Man or boy test

You are encouraged to 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 x i 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 61,786,266 134,202,509 292,011,464 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





Related tasks





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;

This version resembles more Knuth's original version in that the result of B is thrown away.

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 K

Res_A: Integer;

function B return Integer is

begin

M := M - 1 ;

Res_A := A ( M, B' Access , X1, X2, X3, X4 ) ; -- set result of A

return Res_A;

end B;

begin

if M <= 0 then

return X4. all + X5. all ;

else

declare

Dummy: constant Integer := B; -- throw away

begin

return Res_A;

end ;

end if ;

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

integer

F(list l)

{

l[1];

}



integer

eval(list l)

{

l[0](l);

}



integer A(list);



integer

B(list l)

{

A(list(B, l[1] = l[1] - 1, l, l[-5], l[-4], l[-3], l[-2]));

}



integer

A(list l)

{

integer x;



if (l[1] < 1) {

x = eval(l[-2]) + eval(l[-1]);

} else {

x = B(l);

}



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_(A(list(B, 10, f1, fn1, fn1, f1, f0)), "

");



0;

}

Output:

-67

Knuth's example:

begin real procedure A (k, x1, x2, x3, x4, x5); value k; integer k; real x1, x2, x3, x4, x5; 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.

Translation of: ALGOL 60

Works with: ALGOL 68 version Revision 1 - no extensions to language used

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

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

Works with: BBC BASIC for Windows

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

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

" , 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

" , 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

" , A ( Frame ( & a , & k , & f1 , & fn1 , & fn1 , & f1 , & f0 ) ) ) ;

return 0 ;

}

Output:

-67

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

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:

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 ( ) ;

}

}

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

#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

#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 ;

}

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

uses anonymous functions. Tested with g++ version 4.5 and Visual C++ version 16 (Windows SDK 7.1):uses TR1 without C++11.



// 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

( 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 )



( 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 )

def a ( k, x1, x2, x3, x4, x5 )

b = uninitialized -> typeof ( k )

b = -> ( ) { k - = 1 ; a ( k, b, x1, x2, x3, x4 ) }

k < = 0 ? x4. call + x5. call : b. call

end



puts a ( 10 , -> { 1 } , -> { - 1 } , -> { - 1 } , -> { 1 } , -> { 0 } )

Output:

-67

Straightforward Version [ edit ]

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

" , 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).

Lazy Variadic Function Version [ edit ]

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 ;

}

Template Version [ edit ]

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 ;

}

Anonymous Class Version [ edit ]

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 ) ) ;

}

Faster Version [ edit ]

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 ( "...

500 %-(%s \\

%)" ,

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

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 .

func C(i) {

() => i

}



func A(k, x1, x2, x3, x4, x5) {

var b

b = () => {

k -= 1

A(k, b, x1, x2, x3, x4)

}

if k <= 0 {

x4() + x5()

} else {

b()

}

}



print(A(12, C(1), C(-1), C(-1), C(1), C(0)))

Output:

-291

define method a

(k :: <integer>, x1 :: <function>, x2 :: <function>, x3 :: <function>,

x4 :: <function>, x5 :: <function>)

=> (i :: <integer>)



local b() => (i :: <integer>)

k := k - 1;

a(k, b, x1, x2, x3, x4)

end;



if (k <= 0) x4() + x5() else b() end if



end method a;



define method man-or-boy

(x :: <integer>)

=> (i :: <integer>)



a(x, method() 1 end,

method() -1 end,

method() -1 end,

method() 1 end,

method() 0 end)



end method man-or-boy;



format-out("%d

", man-or-boy(10))

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

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.



