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What is the meaning of an expression?

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  What is the meaning of an expression? Roger L Costello <costello@mitre.org> - 2022-01-14 12:15 +0000
    Re: What is the meaning of an expression? anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2022-01-14 18:20 +0000
    Re: What is the meaning of an expression? Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2022-01-15 00:28 +0100
    Re: What is the meaning of an expression? gah4 <gah4@u.washington.edu> - 2022-01-14 17:58 -0800
    Re: What is the meaning of an expression? George Neuner <gneuner2@comcast.net> - 2022-01-15 02:05 -0500
    Re: What is the meaning of an expression? "matt.ti...@gmail.com" <matt.timmermans@gmail.com> - 2022-01-15 06:21 -0800
      Re: What is the meaning of an expression? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2022-02-03 12:50 +0000
    Re: What is the meaning of an expression? Jan Ziak <0xe2.0x9a.0x9b@gmail.com> - 2022-01-16 07:44 -0800
      Re: What is the meaning of an expression? Jan Ziak <0xe2.0x9a.0x9b@gmail.com> - 2022-01-17 15:45 -0800
        Re: What is the meaning of an expression? Jan Ziak <0xe2.0x9a.0x9b@gmail.com> - 2022-01-18 10:03 -0800
          Re: What is the meaning of an expression? gah4 <gah4@u.washington.edu> - 2022-01-18 15:18 -0800
            Re: What is the meaning of an expression? Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2022-01-19 11:54 +0100
              Re: What is the meaning of an expression? Jan Ziak <0xe2.0x9a.0x9b@gmail.com> - 2022-01-19 09:17 -0800
                Re: What is the meaning of an expression? gah4 <gah4@u.washington.edu> - 2022-01-19 14:03 -0800
                Re: What is the meaning of an expression? Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2022-01-20 13:02 +0100
                  Re: What is the meaning of an expression? dave_thompson_2@comcast.net - 2022-01-30 22:51 -0500
              Re: What is the meaning of an expression? Christopher F Clark <christopher.f.clark@compiler-resources.com> - 2022-01-19 20:13 +0200
                Re: What is the meaning of an expression? Thomas Koenig <tkoenig@netcologne.de> - 2022-01-22 20:46 +0000
    Re: What is the meaning of an expression? Thomas Koenig <tkoenig@netcologne.de> - 2022-01-19 20:51 +0000

#2828 — What is the meaning of an expression?

Hello Compiler Experts!

In some book I read this statement:

	The meaning of an expression is
 	the value of the expression.

For example, the meaning of this expression:

	1 + 1

is 2.

Originally I thought I read the statement in some math book, but after
searching through my books and after talking to some mathematicians, I believe
that I did not read it in any math book.

Today while reading the Bison manual, I noticed in it a sentence that said:

	... the meaning of a variable ...

Aha! Perhaps it was in a Bison book or a compiler book that I read the
statement. Is the statement something that you would say? If yes, why do you
say it? The mathematicians and linguists that I spoke to thought the statement
was crazy. Perhaps the statement is appropriate in the context of compilers,
but not elsewhere? Also, from your perspective are these two statements
equivalent:

	The meaning of an expression is
 	the value of the expression.

	The semantics of an expression is
 	the value of the expression.

Do you always use the word "meaning" or do you sometimes use the word
"semantics"? Do the two words mean (no pun intended) the same thing to you,
from a compiler perspective?

/Roger
[I think the meaning here is not to believe everything you read. -John]

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#2829

Roger L Costello <costello@mitre.org> writes:
>Do you always use the word "meaning" or do you sometimes use the word
>"semantics"? Do the two words mean (no pun intended) the same thing to you,
>from a compiler perspective?

"Semantics" is more technical, and not completely synonymous with
"meaning".  When talking about the meaning of a piece of code, we tend
to differentiate between syntax (what is described by a context-free
grammar) and semantics (everything beyond that).  Semantics is divided
into static semantics (how to interpret the code at compile time), and
run-time semantics (what happens at run-time).  Whether you refer to
everything, or just some parts of that when using "meaning" depends on
the context (although I don't think I have seen it used for syntax only).

