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!standard 1.1.4(12)          10-06-03 AI05-0176-1/07
!standard 4.4(7)
!standard 4.5.9(0)
!class Amendment 09-10-28
!status Amendment 2012 10-06-03
!status work item 10-06-18 [rejected by WG 9]
!status ARG Approved 6-1-3 10-02-27
!status work item 09-10-28
!priority Low
!difficulty Easy
!subject Quantified expressions
!summary
Syntax is added for quantified expressions over a finite domain.
!problem
It is very common in formal development to define a predicate over a collection to express the fact that all elements of the collection satisfy a given property or that at least one element of the collection satisfies it. (This is of course borrowed from the language of set theory and fornal logic). For example, the fact that an array A is sorted can be expressed by stating that for all values of an index I in the range from A'First to A'Last - 1 inclusive, the property A(I) <= A (I+1) holds. Mathematical usage is to write, e.g. forall X | P (X), to indicate that all elements X satisfy the property P (X).
When using such notation, the context is supposed to indicate the universe in which the elements X are to be found. This is of course not usable in a programming language that is meant to be executable, and the syntax must indicate the domain of definition of the element (which is some finite set). The common notation is:
for all X in domain | P (X),
Similarly, to indicate that at least one element of the domain satisfies a given property, we might write
for some X in domain | P (X)
The domain can be a discrete range, or an expression that designates a container. The first is typically used when the collection is an array, and the index (the bound variable in the expression) is used to denote an element of the collection in the following predicate. When there is no defined index for the collection, and there is a default iterator for it, the bound variable denotes directly an element of the collection, and we can use the proposed syntax of AI05-0139-2 to write:
for all X of Directory | Name (X)'Length < 20
Where Directory is some container, or an array.
Quantified expressions will prove particularly useful in pre/postconditions and type invariants.
!proposal
Introduce quantified expressions in the language, with their usual meaning: boolean expressions that verify whether all (resp. at least one) element in a collection (array or container) satisfies a given predicate. Introduce a non-reserved keyword: "some" to support this feature.
Quantified expressions have the following syntax:
( for quantifier loop_parameter_specification | Boolean_Expression )
The loop_parameter_specification is the one proposed in AI05-0139-2 for iterators. It includes default iterations over discrete ranges and over containers, as well as user-defined iterations over such.
!wording
Modify 1.1.4(12):
* A vertical line separates alternative items unless it immediately occurs
after an opening curly bracket{ or a loop_parameter_specification}, in which case it stands for itself:
Add to 4.4 (7) a new kind of primary:
quantified_expression
Add a new clause (after the proposed clauses for conditional expressions (AI05-0147) and case expressions (AI05-0188-1):
4.5.9 Quantified expressions
Syntax
quantified_expression ::= for quantifier loop_parameter_specification | predicate quantifier ::= all | some predicate ::= boolean_expression
[Editor's Note: "Some" is not a reserved word and is not given in boldface.]
AARM Ramification: The vertical line ('|') between the loop_parameter_specification and the predicate is an explicit vertical line; it does not separate alternative items as it does elsewhere in the syntax. See 1.1.4.
Wherever the Syntax Rules allow an expression, a quantified_expression may be used in place of the expression, so long as it is immediately surrounded by parentheses.
AARM Discussion: The syntactic category quantified_expression appears only as a primary that is parenthesized. The above rule allows it to additionally be used in other contexts where it would be directly surrounded by parentheses. This is the same rule that is used for conditional_expressions; see 4.5.7 for a detailed discussion of the meaning and effects of this rule.
Name Resolution Rules
The expected type of a quantified_expression is any Boolean type. The predicate in a quantified_expression is expected to be of the same type.
Dynamic Semantics
For the evaluation of a quantified_expression, the loop_parameter_specification is first elaborated. The evaluation of a quantified_expression then evaluates the predicate for each value of the loop parameter. These values are examined in the order specified by the loop_parameter_specification (see 5.5).
The value of the quantified_expression is determined as follows:
* If the quantifier is "all", the expression is True if the evaluation of the
predicate yields True for each value of the loop parameter. It is False otherwise. Evaluation of the quantified_expression stops when all values of the domain have been examined, or when the predicate yields False for a given value. Any exception raised by evaluation of the predicate is propagated.
AARM ramification: The expression is True if the domain contains no values.
* If the quantifier is "some", the expression is True if the evaluation of the
predicate yields True for some value of the loop parameter. It is False otherwise. Evaluation of the quantified_expression stops when all values of the domain have been examined, or when the predicate yields True for a given value. Any exception raised by evaluation of the predicate is propagated.
AARM ramification: The expression is False if the domain contains no values.
Note: Some is not a reserved word.
Examples
The postcondition for a sorting routine on an array A with an index subtype T can be written:
Post => (for all I in A'First .. T'Pred(A'Last) | A (I) <= A (T'Succ (I)))
The assertion that a positive number is composite (as opposed to prime) can be written:
pragma Assert (for some X in 2 .. N / 2 | N mod X = 0);
!discussion
Instead of a vertical bar, we could use a colon or a right arrow to separate the iterator from the condition. The proposed notation is more common in mathematics but the vertical bar has already other uses in Ada syntax.
The order of evaluation is fixed by the iterator used in the loop_parameter_specification, so there is a strong assumption of sequentiality. Not clear how to indicate that a quantified expression can be evaluated in parallel, given that we have no mechanism to parallelize loops either.
!example
(See Wording.)
