(10, INT(return 1), INT(return -1), INT(return -1), INT(return 1), INT(return 0)));
}

C without C99 or gcc extensions:

#include <stdio.h>
#include <stdlib.h>
 
typedef struct frame
{
int (*fn)(struct frame*);
union { int constant; int* k; } u;
struct frame *x1, *x2, *x3, *x4, *x5;
} FRAME;
 
FRAME* Frame(FRAME* f, int* k, FRAME* x1, FRAME* x2, FRAME *x3, FRAME *x4, FRAME *x5)
{
f->u.k = k;
f->x1 = x1;
f->x2 = x2;
f->x3 = x3;
f->x4 = x4;
f->x5 = x5;
return f;
}
 
int F(FRAME* a) { return a->u.constant; }
 
int eval(FRAME* a) { return a->fn(a); }
 
int A(FRAME*);
 
int B(FRAME* a)
{
int k = (*a->u.k -= 1);
FRAME b = { B };
return A(Frame(&b, &k, a, a->x1, a->x2, a->x3, a->x4));
}
 
int A(FRAME* a)
{
return *a->u.k <= 0 ? eval(a->x4) + eval(a->x5) : B(a);
}
 
int main(int argc, char** argv)
{
int k = argc == 2 ? strtol(argv[1], 0, 0) : 10;
FRAME a = { B }, f1 = { F, { 1 } }, f0 = { F, { 0 } }, fn1 = { F, { -1 } };
 
printf("%d\n", A(Frame(&a, &k, &f1, &fn1, &fn1, &f1, &f0)));
return 0;
}

Output:

-67

[edit] C++

works with GCC

Uses "shared_ptr" smart pointers from Boost / TR1 to automatically deallocate objects. Since we have an object which needs to pass a pointer to itself to another function, we need to use "enable_shared_from_this".

#include <iostream>
#include <tr1/memory>
using std::tr1::shared_ptr;
using std::tr1::enable_shared_from_this;
 
struct Arg {
virtual int run() = 0;
virtual ~Arg() { };
};
 
int A(int, shared_ptr<Arg>, shared_ptr<Arg>, shared_ptr<Arg>,
shared_ptr<Arg>, shared_ptr<Arg>);
 
class B : public Arg, public enable_shared_from_this<B> {
private:
int k;
const shared_ptr<Arg> x1, x2, x3, x4;
 
public:
B(int _k, shared_ptr<Arg> _x1, shared_ptr<Arg> _x2, shared_ptr<Arg> _x3,
shared_ptr<Arg> _x4)
: k(_k), x1(_x1), x2(_x2), x3(_x3), x4(_x4) { }
int run() {
return A(--k, shared_from_this(), x1, x2, x3, x4);
}
};
 
class Const : public Arg {
private:
const int x;
public:
Const(int _x) : x(_x) { }
int run () { return x; }
};
 
int A(int k, shared_ptr<Arg> x1, shared_ptr<Arg> x2, shared_ptr<Arg> x3,
shared_ptr<Arg> x4, shared_ptr<Arg> x5) {
if (k <= 0)
return x4->run() + x5->run();
else {
shared_ptr<Arg> b(new B(k, x1, x2, x3, x4));
return b->run();
}
}
 
int main() {
std::cout << A(10, shared_ptr<Arg>(new Const(1)),
shared_ptr<Arg>(new Const(-1)),
shared_ptr<Arg>(new Const(-1)),
shared_ptr<Arg>(new Const(1)),
shared_ptr<Arg>(new Const(0))) << std::endl;
return 0;
}
Works with: C++11
uses anonymous functions. Tested with g++ version 4.5 and Visual C++ version 16 (Windows SDK 7.1):
#include <functional>
#include <iostream>
 
typedef std::function<int()> F;
 
static int A(int k, const F &x1, const F &x2, const F &x3, const F &x4, const F &x5)
{
F B = [=, &k, &B]
{
return A(--k, B, x1, x2, x3, x4);
};
 
return k <= 0 ? x4() + x5() : B();
}
 
static F L(int n)
{
return [n] { return n; };
}
 
int main()
{
std::cout << A(10, L(1), L(-1), L(-1), L(1), L(0)) << std::endl;
return 0;
}
Works with: TR1
uses TR1 without C++11.
#include <tr1/functional>
#include <iostream>
 
typedef std::tr1::function<int()> F;
 
static int A(int k, const F &x1, const F &x2, const F &x3, const F &x4, const F &x5);
 
struct B_class {
int &k;
const F x1, x2, x3, x4;
B_class(int &_k, const F &_x1, const F &_x2, const F &_x3, const F &_x4) :
k(_k), x1(_x1), x2(_x2), x3(_x3), x4(_x4) { }
int operator()() const { return A(--k, *this, x1, x2, x3, x4); }
};
 
static int A(int k, const F &x1, const F &x2, const F &x3, const F &x4, const F &x5)
{
F B = B_class(k, x1, x2, x3, x4);
return k <= 0 ? x4() + x5() : B();
}
 
struct L {
const int n;
L(int _n) : n(_n) { }
int operator()() const { return n; }
};
 
int main()
{
std::cout << A(10, L(1), L(-1), L(-1), L(1), L(0)) << std::endl;
return 0;
}

[edit] C#

C# 2.0 supports anonymous methods which are used in the implementation below:

Works with: C# version 2+
using System;
 
delegate T Func<T>();
 
class ManOrBoy
{
static void Main()
{
Console.WriteLine(A(10, C(1), C(-1), C(-1), C(1), C(0)));
}
 
static Func<int> C(int i)
{
return delegate { return i; };
}
 
static int A(int k, Func<int> x1, Func<int> x2, Func<int> x3, Func<int> x4, Func<int> x5)
{
Func<int> b = null;
b = delegate { k--; return A(k, b, x1, x2, x3, x4); };
return k <= 0 ? x4() + x5() : b();
}
}
 

C# 3.0 supports lambda expressions which are used in the implementation below:

Works with: C# version 3+
using System;
 
class ManOrBoy
{
static void Main()
{
Console.WriteLine(A(10, () => 1, () => -1, () => -1, () => 1, () => 0));
}
 
static int A(int k, Func<int> x1, Func<int> x2, Func<int> x3, Func<int> x4, Func<int> x5)
{
Func<int> b = null;
b = () => { k--; return A(k, b, x1, x2, x3, x4); };
return k <= 0 ? x4() + x5() : b();
}
}

[edit] Clipper

Procedure Main()
Local k
For k := 0 to 20
 ? "A(", k, ", 1, -1, -1, 1, 0) =", A(k, 1, -1, -1, 1, 0)
Next
Return
 
Static Function A(k, x1, x2, x3, x4, x5)
Local ARetVal
Local B := {|| --k, ARetVal := A(k, B, x1, x2, x3, x4) }
If k <= 0
ARetVal := Evaluate(x4) + Evaluate(x5)
Else
B:Eval()
Endif
Return ARetVal
 
Static Function Evaluate(x)
Local xVal
If ValType(x) == "B"
xVal := x:Eval()
Else
xVal := x
Endif
Return xVal


// With Clipper 5.2e compiler and standard RTLINK linker, default settings, only manages up to k=5 before a stack fault:

EVALUATE (0)  Unrecoverable error 650: Processor stack fault

// Using Blinker v5.1 it can get up to k=7 by increasing the stack size via BLINKER PROCEDURE DEPTH 74. But that may be the limit for 16-bit Clipper; increasing the procedure depth further does not help, and eventually results in

