Contents of an exception object

[glen herrmannsfeldt]

(snip)

My understanding is that the word "idempotent" has essentially the
same meaning in programming that it has in mathematics, and it's
the meaning Ike describes, not the one you describe.

This article: <http://en.wikipedia.org/wiki/Idempotence> supports
Ike's position (and mine), and flatly contradicts yours.

The first time I remember seeing it was in descriptions of NFS.
As UDP doesn't provide any protection against loss or duplication
of requests, that was important. In the case of no (or delay in)
acknowledgement, repeat the request.

(snip discussing alternate meaning)

-- glen

 

[Stephen Sprunk]

The first time I remember seeing it was in descriptions of NFS. As
UDP doesn't provide any protection against loss or duplication of
requests, that was important. In the case of no (or delay in)
acknowledgement, repeat the request.

I first learned about it with HTTP; GET requests are supposed to be
idempotent for proper interaction with caches (including the local one
in the browser), whereas other methods are generally not.

SIP, which was designed to run on top of UDP, has idempotent
transactions, which are simple request-response, and non-idempotent
ones, which require a three-way handshake to complete.

A _lot_ of braindead protocols, e.g. SMB (aka CIFS), encounter problems
because they don't treat the two cases differently, which either results
in poor performance (too much handshaking for idempotent requests) or
data consistency errors (not enough handshaking for non-idempotent
requests).

S

 

[glen herrmannsfeldt]

Quick summary: Never mind, I was mistaken.

(snip, someone wrote)
(snip)

Interesting, and it shows some about the complications of mapping
between mathematics and computer science.

My previous post is incorrect, and I apologize for the error.
I did not read the Wikipedia article closely enough. In fact,
it does support a meaning for "idempotent" that's close (but not
identical) to the way Malcolm uses the term.

Quoting from the article:

In computer science, the term idempotent is used more
comprehensively to describe an operation that will produce the
same results if executed once or multiple times. This may have
a different meaning depending on the context in which it is
applied. In the case of methods or subroutine calls with side
effects, for instance, it means that the modified state remains
the same after the first call. In functional programming,
though, an idempotent function is one that has the property
f(f(x)) = f(x) for any value x.

OK, but if you consider a system with a state x, and an operation
that changes the state as x=f(x) (that is, C assignment, not
mathematical equality) then doing the operation twice, that is

x=f(x);
x=f(x);

(now written as C statements with semicolons.)

is the same as:

x=f(x);

As I mentioned previously, I first learned about this through NFS.
And NFS read or write request includes the file offset, such that
duplicating the request gives the same result. (Though maybe not
if requests from different hosts are interleaved.)

Duplicating a file creation or deletion request works, as long as
there is no error reported on the second try. (I am actually not
sure how NFS does this. It is usual, for example, to report an
error on attempt to create a directory that exists.)

I was familiar with the mathematical meaning of the term, and the
similar meaning used in functional programming, and I incorrectly
assumed that the same meaning applied to programming in general.
This is the first time I've encountered the usage of "idempotent" to
refer to a function that merely returns the same result for the same
argument, rather than one with the property that f(f(x)) == f(x).

Since mathematical functions tend not to have state, this isn't
so easy to describe.

I agree with Malcolm that it's unfortunate that the term is used
inconsistently.

(Malcolm's definition still doesn't quite match the meaning mentioned
by the Wikipedia article; a function that depends on other things
can still be idempotent.)

-- glen

 

[glen herrmannsfeldt]

(snip)

For instance, if a file write operation is turned into a remote
procedure call, if the packet is repeated, then the write could happen
twice. If the write operation advances the file pointer, then the
server has to take steps to squash duplicate operations.

But if the write operation is idempotent (carries the absolute
location of the write) then there is little harm in just doing
it as many times as it was received. (Of course, the file
modification timestamp will be that of the most recent write,
that is all.)

The fun thing about NFS, at least in the ones I know, is that it
is the time stamp on the server that applies. I have a nice little
NAS box running NFS that I use to store files on. Sometimes it
restarts, and then fails to set the time, possible instead to
many years ago, or even years in the future. Newly modified files
then get that time. I now have a file created in 1937 (I don't remember
if this was the reason) which always sorts as newest in any ls -t
listing.

-- glen

 

[Stephen Sprunk]

The fun thing about NFS, at least in the ones I know, is that it is
the time stamp on the server that applies.