!corrigendum 1.1.4(12)
Replace the paragraph:
• A vertical line separates alternative items unless it immediately occurs after an opening curly bracket, in which case it stands for itself:
by:
• A vertical line separates alternative items unless it immediately occurs after an opening curly bracket or a loop_parameter_specification, in which case it stands for itself:
!corrigendum 4.4(7)
Replace the paragraph:
primary ::= numeric_literal | null | string_literal | aggregate | name | qualified_expression | allocator | (expression)
by:
primary ::= numeric_literal | null | string_literal | aggregate | name | qualified_expression | allocator | (expression) | (quantified_expression)
!corrigendum 4.5.9(0)
Insert new clause:
Syntax
quantified_expression ::= for quantifier loop_parameter_specification | predicate quantifier ::= all | Some predicate ::= boolean_expression
Wherever the Syntax Rules allow an expression, a quantified_expression may be used in place of the expression, so long as it is immediately surrounded by parentheses.
Name Resolution Rules
The expected type of a quantified_expression is any Boolean type. The predicate in a quantified_expression is expected to be of the same type.
Dynamic Semantics
For the evaluation of a quantified_expression, the loop_parameter_specification is first elaborated. The evaluation of a quantified_expression then evaluates the predicate for each value of the loop parameter. These values are examined in the order specified by the loop_parameter_specification (see 5.5).
The value of the quantified_expression is determined as follows:
• If the quantifier is all, the expression is True if the evaluation of the predicate yields True for each value of the loop parameter. It is False otherwise. Evaluation of the quantified_expression stops when all values of the domain have been examined, or when the predicate yields False for a given value. Any exception raised by evaluation of the predicate is propagated.
• If the quantifier is Some, the expression is True if the evaluation of the predicate yields True for some value of the loop parameter. It is False otherwise. Evaluation of the quantified_expression stops when all values of the domain have been examined, or when the predicate yields True for a given value. Any exception raised by evaluation of the predicate is propagated.
Notes:
Some is not a reserved word.
Examples
The postcondition for a sorting routine on an array A with an index subtype T can be written:
Post => (for all I in A'First .. T'Pred(A'Last) | A (I) <= A (T'Succ (I)))
The assertion that a positive number is composite (as opposed to prime) can be written:
pragma Assert (for some X in 2 .. N / 2 | N mod X = 0);
!ACATS test
Add an ACATS C-Test to test the syntax and semantics.
!appendix
```
From: Robert Dewar
Sent: Thursday, March 5, 2009  2:44 PM

...

And while we are at it, if we are talking useful stuff in PPC's, how about
adding quantifiers while we are at it

(for all X in Sint => Sqrt (X) < 23)

or something like that ...

****************************************************************

From: Ed Schonberg
Sent: Thursday, March 5, 2009  2:52 PM

Would mesh nicely with  some new iterator forms, of course...  There
is no concern here that the iteration might not finish.

****************************************************************

From: Ed Schonberg
Sent: Sunday, March 15, 2009  9:07 AM

> where lhs is the same (possibly complex) lhs. much cleaner and clearer
> to write
>
>   lhs := (if bla then 3 else 4);

Agreed, this will be used abundantly.  I like the default boolean True
interpretation when the else part is missing.

Not convinced about the need for case expressions, but would like to see a
similar proposal for what Randy calls loop expressions, i.e.  quantified
expressions.

****************************************************************

From: Robert Dewar
Sent: Sunday, March 15, 2009  9:30 AM

The tricky issue in quantifiers is how to deal with iterators.

****************************************************************

From: Ed Schonberg
Sent: Sunday, March 15, 2009  9:41 AM

Of course, but the point is to find a very light syntax, so this is not
necessarily tied up to the full iterator proposal that Randy developed. To be
useful is should cover both arrays and containers with a similar syntax, and
should mention elements, not cursors, something like

(for all E in A : F (E) > 0)

If this is defined as a tampering context we can probably simplify semantics and
termination issues. Should this be short-circuited? etc.

****************************************************************

From: Robert Dewar
Sent: Sunday, March 15, 2009  10:20 AM

Definitely short circuited, this is a search for a counterexample and no point
in continuing once a counterexample has been found.

The question to me is does this only work with built in containers, or is there
a way to make your own containers pick up the iteraction.

Also do we have

(exists E in A : F(E) > 0)

con: another keyword

pro: a bit more transparent then

not (for all E in A : F(E) <= 0)

Also, are we sure : is right, I think | might be better

(for all E in A | F (E) > 0)

though I guess to some mathematicians it will read as such that, and perhaps we
should allow the full notation

(for all E in A | E > 0 : F (E) > 0)

read "for all E in A such that E > 0, it is the case that F (E) > 0"

BTW, an implementation is allowed and perhaps encouraged to allow the forall
symbol to replace for all as a representation alternative. Could even require it
(surely a better use of invading mysterious characters in the language proper
than pi in the numerics stuff!)

****************************************************************

From: Bob Duff
Sent: Sunday, March 15, 2009  9:46 AM

...

>...but would like to
> see a similar proposal for what Randy calls loop expressions, i.e.
> quantified expressions.

I've no idea what quantified expressions should look like or mean, so I too
would like to see a proposal.  Didn't Cyrille volunteer to send one to

****************************************************************

From: Edmond Schonberg
Sent: Monday, March 16, 2009  2:08 PM

> I've no idea what quantified expressions should look like or mean, so
> I too would like to see a proposal.  Didn't Cyrille volunteer to send

I'm sure you do, you just forgot!  Quantified expressions are first- order
formulae over sets (that is to say any kind of container). They are either
universal (using the forall quantifier) or existential (using the exists
quantifier).  They use a bound variable to indicate  some property of elements
of the set.  So for example  :   forall X in  S | P (X)

which is True is all elements of S satisfy property P.  The existential
quantifier is redundant, because we can always rewrite:

Exists X in S | P (X)

as

not (forall X in S | not P (X))

but it' cheap and nicer to have both quantifiers.

