On 8/29/2024 12:39 PM, Fred. Zwarts wrote:
Op 29.aug.2024 om 15:44 schreef olcott:
On 8/29/2024 2:46 AM, Mikko wrote:
On 2024-08-28 11:51:51 +0000, olcott said:
On 8/28/2024 2:37 AM, Mikko wrote:
This group is for discussions about the theory of computation and
related
topics. Discussion about people is off-topic.
Try to point to the tiniest lack of clarity in this fully
specified concrete example.
void DDD()
{
HHH(DDD);
return;
}
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
HHH computes the mapping from DDD to behavior that never reaches
its "return" statement on the basis of the x86 emulation of DDD
by HHH according to the semantics of the x86 language.
For all the years people said that this simulation is incorrect
never realizing that they were disagreeing with the semantics
of the x86 language.
Now that I point this out all that I get for "rebuttal" is bluster
and double talk.
The same thing applies to this more complex example that
is simply over-the-head of most reviewers:
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
Nice to see that you don't disagree.
But you should not use subject lines that are off-topic for the group. >>>>
When a specific reviewer makes a specific mistake in
reviewing my work related to this group I must refer
to that specific reviewer's mistake to clear my name.
I could generalize it. No one person here besides myself
sufficiently understands the details of how a simulating
halt decider computes the mapping from an input finite
string to the behavior that this finite sting specifies.
It looks more that you are the only person that does not understand
these details, but who thinks that his dreams are a nice substitute
for facts.
I specifically referred to Ben because he got everything
else correctly. Most everyone else cannot even understand
that correct simulation is defined by HHH emulating DDD
according to the semantics of the x86 language.
Olcott does not even understand what the semantics of the x86 language
is. He thinks that a finite string can have different behaviours
according to the semantics of the x86 language, depending on whether
it is directly executed, or simulated by different simulators, where
the semantics could be different for each simulator.
Pathological self-reference DOES CHANGE THE SEMANTICS.
"This sentence is not true" is neither true nor false
because it is not a truth bearer.
This sentence is not true: "This sentence is not true"
The exact same (finite string) sentence applied to a
copy of itself becomes true because the inner sentence
is not a truth-bearer.
Fred thinks the when DDD is emulated by HHH according to
the semantics of the x86 language and this causes an
emulated HHH to not halt then the emulation is wrong.
Olcott has a strange problem with the English language. He is unable
to express himself. When he talks about what other people say, they
never recognize themselves in his words. When he talks about other
things he always expresses himself in self-contradictory ways. It is
not clear to me whether this is only a problem in expressing himself,
it looks as if he also has a problem in understanding English.
I never said such a thing.
I said that a finite string has a unique meaning according to the
semantics of the x86 language.
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
Anyone that studies linguistic meaning knows that context
does change the meaning. That you are ignorant of this
IS NOT MY MISTAKE !!!
On 8/29/2024 12:39 PM, Fred. Zwarts wrote:
Op 29.aug.2024 om 15:44 schreef olcott:
On 8/29/2024 2:46 AM, Mikko wrote:
On 2024-08-28 11:51:51 +0000, olcott said:
On 8/28/2024 2:37 AM, Mikko wrote:
This group is for discussions about the theory of computation and
related
topics. Discussion about people is off-topic.
Try to point to the tiniest lack of clarity in this fully
specified concrete example.
void DDD()
{
HHH(DDD);
return;
}
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
HHH computes the mapping from DDD to behavior that never reaches
its "return" statement on the basis of the x86 emulation of DDD
by HHH according to the semantics of the x86 language.
For all the years people said that this simulation is incorrect
never realizing that they were disagreeing with the semantics
of the x86 language.
Now that I point this out all that I get for "rebuttal" is bluster
and double talk.
The same thing applies to this more complex example that
is simply over-the-head of most reviewers:
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
Nice to see that you don't disagree.
But you should not use subject lines that are off-topic for the group. >>>>
When a specific reviewer makes a specific mistake in
reviewing my work related to this group I must refer
to that specific reviewer's mistake to clear my name.
I could generalize it. No one person here besides myself
sufficiently understands the details of how a simulating
halt decider computes the mapping from an input finite
string to the behavior that this finite sting specifies.
It looks more that you are the only person that does not understand
these details, but who thinks that his dreams are a nice substitute
for facts.
I specifically referred to Ben because he got everything
else correctly. Most everyone else cannot even understand
that correct simulation is defined by HHH emulating DDD
according to the semantics of the x86 language.
Olcott does not even understand what the semantics of the x86 language
is. He thinks that a finite string can have different behaviours
according to the semantics of the x86 language, depending on whether
it is directly executed, or simulated by different simulators, where
the semantics could be different for each simulator.
Pathological self-reference DOES CHANGE THE SEMANTICS.