Of course; the server can't trust the clients' clocks to be correct or,
more importantly, to agree with each other. Whether the server's clock
happens to be right or wrong is almost irrelevant; one should use the
_same_ clock for all files, and the server's is the obvious one to choose.

I have a nice little NAS box running NFS that I use to store files
on. Sometimes it restarts, and then fails to set the time, possible
instead to many years ago, or even years in the future. Newly
modified files then get that time. I now have a file created in 1937
(I don't remember if this was the reason) which always sorts as
newest in any ls -t listing.

It's common to see clocks come up as 31 Dec 1969 (western hemisphere) or
1 Jan 1970 (eastern hemisphere), which is (time_t)0 on most *ix systems.
The cost of a battery-backed clock is not justified for a device that
should get the correct time from NTP during their boot cycle, though
Wintel boxes typically have them anyway for historical reasons.

Either 2038, i.e. (time_t)0xffffffff, or 1901, i.e. (time_t)0x80000000,
would also be somewhat understandable; I don't see how you got 1937.

S

 

[Stephen Sprunk]

OK, but if you consider a system with a state x, and an operation
that changes the state as x=f(x) (that is, C assignment, not
mathematical equality) then doing the operation twice, that is

x=f(x);
x=f(x);

(now written as C statements with semicolons.)

is the same as:

x=f(x);

Obviously, this doesn't work in C except in the degenerate case where
f(x)==f(f(x)), which isn't a terribly interesting state machine.

A typical solution is to use transaction numbers, with the last N
results cached. If you receive a new request with an existing number,
e.g. your response was lost, you just send back the cached result for
that number rather than performing the transaction again. Note that due
to various factors, transactions may not arrive or complete in numerical
order (or arrive at all!), so a strict N+1 system will have poor
performance over slow and/or noisy networks, if it works at all.

S

 

[Ian Collins]

yes, you can write individual bit-shuffling functions that use known amounts
of memory. But you can't write a general bit-shuffling function without
access to arbitrary memory.

Who writes "general bit-shuffling" functions? What are they?

Nearly all code is written to perform a specific task. Most <32 bit
embedded code uses static fixed memory and shuns recursion. This
enables static code analyses to confirm it will never use more than the
available memory. I've written tools to perform this analysis, it's an
interesting challenge.

 

[glen herrmannsfeldt]

(snip, I wrote)

(snip)

Obviously, this doesn't work in C except in the degenerate case where
f(x)==f(f(x)), which isn't a terribly interesting state machine.

A typical solution is to use transaction numbers, with the last N
results cached. If you receive a new request with an existing number,
e.g. your response was lost, you just send back the cached result for
that number rather than performing the transaction again.

Well, NFS was designed to be stateless. That is, the server (other
than what is on disk) doesn't store any state. If the server
reboots (either intentionally or after a crash) the client retries
the request and goes on as if nothing happened.

A request might say "write these bytes to a disk file at offset
12345", which, if repeated, gives the same result.

(One complication with NFS is file locking, which is a separate
protocol.)

Note that due to various factors, transactions may not arrive
or complete in numerical order (or arrive at all!), so a
strict N+1 system will have poor performance over slow and/or
noisy networks, if it works at all.

Original NFS used UDP, but now TCP is more common. Even so, the
stream contains a series of requests, and if the stream is broken
and restored, the server will continue on. (Some requests might
have been lost in buffers at the time.)

One that I remember from many years ago (SunOS 3.x days), I made
a hard link to a directory (I didn't know you weren't supposed to
do that, and didn't know about symlinks) which immediately crashed
the NFS server system. After some work to restore the server,
including undoing the link, the client immediately retried the
request (since it didn't know why the server crashed).

-- glen

 

[glen herrmannsfeldt]

(snip, I wrote)

It's common to see clocks come up as 31 Dec 1969 (western hemisphere) or
1 Jan 1970 (eastern hemisphere), which is (time_t)0 on most *ix systems.
The cost of a battery-backed clock is not justified for a device that
should get the correct time from NTP during their boot cycle, though
Wintel boxes typically have them anyway for historical reasons.

Either 2038, i.e. (time_t)0xffffffff, or 1901, i.e. (time_t)0x80000000,
would also be somewhat understandable; I don't see how you got 1937.

Sorry, yes, it is July 8, 2037 15:53:53.

-- glen

 

[Malcolm McLean]

And what kind of function is this:

void map(double (*f)(double), double a[], size_t n)
{
for (size_t i = 0; i < n; i++)
a = f(a);
}

A call like map(sqrt, x, 42); would seem to be "bit-shuffling", but call
it like this:

double print(double x) { printf("%f\n", x); return x; }

...

map(print, x, 3);
and it's pure IO.