A (0)  Unrecoverable error 667: Eval stack fault

Harbour however is definitely a man: a 32-bit WinXP executable built with Harbour v3.1 and mingw gcc 4.6.1 manages up to k=13 with the default settings. Increasing the stack size (via the Microsoft utility "editbin /STACK:nnn", or "ulimit -s" in linux) allows it to achieve deeper levels:

A(          0 , 1, -1, -1, 1, 0) =          1 
A(          1 , 1, -1, -1, 1, 0) =          0 
A(          2 , 1, -1, -1, 1, 0) =         -2 
A(          3 , 1, -1, -1, 1, 0) =          0 
A(          4 , 1, -1, -1, 1, 0) =          1 
A(          5 , 1, -1, -1, 1, 0) =          0 
A(          6 , 1, -1, -1, 1, 0) =          1 
A(          7 , 1, -1, -1, 1, 0) =         -1 
A(          8 , 1, -1, -1, 1, 0) =        -10 
A(          9 , 1, -1, -1, 1, 0) =        -30 
A(         10 , 1, -1, -1, 1, 0) =        -67 
A(         11 , 1, -1, -1, 1, 0) =       -138 
A(         12 , 1, -1, -1, 1, 0) =       -291 
A(         13 , 1, -1, -1, 1, 0) =       -642 
A(         14 , 1, -1, -1, 1, 0) =      -1446 
A(         15 , 1, -1, -1, 1, 0) =      -3250 
A(         16 , 1, -1, -1, 1, 0) =      -7244 
A(         17 , 1, -1, -1, 1, 0) =     -16065 
A(         18 , 1, -1, -1, 1, 0) =     -35601 
A(         19 , 1, -1, -1, 1, 0) =     -78985 
A(         20 , 1, -1, -1, 1, 0) =    -175416

[edit] Clojure

(declare a)
 
(defn man-or-boy
"Man or boy test for Clojure"
[k]
(let [k (atom k)]
(a k
(fn [] 1)
(fn [] -1)
(fn [] -1)
(fn [] 1)
(fn [] 0))))
 
(defn a
[k x1 x2 x3 x4 x5]
(let [k (atom @k)]
(letfn [(b []
(swap! k dec)
(a k b x1 x2 x3 x4))]
(if (<= @k 0)
(+ (x4) (x5))
(b)))))
 
(man-or-boy 10)
 

[edit] Common Lisp

(defun man-or-boy (x)
(a x (lambda () 1)
(lambda () -1)
(lambda () -1)
(lambda () 1)
(lambda () 0)))
 
(defun a (k x1 x2 x3 x4 x5)
(labels ((b ()
(decf k)
(a k #'b x1 x2 x3 x4)))
(if (<= k 0)
(+ (funcall x4) (funcall x5))
(b))))
 
(man-or-boy 10)

[edit] D

[edit] Straightforward Version

import core.stdc.stdio: printf;
 
int a(int k, const lazy int x1, const lazy int x2, const lazy int x3,
const lazy int x4, const lazy int x5) pure {
int b() {
k--;
return a(k, b(), x1, x2, x3, x4);
}
return k <= 0 ? x4 + x5 : b();
}
 
void main() {
printf("%d\n", a(10, 1, -1, -1, 1, 0));
}

The DMD compiler is a man. Increasing the maximum stack space to about 1.2 GB the DMD 2.059 compiler computes the result -9479595 for k = 25 in about 6.5 seconds on a 32 bit system (-inline -O -release -L/STACK:1300000000).

[edit] Lazy Variadic Function Version

Lazy Variadic Functions version, as quoted:

If the variadic parameter is an array of delegates with no parameters:
    void foo(int delegate()[] dgs ...);
Then each of the arguments whose type does not match that of the delegate is converted to a delegate.
    int delegate() dg;
    foo(1, 3+x, dg, cast(int delegate())null);
is the same as:
    foo( { return 1; }, { return 3+x; }, dg, null );
int A(int k, int delegate() nothrow @safe[] x...) nothrow @safe {
int b() nothrow @safe {
k--;
return A(k, &b, x[0], x[1], x[2], x[3]);
}
 
return (k > 0) ? b() : x[3]() + x[4]();
}
 
void main() {
import std.stdio;
 
A(10, 1, -1, -1, 1, 0).writeln;
}

[edit] Template Version

auto mb(T)(T mob) nothrow @safe { // Embeding function.
int b() nothrow @safe @nogc {
static if (is(T == int))
return mob;
else
return mob();
}
 
return &b;
}
 
int A(T)(int k, T x1, T x2, T x3, T x4, T x5) nothrow @safe {
static if (is(T == int)) {
return A(k, mb(x1), mb(x2), mb(x3), mb(x4), mb(x5));
} else {
int b() nothrow @safe {
k--;
return A(k, &b, x1, x2, x3, x4);
}
return (k <= 0) ? x4() + x5() : b();
}
}
 
void main() {
import std.stdio;
 
A(10, 1, -1, -1, 1, 0).writeln;
}

[edit] Anonymous Class Version

Similar to Java example:

import std.stdio;
 
interface B {
int run();
}
 
int A(int k, int x1, int x2, int x3, int x4, int x5) {
B mb(int a) {
return new class() B {
int run() {
return a;
}
};
}
 
return A(k, mb(x1), mb(x2), mb(x3), mb(x4), mb(x5));
}
 
int A(int k, B x1, B x2, B x3, B x4, B x5) {
if (k <= 0) {
return x4.run() + x5.run();
} else {
return (new class() B {
int m;
 
this() {
this.m = k;
}
 
int run() {
m--;
return A(m, this, x1, x2, x3, x4);
}
}).run();
}
}
 
void main() {
writeln(A(10, 1, -1, -1, 1, 0));
}

[edit] Faster Version

This version cheats, using a different much faster algorithm.

import std.bigint, std.functional;
 
// Adapted from C code by Goran Weinholt, adapted from Knuth code.
BigInt A(in int k, in int x1, in int x2, in int x3,
in int x4, in int x5) {
static struct Inner {
static BigInt c1_(in int k) {
if (k > 5)
return c1(k - 1) + c2(k - 1);
static immutable t = [0, 0, 0, 1, 2, 3];
return t[k].BigInt;
}
alias c1 = memoize!c1_;
 
static BigInt c2_(in int k) {
if (k > 5)
return c2(k - 1) + c3(k - 1);
static immutable t = [0, 0, 1, 1, 1, 2];
return t[k].BigInt;
}
alias c2 = memoize!c2_;
 
static BigInt c3_(in int k) {
if (k > 5)
return c3(k - 1) + c4(k);
static immutable t = [0, 1, 1, 0, 0, 1];
return t[k].BigInt;
}
alias c3 = memoize!c3_;
 
static BigInt c4_(in int k) {
if (k > 5)
return c1(k - 1) + c4(k - 1) - 1;
static immutable t = [1, 1, 0, 0, 0, 0];
return t[k].BigInt;
}
alias c4 = memoize!c4_;
 
static int c5(in int k) pure nothrow {
return !!k;
}
}
 
with (Inner)
return c1(k) * x1 + c2(k) * x2 + c3(k) * x3 +
c4(k) * x4 + c5(k) * x5;
}
 
void main() {
import std.stdio, std.conv, std.range;
 
foreach (immutable i; 0 .. 40)
writeln(i, " ", A(i, 1, -1, -1, 1, 0));
 
writefln("...\n500 %-(%s\\\n  %)",
A(500, 1, -1, -1, 1, 0).text.chunks(60));
}
Output:
0 1
1 0
2 -2
3 0
4 1
5 0
6 1
7 -1
8 -10
9 -30
10 -67
11 -138
12 -291
13 -642
14 -1446
15 -3250
16 -7244
17 -16065
18 -35601
19 -78985
20 -175416
21 -389695
22 -865609
23 -1922362
24 -4268854
25 -9479595
26 -21051458
27 -46750171
28 -103821058
29 -230560902
30 -512016658
31 -1137056340
32 -2525108865
33 -5607619809
34 -12453091089
35 -27655133488
36 -61414977599
37 -136386945105
38 -302880491178
39 -672620048590
...
500 -36608736847739011154197160517980804737983159473082319871442\
     971269362427356493943811133837572598465628264243340122956824\
     36642737343738734381233089412653032375404781872267320