- anton
--
M. Anton Ertl
anton@mips.complang.tuwien.ac.at
http://www.complang.tuwien.ac.at/anton/

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#2831

On 1/14/22 1:15 PM, Roger L Costello wrote:

> In some book I read this statement:
>
> 	The meaning of an expression is
>   	the value of the expression.

Perhaps in contrast to the meaning of a loop in code?


> Today while reading the Bison manual, I noticed in it a sentence that said:
>
> 	... the meaning of a variable ...

It may mean a state of the program?


You know what I mean:

Expression: I want that evaluated!
Loop: I want that executed repeatedly!
Variable: I want that value rememberd!
#error: I want the compilation aborted!


> [I think the meaning here is not to believe everything you read. -John]

:-)

DoDi

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#2832

On Friday, January 14, 2022 at 9:40:24 AM UTC-8, Roger L Costello wrote:
> Hello Compiler Experts!

> In some book I read this statement:

> The meaning of an expression is
> the value of the expression.

I think that is wrong.

C is a little strange as languages go, but you can have an expression statement like:

   1 + 1

which says to add one and one, and then ignore the result. It has a value, but no meaning.
I suspect most compilers won't even do it, but I never looked.

More common is a function call with side effects, and ignore the value.

printf("Hi there!");

is an expression with the value ignored, but with a meaning.

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#2833

On Fri, 14 Jan 2022 12:15:06 +0000, Roger L Costello
<costello@mitre.org> wrote:

>Hello Compiler Experts!
>
>In some book I read this statement:
>
>	The meaning of an expression is
> 	the value of the expression.
>
>For example, the meaning of this expression:
>
>	1 + 1
>
>is 2.

Just a guess, but it is possible that such a statement might have
accompanied an example of syntax directed translation.


>Is the statement something that you would say?

Informally speaking to someone, I could see myself saying something
like that.  I would never write anything so profound.

No matter what the context, I would (try to) make certain that it was
understood that the statement pertained only to whatever currently was
under discussion.


>The mathematicians and linguists that I spoke to thought the statement
>was crazy.

No doubt. <grin>

The statement is not "crazy" per se, but certainly it is context
dependent and doesn't have any meaning beyond that context.


YMMV,
George

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#2834

> The meaning of an expression is the value of the expression.

That is not true.  This might be said in a magazine article written for laymen
about programming languages, or in a philosophical context that doesn't refer
to practical work.

> The semantics of an expression is the value of the expression.

That's not right either.  The semantics of the *language* determine the
meaning of expressions written in that language.

The meaning of an expression is what you communicate to the compiler or to
readers by writing that expression.

In C, for example,
    int a = 1+1;

means "declare a variable named a of type int, an initialize it with the value
produced by adding the integers 1 and 1".

The expression part of this, "1 + 1", means "the value produced by adding the
integers 1 and 1".   This is *not* the same as "2".  The compiler may
determine that it's equivalent to "2", and will *probably* not write out any
actual addition instructions, but what you *wrote* is an addition, and its
meaning is determined by the semantics of addition as defined in C.

Of course, expressions in most languages can also include function calls and
operators that produce side effects, like "printf("%d",++i);", which certainly
has a meaning even though it produces no meaningful value.

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#2881

On 1/15/2022 2:21 PM, matt.ti...@gmail.com wrote:

> Of course, expressions in most languages can also include function calls and
> operators that produce side effects, like "printf("%d",++i);", which certainly
> has a meaning even though it produces no meaningful value.

Actually, it does.  It returns the number of characters written, or -1
on error.  Therefore, you can write a /meaningful/ hello world like
this,

   int main( int argc, char *argv[] ) { return printf( "hello\n" ); }

Of course, people generally don't like to put the return before the
printf(), and there's no telling what the operating system will do;
think OpenVMS.

--
Johann | email: invalid -> com | www.myrkraverk.com/blog/
I'm not from the Internet, I just work there. | twitter: @myrkraverk

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#2836

On Friday, January 14, 2022 at 6:40:24 PM UTC+1, Roger L Costello wrote:
> For example, the meaning of this expression:
>
> 1 + 1
>
> is 2.