This seems to have been lost in the idempotentcy issue, but this bit is
about your function/procedure distinction.

Does an indirect call count?

There are several issues. The main one is, is the function now defined
in terms of the effect of bits, or in terms of the calls made to the
callback? qsort() for example, isn't guaranteed to call the callback any
set number of times, in any particular order, or on any particular pair
of passed-in values. Also, qsort() is pretty clearly a bit (un-) shuffling
function.
But you can pass qsort() a callback with side effects, you can mis-use it
to write code which depends on a particular order of callback evaluation.

So that's a major proviso. If we allow function pointers, then we've
lost the compiler-imposed guarantee that the function can be replaced
by any with equivalent bit effects. But we can in reality replace qsort()
with any sorting function. The guarantee has to be imposed by the
human programmer keeping to the specified interfaces.

The other issue is, can the function be proved correct if passed a
callback that doesn't do IO? Generally the answer is yes, because you
can fake up IO by passing bytes from memory buffers. But not, for
example, if the IO routines are very low level and rely on being called
with certain timings.

Another issue is that, if you allow function pointers, a perverse
programmer can defeat the system with a a perverse use of function
pointers, basically passing in a table of function pointers to make
liberal IO calls. So you're almost but not quite losing the benefit.

The final issue I can think of is that the use of serialisation
streams is a practical problem for showing correctness. Bit shuffling
functions are defined in terms of their effects on bits, which means
the bits they have access to, which is a finite and usually either
small or simple set (by a simple set, I mean you might have a million
employees, but you do essentially the same operation on each one).
When you pass a stream as a parameter, you lose that, and it doesn't
make any practical difference whether it is in or out of memory
(it makes a theoretical difference, of course). Streams are usually
implemented via callbacks, though they don't have to be.

But callbacks are too useful to ban from bit-shuffling functions.

 

[Malcolm McLean]

Malcolm McLean wrote:


Who writes "general bit-shuffling" functions? What are they?

I do.
Most of what I do is designed to produce an output given an input.
Of course the bits are humanly meaningful. The input bits represent
vertices of polygons, all of which are might be "similar", they
might represent what a human would understand as a worm in various
poses. The output bits represent the worm being taken through its
repertoire of poses. How does it work? You build a matrix of
differences, then take eigenvectors. You throw away all but the top
few eigenvectors, say three, then you move a point around in 3D
space, representing the three top eigenvectors. You then convert the
eigenvectors back to xy space for polygons, and the worm wriggles.

That was a program to help analyse the motion of real worms for a
laboratory. Of course it was then hooked up to a graphics system
so you could actually see the worms, but that step was trivial, all
the interest was in the bit shuffling.

Nearly all code is written to perform a specific task. Most <32 bit
embedded code uses static fixed memory and shuns recursion. This
enables static code analyses to confirm it will never use more than the
available memory. I've written tools to perform this analysis, it's an
interesting challenge.

So that's another bit shuffling function, surely?

 

[James Harris]

You can get an effect that suits your purposes, but IMO it won't be
similar to exceptions.

Not the original query but I don't mind explaining what I have got set up.
It is not a "normal" exception mechanism in that it is not automatic.
However, exceptions can be thrown, caught, replaced, cancelled and rethrown.
Once thrown they persist until they are cancelled or replaced. They are easy
to catch and handle. That lot seems to me fairly close to covering the
essentials!

Downsides: Unwinding is manual and I don't at present add any call stack
info to an exception object.

The call stack info is not normally needed because I catch the exceptions
and deal with them rather than reporting them.

How?

See below.

How? I cannot see how that would be possible without language support,
or very intrusive changes to all code which might be "unwound" by an
exception.

The latter.

In fact the changes are not that intrusive. After a call to something which
could throw an exception (or which could itself call something which could
generate an exception) I usually have just

if (exception) return;

(Or "if (exception) return 0;" if the function returns an integer, etc.)

Naturally given the above, resources can be freed before returning, if
needed. For example, here's a piece of code where two things need to be
dealt with: interrupts have been turned off and a timeout has to be
cancelled. So the code restores the interrupt state and cancels the timeout
before returning.

if (exception) {
cpuintrx_set(intstate);
timeout_clear(tmo);
return 0;
}

Handling timeouts has been the main use for this so far. I am interfacing
with hardware and have a number of places where I have nested timeouts. If
the lowest level of timeout expires it throws an exception which gets caught
higher up in the module which set the timeout. That module can then decide
what to do but it can also be operating under a timeout from a higher level.
That is unaffected. It just works. There is a stack of timeout times but
just one exception word.