[edit] Delphi

The latest editions of Delphi support anonymous methods, providing a way to implement call by name semantics.

type
TFunc<T> = reference to function: T;
 
function C(x: Integer): TFunc<Integer>;
begin
Result := function: Integer
begin
Result := x;
end;
end;
 
function A(k: Integer; x1, x2, x3, x4, x5: TFunc<Integer>): Integer;
var
b: TFunc<Integer>;
begin
b := function: Integer
begin
Dec(k);
Result := A(k, b, x1, x2, x3, x4);
end;
if k <= 0 then
Result := x4 + x5
else
Result := b;
end;
 
begin
Writeln(A(10, C(1), C(-1), C(-1), C(1), C(0))); // -67 output
end.

[edit] Déjà Vu

Translation of: Python
a k x1 x2 x3 x4 x5:
local b:
set :k -- k
a k @b @x1 @x2 @x3 @x4
if <= k 0:
+ x4 x5
else:
b
local x i:
labda:
i
 
!. a 10 x 1 x -1 x -1 x 1 x 0

[edit] E

Provided that it is marked in the caller and callee, E can perfectly emulate the requested call-by-name behavior by passing slots instead of values:

def a(var k, &x1, &x2, &x3, &x4, &x5) {
def bS; def &b := bS
bind bS {
to get() {
k -= 1
return a(k, &b, &x1, &x2, &x3, &x4)
}
}
return if (k <= 0) { x4 + x5 } else { b }
}
 
def p := 1
def n := -1
def z := 0
println(a(10, &p, &n, &n, &p, &z))

Here each of the "x" parameters is effectively call-by-name. b is bound to a custom slot definition.

[edit] Ela

Stack overflow is not a problem in Ela (but "out of memory" is):

open list cell console
 
a k x1 x2 x3 x4 x5 | k <= 0 = x4! + x5!
| else = b!
where b () = m-- $ a (valueof m) b x1 x2 x3 x4
m = ref k
m-- = m |> mutate (valueof m - 1)
 
a 10 (\() -> 1) (\() -> --1) (\() -> --1) (\() -> 1) (\() -> 0)

Ela itself is a pure language and doesn't provide a support for mutating variables (doesn't have variables basically). However stateful programming features can be added through foreign functions. This implementation uses "reference cells" from Cell module (similar to reference cells in OCaml).

[edit] Erlang

Erlang variables cannot be changed after binding, so k is decremented by sending a message to a process.

kloop(K) ->
    receive
        {decr,Pid} -> Pid ! K-1, kloop(K-1);
        _          -> ok
    end.
 
 
a(K, X1, X2, X3, X4, X5) ->
    Kproc = spawn(fun() -> kloop(K) end),
    B = fun (B) -> 
                Kproc ! {decr, self()},
                receive Kdecr ->
                        a(Kdecr, fun() -> B(B) end, X1, X2, X3, X4)
                end
        end,
    if
        K =< 0  -> Kproc ! X4() + X5();
        true    -> Kproc ! B(B)
    end.
 
 
manorboy(N) ->                
     a(N, fun() -> 1 end, fun() -> -1 end, fun() -> -1 end, fun() -> 1 end, fun() -> 0 end ).

[edit] F#

Straightforward version:

 
[<EntryPoint>]
let main (args : string[]) =
let k = int(args.[0])
 
let l x = fun() -> x
 
let rec a k x1 x2 x3 x4 x5 =
if k <= 0 then
x4() + x5()
else
let k = ref k
let rec b() =
k := !k - 1
a !k b x1 x2 x3 x4
b()
 
a k (l 1) (l -1) (l -1) (l 1) (l 0)
|> printfn "%A"
 
0
 

Using a trampoline to avoid stack overflows when k >= 20:

 
type Tramp<'t> =
| Delay of (unit -> Tramp<'
t>)
| Bind of Tramp<'t> * ('t -> Tramp<'t>)
| Return of '
t
| ReturnFrom of Tramp<'t>
 
type Tramp() =
member this.Delay(f) = Delay f
member this.Bind(x, f) = Bind(x, f)
member this.Return(x) = Return x
member this.ReturnFrom(x) = ReturnFrom x
 
let tramp = Tramp()
 
let run (tr : Tramp<'
t>) =
let rec loop tr stack =
match tr with
| Delay f -> loop (f()) stack
| Bind(x, f) -> loop x (f :: stack)
| Return x ->
match stack with
| [] -> x
| f :: stack' -> loop (f x) stack'
| ReturnFrom tr -> loop tr stack
loop tr []
 
[<EntryPoint>]
let main (args : string[]) =
let k = int(args.[0])
 
let l x = fun() -> Return x
 
tramp {
let rec a k x1 x2 x3 x4 x5 =
tramp {
if k <= 0 then
let! x4' = x4()
let! x5'
= x5()
return x4' + x5'
else
let k = ref k
let rec b() =
tramp {
k := !k - 1
return! a !k b x1 x2 x3 x4
}
return! b()
}
 
return! a k (l 1) (l -1) (l -1) (l 1) (l 0)
}
|> run
|> printfn "%A"
 
0
 

[edit] Fantom

Fantom has closures, so:

 
class ManOrBoy
{
Void main()
{
echo(A(10, |->Int|{1}, |->Int|{-1}, |->Int|{-1}, |->Int|{1}, |->Int|{0}));
}
 
static Int A(Int k, |->Int| x1, |->Int| x2, |->Int| x3, |->Int| x4, |->Int| x5)
{
|->Int|? b
b = |->Int| { k--; return A(k, b, x1, x2, x3, x4) }
return k <= 0 ? x4() + x5() : b()
}
}
 

yields

  -67

[edit] Fortran

Fortran 2008 (uses an internal procedure as function argument). Tested with g95 and gfortran 4.6.

module man_or_boy
 
implicit none
 
contains
 
recursive integer function A(k,x1,x2,x3,x4,x5) result(res)
integer, intent(in) :: k
interface
recursive integer function x1()
end function
recursive integer function x2()
end function
recursive integer function x3()
end function
recursive integer function x4()
end function
recursive integer function x5()
end function
end interface
integer :: m
if ( k <= 0 ) then
res = x4()+x5()
else
m = k
res = B()
end if
 
contains
 
recursive integer function B() result(res)
m = m-1
res = A(m,B,x1,x2,x3,x4)
end function B
 
end function A
 
 
recursive integer function one() result(res)
res = 1
end function
 
recursive integer function minus_one() result(res)
res = -1
end function
 
recursive integer function zero() result(res)
res = 0
end function
 
end module man_or_boy
 
program test
use man_or_boy
write (*,*) A(10,one,minus_one,minus_one,one,zero)
end program test

[edit] Go

package main
import "fmt"
 
func a(k int, x1, x2, x3, x4, x5 func() int) int {
var b func() int
b = func() int {
k--
return a(k, b, x1, x2, x3, x4)
}
if k <= 0 {
return x4() + x5()
}
return b()
}
 
func main() {
x := func(i int) func() int { return func() int { return i } }
fmt.Println(a(10, x(1), x(-1), x(-1), x(1), x(0)))
}

Another version that uses named result parameters the way the original Algol uses the function name. This includes B setting the result of its enclosing A.

package main
 
import "fmt"
 
func A(k int, x1, x2, x3, x4, x5 func() int) (a int) {
var B func() int
B = func() (b int) {
k--
a = A(k, B, x1, x2, x3, x4)
b = a
return
}
if k <= 0 {
a = x4() + x5()
} else {
B()
}
return
}
 
func main() {
K := func(x int) func() int { return func() int { return x } }
fmt.Println(A(10, K(1), K(-1), K(-1), K(1), K(0)))
}

[edit] Gosu

Using Gosu Version 0.10.2.