The run-time semantics of such a construct are short-circuited, i.e.
the implicit iteration stops as soon as an example has been found.

The necessary constituents are a container and a predicate. The scope of the
bound variable is the body of the predicate. Now figure out the best syntax for
this, preferably one that feels natural in Ada!

****************************************************************

From: Randy Brukardt
Sent: Monday, March 16, 2009  2:17 PM

> I'm sure you do, you just forgot!  Quantified expressions are
> first- order formulae over sets (that is to say any kind of
> container). They are either universal (using the forall
> quantifier) or existential (using the exists quantifier).
> They use a bound variable to indicate some property of elements of the
> set.

Could you translate this into English? This sounds like some philosophy class
run amok. :-)

(Specifically, what do you mean by "universal" and "existential" here??)

****************************************************************

From: Edmond Schonberg
Sent: Monday, March 16, 2009  2:36 PM

Now now, just look at the examples. A universally quantified
expression says:   all elements of this set  have this particular
property.
An existentially quantified one says :  there does exist one element of this
set that satisfies this property .  Both of these are in fact loops over a
set, and their naive implementation is:

forall := false;
Elmt := First_Element (S);
while Present (Elmt) loop
if not P(X) then
forall := False;
exit;
end if;
Next_Elmt (Elmt);
end loop;

And the converse for Exists.  This conventional interpretation means that a
universally quantified expression over a null set is always true (all the
elements of the empty set are green, for example).

The rest is syntax.  Conventional mathematical notation is    Forall
(X)  (P (X))   which is tricky to implement because it doesn't say
where X comes from  (the domain is implicit in the condition itself).
For an executable programming language you want to specify the domain
explicitly, and unless you have lazy evaluation you want the domain to be
finite.  A number of years ago SETL chose the notation
(forall X in S | P(X)).   Instead of the vertical bar I've seen
suggestions for a colon, maybe closer to existing conventions in C- languages.

****************************************************************

From: Randy Brukardt
Sent: Monday, March 16, 2009  3:01 PM

Thanks for the clear explanation. This one I understand (and probably use from
time-to-time, I just didn't know it had a name).

****************************************************************

From: Robert Dewar
Sent: Monday, March 16, 2009  2:39 PM

> Could you translate this into English? This sounds like some
> philosophy class run amok. :-)

No, more like a review of a very elementary math course :-)

> (Specifically, what do you mean by "universal" and "existential"
> here??)

Well here I can't follow Randy's I-dont-know-no-stinking-math philosophy
universal and existential quantifiers seem totally familiar and natural to me.

****************************************************************

From: Randy Brukardt
Sent: Monday, March 16, 2009  2:59 PM

> No, more like a review of a very elementary math course :-)

Sorry, Robert, the last formal math course I took was 29 years ago. Unless I've
had reason to use the information in my day-to-day work, I've almost certainly
forgotten it.

> > (Specifically, what do you mean by "universal" and "existential"
> > here??)
>
> Well here I can't follow Randy's I-dont-know-no-stinking-math
> philosophy universal and existential quantifiers seem totally familiar
> and natural to me.

I think it is the terms "universal quantifiers" and "existential quantifiers"
here that threw me; Ed explains an "if all" and "if exist" (that's the backwards
E if I remember right) relationship. That I understand; I still don't remember
ever hearing them given these names. Sorry if that offends your sense of math
correctness (a version of political correctness, I think).

****************************************************************

From: Robert Dewar
Sent: Monday, March 16, 2009  4:33 PM

> I think it is the terms "universal quantifiers" and "existential
> quantifiers" here that threw me; Ed explains an "if all" and "if exist"
> (that's the backwards E if I remember right) relationship. That I
> understand; I still don't remember ever hearing them given these names.

See you *do* remember stuff from all that time ago :-)

> Sorry if that offends your sense of math correctness (a version of
> political correctness, I think).

Something like that no doubt, it's part of the secret handshake of
mathematicians :-)

****************************************************************

From: Tucker Taft
Sent: Monday, March 16, 2009  3:14 PM

Randy, I think you should probably drag out one of those old math textbooks if
we are going to be talking about preconditions and postconditions. Existential
(there exists) and universal (for all) quantifiers are pretty fundamental (as is
"implies" by the way ;-).

I think it is healthy for us to reexamine whether these standard logic notions
are appropriate for a programming language (at least you convinced me that
"implies" doesn't quite work for our purposes), but we should at least be able
to use the vocabulary of first-order logic in our *discussions*.

There are a lot of good books out there, and of course there is Wikipedia, which
probably has all you need.  A good starting point might be:

http://en.wikipedia.org/wiki/First-order_logic

One book I have used is:

Software Engineering Mathematics
by Jim Woodcock and Martin Loomes
SEI series in Software Engineering, 1988.

This one is clearly aimed at programmers who want to get more "formal" in their
approach to software engineering.  It also happens to use "Zed" notation (simply
"Z" in the UK), which is pretty popular among the formal methods crowd.

****************************************************************

From: Randy Brukardt
Sent: Monday, March 16, 2009  3:44 PM

> Randy, I think you should probably drag out one of those old math
> textbooks if we are going to be talking about preconditions and
> postconditions.
> Existential (there exists) and universal (for all) quantifiers are
> pretty fundamental (as is "implies" by the way ;-).

I agree that they are fundamental, I just had never heard these names before.

...
> I think it is healthy for us to
> reexamine whether these standard logic notions are appropriate for a
> programming language (at least you convinced me that "implies" doesn't
> quite work for our purposes), but we should at least be able to use
> the vocabulary of first-order logic in our *discussions*.