The meaning of 1+1 is a transition between two states. The machine is in state
A before the expression is processed and is in state B after the processing
ends (usually, A and B are different states, albeit in some cases A is the
same as B). A and B are stored in cells of memory (usually: A and B are
distributed over many binary cells). The binary cells can in some cases
influence the emission of photons (such as: bits of GPU's frame-buffer; the
placement of particles of black powder on a white paper coming from a printing
machine).

-atom
[We seem to be pretty deep in this tarpit now. -John]

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#2839

On Sunday, January 16, 2022 at 6:27:58 PM UTC+1, Jan Ziak wrote:
> On Friday, January 14, 2022 at 6:40:24 PM UTC+1, Roger L Costello wrote:
> > For example, the meaning of this expression:
> >
> > 1 + 1
> >
> > is 2.
>
> The meaning of 1+1 is a transition between two states. ....
>
> -atom
> [We seem to be pretty deep in this tarpit now. -John]

@John It's not about a tarpit. If a person believes that the [only] meaning of
1+1 is 2 then it increases the probability that the person does not know about
modulo arithmetic: (1+1 mod 2) is 0. Thus, it is better to adopt the more
general viewpoint that the meaning of an expression is a transition between
two [machine] states. A next concern is the complexity of those states.

-atom
[Now we're even deeper in the tarpit.  Is the "meaning" a mathematical statement,
an instruction to a compiler to generate code computing the value of an expression,
something else?  I don't know, and it's pretty clear none of the rest of us do either.
-John]

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#2840

> Now we're even deeper in the tarpit. Is the "meaning" a mathematical statement,
> an instruction to a compiler to generate code computing the value of an expression,
> something else? I don't know, and it's pretty clear none of the rest of us do either.
> -John

In my opinion, your comments are moving this discussion in the wrong
direction. In the context of compilers: a compiler isn't in control of the
meaning of the source code input into the compiler, because the input might be
a Universal Turing Machine. The compiler knows for certain that the source
code is moving a machine from one state to another state (while not in a
terminating state: perform a state transition) while the source code is being
executed - a compiler isn't trying to answer the question of what the _final_
meanings of those state transitions are. If the compiler tried to answer such
a question, then the compiler might never stop compiling the source code. The
set of terminating states is specified by the source code, not by the
compiler.

-atom
[If you go back the the start of the thread, someone asked about
a statement that "The meaning of an expression is the value of the expression."
I suppose we could ask what it means to a compiler but that seems awfully
anthropomorphic. -John]

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#2841

(snip, and our moderator wrote)

> [If you go back the the start of the thread, someone asked about
> a statement that "The meaning of an expression is the value of the expression."
> I suppose we could ask what it means to a compiler but that seems awfully
> anthropomorphic. -John]

This is reminding me too much about the episodes of Star Trek
where Kirk and Spock have to destroy a computer.  (None of which
ever seem to have a compiler.)

They give a logical inconsistency, which the computer works
on for a while, until smoke comes out and we know it is dead.
(And the computers always talk, making the anthropomorphising
easier.)

As for actual compilers, what do they do with logical inconsistencies?

As above, normally they should just compile what they are given,
and not try to actually process it.  But more and more compilers optimize
code, which means (often enough) that they do processing that would
otherwise be done at run time.

My favorite optimization story, which I heard many years ago when it
was already old, is from the OS/360 Fortran H days.  It seems that
there was a popular Fortran benchmark program that evaluated
some very complicated expression, mostly with the use of statement
functions.  (The sometimes useful, but now deprecated Fortran
feature.)  Fortran H expands statement function inline (it seems
unlike others at the time.)

The result of this, was that the compiler evaluated the
whole complex expression at compile time (very slowly),
and printed the result at run time (very quickly).

So, back to anthropomorphic computers and logical
inconsistencies.  How good are compilers, especially ones
that evaluate constant expressions at compile time, at
dealing with logic failure?  And especially, as the question
needs, expressions that don't have a value?

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#2842

On 1/19/22 12:18 AM, gah4 wrote:

> So, back to anthropomorphic computers and logical
> inconsistencies.  How good are compilers, especially ones
> that evaluate constant expressions at compile time, at
> dealing with logic failure?

Optimization is a special science. A compiler might evaluate a constant
expression properly, in the sense that evaluation at runtime might fail
due to overflows of too narrow types in compiled code.