This is not stictly identical with Wirth's example.

function A(in_k: int, x1(): int, x2(): int, x3(): int, x4(): int, x5(): int): int  {
var k = in_k
var B(): int // B is a function variable
B = \ -> {
k = k-1;
return A(k, B, x1, x2, x3, x4)
}
return k<=0 ? x4()+x5() : B()
}
print(A(10, \ -> 1, \ -> -1, \ -> -1, \ -> 1, \ -> 0))

Output:

 -67

[edit] Groovy

Solution:

def a; a = { k, x1, x2, x3, x4, x5 ->
def b; b = {
a (--k, b, x1, x2, x3, x4)
}
k <= 0 ? x4() + x5() : b()
}
 
def x = { n -> { it -> n } }

Test 1:

println (a(10, x(1), x(-1), x(-1), x(1), x(0)))

This test overflowed the stack at the default stack size. On my system I required "-Xss1409k" or larger to run successfully.

Output:

-67

Test 2:

(0..20).each { k ->
printf ("%3d: %7d\n", k, a(k, x(1), x(-1), x(-1), x(1), x(0)))
}

This test required "-Xss345m" to avoid overflow.

Output:

  0:       1
  1:       0
  2:      -2
  3:       0
  4:       1
  5:       0
  6:       1
  7:      -1
  8:     -10
  9:     -30
 10:     -67
 11:    -138
 12:    -291
 13:    -642
 14:   -1446
 15:   -3250
 16:   -7244
 17:  -16065
 18:  -35601
 19:  -78985
 20: -175416

[edit] Haskell

Haskell is a pure language, so the impure effects of updating k must be wrapped in the IO or ST monad:

 import Control.Monad
import Data.IORef
 
a k x1 x2 x3 x4 x5 = do r <- newIORef k
let b = do k <- pred !r
a k b x1 x2 x3 x4
if k <= 0 then liftM2 (+) x4 x5 else b
where f !r = modifyIORef r f >> readIORef r
 
main = a 10 #1 #(-1) #(-1) #1 #0 >>= print
where (#) f = f . return

On an AMD Opteron 6282 SE using GHC 7.8.2 this program can compute k = 30 in 1064 s and 156.2 GiB.

384,694,618,688 bytes allocated in the heap
393,966,884,256 bytes copied during GC
 73,969,319,136 bytes maximum residency (20 sample(s))
    488,551,728 bytes maximum slop
         159874 MB total memory in use (0 MB lost due to fragmentation)

                                      Tot time (elapsed)      Avg pause    Max pause
 Gen  0     711625 colls,     0 par   456.87s   10710.35s       0.0151s       3.1180s
 Gen  1         20 colls,     0 par   273.65s    9674.71s     483.7353s    5204.3968s

 INIT    time     0.00s  (    0.00s elapsed)
 MUT     time   332.81s  (14301.58s elapsed)
 GC      time   730.52s  (20385.06s elapsed)
 EXIT    time     0.43s  (   12.66s elapsed)
 Total   time  1063.76s  (34699.30s elapsed)

 %GC     time      68.7%  (58.7% elapsed)

 Alloc rate    1,155,911,179 bytes per MUT second

 Productivity  31.3% of total user, 1.0% of total elapsed

[edit] Icon and Unicon

There are a few challenges to implementing MoB in Icon/Unicon.

  • There are no nested procedures and non-local variables that go with them
  • There is no selectable call by value .vs. call by name/reference. Knowledge of the implicit mutable/immutable types is needed.
  • Procedure calls can't be deferred transparently but can be deferred through co-expressions
  • Co-expressions aren't enough as they trap local copies of variables which follow Icon rules for mutability/immutability

The initial solution below involved the use of co-expressions which seemed a natural tool to solve MoB. It turns out that co-expressions aren't necessary to solve this task. Co-expressions are very powerful and MoB really doesn't exercise their full capability. There is a lighter weight solution and also a cheat solution which is a further simplification. The light weight version exploits that procedures are a data type and can be passed around and assigned. This allows us to defer calling 'B' which is just what is required. The change introduces a new record definition 'defercall' and changes only two lines of the original solution in 'eval' and 'B'. The cheat would be to have 'eval' know that it always called 'B'.

MoB is intense and can be pushed to challenge any machine. If you run this and the program hangs up or fails with an inadequate space for static allocation error, you may need to tweak the way Icon/Unicon allocates memory. This is controlled through the environment variables COEXPSIZE, MSTKSIZE, BLKSIZE (see Icon and Unicon Environment Variables).

Notes:

  • The co-expression version will require adjustment to COEXPRSIZE, and possibly BLKSIZE and MSTKSIZE.
    • Mob 13 ran on a machine with 4GB RAM running Unicon Win32 using COEXPSIZE=71000; BLKSIZE=2000000; and MSTKSIZE=1000000.
    • Mob 15 ran on on a 64-bit linux box with 16GB RAM with COEXPSIZE to 200000 (and everything else defaulting).
  • The non-co-expression version required adjustment to BLKSIZE and MSTKSIZE.
    • Mob 21 ran on the same 4GB machine with BLKSIZE=10000000; and MSTKSIZE=70000000
    • Mob 23 ran on the same 4GB machine with BLKSIZE=20000000; and MSTKSIZE=300000000

The co-expression version.

record mutable(value)                                         # we need mutable integers
# ... be obvious when we break normal scope rules
procedure main(arglist) # supply the initial k value
k := integer(arglist[1])|10 # .. or default to 10=default
write("Man or Boy = ", A( k, 1, -1, -1, 1, 0 ) )
end
 
procedure eval(ref) # evaluator to distinguish between a simple value and a code reference
return if type(ref) == "co-expression" then @ref else ref
end
 
procedure A(k,x1,x2,x3,x4,x5) # Knuth's A
k := mutable(k) # make k mutable for B
return if k.value <= 0 then # -> boy compilers may recurse and die here
eval(x4) + eval(x5) # the crux of separating man .v. boy compilers
else # -> boy compilers can run into trouble at k=5+
B(k,x1,x2,x3,x4,x5)
end
 
procedure B(k,x1,x2,x3,x4,x5) # Knuth's B
k.value -:= 1 # diddle A's copy of k
return A(k.value, create |B(k,x1,x2,x3,x4,x5),x1,x2,x3,x4) # call A with a new k and 5 x's
end

Below are the code changes for the non-co-expression version. A new record type is introduced and the two return expressions are changed slightly.

record defercall(proc,arglist)                                # light weight alternative to co-expr for MoB
 
procedure eval(ref) # evaluator to distinguish between a simple value and a code reference
return if type(ref) == "defercall" then ref.proc!ref.arglist else ref
end
 
procedure B(k,x1,x2,x3,x4,x5) # Knuth's B
k.value -:= 1 # diddle A's copy of k
return A(k.value, defercall(B,[k,x1,x2,x3,x4,x5]),x1,x2,x3,x4)# call A with a new k and 5 x's
end

[edit] Io

Io is nothing if not aggressively manly.