"This sentence is not true" is neither true nor false
because it is not a truth bearer.
This sentence is not true: "This sentence is not true"
The exact same (finite string) sentence applied to a
copy of itself becomes true because the inner sentence
is not a truth-bearer.
Fred thinks the when DDD is emulated by HHH according to
the semantics of the x86 language and this causes an
emulated HHH to not halt then the emulation is wrong.
Olcott has a strange problem with the English language. He is unable
to express himself. When he talks about what other people say, they
never recognize themselves in his words. When he talks about other
things he always expresses himself in self-contradictory ways. It is
not clear to me whether this is only a problem in expressing himself,
it looks as if he also has a problem in understanding English.
I never said such a thing.
I said that a finite string has a unique meaning according to the
semantics of the x86 language.
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
Anyone that studies linguistic meaning knows that context
does change the meaning. That you are ignorant of this
IS NOT MY MISTAKE !!!
On 8/29/2024 1:11 PM, Fred. Zwarts wrote:
Op 29.aug.2024 om 19:53 schreef olcott:
On 8/29/2024 12:39 PM, Fred. Zwarts wrote:
Olcott does not even understand what the semantics of
the x86 language is. He thinks that a finite string can
have different behaviours according to the semantics
of the x86 language, depending on whether it is directly
executed, or simulated by different simulators, where the
semantics could be different for each simulator.
Pathological self-reference DOES CHANGE THE SEMANTICS.
"This sentence is not true" is neither true nor false
because it is not a truth bearer.
This sentence is not true: "This sentence is not true"
The exact same (finite string) sentence applied to a
copy of itself becomes true because the inner sentence
is not a truth-bearer.
You are changing the subject to irrelevant other subjects.
I am provided a specific concrete counter-example that
correctly refutes your claim that finite strings have
the exact same meaning regardless of context.
It is incorrect to ignore context.
You are incorrect to ignore context.
On 8/29/2024 12:39 PM, Fred. Zwarts wrote:
Op 29.aug.2024 om 15:44 schreef olcott:
On 8/29/2024 2:46 AM, Mikko wrote:
On 2024-08-28 11:51:51 +0000, olcott said:
On 8/28/2024 2:37 AM, Mikko wrote:
This group is for discussions about the theory of computation and related
topics. Discussion about people is off-topic.
Try to point to the tiniest lack of clarity in this fully
specified concrete example.
void DDD()
{
HHH(DDD);
return;
}
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
HHH computes the mapping from DDD to behavior that never reaches
its "return" statement on the basis of the x86 emulation of DDD
by HHH according to the semantics of the x86 language.
For all the years people said that this simulation is incorrect
never realizing that they were disagreeing with the semantics
of the x86 language.
Now that I point this out all that I get for "rebuttal" is bluster
and double talk.
The same thing applies to this more complex example that
is simply over-the-head of most reviewers:
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
Nice to see that you don't disagree.
But you should not use subject lines that are off-topic for the group. >>>>
When a specific reviewer makes a specific mistake in
reviewing my work related to this group I must refer
to that specific reviewer's mistake to clear my name.
I could generalize it. No one person here besides myself
sufficiently understands the details of how a simulating
halt decider computes the mapping from an input finite
string to the behavior that this finite sting specifies.
It looks more that you are the only person that does not understand
these details, but who thinks that his dreams are a nice substitute for
facts.
I specifically referred to Ben because he got everything
else correctly. Most everyone else cannot even understand
that correct simulation is defined by HHH emulating DDD
according to the semantics of the x86 language.
Olcott does not even understand what the semantics of the x86 language
is. He thinks that a finite string can have different behaviours
according to the semantics of the x86 language, depending on whether it
is directly executed, or simulated by different simulators, where the
semantics could be different for each simulator.
Pathological self-reference DOES CHANGE THE SEMANTICS.
"This sentence is not true" is neither true nor false
because it is not a truth bearer.
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
On 8/30/2024 3:02 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
On 8/29/2024 12:39 PM, Fred. Zwarts wrote:
Op 29.aug.2024 om 15:44 schreef olcott:
On 8/29/2024 2:46 AM, Mikko wrote:
On 2024-08-28 11:51:51 +0000, olcott said:
On 8/28/2024 2:37 AM, Mikko wrote:
This group is for discussions about the theory of computation
and related
topics. Discussion about people is off-topic.
Try to point to the tiniest lack of clarity in this fully
specified concrete example.
void DDD()
{
HHH(DDD);
return;
}
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
HHH computes the mapping from DDD to behavior that never reaches >>>>>>> its "return" statement on the basis of the x86 emulation of DDD
by HHH according to the semantics of the x86 language.
For all the years people said that this simulation is incorrect >>>>>>> never realizing that they were disagreeing with the semantics
of the x86 language.
Now that I point this out all that I get for "rebuttal" is bluster >>>>>>> and double talk.