;; copied from 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 ) )

→ - 67

( A 13 ( lambda ( ) 1 ) ( lambda ( ) - 1 ) ( lambda ( ) - 1 ) ( lambda ( ) 1 ) ( lambda ( ) 0 ) )

→ - 642

( A 14 .. )

❗ InternalError : too much recursion - JS internal error ( please, report it ) -

→ stack overflow using FireFox



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

open monad io unsafe.cell unsafe.console



liftM2 f m1 m2 = do

x1 <- m1

x2 <- m2

return (f x1 x2)



a k x1 x2 x3 x4 x5 = do

r <- return $ ref k

let b = & do k <- return $ pred (valueof r)

a k b x1 x2 x3 x4

if k <= 0 then liftM2 (+) x4 x5 else b



_ = a 10 (!!1) (!! -1) (!! -1) (!!1) (!!0) >>= (putStr << show) ::: IO

where (!!) f = & return f ::: IO

ELENA 4.1:

import extensions;



A(k,x1,x2,x3,x4,x5)

{

var m := new ref<int>(k);



var b := { m -= 1; ^ A(m,this self,x1,x2,x3,x4) };



if (m <= 0)

{

^ x4() + x5()

}

else

{

^ b()

}

}



public program()

{

for(int n := 0, n <= 14, n += 1)

{

console.printLine(A(n,{^1},{^-1},{^-1},{^1},{^0}))

}

}

Output:

1 0 -2 0 1 0 1 -1 -10 -30 -67 -138 -291 -642 -1446

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 ).

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



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

Works with: gforth version 0.7.9_20180830

Gforth provides flat closures [{: ... :}L ... ;] that are initialized from the stack. You have to perform flat-closure conversion and assignment conversion manually (and this has been done here).

: A {: w^ k x1 x2 x3 xt: x4 xt: x5 | w^ B :} recursive

k @ 0<= IF x4 x5 f+ ELSE

B k x1 x2 x3 action-of x4 [{: B k x1 x2 x3 x4 :}L

-1 k +!

k @ B @ x1 x2 x3 x4 A ;] dup B !

execute THEN ;

10 [: 1e ;] [: -1e ;] 2dup swap [: 0e ;] A f.

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

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 )))

}



By exploiting interfaces, one can more closely parallel the original Algol's polymorphic parameters.

package main



import "fmt"



func eval ( v interface {}) int {

switch v := v . ( type ) {

case int :

return v

case func () int :

return v ()

}

panic ( "bad type" )

return 0

}



func A ( k int , x1 , x2 , x3 , x4 , x5 interface {}) ( 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 = eval ( x4 ) + eval ( x5 )

} else {

_ = B ()

}

return

}



func main () {

fmt . Println ( A ( 10 , 1 , - 1 , - 1 , 1 , 0 ))

}

Inspired by D's "faster" version, here's another that uses a different algorithm to compute the result.

package main



import (

"fmt"

"math/big"

)



func A ( k int ) * big. Int {

one := big . NewInt ( 1 )

c0 := big . NewInt ( 3 )

c1 := big . NewInt ( 2 )

c2 := big . NewInt ( 1 )

c3 := big . NewInt ( 0 )

for j := 5 ; j < k ; j ++ {

c3 . Sub ( c3 . Add ( c3 , c0 ), one )

c0 . Add ( c0 , c1 )

c1 . Add ( c1 , c2 )

c2 . Add ( c2 , c3 )

}

return c0 . Add ( c0 . Sub ( c0 . Sub ( c0 , c1 ), c2 ), c3 )

}



func p ( k int ) {

fmt . Printf ( "A(%d) = " , k )

if s := A ( k ) . String (); len ( s ) < 60 {

fmt . Println ( s )

} else {

fmt . Printf ( "%s...%s (%d digits)

" ,

s [: 6 ], s [ len ( s ) - 5 :], len ( s ) - 1 )

}

}



func main () {

p ( 10 )

p ( 30 )

p ( 500 )

p ( 10000 )

p ( 1e6 )

}

Output:

A(10) = -67 A(30) = -512016658 A(500) = -36608...67320 (172 digits) A(10000) = -19928...34899 (3464 digits) A(1000000) = -67341...95219 (346497 digits)

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

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

" , 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

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

import Data . IORef ( modifyIORef , newIORef , readIORef )



a

:: ( Enum a , Num b , Num a , Ord a )