Range
 
a := method(k, xs,
b := block(
k = k -1
a(k, list(b, xs slice(0,4)) flatten))
if(k <= 0,
(xs at(3) call) + (xs at(4) call),
b call))
 
f := method(x, block(x))
1 to(500) foreach(k,
(k .. " ") print
a(k, list(1, -1, -1, 1, 0) map (x, f(x))) println)

[edit] J

Given

A=:4 :0
L=.cocreate'' NB. L is context where names are defined.
k__L=:x
'`x1__L x2__L x3__L x4__L x5__L'=:y
if.k__L<:0 do.a__L=:(x4__L + x5__L)f.'' else. L B '' end.
(coerase L)]]]a__L
)
 
B=:4 :0
L=.x
k__L=:k__L-1
a__L=:k__L A L&B`(x1__L f.)`(x2__L f.)`(x3__L f.)`(x4__L f.)
)


   10 A 1:`_1:`_1:`1:`0:
_67

[edit] Java

We use anonymous classes to represent closures.

Java Version 8 and up

import java.util.function.DoubleSupplier;
 
public class ManOrBoy {
 
static double A(int k, DoubleSupplier x1, DoubleSupplier x2,
DoubleSupplier x3, DoubleSupplier x4, DoubleSupplier x5) {
 
DoubleSupplier B = new DoubleSupplier() {
int m = k;
public double getAsDouble() {
return A(--m, this, x1, x2, x3, x4);
}
};
 
return k <= 0 ? x4.getAsDouble() + x5.getAsDouble() : B.getAsDouble();
}
 
public static void main(String[] args) {
System.out.println(A(10, () -> 1.0, () -> -1.0, () -> -1.0, () -> 1.0, () -> 0.0));
}
}

Java Version 7

public class ManOrBoy {
interface Arg {
public int run();
}
 
public static int A(final int k, final Arg x1, final Arg x2,
final Arg x3, final Arg x4, final Arg x5) {
if (k <= 0)
return x4.run() + x5.run();
return new Arg() {
int m = k;
public int run() {
m--;
return A(m, this, x1, x2, x3, x4);
}
}.run();
}
public static Arg C(final int i) {
return new Arg() {
public int run() { return i; }
};
}
 
public static void main(String[] args) {
System.out.println(A(10, C(1), C(-1), C(-1), C(1), C(0)));
}
}

[edit] JavaScript

In Chrome we get a "Maximum call stack size exceeded" when a > 13. In Firefox we get "too much recursion" when a > 12.

function a(k, x1, x2, x3, x4, x5) {
function b() {
k = k - 1;
return a(k, b, x1, x2, x3, x4);
}
return k <= 0 ? x4() + x5() : b();
}
 
// this uses lambda wrappers around the numeric arguments
function x(n) {
return function () {
return n;
};
}
alert(a(10, x(1), x(-1), x(-1), x(1), x(0)));

[edit] Lua

function a(k,x1,x2,x3,x4,x5)
local function b()
k = k - 1
return a(k,b,x1,x2,x3,x4)
end
if k <= 0 then return x4() + x5() else return b() end
end
 
function K(n)
return function()
return n
end
end
 
print(a(10, K(1), K(-1), K(-1), K(1), K(0)))

[edit] Mathematica

This Mathematica code was derived from the Ruby example appearing below.

$RecursionLimit = 1665; (* anything less fails for k0 = 10 *)

a[k0_, x1_, x2_, x3_, x4_, x5_] := Module[{k, b },
  k = k0;
  b = (k--; a[k, b, x1, x2, x3, x4]) &;
  If[k <= 0, x4[] + x5[], b[]]]
a[10, 1 &, -1 &, -1 &, 1 &, 0 &] (* => -67 *)

[edit] Modula-3

MODULE Main;
IMPORT IO;
 
TYPE Function = PROCEDURE ():INTEGER;
 
PROCEDURE A(k: INTEGER; x1, x2, x3, x4, x5: Function): INTEGER =
 
PROCEDURE B(): INTEGER =
BEGIN
DEC(k);
RETURN A(k, B, x1, x2, x3, x4);
END B;
 
BEGIN
IF k <= 0 THEN
RETURN x4() + x5();
ELSE
RETURN B();
END;
END A;
 
PROCEDURE F0(): INTEGER = BEGIN RETURN 0; END F0;
PROCEDURE F1(): INTEGER = BEGIN RETURN 1; END F1;
PROCEDURE Fn1(): INTEGER = BEGIN RETURN -1; END Fn1;
 
BEGIN
IO.PutInt(A(10, F1, Fn1, Fn1, F1, F0));
IO.Put("\n");
END Main.

[edit] Nimrod

import future
 
proc a(k: int; x1, x2, x3, x4, x5: proc(): int): int =
var k = k
proc b(): int =
dec k
a(k, b, x1, x2, x3, x4)
if k <= 0: x4() + x5()
else: b()
 
echo a(10, () => 1, () => -1, () => -1, () => 1, () => 0)

[edit] Objective-C

Works with: Cocoa version Mac OS X 10.6+
#import <Foundation/Foundation.h>
 
typedef NSInteger (^IntegerBlock)(void);
 
NSInteger A (NSInteger kParam, IntegerBlock x1, IntegerBlock x2, IntegerBlock x3, IntegerBlock x4, IntegerBlock x5) {
__block NSInteger k = kParam;
__block __weak IntegerBlock weak_B;
IntegerBlock B;
weak_B = B = ^ {
return A(--k, weak_B, x1, x2, x3, x4);
};
return k <= 0 ? x4() + x5() : B();
}
 
IntegerBlock K (NSInteger n) {
return ^{return n;};
}
 
int main (int argc, const char * argv[]) {
@autoreleasepool {
NSInteger result = A(10, K(1), K(-1), K(-1), K(1), K(0));
NSLog(@"%d\n", result);
}
return 0;
}

Without ARC, the above should be:

#import <Foundation/Foundation.h>
 
typedef NSInteger (^IntegerBlock)(void);
 
NSInteger A (NSInteger kParam, IntegerBlock x1, IntegerBlock x2, IntegerBlock x3, IntegerBlock x4, IntegerBlock x5) {
__block NSInteger k = kParam;
__block IntegerBlock B;
B = ^ {
return A(--k, B, x1, x2, x3, x4);
};
return k <= 0 ? x4() + x5() : B();
}
 
IntegerBlock K (NSInteger n) {
return [[^{return n;} copy] autorelease];
}
 
int main (int argc, const char * argv[]) {
NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
NSInteger result = A(10, K(1), K(-1), K(-1), K(1), K(0));
NSLog(@"%d\n", result);
[pool drain];
return 0;
}


without Blocks or ARC:

@protocol IntegerFun <NSObject>
-(NSInteger)call;
@end
 
NSInteger A (NSInteger kParam, id<IntegerFun> x1, id<IntegerFun> x2, id<IntegerFun> x3, id<IntegerFun> x4, id<IntegerFun> x5);
 
@interface B_Class : NSObject <IntegerFun> {
NSInteger *k;
id<IntegerFun> x1, x2, x3, x4;
}
-(id)initWithK:(NSInteger *)k x1:(id<IntegerFun>)x1 x2:(id<IntegerFun>)x2 x3:(id<IntegerFun>)x3 x4:(id<IntegerFun>)x4;
@end
 