The same thing applies to this more complex example that
is simply over-the-head of most reviewers:
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
Nice to see that you don't disagree.
But you should not use subject lines that are off-topic for the
group.
When a specific reviewer makes a specific mistake in
reviewing my work related to this group I must refer
to that specific reviewer's mistake to clear my name.
I could generalize it. No one person here besides myself
sufficiently understands the details of how a simulating
halt decider computes the mapping from an input finite
string to the behavior that this finite sting specifies.
It looks more that you are the only person that does not understand
these details, but who thinks that his dreams are a nice substitute
for facts.
I specifically referred to Ben because he got everything
else correctly. Most everyone else cannot even understand
that correct simulation is defined by HHH emulating DDD
according to the semantics of the x86 language.
Olcott does not even understand what the semantics of the x86
language is. He thinks that a finite string can have different
behaviours according to the semantics of the x86 language, depending
on whether it is directly executed, or simulated by different
simulators, where the semantics could be different for each simulator. >>>>
Pathological self-reference DOES CHANGE THE SEMANTICS.
No, it does not.
"This sentence is not true" is neither true nor false
because it is not a truth bearer.
Its meaning never changed.
I showed you the before any after, that was before
it changed this is the after"
*This sentence is not true: "This sentence is not true". is true*
It changed because of one level of indirection applied to
pathological self-reference.
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
and all four of them are emulated by the world
class x86 emulator libx86emu
It is easy to see that when the executed HHH emulates
DDD that it does this correctly when we look at the
execution trace and see the the first four instructions
of DDD are listed.
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
New slave_stack at:1038c4
Begin Local Halt Decider Simulation Execution Trace Stored at:1138cc [00002172][001138bc][001138c0] 55 push ebp ; housekeeping
[00002173][001138bc][001138c0] 8bec mov ebp,esp ; housekeeping
[00002175][001138b8][00002172] 6872210000 push 00002172 ; push DDD [0000217a][001138b4][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
New slave_stack at:14e2ec
[00002172][0015e2e4][0015e2e8] 55 push ebp ; housekeeping
[00002173][0015e2e4][0015e2e8] 8bec mov ebp,esp ; housekeeping
[00002175][0015e2e0][00002172] 6872210000 push 00002172 ; push DDD [0000217a][0015e2dc][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
Then this emulated DDD calls an emulated HHH(DDD).
It is easy to see that when the executed HHH emulates
itself emulated DDD that it does this correctly when we
look at the execution trace and see the the first four
instructions of DDD are listed again.
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
and all four of them are emulated by the world
class x86 emulator libx86emu
It is easy to see that when the executed HHH emulates
DDD that it does this correctly when we look at the
execution trace and see the the first four instructions
of DDD are listed.
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
New slave_stack at:1038c4
Begin Local Halt Decider Simulation Execution Trace Stored at:1138cc [00002172][001138bc][001138c0] 55 push ebp ; housekeeping
[00002173][001138bc][001138c0] 8bec mov ebp,esp ; housekeeping
[00002175][001138b8][00002172] 6872210000 push 00002172 ; push DDD [0000217a][001138b4][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
New slave_stack at:14e2ec
[00002172][0015e2e4][0015e2e8] 55 push ebp ; housekeeping
[00002173][0015e2e4][0015e2e8] 8bec mov ebp,esp ; housekeeping
[00002175][0015e2e0][00002172] 6872210000 push 00002172 ; push DDD [0000217a][0015e2dc][0000217f] e853f4ffff call 000015d2 ; call HHH(DDD)
Local Halt Decider: Infinite Recursion Detected Simulation Stopped
Then this emulated DDD calls an emulated HHH(DDD).
It is easy to see that when the executed HHH emulates
itself emulated DDD that it does this correctly when we
look at the execution trace and see the the first four
instructions of DDD are listed again.
It specifies the meanings
but not any finite strings to carry these meanings. The meanings
exist independently of any finite string. A solution or a partial
solution to the problem specifies how each of these meanings shall
be expressed with a finite string for other parts of the solution.
On 8/30/2024 8:22 AM, Mikko wrote:
On 2024-08-30 12:57:49 +0000, olcott said:
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
The correct behaviour is the computation that the user wants to
ask about. If the input string specifies a different behaviour
then the input string is worng, not the behaviour.
int sum(int x, int y) { return x + y; }
And in the exact same way Bill wants to get the
sum of 5+6 from sum(3,2).
HHH must use its actual input as its basis
and it not allowed to use anything else.
DDD emulated by HHH according to the semantics of the x86
language cannot possibly stop running unless aborted and
cannot possibly reach its only final halt state no matter
what HHH does.
Therefore DDD never halts even if everyone> in the universe includingmyself disagrees.