=> a -> IO b -> IO b -> IO b -> IO b -> IO b -> IO b

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 ( + ) <$> x4 <*> x5

else b

where

f ! r = modifyIORef r f >> readIORef r



main :: IO ( )

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

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

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 )

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

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 ) ) ) ;

}

}

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 -= 1 ;

return a ( k , b , x1 , x2 , x3 , x4 ) ;

}

return ( k > 0 ) ? b ( ) : x4 ( ) + x5 ( ) ;

}



// 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 ) ) ) ;

Implemented using ES6 syntax

var x = n => ( ) => n ;



var a = ( k , x1 , x2 , x3 , x4 , x5 ) => {

var b = ( ) => a ( -- k , b , x1 , x2 , x3 , x4 ) ; //decrement k before use

return ( k > 0 ) ? b ( ) : x4 ( ) + x5 ( ) ;

} ;

From Javascript entry.

/* Knuth's Man or boy test (local references in recursion), in Jsish */

/* As noted, needs a fair sized stack depth, default is 200 in jsish v2.8.24 */

Interp. conf ( { maxDepth : 2048 } ) ;



function a ( k , x1 , x2 , x3 , x4 , x5 ) {

function b ( ) {

k -= 1 ;

return a ( k , b , x1 , x2 , x3 , x4 ) ;

}

return ( k > 0 ) ? b ( ) : x4 ( ) + x5 ( ) ;

}



// this uses lambda wrappers around the numeric arguments

function x ( n ) {

return function ( ) {

return n ;

} ;

}



puts ( a ( 10 , x ( 1 ) , x ( - 1 ) , x ( - 1 ) , x ( 1 ) , x ( 0 ) ) ) ;



/*

=!EXPECTSTART!=

-67

=!EXPECTEND!=

*/

Output:

prompt$ jsish -u manOrBoyTest.jsi [PASS] manOrBoyTest.jsi prompt$ jsish manOrBoyTest.jsi -67

function a(k, x1, x2, x3, x4, x5)

b = ()-> a(k-=1, b, x1, x2, x3, x4);

k <= 0 ? (x4() + x5()) : b();

end



println(a(10, ()->1, ()->-1, ()->-1, ()->1, ()->0));

Using the default JVM stack size, could only get to k = 12 before experiencing an overflow:

// version 1.1.3



typealias Func = ( ) - > Int



fun a ( k : Int, x1 : Func, x2 : Func, x3 : Func, x4 : Func, x5 : Func ) : Int {

var kk = k

fun b ( ) : Int = a ( --kk, :: b, x1, x2, x3, x4 )

return if ( kk <= 0 ) x4 ( ) + x5 ( ) else b ( )

}



fun main ( args : Array < String > ) {

println ( " k a" )

for ( k in 0 .. 12 ) {

println ( "${" % 2d ".format(k)}: ${a(k, { 1 }, { -1 }, { -1 }, { 1 }, { 0 })}" )

}

}



Output:

k a 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

fun A (k, xa, xb, xc, xd, xe) {

print k;

fun B() {

k = k - 1;

return A(k, B, xa, xb, xc, xd);

}

if (k <= 0) {

return xd() + xe();

} else {

return B();

}

}



fun I0() { return 0; }

fun I1() { return 1; }

fun I_1() { return -1; }



print A(10, I1, I_1, I_1, I1, I0);

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 ) ) )

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 *)

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 ( "

" ) ;

END Main.

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)

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 ( ) ;

}

}



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

" , 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

" , 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

" , result ) ;



[ pool release ] ;

return 0 ;

}

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

" ( a 10 ( fun ( ) -> 1 ) ( fun ( ) -> - 1 ) ( fun ( ) -> - 1 ) ( fun ( ) -> 1 ) ( fun ( ) -> 0 ) )

Ol designed as purely functional language, so such 'tricks' with side effects are not allowed.