@implementation B_Class
-(id)initWithK:(NSInteger *)_k x1:(id<IntegerFun>)_x1 x2:(id<IntegerFun>)_x2 x3:(id<IntegerFun>)_x3 x4:(id<IntegerFun>)_x4 {
if ((self = [super init])) {
k = _k;
x1 = [_x1 retain];
x2 = [_x2 retain];
x3 = [_x3 retain];
x4 = [_x4 retain];
}
return self;
}
-(void)dealloc {
[x1 release];
[x2 release];
[x3 release];
[x4 release];
[super dealloc];
}
-(NSInteger)call {
return A(--*k, self, x1, x2, x3, x4);
}
@end
 
NSInteger A (NSInteger k, id<IntegerFun> x1, id<IntegerFun> x2, id<IntegerFun> x3, id<IntegerFun> x4, id<IntegerFun> x5) {
id<IntegerFun> B = [[[B_Class alloc] initWithK:&k x1:x1 x2:x2 x3:x3 x4:x4] autorelease];
return k <= 0 ? [x4 call] + [x5 call] : [B call];
}
 
@interface K : NSObject <IntegerFun> {
NSInteger n;
}
-(id)initWithN:(NSInteger)n;
@end
 
@implementation K
-(id)initWithN:(NSInteger)_n {
if ((self = [super init])) {
n = _n;
}
return self;
}
-(NSInteger)call {
return n;
}
@end
 
int main(int argc, const char *argv[]) {
NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
 
NSInteger result = A(10,
[[[K alloc] initWithN:1] autorelease],
[[[K alloc] initWithN:-1] autorelease],
[[[K alloc] initWithN:-1] autorelease],
[[[K alloc] initWithN:1] autorelease],
[[[K alloc] initWithN:0] autorelease]);
NSLog(@"%ld\n", result);
 
[pool release];
return 0;
}

[edit] Objeck

Using anonymous classes instead of closures

interface Arg {
method : virtual : public : Run() ~ Int;
}
 
class ManOrBoy {
New() {}
 
function : A(mb : ManOrBoy, k : Int, x1 : Arg, x2 : Arg, x3 : Arg, x4 : Arg, x5 : Arg) ~ Int {
if(k <= 0) {
return x4->Run() + x5->Run();
};
 
return Base->New(mb, k, x1, x2, x3, x4) implements Arg {
@mb : ManOrBoy; @k : Int; @x1 : Arg; @x2 : Arg; @x3 : Arg; @x4 : Arg; @m : Int;
 
New(mb : ManOrBoy, k : Int, x1 : Arg, x2 : Arg, x3 : Arg, x4 : Arg) {
@mb := mb; @k := k; @x1 := x1; @x2 := x2; @x3 := x3; @x4 := x4; @m := @k;
}
 
method : public : Run() ~ Int {
@m -= 1;
return @mb->A(@mb, @m, @self, @x1, @x2, @x3, @x4);
}
}->Run();
}
 
function : C(i : Int) ~ Arg {
return Base->New(i) implements Arg {
@i : Int;
New(i : Int) {
@i := i;
}
 
method : public : Run() ~ Int {
return @i;
}
};
}
 
function : Main(args : String[]) ~ Nil {
mb := ManOrBoy->New();
mb->A(mb, 10, C(1), C(-1), C(-1), C(1), C(0))->PrintLine();
}
}
 

[edit] OCaml

OCaml variables are not mutable, so "k" is wrapped in a mutable object, which we access through a reference type called "ref".

let rec a k x1 x2 x3 x4 x5 =
if k <= 0 then
x4 () + x5 ()
else
let m = ref k in
let rec b () =
decr m;
a !m b x1 x2 x3 x4
in
b ()
 
let () =
Printf.printf "%d\n" (a 10 (fun () -> 1) (fun () -> -1) (fun () -> -1) (fun () -> 1) (fun () -> 0))

[edit] Oz

We emulate the ALGOL60 example as closely as possible. Like most of the examples, we use functions to emulate call-by-name.

Oz variables are immutable, so we use a mutable reference ("cell") for K. The ALGOL example uses call-by-value for K. Oz uses call-by-reference, therefore we copy K explicitly when we call A recursively.

We use explicit "return variables" to emulate the strange behaviour of the ALGOL B procedure which assigns a value to A's return value.

declare
fun {A K X1 X2 X3 X4 X5}
ReturnA = {NewCell undefined}
fun {B}
ReturnB = {NewCell undefined}
in
K := @K - 1
ReturnA := {A {NewCell @K} B X1 X2 X3 X4}
ReturnB := @ReturnA
@ReturnB
end
in
if @K =< 0 then ReturnA := {X4} + {X5} else _ = {B} end
@ReturnA
end
 
fun {C V}
fun {$} V end
end
in
{Show {A {NewCell 10} {C 1} {C ~1} {C ~1} {C 1} {C 0}}}

[edit] Perl

sub A {
my ($k, $x1, $x2, $x3, $x4, $x5) = @_;
my($B);
$B = sub { A(--$k, $B, $x1, $x2, $x3, $x4) };
$k <= 0 ? &$x4 + &$x5 : &$B;
}
 
print A(10, sub{1}, sub {-1}, sub{-1}, sub{1}, sub{0} ), "\n";

[edit] Perl 6

This solution avoids creating the closure B if $k <= 0 (that is, nearly every time).

sub A($k is copy, &x1, &x2, &x3, &x4, &x5) {
$k <= 0
?? x4() + x5()
!! (my &B = { A(--$k, &B, &x1, &x2, &x3, &x4) })();
};
 
say A(10, {1}, {-1}, {-1}, {1}, {0});
Output:
-67

[edit] PHP

Works with: PHP version 5.3+
<?php
function A($k,$x1,$x2,$x3,$x4,$x5) {
$b = function () use (&$b,&$k,$x1,$x2,$x3,$x4) {
return A(--$k,$b,$x1,$x2,$x3,$x4);
};
return $k <= 0 ? $x4() + $x5() : $b();
}
 
echo A(10, function () { return 1; },
function () { return -1; },
function () { return -1; },
function () { return 1; },
function () { return 0; }) . "\n";
?>
Works with: PHP version pre-5.3 and 5.3+
<?php
function A($k,$x1,$x2,$x3,$x4,$x5) {
static $i = 0;
$b = "myfunction_$i";
$i++;
eval('function '.$b.'() {
static $k = '
.$k.';
return A(--$k, '
.var_export($b,true).',
'
.var_export($x1,true).',
'
.var_export($x2,true).',
'
.var_export($x3,true).',
'
.var_export($x4,true).');
}'
);
return $k <= 0 ? $x4() + $x5() : $b();
}
 
echo A(10, create_function('', 'return 1;'),
create_function('', 'return -1;'),
create_function('', 'return -1;'),
create_function('', 'return 1;'),
create_function('', 'return 0;')) . "\n";
?>

[edit] PicoLisp

As PicoLisp uses exclusively shallow dynamic binding, stack frames have to be explicitly constructed.

(de a (K X1 X2 X3 X4 X5)
(let (@K (cons K) B (cons)) # Explicit frame
(set B
(curry (@K B X1 X2 X3 X4) ()
(a (dec @K) (car B) X1 X2 X3 X4) ) )
(if (gt0 (car @K)) ((car B)) (+ (X4) (X5))) ) )
 
(a 10 '(() 1) '(() -1) '(() -1) '(() 1) '(() 0))

Output:

-> -67

[edit] PL/I

morb: proc options (main) reorder;
 dcl sysprint file;

 put skip list(a((10), lambda1, lambdam1, lambdam1, lambda0, lambda0));

 a: proc(k, x1, x2, x3, x4, x5) returns(fixed bin (31)) recursive;
   dcl k                    fixed bin (31);
   dcl (x1, x2, x3, x4, x5) entry returns(fixed bin (31));

   b: proc returns(fixed bin(31)) recursive;
     k = k - 1;
     return(a((k), b, x1, x2, x3, x4));
   end b;

   if k <= 0 then
     return(x4 + x5); 
   else
     return(b);
 end a;

 lambdam1: proc returns(fixed bin (31)); return(-1); end lambdam1;
 lambda0:  proc returns(fixed bin (31)); return(1);  end lambda0;
 lambda1:  proc returns(fixed bin (31)); return(1);  end lambda1;
end morb;

The above PL/I code has been tested on OS PL/I V2.3.0, Enterprise PL/I V3R9M0 and PL/I for Windows V8.0. The limit for OS PL/I on a z/OS machine with 4Gb seems to be A=15, the limit for Enterprise PL/I on the same machine seems to be A=23, and the limit for PL/I for Windows on a 16Gb system seems to be A=26.