Not with me, sorry. I didn't take the logic class at UW, taking statistics and
probability instead. (I think the former may have been taken while I was still a
ChemE, so I had the credits when I transferred to a CS major.)

> There are a lot of good books out there, and of course there is
> Wikipedia, which probably has all you need.  A good starting point
> might be:
>
>    http://en.wikipedia.org/wiki/First-order_logic

OK, thanks for the reference. A quick look at this shows its going to take a lot
longer than a few minutes to make sense out of this. It'll have to wait a few
weeks at least, until ASIS and the minutes and the conference call are done.

[BTW, I think "first-order logic" is "and", "or", and "not". Anything more
complicated than that clearly has a higher order. ;-)]

****************************************************************

From: Edmond Schonberg
Sent: Monday, March 16, 2009  3:33 PM

> I think it is healthy for us to
> reexamine whether these standard logic notions are appropriate for a
> programming language (at least you convinced me that "implies" doesn't
> quite work for our purposes), but we should at least be able to use
> the vocabulary of first-order logic in our *discussions*.

I think the semantics of quantified expressions are intuitive and
straightforward to implement.  They are particularly useful in pre- and
postconditions but have more general uses.  The transformation of a quantified
expression into a loop is immediate, and also leads naturally to nested loops
when a condition is defined over elements of
two sets:   (forall X in S1, Y in S2 :  P (X, Y))

One nice thing about these implicit iterators is that they do not mention
cursors but speak directly about elements.  I suppose that the expression can be
defined to be a tampering context, so that any perverse use of the condition to
modify an element will be rejected.

The more general question is whether this is too much machinery to add to the
language at this point.

****************************************************************

From: Tucker Taft
Sent: Monday, March 16, 2009  3:57 PM

The obvious alternative is to rely on programmers writing appropriate named
functions that do the iteration internally.  I don't think forcing the
definition of named functions is appropriate for conditional expressions, but
for quantified expressions, I think expecting the programmer to program up an
appropriate named function is not too much to ask.

So I see these quantified expressions as significantly lower priority than
conditional expressions.

****************************************************************

From: Robert Dewar
Sent: Monday, March 16, 2009  4:38 PM

Note that in Setl you routinely write an expression which is pronounced

for all x in some-set such that p(x) is true, it is the
case that q (x) is also true.

that "such that" phrase is certainly convenient to have in practice, and the
mathematical crowd will be quick to point this out as a use of implies

forall X in some-set | p(x) -> q(x)

and in that context the -> reads pretty nicely I think but most likely

forall X in someset | (if p(x) then q(x))

the reason I like the such that phrase is that it is not so much that you want
to consider that somehow p(x) implies q(x), it is more like you only want to
consider the subset for which p(x) is true. This is logically equivalent, but
feels different, so a notation like

forall X in someset | p(x) : q(x)

reads clearer to me (though I think I would prefer to use the vertical bar for
the "it is the case that", rather than colon.

****************************************************************

From: Robert Dewar
Sent: Monday, March 16, 2009  4:41 PM

> The obvious alternative is to rely on programmers writing appropriate
> named functions that do the iteration internally.  I don't think
> forcing the definition of named functions is appropriate for
> conditional expressions, but for quantified expressions, I think
> expecting the programmer to program up an appropriate named function
> is not too much to ask.
>
> So I see these quantified expressions as significantly lower priority
> than conditional expressions.

Well there is the issue of bodies in the spec, and it does not seem that you can
use renaming of expressions to achieve this if you don't have quantified
expressions.

I find the bodies-in-spec issue to be a significant one!

****************************************************************

From: Bob Duff
Sent: Monday, March 16, 2009  5:15 PM

> I'm sure you do, you just forgot! ...

Thanks for the mathematical logic lesson, but I think you misunderstood what I
meant.  ;-)

I understand what universal quantifiers are in maths, and I haven't forgotten my
logic course (at least, I haven't forgotten the basics).  I even taught this
stuff to Bill some time ago, and he understands, for example, why "all pink
unicorns are green" is true.

What I meant is that I don't know how this stuff should be translated into a
programming language, especially an imperative programming language like, say,
syntactic sugar for a loop.  No big deal But it sounded like Cyrille was
thinking of something more "math-y".

Maths doesn't have loops.  Nor side effects.  Nor "run time" vs. "compile time".
In maths we are comfortable talking about infinite sets, and combinatorially
huge sets.

A type (in Ada) has (or is?) a set of values.  I was wondering if one can say
things like "for all values X, Y, and Z of type String, X >= Y and Y >= Z
implies X >= Z".  This means all _possible_ values, not just all values that
some program happens to have computed so far.  And a mathemetician would point
out that Natural'Last can be arbitrarily large, and would like to prove the
above for all possible implementations of Ada.  But that's apparently not what
you mean by universal quantifiers in Ada.

****************************************************************

From: Robert Dewar
Sent: Monday, March 16, 2009  7:10 PM

Clearly the sets in this case have to be finite, and the notion of quantifiers
over finite sets is well established in mathematics. So, no you cannot have
non-effective quantifiers over infinite sets, you could expect to say;

(for all A in Integer | P (A));

but it would take a long time to compute this :-)

****************************************************************

From: Robert I. Eachus
Sent: Monday, March 16, 2009  8:39 PM

Let me try to bring this discussion out of the blue sky and back to the
practical.  The primary goal of any extensions to Ada should be:to make programs
easier to write. As long as doing so does not make the programs more difficult
to read and understand, and as long as the extensions do not make it easier to
write bad (in some existential sense) programs than good programs.  There are
going to be many other criteria about making the language easier or harder to
learn, to implement, or to prove correct.  Plus to some extent a concern about
creating too big a language or a language that is not Ada.