But! For some reasons in version 1.2 a very limited mutators (set-ref!, set-car!, set-cdr!) are added; so this task can be implemented as usual. Please, be aware that mutators receives only values (small numbers, constants) or previously (before the mutating dest) declared objects.



; Because argument "k" is a small number, it's a value, not an object.

; So we must 'pack' it in object - 'box' it; And 'unbox' when we try to get value.



( define ( box x ) ( list x ) )

( define ( unbox x ) ( car x ) )

( define ( copy x ) ( box ( unbox x ) ) )



( define ( A k x1 x2 x3 x4 x5 )

( define ( B )

( set - car ! k ( - ( unbox k ) 1 ) )

( A ( copy k ) B x1 x2 x3 x4 ) )



( if ( <= ( unbox k ) 0 )

( + ( x4 ) ( x5 ) )

( B ) ) )



( define ( man - or - boy N )

( A ( box N )

( lambda ( ) 1 )

( lambda ( ) - 1 )

( lambda ( ) - 1 )

( lambda ( ) 1 )

( lambda ( ) 0 ) ) )



( print ( man - or - boy 10 ) )

( print ( man - or - boy 15 ) )

( print ( man - or - boy 20 ) )



Output:

-67 -3250 -175416

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 } } }

program manorboy ( output ) ;



function zero : integer ; begin zero : = 0 end ;

function one : integer ; begin one : = 1 end ;

function negone : integer ; begin negone : = - 1 end ;



function A (

k : integer ;

function x1 : integer ;

function x2 : integer ;

function x3 : integer ;

function x4 : integer ;

function x5 : integer

) : integer ;



function B : integer ;

begin k : = k - 1 ;

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

end ;



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

end ;



begin writeln ( A ( 10 , one , negone , negone , one , zero ) )

end .

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 } ) , "

" ;

Ugh. Phix does not allow this sort of nonsense implicitly, so you have to get a bit dirty creative.

Explicitly allocates space (which is automatically freed) for the various "k contexts". Manages up to k=23 in about 10s, but crashes on k=24.

forward function A(integer k, object x1, x2, x3, x4, x5)



function B(sequence s)

object {kptr,x1,x2,x3,x4} = s

integer k = peek4s(kptr)-1

poke4(kptr,k)

return A(k,{kptr,x1,x2,x3,x4},x1,x2,x3,x4)

end function



function A(integer k, object x1, x2, x3, x4, x5)

if k<=0 then

return iff(sequence(x4)?B(x4):x4)+

iff(sequence(x5)?B(x5):x5)

end if

atom kptr = allocate(4,1)

poke4(kptr,k)

return B({kptr,x1,x2,x3,x4})

end function



for k=0 to 10 do

?{"k=",k,A(k,1,-1,-1,1,0)}

end for

Output:

{"k=",0,1} {"k=",1,0} {"k=",2,-2} {"k=",3,0} {"k=",4,1} {"k=",5,0} {"k=",6,1} {"k=",7,-1} {"k=",8,-10} {"k=",9,-30} {"k=",10,-67}

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 ; } ) . "

" ;

?>

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;' ) ) . "

" ;

?>

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

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.

The «Russian» compiler (that is based on Kildall’s compiler PL/I-86) produced the best results. However, two tricks were used there: a) hardware stack pointer was set directly to allocated memory by quasi-assembler’s instruction; b) stack of parameters was replaced by array of parameters and contexts. The result is A=27 for Win32 (Windows-XP) and A=31 for Win64 (Windows-7). Source code test for Win32 see: http://rsdn.org/article/pl1/PL1ex7/pl1ex7.xml In source code test for Win64 FIXED(31) was replaced by FIXED(63) and pseudo-variable ?ESP by ?RSP.

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) =>

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

Py3k [ edit ]

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 ) )

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.