[edit] Pop11

define A(k, x1, x2, x3, x4, x5);
    define B();
        k - 1 -> k;
        A(k, B, x1, x2, x3, x4)
    enddefine;
    if k <= 0 then
        x4() + x5()
    else
        B()
    endif
enddefine;

define one(); 1 enddefine;
define minus_one(); -1 enddefine;
define zero(); 0 enddefine;
A(10, one, minus_one, minus_one, one, zero) =>

[edit] Python

Works with: Python version 2.5
#!/usr/bin/env python
import sys
sys.setrecursionlimit(1025)
 
def a(in_k, x1, x2, x3, x4, x5):
k = [in_k]
def b():
k[0] -= 1
return a(k[0], b, x1, x2, x3, x4)
return x4() + x5() if k[0] <= 0 else b()
 
x = lambda i: lambda: i
print(a(10, x(1), x(-1), x(-1), x(1), x(0)))
 

A better-looking alternative to using lists as storage are function attributes:

#!/usr/bin/env python
import sys
sys.setrecursionlimit(1025)
 
def a(k, x1, x2, x3, x4, x5):
def b():
b.k -= 1
return a(b.k, b, x1, x2, x3, x4)
b.k = k
return x4() + x5() if b.k <= 0 else b()
 
x = lambda i: lambda: i
print(a(10, x(1), x(-1), x(-1), x(1), x(0)))
 

Output:

-67

[edit] Py3k

Works with: Python version 3.0
#!/usr/bin/env python
import sys
sys.setrecursionlimit(1025)
 
def A(k, x1, x2, x3, x4, x5):
def B():
nonlocal k
k -= 1
return A(k, B, x1, x2, x3, x4)
return x4() + x5() if k <= 0 else B()
 
print(A(10, lambda: 1, lambda: -1, lambda: -1, lambda: 1, lambda: 0))

[edit] R

Like many implementations this uses lambda wrappers around the numeric arguments and explicit function calls in the x4() + x5() step to force the order of evaluation and handle value/call duality.

n <- function(x) function()x
 
A <- function(k, x1, x2, x3, x4, x5) {
B <- function() A(k <<- k-1, B, x1, x2, x3, x4)
if (k <= 0) x4() + x5() else B()
}
 
A(10, n(1), n(-1), n(-1), n(1), n(0))

That is the way any sane person would implement Man-or-Boy. However, we can be a bit more evil than that. Here call.by.name is a function that rewrites the function definition given as its input:

call.by.name <- function(...) {
cl <- as.list(match.call())
sublist <- lapply(cl[2:(length(cl)-1)],
function(name) substitute(substitute(evalq(.,.caller),
list(.=substitute(name))),
list(name=name)))
names(sublist) <- enquote(cl[2:(length(cl)-1)])
subcall <- do.call("call", c("list", lapply(sublist, enquote)))
fndef <- cl[[length(cl)]]
fndef[[3]] <- substitute({
.caller <- parent.frame()
eval(substitute(body, subcall))
}, list(body=fndef[[3]], subcall=subcall))
eval.parent(fndef)
}

allowing us to write A in a way that mirrors ALGOL60 semantics closely:

A <- call.by.name(x1, x2, x3, x4, x5,
function(k, x1, x2, x3, x4, x5) {
Aout <- NULL
B <- function() {
k <<- k - 1
Bout <- Aout <<- A(k, B(), x1, x2, x3, x4)
}
if (k <= 0) Aout <- x4 + x5 else B()
Aout
}
)

One has to increase the recursion limit a bit, but it gives correct answers:

> options(expressions=10000)
> mapply(A, 0:10, 1, -1, -1, 1, 0)
[1] 1 0 -2 0 1 0 1 -1 -10 -30 -67

If you inspect A without the original source you will see what has happened: call.by.name rewrote A so that it looks like this:

> print(A, useSource=FALSE)
function (k, x1, x2, x3, x4, x5)
{
.caller <- parent.frame()
eval(substitute({
Aout <- NULL
B <- function() {
k <<- k - 1
Bout <- Aout <<- A(k, B(), x1, x2, x3, x4)
}
if (k <= 0) Aout <- x4 + x5 else B()
Aout
}, list(x1 = substitute(evalq(., .caller), list(. = substitute(x1))),
x2 = substitute(evalq(., .caller), list(. = substitute(x2))),
x3 = substitute(evalq(., .caller), list(. = substitute(x3))),
x4 = substitute(evalq(., .caller), list(. = substitute(x4))),
x5 = substitute(evalq(., .caller), list(. = substitute(x5))))))
}

That is, instead of evaluating its arguments normally, A captures their original expressions, and instead of evaluating its body normally, A substitutes calls to evalq the captured argument expressions in the calling frame. After a few levels of recursion this way, you end up evaluating expressions like A(k, B(), evalq(B(), .caller), evalq(evalq(B(), .caller), .caller), evalq(evalq(evalq(1, .caller), .caller), .caller), evalq(evalq(evalq(-1, .caller), .caller), .caller)), so this is not very efficient, but works.

[edit] Racket

Copied from Scheme, works fine:

#lang racket
 
(define (A k x1 x2 x3 x4 x5)
(define (B)
(set! k (- k 1))
(A k B x1 x2 x3 x4))
(if (<= k 0)
(+ (x4) (x5))
(B)))
 
(A 10 (lambda () 1) (lambda () -1) (lambda () -1) (lambda () 1) (lambda () 0))

[edit] REXX

The REXX language only passes by value, not by name.   However, there is a way to treat passed arguments as names.
However, using the code below, it only works for   n   up to (and including)   3.

/*REXX program performs the "man or boy" test as far as possible for N. */
do n=0 /*increment N from 0 forever.*/
say 'n='n a(N,x1,x2,x3,x4,x5) /*display the result to the term.*/
end /*n*/ /* [↑] do until something breaks*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────A subroutine────────────────────────*/
a: procedure; parse arg k,x1,x2,x3,x4,x5
if k<=0 then return f(x4)+f(x5)
else return f(b)
/*──────────────────────────────────one─liner subroutines───────────────*/
b: k=k-1; return a(k,b,x1,x2,x3,x4)
f: interpret 'v=' arg(1)"()"; return v
x1: procedure; return 1
x2: procedure; return -1
x3: procedure; return -1
x4: procedure; return 1

output

n=0 1
n=1 0
n=2 -2
n=3 0

[edit] Ruby

Note: the lambda call can be replaced with Proc.new and still work.

def a(k, x1, x2, x3, x4, x5)
b = lambda { k -= 1; a(k, b, x1, x2, x3, x4) }
k <= 0 ? x4[] + x5[] : b[]
end
 
puts a(10, lambda {1}, lambda {-1}, lambda {-1}, lambda {1}, lambda {0})

[edit] Scala

def A(in_k: Int, x1: =>Int, x2: =>Int, x3: =>Int, x4: =>Int, x5: =>Int): Int = {
var k = in_k
def B: Int = {
k = k-1
A(k, B, x1, x2, x3, x4)
}
if (k<=0) x4+x5 else B
}
println(A(10, 1, -1, -1, 1, 0))

[edit] Snap!