So what would we expect to gain or lose from adding for all to Ada?  We
currently have for subtypes:

for I in Subtype'Range loop...end loop;

The same syntax works for arrays:

for I in A'Range loop..end loop;

But for lists and other containers? Define what should be the body of the loop
as a procedure with a parameter of type Cursor,  inside the body of the
procedure use calls to Element, and replace Element, or create more procedure
declarations, and finally call Iterate passing the container and the procedure.
In my humble opinion, the worst part of all that is not needing to know about
throwaway things like Cursors, but having to write often simple code  out of
line.

declare
procedure Nonsense_Name(C: in Cursor) is
begin
if Element(C).Last_Modified = Today
then Update_Element(Container, C, Daily_Backup;
end if;
end Nonsense_Name;
begin
Iterate(Container; Nonsense_Name;
end;
-- if Daily_Backup has other parameters, I need another wrapper procedure.

Not very lightweight, especially if you use declare blocks to keep the wrapper
procedure close by. If you could pass a declare block in-line  it would make
iterators much more comfortable to use and easier on readers as well.
(Implementation shouldn't be that hard, this is really syntactic sugar, with
access subprogram parameters already in the language.)  Renaming Iterate: ;=)

For_All(Element, Container,
(if Element.Last_Modified = Today then Daily_Backup(Element); end if));

-- assumes that a declare block passed as a parameter would be wrapped
-- in parentheses, not declare..end

Is it worth stopping there, or is it worth going further? When Ada was first
being defined, I suggested defining a couple of "extra" operator names with no
associated operations.  These could be used to name operations which didn't
match the standard set of operations.  I don' t know if that ever got as far as
being thrown out in scope reductions in the 1983 or 1995 standards.  But here
what we would really like is a template which takes two arguments and a block of
code:

for all Element in Container do
begin
if Element.Last_Modified = Today
then Daily_Backup(Element);
end if;
end;

There could be generic templates like this declared in Standard that could be
instantiated for (pairs of) types to create both for all and exists type
functionality.  However, I think I am reaching well beyond what should be
considered for the next version of Ada.  Besides, the huge improvement comes
from putting the sequence of statements in line, the syntactic sugar is pretty,

The anonymous declare block parameters may be a winner, especially if it can be
merged with Randy's function renaming idea, by doing the same with renaming
expressions as functions:

function <identifier> <parameter and result profile>  renames <expression> end [identifier];

Hmm.  I think I see a problem, the first things I want to write are things like
Factorial or Ackermann's function:

function Factorial(N: Positive) return Integer
renames (if N = 0 then 1 else N * Factorial (N-1)); end Factorial;

function Ackermann(M, N: Positive) return Integer renames
(if M = 0 then N+ 1
elsif N = 0 then Ackermann(M-1, N)
else N * Ackermann (M-1, Ackermann(M,N-1)))
end Ackermann;

Should the recursive calls be disallowed (probably by making the name not
visible)?  Or do we just accept that theorem provers can run into lots of cases
where the proof is possible, but takes a lot of CPU cycles?  Certainly these
functions are well defined, even if it does make more sense to use a BigNum type
for the results.  (For that matter it might be nice to add an Unbounded_Integer
type in the Numerics annex.)

Note that this example code for Ackermann, is really just syntactic sugar.
Well...  I save three return keywords, and some semicolons in exchange for some
parentheses.  I don't have a begin, but I do have a renames.  The huge mental
savings come from combining the spec and body, and putting the body (hopefully)
where it is needed.

Looking back, my practical may look pretty blue sky to some of you, but don't
lose my point.  Providing access to subprogram parameters makes a lot of things
more doabile in Ada, but in practice the "out lining" of the code becomes pretty
heavy.  I try to use declare blocks to bring code back to almost where it should
be, but it is still pretty heavy for what should be simple operations.  Randy's
renaming of expressions as functions has the same intended purpose, but in the
case of package specifications, declare blocks don't help.

****************************************************************

From: Randy Brukardt
Sent: Monday, March 16, 2009  9:03 PM

Proper iterators for Ada are discussed in AI05-0139-1, and were discussed at the
Tallahassee meeting.

Proper accessors for Ada are discussed in AI05-0142-1, on several recent threads
anonymous access types), and will be on the agenda of the upcoming subcommittee
meeting.

We're obviously interested in improving Ada in these areas. But it's not
particularly helpful to rehash all of the points that have already been covered
in these AIs and their e-mail threads.

****************************************************************

From: Edmond Schonberg
Sent: Monday, March 16, 2009  9:26 PM

[Editor's note: Forked back from AC-0180.]
> I agree. Large Boolean expressions are notoriously hard to read and
> debug.

I think we all agree on that. But to come back to the topic, quantified
expressions by themselves are compact and easy to read, and  therefore are a
good choice to have in preconditions.   Sortedness?
(for all I in A'first .. A'last -1 : A(I) <= A (I+1))

If the preconditions have a very complex description that requires them being
off-line, this may be a design issue, not a problem with boolean expressions per
se!

****************************************************************

From: Tucker Taft
Sent: Monday, March 16, 2009  10:54 PM

I think if we talk about object-oriented abstractions, then the "class-wide" /
"inheritable" preconditions are almost certainly going to be described using
(abstract) primitive functions, which are inevitably something you can't put in
the spec.  E.g. for an abstract Stack, the precondition on "Pop(Stack)" is "not
Is_Empty(Stack)" and it is clear that Is_Empty will have to be defined
differently for each concrete extension of the abstract Stack type.