Frankly, it's awesome to have this in C! There is not much coding to do and
the result is useful and simple.

You can guess the rest but to be clear.... As you can see, exception == 0
means no exception. Where an exception is to be handled the code might be

switch (exception) {
case 0: break; /* No exception */
case EXCEPTION_TIMEOUT:
/* Deal with a timeout */
exception_cancel();
break;
case EXCEPTION_NOMEM:
/* Deal with memory depletion */
exception_cancel();
break;
default:
return 0; /* Pass unhandled exception to caller */
}

Or it could be

if (exception) {
switch (exception) {
... etc

The coding for these is similar to the coding for an automatic mechanism so
there is no loss there.

Ok, I don't think you mentioned that before.

The intial query was about potential contents of the exception object, not
about the mechanism.

Then you would have to
implement abort() yourself -- it could write a register/stack trace to
flash or whatever, and then blink a LED forever, or start a debugger,
or whatever your machine can offer.

I can write to the screen; that's not a problem. In fact my top-level module
has a catch all. If an exception reaches it it writes what the exception was
and, without a call stack, the file and line number where the exception was
thrown, something like

user-defined exception in src/kbc_io.c at line 203

James

 

[Nobody]

"The latter" implies that two options have been provided, and specifies
selection of the second option; "The former" is how you would identify
selection of the first option. I don't recognize an option (two-valued
or otherwise) having been provided. Perhaps it would help if you could
identify the two options that "The former" and "The latter" would refer to?

AFAICT:

The two options are separated by the word "or".

The first option is "a similar effect". The second option is "at least one
that suits my purposes".

The OP implied that they're roughly the same thing. Jorgen took advantage
of the phrasing and responded as if it had been posed as an explicit
choice between two distinct alternatives.

 

[Ben Bacarisse]

And what kind of function is this:

void map(double (*f)(double), double a[], size_t n)
{
for (size_t i = 0; i < n; i++)
a = f(a);
}

A call like map(sqrt, x, 42); would seem to be "bit-shuffling", but call
it like this:

double print(double x) { printf("%f\n", x); return x; }
...
map(print, x, 3);

and it's pure IO.

This seems to have been lost in the idempotentcy issue, but this bit is
about your function/procedure distinction.

But callbacks are too useful to ban from bit-shuffling functions.

It looks like the answer is yes -- it's a bit-shuffling function
according to your classification.

What about the converse? Is the function

void format_int(FILE *fp, int i) { fprintf(fp, "%08d", x); }

An IO procedure even when called with a FILE * representing an in-memory
stream? (It does not apply to standard C, but it's a very common
extension to provide such a thing.)

 

[Ben Bacarisse]

The latter.

In fact the changes are not that intrusive. After a call to something which
could throw an exception (or which could itself call something which could
generate an exception) I usually have just

if (exception) return;

I don't see it yet. How does control get here if the called function
(or one it calls) throws an exception?

<snip>

 

[Malcolm McLean]

It looks like the answer is yes -- it's a bit-shuffling function
according to your classification.

What about the converse? Is the function

void format_int(FILE *fp, int i) { fprintf(fp, "%08d", x); }

An IO procedure even when called with a FILE * representing an in-memory
stream? (It does not apply to standard C, but it's a very common
extension to provide such a thing.)

As I said, stream parameters are a difficult case.
If we provide a version of fprintf() that cannot attach to an external
stream, then indeed it becomes a bit-shuffling function.
It's possible to fake up most IO devices, converting procedures into
bit-shuffling functions. But whilst that's often good and useful
for getting most errors out, it cannot be the final test of correctness.

The other question is whether the function still remains correct
if we replace fprintf() with another piece of code which has the same
effect on bits. Probably it doesn't. If we replace fprintf() with
sprintf(fp->internalbuff, "%08d", x), you'll probably say that the
function is now broken. So the structure's opaque. Shouldn't really
be allowed, because the bit-shuffling function is then defined as
correct /incorrect based on the subroutine calls it makes, whilst
bit-shuffling functions should be defined as correct / incorrect
based on bit state on entry / exit.
However if the subroutines are bit-shuffling functions, then that's
not a problem, because those subroutines are defined in terms of
bit state, even if the definition is cast at rather higher level
than the bit level.