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))

(formerly 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

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 zero forever. */

say 'n=' n a ( N,x1,x2,x3,x4,x5 ) /*display the result to the terminal. */

end /*n*/ /* [↑] do until something breaks. */

exit /*stick a fork in it, we're all done. */

/*──────────────────────────────────────────────────────────────────────────────────────*/

a: procedure ; parse arg k, x1, x2, x3, x4, x5

if k < = 0 then return f ( x4 ) + f ( x5 )

else return f ( b )

/*──────────────────────────────────────────────────────────────────────────────────────*/

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

x5: procedure ; return 0

output

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

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 } )

use std::cell::Cell;



trait Arg {

fn run(&self) -> i32;

}



impl Arg for i32 {

fn run(&self) -> i32 { *self }

}



struct B<'a> {

k: &'a Cell<i32>,

x1: &'a Arg,

x2: &'a Arg,

x3: &'a Arg,

x4: &'a Arg,

}



impl<'a> Arg for B<'a> {

fn run(&self) -> i32 {

self.k.set(self.k.get() - 1);

a(self.k.get(), self, self.x1, self.x2, self.x3, self.x4)

}

}



fn a(k: i32, x1: &Arg, x2: &Arg, x3: &Arg, x4: &Arg, x5: &Arg) -> i32 {

if k <= 0 {

x4.run() + x5.run()

} else {

B{

k: &Cell::new(k),

x1, x2, x3, x4

}.run()

}

}



pub fn main() {

println!("{}", a(10, &1, &-1, &-1, &1, &0));

}

Another solution where we have B take itself as an argument in order to recursively call itself:

use std::cell::Cell;



fn a(k: i32, x1: &Fn() -> i32, x2: &Fn() -> i32, x3: &Fn() -> i32, x4: &Fn() -> i32, x5: &Fn() -> i32) -> i32 {

let k1 = Cell::new(k);

struct B<'a> { f: &'a Fn(&B) -> i32 }

let b = B {

f: &|b| {

k1.set(k1.get() - 1);

return a(k1.get(), &||(b.f)(b), x1, x2, x3, x4)

}

};

let b = ||(b.f)(&b);

return if k <= 0 {x4() + x5()} else {b()}

}



pub fn main() {

println!("{}", a(10, &||1, &||-1, &||-1, &||1, &||0));

}

Another solution that gives a reference-counted function a weak reference to itself:

Translation of: Objective-C

use std::cell::Cell;

use std::cell::RefCell;

use std::rc::Rc;

use std::rc::Weak;



fn a(k: i32, x1: &Fn() -> i32, x2: &Fn() -> i32, x3: &Fn() -> i32, x4: &Fn() -> i32, x5: &Fn() -> i32) -> i32 {

let weak_holder: Rc<RefCell<Weak<Fn() -> i32>>> = Rc::new(RefCell::new(Weak::<fn() -> i32>::new()));

let weak_holder2 = weak_holder.clone();

let k_holder = Cell::new(k);

let b: Rc<Fn() -> i32> = Rc::new(move || {

let b = weak_holder2.borrow().upgrade().unwrap();

k_holder.set(k_holder.get() - 1);

return a(k_holder.get(), &*b, x1, x2, x3, x4);

});

weak_holder.replace(Rc::downgrade(&b));



return if k <= 0 {x4() + x5()} else {b()}

}



pub fn main() {

println!("{}", a(10, &||1, &||-1, &||-1, &||1, &||0));

}

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 ) )

( 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 ) )

func a ( k, x1, x2, x3, x4, x5 ) {

func b { a ( -- k, b, x1, x2, x3, x4 ) } ;

k < = 0 ? ( x4 ( ) + x5 ( ) ) : b ( ) ;

}

say a ( 10 , -> { 1 } , -> { - 1 } , -> { - 1 } , -> { 1 } , -> { 0 } ) ; #=> -67

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

func a ( k, x1, x2, x3, x4, x5 ) {

k < = 0 ? ( x4 ( ) + x5 ( ) )

: func b { a ( -- k, b, x1, x2, x3, x4 ) } ( ) ;

}

say a ( 10 , -> { 1 } , -> { - 1 } , -> { - 1 } , -> { 1 } , -> { 0 } ) ; #=> -67