If we are talking about scalar or array-of-scalar abstractions I can see these
things being fully defined in the spec, but for an abstraction which is truly
"abstract" (either in the O-O sense or in the private-type sense), then the
predicates are themselves going to involve abstract/private functions.  These
abstract predicates are in some sense "defined" by where they appear in
preconditions and postconditions.  E.g., if the postcondition of "Push(Stack) is
"not Is_Empty(Stack)", and the precondition of "Pop(Stack)" is the same, then we
know that a Pop immediately following a Push is safe.

If we went further and defined a "Depth(Stack)" then we could get more specific,
such as having a postcondition for Push of "Depth(Stack) = Depth(Stack)'old + 1"
and a precondition on Pop of "Depth(Stack) > 0", and a postcondition of
"Depth(Stack) = Depth(Stack)'old - 1". Combined with a postcondition on
Depth(Stack) itself of "Depth'Result >= 0" then we can begin to understand the
stack-like nature of a Stack, without ever seeing the body for "Depth".

I believe that most "interesting" abstractions will have this characteristic,
that is, where it will be necessary to define "helper" functions to specify pre-
and postconditions, and the meaning of the helper functions will be implicit in
how they are used in pre- and postconditions (I'll admit that sounds circular),
and not require visibility on the body of these helper functions, some of which
may be "abstract" when talking about O-O type hierarchies.

Given this, I am dubious about investing heavily in quantified expression
syntax.  Even for things like "sorted" I think you can't expect many compilers
to glean the truth of your "for all" expression from the code, but if you claim
via a postcondition of your sort routine that "Sorted(QSort'Result)" and
elsewhere you have a precondition of "Sorted(A)", then it would not be too much
of a leap for the compiler to expect you to have defined "A" by using QSort or
some other sorting routine, before calling a function that expected "Sorted(A)"
to be True.

To put this another way, I believe that from the *caller* side, pre- and
postconditions will be treated more "symbolically," where it is the matching up
of postconditions and preconditions which will be used to be sure that an object
is in the right "state" before being passed to some operation.

On the *callee* side, I believe the pre- and postconditions will actually be
analyzed in their full glory, because that is the place where they are
guaranteed to actually mean something, since that is where you have full access
to the representation, and in an O-O context, you actually know the concrete
type of the thing you are manipulating.

****************************************************************

From: Bob Duff
Sent: Monday, November 16, 2009  10:54 PM

AI05-0176-1, Quantified expressions was mentioned recently.

I think we should have an e-mail discussion of this issue, which was raised by
John Barnes at the recent meeting:

If we're going to have the universal quantifier "for all", we ought to also have
the existential quantifier.  John suggested the syntax "for some", which I like.

It looks pretty silly to have one without the other -- reading the double
negative (not (for all... (not...))) is pretty ugly.  Sort of like having "and
then" but not "or else" in the language.

Are we willing to tolerate the new reserved word "some"?

I'm not sure where I stand, but I'm in kind of a "both or neither" mood right
now.

****************************************************************

From: Robert Dewar
Sent: Monday, November 16, 2009  5:11 PM

The other possibility is of course exists. How about we do a run on the GNAT
test suite to see how much use of either identifier there is. I will post
results on this ASAP.

****************************************************************

From: Bob Duff
Sent: Monday, November 16, 2009  5:36 PM

Good idea.

FWIW, "for some" reads nicely to me.  I'm not sure whether you're suggesting
"for exists" or "if exists".  To me, "for exists" looks weird.  But I don't like
"if exists" either, because it's a loop, so should have "for".

I shall refrain from suggesting a backwards E, which I guess exists (heh heh)
somewhere in Unicode.  ;-)

****************************************************************

From: Robert Dewar
Sent: Monday, November 16, 2009  5:46 PM

to me it is fine to write

if for all ...

if exists

really the first line should be

if forall ...

and really we should allow the special symbols (gosh, we have them available in
the 32-bit character set I am sure :-) :-) :-)

while for some ...

seems less nice to me than

while exists

but then I am biased by having programmed using while exists and while forall

> I shall refrain from suggesting a backwards E, which I guess exists
> (heh heh) somewhere in Unicode.  ;-)

Well as per above, you are only allowed to suggest this if you suggest the
corresponding symbol for FORALL :-)

****************************************************************

From: Edmond Schonberg
Sent: Monday, November 16, 2009  5:49 PM

"exists"  stands by itself to define a quantified expression:       if
exists X in S: ....     or    while exists X in S: ....

I find it slightly preferable to  "for some"

****************************************************************

From: Gary Dismukes
Sent: Monday, November 16, 2009  5:49 PM

> FWIW, "for some" reads nicely to me.  I'm not sure whether you're
> suggesting "for exists" or "if exists".  To me, "for exists" looks
> weird.  But I don't like "if exists" either, because it's a loop, so should
> have "for".

I suspect that 'some' is very rare, whereas I can easily imagine there are
programs using 'exists' (as a predicate function name).

> I shall refrain from suggesting a backwards E, which I guess exists
> (heh heh) somewhere in Unicode.  ;-)

;-)

****************************************************************

From: Tucker Taft
Sent: Monday, November 16, 2009  7:09 PM

Actually, we do have the mathematical symbols to draw on. Pi got its nose in the
tent for Ada 2005, Perhaps we could adopt ? and ? directly.

****************************************************************

From: Bob Duff
Sent: Monday, November 16, 2009  7:12 PM

Edmond Schonberg wrote:

> "exists"  stands by itself to define a quantified expression:       if
> exists X in S: ....     or    while exists X in S: ....
