Man or boy test

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.

Knuth's example

In ALGOL 60:

begin
real procedure A;
value k; integer k;
real x1, x2, x3, x4, x5;
begin
real procedure B;
begin k := k - 1;
B := A := A
end;
if k ≤ 0 then A := x4 + x5 else B
end;
outreal
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 for k = 10, the correct answer is −67, despite the fact that in the original article Knuth conjectured it to be −121. Even modern machines quickly run out of stack space for larger values of k, which are tabulated below.


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
15
16
17
18
19
20
21
22
23
24
25
26

Explanation

There are three Algol features used in this program that can be difficult to implement properly in a compiler:

Nested function definitions: Since B is being defined in the local context of A, the body of B has access to symbols that are local to A — most notably k, which it modifies, but also x1, x2, x3, x4, and x5. This is straightforward in the Algol descendant Pascal, but not possible in the other major Algol descendant C.
Function references: The B in the recursive call A is not a call to B, but a reference to B, which will be called only when k is greater than zero. This is straightforward in standard Pascal, and also in C. Some variants of Pascal do not support procedure references, but when the set of functions that may be referenced is known beforehand, this can be worked around.
Constant/function dualism: The x1 through x5 parameters of A may be numeric constants or references to the function B — the x4 + x5 expression must be prepared to handle both cases as if the formal parameters x4 and x5 had been replaced by the corresponding actual parameter. This is probably more of a problem in statically typed languages than in dynamically typed languages, but the standard workaround is to reinterpret the constants 1, 0, and −1 in the main call to A as functions without arguments that return these values.

These things are, however, not what the test is about; they are merely prerequisites for the test to at all be meaningful. What the test is about is whether the different references to B resolve to the correct instance of B — one that has access to the same A-local symbols as the B that created the reference. A "boy" compiler might, for example, instead compile the program so that B always accesses the topmost A call frame.