>  And especially, as the question
> needs, expressions that don't have a value?

Aren't these called *statements*?
Syntax does not normally allow for expressions without values,
semantics disallow the use of subroutines without a return type as part
of an expression.

Expressions always have a value, but if that value is not used further
then the compiler can ignore that part of the source code. Problems can
arise from unrecognized side effects or exceptions eliminated by dead
code elimination.

DoDi

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#2843

On Wednesday, January 19, 2022 at 4:13:36 PM UTC+1, Hans-Peter Diettrich
wrote:
> On 1/19/22 12:18 AM, gah4 wrote:
>
> > So, back to anthropomorphic computers and logical
> > inconsistencies. How good are compilers, especially ones
> > that evaluate constant expressions at compile time, at
> > dealing with logic failure?
> Optimization is a special science. A compiler might evaluate a constant
> expression properly, in the sense that evaluation at runtime might fail
> due to overflows of too narrow types in compiled code.

An analogy: There exist two kinds of compression algorithms: lossy and
lossless. Similarly, there exist two kinds of optimization algorithms. If it
is a lossless optimization algorithm, then any kind of difference between
compile-time evaluation and run-time evaluation is a software bug in the
optimizer. If it is a lossy optimization algorithm, then it should be
sufficiently clearly specified what kind of information is permitted to be
lost during the optimization process.

> > And especially, as the question
> > needs, expressions that don't have a value?
> Aren't these called *statements*?

One could imagine that, as a minimal requirement that has to be fulfilled by
any statement, the "value" of a statement X must include information about
what the next statement is after X is done executing, unless the programmer or
the compiler proves that the statement never terminates by itself.

Back to the original post by Roger L Costello: A problem with both "The
meaning of an expression is its value" and "The semantics of an expression is
the value of the expression" is that some expressions never return a value
because their values aren't computable; we are only able to observe that,
while the expression is being computed/evaluated, it is executing as a
sequence of well-defined steps where each of the steps is known to
evaluate/terminate quickly. If a person adopts the belief that "The
meaning/semantics of an expression is its value" then consequently the person
will later be forced to adopt the belief that it is impossible to know the
meaning of certain kinds of expressions.

-atom

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#2846

(snip, I wrote)
> > > So, back to anthropomorphic computers and logical
> > > inconsistencies. How good are compilers, especially ones
> > > that evaluate constant expressions at compile time, at
> > > dealing with logic failure?

(snip)
> An analogy: There exist two kinds of compression algorithms: lossy and
> lossless. Similarly, there exist two kinds of optimization algorithms. If it
> is a lossless optimization algorithm, then any kind of difference between
> compile-time evaluation and run-time evaluation is a software bug in the
> optimizer. If it is a lossy optimization algorithm, then it should be
> sufficiently clearly specified what kind of information is permitted to be
> lost during the optimization process.

I find the other way around more interesting.

There is a popular Fortran compiler that uses an high precision arithmetic
package to evaluate constant expressions.  As I understand it, it will
accurately calculate sin(1e100).   At run time, though, you only have
normal machine precision.

In most science/engineering problems, data has an uncertainty, and
floating point well represents data with a relative uncertainty. There
is no reasonable answer to sin(x) when x has an uncertainty
of more than 2*pi.  (There is an extremely small branch of mathematics
where problems like this might occur. But never in physics or engineering.)

But in any case, calculating constant expressions more accurately
(or less accurately) means that they won't be equal to the same thing
calculated at run time. (Now, people are supposed to know not to
compare floating point values for equality, but it is still surprising.)

Early Fortran didn't have constant expressions, so any such evaluation
was optional optimization.  More recent versions do, though, so there
are some things that the compiler is required to evaluate at compile time.

I believe that there are cases equivalent to the mentioned C++ cases.

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#2848

On 1/19/22 6:17 PM, Jan Ziak wrote:
> On Wednesday, January 19, 2022 at 4:13:36 PM UTC+1, Hans-Peter Diettrich
> wrote:
>> On 1/19/22 12:18 AM, gah4 wrote:

>>> And especially, as the question
>>> needs, expressions that don't have a value?
>> Aren't these called *statements*?
>
> One could imagine that, as a minimal requirement that has to be fulfilled by
> any statement, the "value" of a statement X must include information about
> what the next statement is after X is done executing, unless the programmer or
> the compiler proves that the statement never terminates by itself.