>
> I find it slightly preferable to  "for some"

Ed, your comment, and Robert's similar comment, seem somewhat convincing to me,
but I think I need to see the full BNF syntax before I can really "see" it.

Gary's comment:

> I suspect that 'some' is very rare, whereas I can easily imagine there
> are programs using 'exists' (as a predicate function name).

is a strong argument for 'some', but let's see the result of Robert's experiment
first.

> > I shall refrain from suggesting a backwards E, which I guess exists
> > (heh heh) somewhere in Unicode.  ;-)
>
> Well as per above, you are only allowed to suggest this if you suggest
> the corresponding symbol for FORALL :-)

Yes, of course.  ;-)  I shall also refrain from suggesting an upside-down A.
I couldn't type an upside-down A on my keyboard to save my life!

My opinion: You shouldn't have to know any more than 4'th grade math to learn
how to program.

****************************************************************

From: Tucker Taft
Sent: Monday, November 16, 2009  8:59 PM

> Actually, we do have the mathematical symbols to draw on. Pi got its
> nose in the tent for Ada 2005,

That was a mistake, IMHO.

> Perhaps we could adopt ? and ? directly.

Cool!  Those look like upside-down A and backwards E on my screen!  I've no idea how you typed them in.

I hope you're kidding, Tuck.  We really don't want the predefined stuff to
depend on anything but 7-bit ASCII.  It's fine to allow another 2**N characters,
for N=31 or whatever, but let's not put that in the predefined stuff.

P.S. Actually, that upside-down A has an extra serif on the side that looks
weird to me.  And probably looks weird to Donald Knuth.

****************************************************************

From: Randy Brukardt
Sent: Monday, November 16, 2009  9:16 PM

> > Actually, we do have the mathematical symbols to draw on. Pi got its
> > nose in the tent for Ada 2005,
>
> That was a mistake, IMHO.

That's just an identifier, and there is an ASCII equivalent. Any user could have
done the same.

> > Perhaps we could adopt ? and ? directly.
>
> Cool!  Those look like upside-down A and backwards E on my screen!
> I've no idea how you typed them in.

On my screen, I just see ? and ?. Not very helpful. (I'd type them in opening
the symbol page in OpenOffice or Word, inserting them into a blank document, and
then cut-and-pasting them into my e-mail. Not fun. Probably a programming editor
would have a similar page, so it wouldn't be quite that bad in practice.) In any
case, I have to remove characters like that from the filed mail, or I get
complaints about "garbage" in the files. So please minimize the use of them
here.

> I hope you're kidding, Tuck.  We really don't want the predefined
> stuff to depend on anything but 7-bit ASCII.  It's fine to allow
> another 2**N characters, for N=31 or whatever, but let's not put that
> in the predefined stuff.

I wouldn't object if they were identifiers and there were regular ASCII
representations available as well. (As in the PI case.) But to use them *in
place* of reserved words is really nasty. So I too hope Tucker was kidding.

****************************************************************

From: Tucker Taft
Sent: Monday, November 16, 2009  9:44 PM

>> Perhaps we could adopt ? and ? directly.
>
> Cool!  Those look like upside-down A and backwards E on my screen!
> I've no idea how you typed them in.

The joys of using a Mac (and UTF-8).  ;-)

...
> P.S. Actually, that upside-down A has an extra serif on the side that
> looks weird to me.  And probably looks weird to Donald Knuth.

The pain of infinite font choices. ;-(

****************************************************************

From: Randy Brukardt
Sent: Monday, November 16, 2009  11:52 PM

> > Cool!  Those look like upside-down A and backwards E on my screen!
> > I've no idea how you typed them in.
>
> The joys of using a Mac (and UTF-8).  ;-)

For what it's worth (probably \$0.00 :-), neither of those characters appear in
the "special symbols" page of OpenOffice for the fonts provided with Windows XP.
I believe OpenOffice shows all of the characters defined in the fonts (it is
around a thousand characters for Times New Roman, including a lengthy set of
Arabic characters -- but only a handful of math characters); it is nice enough
to show the (Unicode) encoding of the characters. I suppose its possible that I
looked in the wrong place; what codes are those characters??

****************************************************************

From: Randy Brukardt
Sent: Monday, November 16, 2009  11:59 PM

Following up, I found these in the Symbol font, with character codes F022 and
F024; those codes are in the "private use area" and doesn't have the same glyphs
in other fonts. So I'm pretty sure that typical Windows fonts don't have those
characters. Which suggests against using them (having to use a special font to
display them is obnoxious at best). (Haven't checked Windows 7 yet, perhaps it
has more characters.)

****************************************************************

From: Jean-Pierre Rosen
Sent: Tuesday, November 17, 2009  4:09 AM

> "exists"  stands by itself to define a quantified expression:       if
> exists X in S: ....     or    while exists X in S: ....
>
> I find it slightly preferable to  "for some"
>
So do I - but of course I am part of the gang under SETL influence ;-)

****************************************************************

From: Robert Dewar
Sent: Tuesday, November 17, 2009  6:34 AM

> Actually, we do have the mathematical symbols to draw on. Pi got its
> nose in the tent for Ada 2005, Perhaps we could adopt ? and ?
> directly.

Tee hee, someone rose to the bait!

The introduction of Pi in the library was a HUGE pain, it required all sorts of special fiddling for us to deal with.
I really don't want to get into this for the language itself.
We could possibly allow these as alternatives, but you don't want to insist on
them. In many environments this would simply make the features unavailable.