What do I mean by that?

sprintf("%08x", x);

we can define the behaviour of the function as "to write 8 ascii characters
in the range 0-f, representing a hexadecimal number". So any implementation
of sprintf() that returns the result 0000000a when passed "10" is correct,
at least for that input.

but

sprintf("%p", ptr)

we can define as "the behaviour of this function is to write a humanly-
meaningful representation of the pointer ptr.

So we can implement sprintf to return "8000DA7A", or "8000-da7a:",
both are correct. We've defined correctness in a non-mathematical way.
Computers can cope with that, so can human programmers. But a formal
definition in terms of functions that map input to output can't. So
we can actually have opaque structures, we don't need to ban them,
but we need to understand that the bit-shuffling subroutines are
defined at a high level, in terms of what the bits represent, not
what their actual on/off state is.

Parameters which are streams, indirect calls, and opaque structures are
difficult areas. But they're not fatal. The simple rule that a
bit-shuffling function cannot call IO or do IO remains. It's just
that some of the implications go a bit deeper than might first appear.

 

[Ben Bacarisse]

As I said, stream parameters are a difficult case.
If we provide a version of fprintf() that cannot attach to an external
stream, then indeed it becomes a bit-shuffling function.
It's possible to fake up most IO devices, converting procedures into
bit-shuffling functions. But whilst that's often good and useful
for getting most errors out, it cannot be the final test of correctness.

The other question is whether the function still remains correct
if we replace fprintf() with another piece of code which has the same
effect on bits. Probably it doesn't. If we replace fprintf() with
sprintf(fp->internalbuff, "%08d", x), you'll probably say that the
function is now broken. So the structure's opaque. Shouldn't really
be allowed, because the bit-shuffling function is then defined as
correct /incorrect based on the subroutine calls it makes, whilst
bit-shuffling functions should be defined as correct / incorrect
based on bit state on entry / exit.
However if the subroutines are bit-shuffling functions, then that's
not a problem, because those subroutines are defined in terms of
bit state, even if the definition is cast at rather higher level
than the bit level.

What do I mean by that?

sprintf("%08x", x);

we can define the behaviour of the function as "to write 8 ascii characters
in the range 0-f, representing a hexadecimal number". So any implementation
of sprintf() that returns the result 0000000a when passed "10" is correct,
at least for that input.

but

sprintf("%p", ptr)

we can define as "the behaviour of this function is to write a humanly-
meaningful representation of the pointer ptr.

So we can implement sprintf to return "8000DA7A", or "8000-da7a:",
both are correct. We've defined correctness in a non-mathematical way.
Computers can cope with that, so can human programmers. But a formal
definition in terms of functions that map input to output can't. So
we can actually have opaque structures, we don't need to ban them,
but we need to understand that the bit-shuffling subroutines are
defined at a high level, in terms of what the bits represent, not
what their actual on/off state is.

Parameters which are streams, indirect calls, and opaque structures are
difficult areas. But they're not fatal. The simple rule that a
bit-shuffling function cannot call IO or do IO remains. It's just
that some of the implications go a bit deeper than might first
appear.

I could not determine an answer to my question from this. Maybe some
functions can't classified?

 

[James Harris]

I don't see it yet. How does control get here if the called function
(or one it calls) throws an exception?

Basically, each function in the call chain would have the same
test-and-return line at selected points - usually after each call to a
function which could result in an exception - though there are variations.

It is probably clearest if I try to explain what I mean by variations by
making up an example showing different scenarios. Bear in mind that the
overall idea is something I am experimenting with. It is not yet a fully
worked solution that I would recommend to others. It is just something that
seems to be working well for me.

Imagine there are four functions which form a call chain as in

A -> B -> C -> D

So function A calls B, B calls C, and C calls D. Each deals with exceptions
differently but they have to work together. Let's say that D may throw an
exception. Function C does not handle any exceptions at all. That is
probably the most common case. B handles some specific exceptions. Function
A is the final "catcher" for the application and handles all catchable
exceptions one way or another. It could take remedial action in some cases
but in this example it will just report them to a person.

The code in the four functions would be along the following lines.