Can you please specify the language you have in mind?

Languages like C or Pascal distinguish expressions from statements in
their grammar. Allowed is to ignore the value (result) of an expression
evaluation but not to use a non-expression as a value.


> Back to the original post by Roger L Costello: A problem with both "The
> meaning of an expression is its value" and "The semantics of an expression is
> the value of the expression" is that some expressions never return a value

ARAIR K&R C defined the value of a function call to be the value
contained in the accumulator after return. A decision with horrible
consequences if you look at compiler and library source code of that
time. OTOH it derogates the meaning of an expression if at any time one
can find a value in the defined result register.

So I think that it's moot to discuss obscure languages that do not
strictly distinguish expressions from statements. At the abstract level
we could try to define what *is* an expression, with my favorite:
"Evaluation of an expression yields a value."
Then it should be clear that the meaning of an expression is a value.

DoDi
[Early C didn't have default return values, but since the compilers also
didn't do much type checking, I can believe there was a code that
worked by accident becaues the value of the last expression in a function
happened to be in the register where the caller looked for the result.
It's sort of like the Berkeley bug, that there was always a zero byte at
memory location zero so dereferencing null pointers sort of worked. -John]

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#2878

On Thu, 20 Jan 2022 13:02:34 +0100, Hans-Peter Diettrich
<DrDiettrich1@netscape.net> wrote:
...
> ARAIR K&R C defined the value of a function call to be the value
> contained in the accumulator after return. A decision with horrible
> consequences if you look at compiler and library source code of that
> time. OTOH it derogates the meaning of an expression if at any time one
> can find a value in the defined result register.
...
> [Early C didn't have default return values, but since the compilers also
> didn't do much type checking, I can believe there was a code that
> worked by accident becaues the value of the last expression in a function
> happened to be in the register where the caller looked for the result. ...]

Through K&R1 C didn't have 'void' -- all functions had some return
type, which if not written defaulted to 'int' (as in BCPL and B). The
_compilers_ did typecheck but not most _linkers_ so a mismatch across
separately-compiled files was one way to get this problem; one of the
features of 'lint' was to catch such. (FORTRAN had the same issue, and
there were some tools for it, but I don't recall one as prominent.
COBOL, at least then, didn't have value-returning subprograms,
although it could have mismatch on arguments. I don't recall what
Pascals did -- when they had separate compilation at all -- and never
saw a non-toy algol. C++ overloading effectively required typesafe
linkage, and Ada assumed a 'repository' preventing mismatches.)

Another way is if you 'fall off the end' of a (non-void) function, or
through the first standard (C89/90) you wrote and executed a return
statement with no expression; before void this was widely used for
functions with no useful value. If the callsite doesn't discard the
notional 'value' of a call that does one of these, it is officially
undefined behavior and in practice usually takes whatever value is
lying about in the register used by the calling sequence -- but on
PDP-11 and Interdata at least that wasn't 'the accumulator' because
they had no such thing.

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#2844

Not to continue to belabor this overly drawn-out discussion, but
gah4's question of feeding a compiler a logical inconsistency and
having it crash is vaguely relevant.

I have two examples.  The first one, hearsay, from what I consider
normally reliable sources.

The template mechanism of C++ is Turing Complete and unfortunately,
some programmers have taken advantage of that in an attempt to
optimize their programs to an unreasonable extent.  The result is
compilations that take hours for programs that run in seconds and may
only be run once.  I can only imagine someone writing an NP-complete
problem, say 3-SAT as a template and wondering why their compilation
never finishes when they give it a problem with one hundred variables.

The template mechanism may be Turing Complete, but the implementation
doesn't have all the limitations and declarations that make programs
tractable. Moreover, no one has spent years optimizing the template
processor for such cases, and it is not clear that it would be
possible to do so. We don't know how to solve the halting problem. And
the template processor is supposed to *be* the Oracle, not require
one.