Snap-man-or-boy.png

[edit] Scheme

(define (A k x1 x2 x3 x4 x5)
(define (B)
(set! k (- k 1))
(A k B x1 x2 x3 x4))
(if (<= k 0)
(+ (x4) (x5))
(B)))
 
(A 10 (lambda () 1) (lambda () -1) (lambda () -1) (lambda () 1) (lambda () 0))

[edit] Smalltalk

Number>>x1: x1 x2: x2 x3: x3 x4: x4 x5: x5
   | b k |
   k := self.
   b := [ k := k - 1. k x1: b x2: x1 x3: x2 x4: x3 x5: x4 ].
   ^k <= 0 ifTrue: [ x4 value + x5 value ] ifFalse: b

10 x1: [1] x2: [-1] x3: [-1] x4: [1] x5: [0]

[edit] Sparkling

Sparkling does not directly support modifying external local variables. To work around this limitation, we wrap the k variable in an array, which is mutable.

function a(k, x1, x2, x3, x4, x5) {
let kk = { "k": k.k };
let b = function b() {
kk.k--;
return a(kk, b, x1, x2, x3, x4);
};
return kk.k <= 0 ? x4() + x5() : b();
}
 
function x(n) {
return function () {
return n;
};
}
 
print(a({ "k": 10 }, x(1), x(-1), x(-1), x(1), x(0)));

[edit] Standard ML

Standard ML variables are not mutable, so "k" is wrapped in a mutable object, which we access through a reference type called "ref".

fun a (k, x1, x2, x3, x4, x5) =
if k <= 0 then
x4 () + x5 ()
else let
val m = ref k
fun b () = (
m := !m - 1;
a (!m, b, x1, x2, x3, x4)
)
in
b ()
end
 
val () =
print (Int.toString (a (10, fn () => 1, fn () => ~1, fn () => ~1, fn () => 1, fn () => 0)) ^ "\n")

[edit] Swift

func A(var k: Int, x1: () -> Int, x2: () -> Int, x3: () -> Int, x4: () -> Int, x5: () -> Int) -> Int {
var B: (() -> Int)!
B = {
k--
return A(k, B, x1, x2, x3, x4)
}
if k <= 0 {
return x4() + x5()
} else {
return B()
}
}
 
println(A(10, {1}, {-1}, {-1}, {1}, {0}))

[edit] Tcl

There are two nontrivial features in the "man or boy" test. One is that the parameters x1 though x5 are in general going to be function calls that don't get evaluated until their values are needed for the addition in procedure A, which means that these in Tcl are going to be scripts, and therefore it is necessary to introduce a helper procedure C that returns a constant value. The other is that procedure B needs to refer to variables in the local context of its "parent" instance of procedure A. This is precisely what the upvar core command does, but the absolute target level needs to be embedded into the script that performs the delayed call to procedure B (upvar is more often used with relative levels).

proc A {k x1 x2 x3 x4 x5} {
expr {$k<=0 ? [eval $x4]+[eval $x5] : [B \#[info level]]}
}
proc B {level} {
upvar $level k k x1 x1 x2 x2 x3 x3 x4 x4
incr k -1
A $k [info level 0] $x1 $x2 $x3 $x4
}
proc C {val} {return $val}
interp recursionlimit {} 1157
A 10 {C 1} {C -1} {C -1} {C 1} {C 0}

The [info level 0] here is a sort of "self" idiom; it returns the command (with arguments) that called the current procedure.

Since the values of x1 through x4 are never modified, it is also possible to embed these as parameters of B, thereby slightly purifying the program:

proc AP {k x1 x2 x3 x4 x5} {expr {$k<=0 ? [eval $x4]+[eval $x5] : [BP \#[info level] $x1 $x2 $x3 $x4]}}
proc BP {level x1 x2 x3 x4} {AP [uplevel $level {incr k -1}] [info level 0] $x1 $x2 $x3 $x4}
proc C {val} {return $val}
interp recursionlimit {} 1157
AP 10 {C 1} {C -1} {C -1} {C 1} {C 0}

[edit] Visual Prolog

Visual Prolog (like any other Prolog) does not allow variables to be changed. But behavior can easily be mimicked by using a varM (modifiable variable), which is actually an object containing a value of the relevant type in a modifiable entity (a so called fact variable). Secondly, anonymous function (lambda-expression) cannot be recursive, but this is mimicked by using yet a varM to hold the function.

(Token coloring of Visual Prolog in this wiki is unfortunately wrong, because styles are used across languages. A correctly colored version can be seen in Man or boy test in the Visual Prolog wiki).

 
implement main
open core
 
clauses
run():-
console::init(),
stdio::write(a(10, {() = 1}, {() = -1}, {() = -1}, {() = 1}, {() = 0})).
 
class predicates
a : (integer K, function{integer} X1, function{integer} X2, function{integer} X3, function{integer} X4, function{integer} X5) -> integer Result.
clauses
a(K, X1, X2, X3, X4, X5) = R :-
KM = varM::new(K),
BM = varM{function{integer}}::new({() = 0}),
BM:value :=
{ () = BR :-
KM:value := KM:value-1,
BR = a(KM:value, BM:value, X1, X2, X3, X4)
},
R = if KM:value <= 0 then X4() + X5() else BM:value() end if.
 
end implement main

[edit] Vorpal

Adapted from the Lua example. In vorpal, all execution is a message to an object. This task primarily involves functions, so we have the apply the function objects to self for them to execute. Correctly, prints -67.

self.a = method(k, x1, x2, x3, x4, x5){
b = method(){
code.k = code.k - 1
return( self.a(code.k, code, code.x1, code.x2, code.x3, code.x4) )
}
b.k = k
b.x1 = x1
b.x2 = x2
b.x3 = x3
b.x4 = x4
b.x5 = x5
 
if(k <= 0){
return(self.apply(x4) + self.apply(x5))
}
else{
return(self.apply(b))
}
}
 
self.K = method(n){
f = method(){
return(code.n)
}
f.n = n
return(f)
}
 
self.a(10, self.K(1), self.K(-1), self.K(-1), self.K(1), self.K(0)).print()

[edit] zkl

The compiler is OK but the VM is a girlie-man VM. Due to the way closures are built, the stack blows quickly when closures recurse. So, while the code can be written per Knuth, it is unable to do anything. So, classes are used to simulate the closures. Also (5)()-->5 so no problems there.

fcn A(k, x1, x2, x3, x4, x5){ // -->1,0,-2,0,1,0,1,-1,-10,-30,-67,-138	
B:=CB(k, x1, x2, x3, x4, x5);
if(k <= 0) x4()+x5() else B.B();
}
 
foreach k in (12){
println("k=%2d A=%d".fmt(k, A(k, 1, -1, -1, 1, 0)))
}
 
class CB{ var k, x1, x2, x3, x4, x5;
fcn init{ k, x1, x2, x3, x4, x5 = vm.arglist; }
fcn B{
k= k - 1;
A(k, B, x1, x2, x3, x4);
}
}
Output:
k= 0 A=1
k= 1 A=0
k= 2 A=-2
k= 3 A=0
k= 4 A=1
k= 5 A=0
k= 6 A=1
k= 7 A=-1
k= 8 A=-10
k= 9 A=-30
k=10 A=-67
k=11 A=-138
and the stack blows
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