Alternatively, we can implement it as a class also:

class MOB {

method a ( k, x1, x2, x3, x4, x5 ) {

func b { self . a ( -- k, b, x1, x2, x3, x4 ) } ;

k < = 0 ? ( x4 ( ) + x5 ( ) ) : b ( ) ;

}

}



var obj = MOB ( ) ;

say obj. a ( 10 , -> { 1 } , -> { - 1 } , -> { - 1 } , -> { 1 } , -> { 0 } ) ;

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]

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)));

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)) ^ "

")

Works with: Swift version 3.x+

As of Swift 3.0, closure parameters are "non-escaping" by default. The Man or Boy Test requires the closures to be escaping, and thus we must now annotate the closure parameters with the "@escaping" attribute.

func A(_ k: Int,

_ x1: @escaping () -> Int,

_ x2: @escaping () -> Int,

_ x3: @escaping () -> Int,

_ x4: @escaping () -> Int,

_ x5: @escaping () -> Int) -> Int {

var k1 = k



func B() -> Int {

k1 -= 1

return A(k1, B, x1, x2, x3, x4)

}



if k1 <= 0 {

return x4() + x5()

} else {

return B()

}

}



print(A(10, {1}, {-1}, {-1}, {1}, {0}))

Works with: Swift version 2.x

func A(k: Int, _ x1: () -> Int, _ x2: () -> Int, _ x3: () -> Int, _ x4: () -> Int, _ x5: () -> Int) -> Int {

var k1 = k

func B() -> Int {

k1-=1

return A(k1, B, x1, x2, x3, x4)

}

if k1 <= 0 {

return x4() + x5()

} else {

return B()

}

}



print(A(10, {1}, {-1}, {-1}, {1}, {0}))

Works with: Swift version 1.x

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}))

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 }

SQL is kinda limited, and TSQL is not much better. Unfortunately it fails the Man test due to Stack Level being limited to 32.



CREATE PROCEDURE dbo. LAMBDA_WRAP_INTEGER



@v INT



AS

DECLARE @name NVARCHAR ( MAX ) = 'LAMBDA_' + UPPER ( REPLACE ( NEWID ( ) , '-' , '_' ) )

DECLARE @ SQL NVARCHAR ( MAX ) = '

CREATE PROCEDURE dbo.' + @name + '

AS



RETURN ' + CAST ( @v AS NVARCHAR ( MAX ) )



EXEC ( @ SQL )

RETURN OBJECT_ID ( @name )

GO



CREATE PROCEDURE dbo. LAMBDA_EXEC

@id INT



AS

DECLARE @name SYSNAME = OBJECT_NAME ( @id )

, @retval INT

EXEC @retval = @name

RETURN @retval

GO



-- B-procedure

CREATE PROCEDURE dbo. LAMBDA_B

@name_out SYSNAME OUTPUT

, @q INT

AS

BEGIN



DECLARE @ SQL NVARCHAR ( MAX )

, @name NVARCHAR ( MAX ) = 'LAMBDA_B_' + UPPER ( REPLACE ( NEWID ( ) , '-' , '_' ) )



SELECT @ SQL = N '

CREATE PROCEDURE dbo.' + @name + N '



AS



DECLARE @retval INT, @k INT, @x1 INT, @x2 INT, @x3 INT, @x4 INT



SELECT @k = k - 1, @x1 = x1, @x2 = x2, @x3 = x3, @x4 = x4

FROM #t_args t

WHERE t.i = ' + CAST ( @q AS NVARCHAR ( MAX ) ) + '



UPDATE t

SET k = k -1

FROM #t_args t

WHERE t.i = ' + CAST ( @q AS NVARCHAR ( MAX ) ) + '



EXEC @retval = LAMBDA_A @k, @@PROCID, @x1, @x2, @x3, @x4

RETURN @retval'

EXEC ( @ SQL )