Function A catches all catchable exceptions and reports them. So after a
call to B it only needs to test whether variable "exception" is non-zero and
if it is to act accordingly.

void A(void) {
.... other code ....
B();
if (exception) {
printf("\n%s exception in %s at line %u\n",
exception_typename_get(exception),
exception_filename_get(),
exception_linenum_get());
}
.... other code ....
}

Function B handles some specific exception types so it might use a switch
statement in order to select which path to take. This is similar to the
traditional use of multiple catch clauses.

void B(void) {
.... other code ....
C();
switch (exception) {
case 0:
break; /* Nothing went wrong */
case EXCEPTION_RANGE:
/* Handle range exception */
exception_cancel();
break;
default:
return; /* Not handled here. Go to caller */
}
.... other code ....
}

Function C doesn't catch any exceptions at all so if one occurs it
immediately returns to its caller.

void C(void) {
.... other code ....
D();
if (exception) return;
.... other code ....
}

Finally, function D doesn't handle exceptions but may throw one or two.

void D(void) {
.... other code ....
if (condition1) {
exception_throw(EXCEPTION_RANGE, __FILE__, __LINE__,
"D", 0);
return;
}
.... other code ....
if (condition2) {
exception_throw(EXCEPTION_USER, __FILE__, __LINE__,
"D", 0);
return;
}
.... other code ....
}

Note that 'throwing' the exception just sets the exception variables. D must
still return to its caller.

In the above scenario, if D throws EXCEPTION_RANGE the effect will be as if
function C was skipped and the exception will be caught by B. If D throws
EXCEPTION_USER the effect will be as if both C and B were skipped and the
exception will be caught by function A.

Note that although B catches the EXCEPTION_RANGE type it does not have to
deal with all such exceptions. After other tests on what specifically went
wrong it could decide either to deal with the issue - in which case it will
call exception_cancel() - or that it doesn't want to deal with the issue -
in which case it will return to its caller with the exception object
unchanged.

The above illustrative code is just as typed in and is untested. I may have
missed something but I hope it gives the idea.

Comments welcome.

James

 

[Malcolm McLean]

I could not determine an answer to my question from this. Maybe some
functions can't classified?

sleep() is an oddball.

But functions either call IO or they don't, defining memory as "not IO",
even though physically the memory might be implemented as a peripheral
device. So that's relatively crisp definition, it can be enforced
automatically.

But callbacks are an interesting special case. You need to enforce
callbacks not modifying any internal or intermediate state used by a
bit-shuffling function, except for the bits that the callback is passed
to modify, or it's not really right to call it a "function",
and you need to enforce that the program doesn't rely on any particular
order or number of calls to the callback. Most programmers do that
anyway, but it's not a nice simple rule like the previous one.

If we're not relying on any particular order or number of callback
calls, it's difficult to see how programs can do IO in the callback
and still have correct behaviour for any pattern of calls.

Most IO can be replaced by non-IO dummy or stub functions, and the
procedures tested for correctness. That's a common technique. If you
don't have barcode reader, write a little function that returns one
from a list of ten barcodes. But it's difficult to test everything
like that.

The idea is simple, the implications aren't so simple.

 

[Ben Bacarisse]

sleep() is an oddball.

What about raise, longjmp, atexit, thrd_create (and friends), mtx_lock
(etc.)? Are they oddballs or simple to classify?

But functions either call IO or they don't, defining memory as "not IO",
even though physically the memory might be implemented as a peripheral
device. So that's relatively crisp definition, it can be enforced
automatically.

But callbacks are an interesting special case. You need to enforce
callbacks not modifying any internal or intermediate state used by a
bit-shuffling function, except for the bits that the callback is passed
to modify, or it's not really right to call it a "function",
and you need to enforce that the program doesn't rely on any particular
order or number of calls to the callback. Most programmers do that
anyway, but it's not a nice simple rule like the previous one.

I don't know what you are saying here. I just can't follow the words.
Is a simple yes/no answer possible for the two examples I gave? If not,
that's fine, I'd just like to know.

Your classification is based on the function, but the examples were
supposed to suggest that it's sometimes the call that determines what
the function does (bit-shuffling or IO).

If we're not relying on any particular order or number of callback
calls, it's difficult to see how programs can do IO in the callback
and still have correct behaviour for any pattern of calls.

Most IO can be replaced by non-IO dummy or stub functions, and the
procedures tested for correctness. That's a common technique. If you
don't have barcode reader, write a little function that returns one
from a list of ten barcodes. But it's difficult to test everything
like that.

The idea is simple, the implications aren't so simple.

I'd say simplistic rather than simple -- I think it misses the
complexity of most programming languages. Maybe it will seem simple
when it's defined well-enough for me to see what functions are in which
category.