The second one was from my own experience working on the Alpha
optimizer at DEC.  The C++ compiler was one of the last pieces of
software to use the one based upon Fred Chow's work.  That was my
responsibility at the time (the optimizer, not the C++ compiler).  In
any case, the front end writers were very aggressive in inlining
subroutines and doing whole-program optimization by that trick.  The
result was very massive files of the intermediate representation.  The
result, for certain large (and important) C++ programs the compiler
would work for days before it had filled up all the paging space on
the engineering cluster at DEC, which was multiple disks of paging and
as a result crashed not only the compiler, but in some cases the
entire cluster.   This made for some very unhappy users, because they
had waited days and they still didn't get a successful compilation.

Fortunately, a small amount of analysis on my part allowed me to
realize that most of the optimizers data structures while N-squared in
size, were actually filled with mostly zero values. Thus, with a
couple days of work I was able to come up with easily implemented
compression schemes that drastically reduced that footprint.  The
result was that the compilation finished in mere minutes, not days,
and more importantly, actually finished, not filled the paging disk
and crashed.

-----

Thus, in that respect the "meaning" of an expression might be vaguely
relevant if the compiler is required to "figure it out".  And, so
while it doesn't take a logical inconsistency to crash a compiler, we
do have the means to do so.  It isn't actually that hard.

--
******************************************************************************
Chris Clark                  email: christopher.f.clark@compiler-resources.com
Compiler Resources, Inc.  Web Site: http://world.std.com/~compres
23 Bailey Rd                 voice: (508) 435-5016
Berlin, MA  01503 USA      twitter: @intel_chris
------------------------------------------------------------------------------

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#2858

Christopher F Clark <christopher.f.clark@compiler-resources.com> schrieb:

> The second one was from my own experience working on the Alpha
> optimizer at DEC.  The C++ compiler was one of the last pieces of
> software to use the one based upon Fred Chow's work.  That was my
> responsibility at the time (the optimizer, not the C++ compiler).  In
> any case, the front end writers were very aggressive in inlining
> subroutines and doing whole-program optimization by that trick.

When to inline and when not to inline is still a major issue today.

> The result was very massive files of the intermediate representation.  The
> result, for certain large (and important) C++ programs the compiler
> would work for days before it had filled up all the paging space on
> the engineering cluster at DEC, which was multiple disks of paging and
> as a result crashed not only the compiler, but in some cases the
> entire cluster.   This made for some very unhappy users, because they
> had waited days and they still didn't get a successful compilation.

https://xkcd.com/303/ and https://dilbert.com/strip/1998-06-04
come to mind :-)


> Fortunately, a small amount of analysis on my part allowed me to
> realize that most of the optimizers data structures while N-squared in
> size, were actually filled with mostly zero values.

Quadratic algorithms (if in space or in time) are a progressively
bad idea.  Programs are getting bigger, and anybody who thinkis
a quadratic algrorithm is OK, will be hit sooner or later with a
(real-life) test case which brings it out into the open.

Just a random example:  Some time ago, a test case for gcc was
submitted which used up hours and Gigabytes for compiliation.
It consisted of a single basic block in a subroutine, with thousands
of variables and thousands of assignments (getting translated into
ten thousands of SSA statements).

This code was not written by a human, but by a computer algrebra
system expanding some complicated formula.

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#2845

Roger L Costello <costello@mitre.org> schrieb:

> In some book I read this statement:
>
> 	The meaning of an expression is
>  	the value of the expression.

Jumping in late...

Computer science teminology can unfortunately be imprecise, and
different people and different documents use different words for
meaing the same thing, and vice versa.

If you  want to know what expression means in a particular language,
look at its standards documents.  For example, Fortran states
(F2018, 10.1.1)

# An expression represents either a data object reference
# or a computation, and its value is either a scalar or an
# array. Evaluation of an expression produces a value, which has a
# type, type parameters (if appropriate), and a shape (10.1.9).

whereas C states (n2596)

# An expression is a sequence of operators and operands that
# specifies computation of a value,92) or that designates an object
# or a function, or that generates side effects, or that performs
# a combination thereof.

so the two languages obviously have different meanings for the
term, and applying one definition to the other language is likely
to lead to confusion (such as about side effects in Fortran
expressions).

I find no definiton of "meaining" in either standard, so although
your question contains the word "meaning", I do not think it
is meaningful.  Know what I mean?

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