SELECT @name_out = @name

END



GO

-- A-procedure

CREATE PROCEDURE dbo. LAMBDA_A

(



@k INT

, @x1 INT

, @x2 INT

, @x3 INT

, @x4 INT

, @x5 INT

)

AS

SET NOCOUNT ON ;

DECLARE @res1 INT

, @res2 INT

, @Name SYSNAME

, @q INT



-- First add the arguments to the "stack"

INSERT INTO #t_args ( k, x1, x2, x3, x4, x5

)

SELECT @k, @x1, @x2, @x3, @x4, @x5



SELECT @q = SCOPE_IDENTITY ( )



IF @k <= 0

BEGIN

EXEC @res1 = dbo. LAMBDA_EXEC @x4

EXEC @res2 = dbo. LAMBDA_EXEC @x5

RETURN @res1 + @res2

END

ELSE

BEGIN

EXEC dbo. LAMBDA_B @name_out = @Name OUTPUT , @q = @q

EXEC @res1 = @Name

RETURN @res1

END



GO



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

-- Test script

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



DECLARE @x1 INT

, @x2 INT

, @x0 INT

, @x4 INT

, @x5 INT

, @K INT

, @retval INT



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

-- Create wrapped integers to pass as arguments

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

EXEC @x1 = LAMBDA_WRAP_ IN TEGER 1

EXEC @x2 = LAMBDA_WRAP_ IN TEGER - 1

EXEC @x0 = LAMBDA_WRAP_ IN TEGER 0



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

-- Argument storage table

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

CREATE TABLE #t_args (

k INT

, x1 INT

, x2 INT

, x3 INT

, x4 INT

, x5 INT

, i INT IDENTITY

)



SELECT @K = 1



-- Anything above 5 blows up the stack

WHILE @K <= 4

BEGIN

EXEC @retval = dbo. LAMBDA_A @K, @x1, @x2, @x2, @x1, @x0

PRINT 'For k=' + CAST ( @K AS VARCHAR ) + ', result=' + CAST ( @retval AS VARCHAR )



SELECT @K = @K + 1

END





Outputs: For k=1, result=0 For k=2, result=-2 For k=3, result=0 For k=4, result=1

The goal in this solution is to emulate the Algol 60 solution as closely as possible, and not merely get the correct result. For that, we could just crib the Common Lisp or Scheme solution, with more succinct syntax, like this:

(defun A (k x1 x2 x3 x4 x5)

(labels ((B ()

(dec k)

[A k B x1 x2 x3 x4]))

(if (<= k 0) (+ [x4] [x5]) (B))))



(prinl (A 10 (ret 1) (ret -1) (ret -1) (ret 1) (ret 0)))

To do a proper job, we define a call-by-name system as a set of functions and macros. With these, the function A can be defined as a close transliteration of the Algol, as can the call to A with the integer constants:

(defun-cbn A (k x1 x2 x3 x4 x5)

(let ((k k))

(labels-cbn (B ()

(dec k)

(set B (set A (A k (B) x1 x2 x3 x4))))

(if (<= k 0)

(set A (+ x4 x5))

(B))))) ;; value of (B) correctly discarded here!



(prinl (A 10 1 -1 -1 1 0))

We define the global function with defun-cbn ("cbn" stands for "call by name") and the inner function with labels-cbn . These functions are actually macros which call hidden call-by-value functions. The macros create all the necessary thunks out of their argument expressions, and the hidden functions use local macros to provide transparent access to their arguments from their bodies.

Even the fact that a return value is established by an assignment to the function name is simulated. Note that in A and B , we must assign to the variables A and B respectively to establish the return value. This in turn allows the faithful rendition of the detail in the original that the if form discards the value of the call to B . Establishing a return value by assignment, as in Algol, is achieved thanks to the Lisp-2 base of TXR Lisp; we can simultaneously bind a symbol to a function and variable in the same scope.

Also, k is treated as a call-by-name argument also, and is explicitly subject to a rebinding inside A , as is apparently the case in the Algol code. This detail is necessary; if we do not rebind k , then it is a by-name reference to the caller's k , which is a by-name reference to its caller's k and so on.