On 8/30/2024 8:22 AM, Mikko wrote:
On 2024-08-30 12:57:49 +0000, olcott said:
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
The correct behaviour is the computation that the user wants to
ask about. If the input string specifies a different behaviour
then the input string is worng, not the behaviour.
int sum(int x, int y) { return x + y; }
And in the exact same way Bill wants to get the
sum of 5+6 from sum(3,2).
HHH must use its actual input as its basis
and it not allowed to use anything else.
DDD emulated by HHH according to the semantics of the x86
language cannot possibly stop running unless aborted and
cannot possibly reach its only final halt state no matter
what HHH does. Therefore DDD never halts even if everyone
in the universe including myself disagrees.
On 8/31/2024 10:24 AM, Fred. Zwarts wrote:
Op 31.aug.2024 om 14:26 schreef olcott:
On 8/30/2024 8:22 AM, Mikko wrote:
On 2024-08-30 12:57:49 +0000, olcott said:
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
The correct behaviour is the computation that the user wants to
ask about. If the input string specifies a different behaviour
then the input string is worng, not the behaviour.
int sum(int x, int y) { return x + y; }
And in the exact same way Bill wants to get the
sum of 5+6 from sum(3,2).
HHH must use its actual input as its basis
and it not allowed to use anything else.
HHH is given a finite string of a halting program.
ARE YOU FREAKING BRAIN DEAD?
HALTING ONLY MEANS REACHING A FINAL HALT STATE
AND DDD EMULATED BY HHH CANNOT POSSIBLY DO THIS.
void DDD()
{
HHH(DDD);
return;
}
_DDD()
[00002172] 55 push ebp ; housekeeping
[00002173] 8bec mov ebp,esp ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404 add esp,+04
[00002182] 5d pop ebp
[00002183] c3 ret
Size in bytes:(0018) [00002183]
On 8/30/2024 8:22 AM, Mikko wrote:
On 2024-08-30 12:57:49 +0000, olcott said:
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
The correct behaviour is the computation that the user wants to
ask about. If the input string specifies a different behaviour
then the input string is worng, not the behaviour.
int sum(int x, int y) { return x + y; }
And in the exact same way Bill wants to get the
sum of 5+6 from sum(3,2).
On 9/1/2024 6:13 AM, Mikko wrote:
On 2024-08-31 12:26:15 +0000, olcott said:
On 8/30/2024 8:22 AM, Mikko wrote:
On 2024-08-30 12:57:49 +0000, olcott said:
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
The correct behaviour is the computation that the user wants to
ask about. If the input string specifies a different behaviour
then the input string is worng, not the behaviour.
int sum(int x, int y) { return x + y; }
And in the exact same way Bill wants to get the
sum of 5+6 from sum(3,2).
If Bill wants to get the sum of 5 + 6 then there are two possibilites:
either you give him a tool that can give him the sum and instrunctions
of use of that tool; or you don't, in which case Bill may ask someone
else.
Bill cannot get the sum of 5+6 from sum(3,2)
the same way that HHH cannot report on the
behavior of the directly executed DDD() on
the basis of DDD emulated by HHH where DDD and
HHH have a pathological relationship.
For three years people have tried to get away with
simply ignoring the elephant in the room of the
pathological relationship between DDD and HHH.
They keep assuming that the behavior of DDD with
a pathological relationship to HHH must be the same
behavior as DDD having no pathological relationship
to HHH1 AGAINST THE VERIFIED FACTS.
When someone contradicts the verified facts this is
the most certain way to determine that they are not
telling the truth.
it now seems like they may have been too indoctrinated
to pay close enough attention to see that their position
directly contradicts verified facts.
Because these things are so dead obvious to me it initially
seemed that they were contradicting the verified facts out
of sadistic pleasure of playing head games.
On 9/1/2024 6:13 AM, Mikko wrote:
On 2024-08-31 12:26:15 +0000, olcott said:
On 8/30/2024 8:22 AM, Mikko wrote:
On 2024-08-30 12:57:49 +0000, olcott said:
On 8/30/2024 3:11 AM, Mikko wrote:
On 2024-08-29 17:53:44 +0000, olcott said:
I just proved that the basic notion of finite strings
having unique meanings independently of their context
is incorrect.
The context is the halting problem.
The behavior of
the directly executed DDD and executed HHH
is different from the behavior of
the emulated DDD and the emulated HHH
The correct behaviour is the computation that the user wants to
ask about. If the input string specifies a different behaviour
then the input string is worng, not the behaviour.
int sum(int x, int y) { return x + y; }
And in the exact same way Bill wants to get the
sum of 5+6 from sum(3,2).
If Bill wants to get the sum of 5 + 6 then there are two possibilites:
either you give him a tool that can give him the sum and instrunctions
of use of that tool; or you don't, in which case Bill may ask someone
else.
Bill cannot get the sum of 5+6 from sum(3,2)
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