Call-by-name is achieved by representing arguments as structure objects that hold get/set lambdas, serving as access thunks, hidden behind macros. These thunks allow two-way access: the passed values can be stored, not only accessed. This creates a problem when the actual arguments are constants or function calls; that is solved. Constants are recognized and re-bound to hidden variables, which are passed in their place. Function calls are passed as thunks configured to reject store attempts with a run-time error.

The complete code follows:

(defstruct (cbn-thunk get set) nil get set)



(defmacro make-cbn-val (place)

(with-gensyms (nv tmp)

(cond

((constantp place)

^(let ((,tmp ,place))

(new cbn-thunk

get (lambda () ,tmp)

set (lambda (,nv) (set ,tmp ,nv)))))

((bindable place)

^(new cbn-thunk

get (lambda () ,place)

set (lambda (,nv) (set ,place ,nv))))

(t

^(new cbn-thunk

get (lambda () ,place)

set (lambda (ign) (error "cannot set ~s" ',place)))))))



(defun cbn-val (cbs)

(call cbs.get))



(defun set-cbn-val (cbs nv)

(call cbs.set nv))



(defplace (cbn-val thunk) body

(getter setter

(with-gensyms (thunk-tmp)

^(rlet ((,thunk-tmp ,thunk))

(macrolet ((,getter () ^(cbn-val ,',thunk-tmp))

(,setter (val) ^(set-cbn-val ,',thunk-tmp ,val)))

,body)))))



(defun make-cbn-fun (sym args . body)

(let ((gens (mapcar (ret (gensym)) args)))

^(,sym ,gens

(symacrolet ,[mapcar (ret ^(,@1 (cbn-val ,@2))) args gens]

,*body))))



(defmacro cbn (fun . args)

^(call (fun ,fun) ,*[mapcar (ret ^(make-cbn-val ,@1)) args]))



(defmacro defun-cbn (name (. args) . body)

(with-gensyms (hidden-fun)

^(progn

(defun ,hidden-fun ())

(defmacro ,name (. args) ^(cbn ,',hidden-fun ,*args))

(set (symbol-function ',hidden-fun)

,(make-cbn-fun 'lambda args

^(block ,name (let ((,name)) ,*body ,name)))))))



(defmacro labels-cbn ((name (. args) . lbody) . body)

(with-gensyms (hidden-fun)

^(macrolet ((,name (. args) ^(cbn ,',hidden-fun ,*args)))

(labels (,(make-cbn-fun hidden-fun args

^(block ,name (let ((,name)) ,*lbody ,name))))

,*body))))



(defun-cbn A (k x1 x2 x3 x4 x5)

(let ((k k))

(labels-cbn (B ()

(dec k)

(set B (set A (A k (B) x1 x2 x3 x4))))

(if (<= k 0)

(set A (+ x4 x5))

(B))))) ;; value of (B) correctly discarded here!



(prinl (A 10 1 -1 -1 1 0))

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

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()

In Wren, a fiber's stack starts quite small but is then increased as needed, apparently limited only by available memory. Anyway, satisfying the test for k up to 20 is unlikely to be a problem on a modern machine.

import "/fmt" for Fmt



var a

a = Fn . new { | k , x1 , x2 , x3 , x4 , x5 |

var b

b = Fn . new {

k = k - 1

System . write ( "" ) // guards against a VM recursion bug

return a . call ( k , b , x1 , x2 , x3 , x4 )

}

return ( k <= 0 ) ? x4 . call ( ) + x5 . call ( ) : b . call ( )

}



System . print ( " k a" )

for ( k in 0 .. 20 ) {

Fmt . print ( "$2d : $ d" , k , a . call ( k , Fn . new { 1 } , Fn . new { - 1 } , Fn . new { - 1 } , Fn . new { 1 } , Fn . new { 0 } ) )

}

Output:

k a 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

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