****************************************************************

From: Robert Dewar
Sent: Tuesday, November 17, 2009  6:36 AM

>> I suspect that 'some' is very rare, whereas I can easily imagine
>> there are programs using 'exists' (as a predicate function name).
>
> is a strong argument for 'some', but let's see the result of Robert's
> experiment first.

I don't think "I suspect" can ever be a "strong argument". Indeed let's wait for
the result of the experiment.

****************************************************************

From: Robert Dewar
Sent: Tuesday, November 17, 2009  6:37 AM

> Cool!  Those look like upside-down A and backwards E on my screen!
> I've no idea how you typed them in.

not on my screen :-)

****************************************************************

From: Robert Dewar
Sent: Tuesday, November 17, 2009  6:38 AM

> That's just an identifier, and there is an ASCII equivalent. Any user
> could have done the same.

NOT!

They could not have done it in the standard library, and it has been a HUGE pain
for us to accomodate this one special case.

****************************************************************

From: Bob Duff
Sent: Tuesday, November 17, 2009  8:20 AM

> > Cool!  Those look like upside-down A and backwards E on my screen!
> > I've no idea how you typed them in.
>
> not on my screen :-)

Now you've mailed them back to me, they look different.
The for-all symbol looks like an 'a' with a '^' on top, followed by a '^',
followed by a Euro symbol (three characters).

And when Randy mailed them back to me, they both looked like '?'.

Q.E.D. (that we shouldn't touch such characters with a barge pole)

****************************************************************

From: Erhard Ploedereder
Sent: Tuesday, November 17, 2009  3:19 AM

RE: "for some" vs. "exists"....

Is this a contest at all? Is there anybody who prefers "for some" to "exists"?
(in boolean expressions)

****************************************************************

From: Tucker Taft
Sent: Tuesday, November 17, 2009  11:52 AM

I think I prefer "for some" because it better suggests the loop involved.  I am
also somewhat swayed by the fact that "exists" will never fly as a reserved
word, whereas I could imagine handling "for some" either by making "some"
reserved, or by only reserving it in this context.

****************************************************************

From: Bob Duff
Sent: Tuesday, November 17, 2009  12:00 PM

Same here.  Also, I don't see any need to be overly mathematical in our
notation.  (E.g. I much prefer using the words "and" and "or" over the operators
maths folks sometimes use -- even if those operators were part of 7-bit ascii
and appeared on my keyboard.)

But I'm not sure, because I haven't seen the exact BNF being proposed for
'exists'.

By the way, some people are fanatically opposed to semi-reserved keywords.  Not
me.

****************************************************************

From: Randy Brukardt
Sent: Tuesday, November 17, 2009  12:06 PM

> Is this a contest at all? Is there anybody who prefers "for some" to
> "exists"? (in boolean expressions)

I don't like either much. Moreover, "Exists" does not fly as a reserved word for
me. I found a number of instances of parameters and variables named "Exists" in
part of the Janus/Ada compiler (a small sample, but I think it is instructive):

---

procedure Find_SYM (Current_Class : in out J2Typ_Decs.Library_Type;
Line       : in Target.Line_Numbers;
Pos        : in Target.Line_Position;
Can_Create : in Boolean;
Exists     : out Boolean);

---

Exists : Boolean;
Can_Create => FALSE, Exists => Exists);
if Exists then

(There are two more instances like this in this package; these are all making
calls on Find_SYM)

---

Perhaps these would have been better named "File_Exists" or something like that
(there are a *lot* of those in the Janus/Ada compiler), but I doubt that our
code is atypical. Thus I think the incompatibility caused by "Exists" as a
reserved word is unacceptable.

---

I didn't try all of the compiler tools or any of our other code (as I did the
looking with a simple text search).

I tried a similar search for Some; I didn't find any declarations, but it's hard
to tell because of the number of comments and larger identifiers containing the
text "Some". We need a smarter tool for that. Presumably, the AdaCore experiment
will give a more definitive answer.

****************************************************************

From: Robert Dewar
Sent: Tuesday, November 17, 2009  12:09 PM

> By the way, some people are fanatically opposed to semi-reserved
> keywords.  Not me.

Not me either, but I don't like to allow them unless they appear in a position
where the identifier could not occur reading left to right

for some in x .. y loop

for some x ...     loop

seems uncomfortable to me

****************************************************************

From: Robert Dewar
Sent: Tuesday, November 17, 2009  12:10 PM

Note that if you tolerate semi-reserved keywords, exists is fine because you
will always have an identifier after exists

****************************************************************

From: Jean-Pierre Rosen
Sent: Wednesday, November 18, 2009  1:48 AM

> I tried a similar search for Some; I didn't find any declarations, but
> it's hard to tell because of the number of comments and larger
> identifiers containing the text "Some". We need a smarter tool for that.
check entities (all some, all exists);

****************************************************************

From: Edmond Schonberg
Sent: Wednesday, February 3, 2010  5:21 PM

here is a more fleshed-out proposal.  It may still depend on the new iterator
machinery, but most of it stands on its own.  I think we have to bite the bullet
and introduce the keyword "exists".

[This is version /02 - Editor.]

****************************************************************

From: Randy Brukardt
Sent: Wednesday, February 3, 2010  5:21 PM

> here is a more fleshed-out proposal.  It may still depend on the new
> iterator machinery, but most of it stands on its own.
>  I think we have to bite the bullet and introduce the keyword
> "exists".

That's a huge bullet. When we discussed this back in November, I did a quicky
look at the code of a portion of Janus/Ada (about 25%) and found more than 20
parameters and objects named "Exists". I just did a look at the public part of
Claw and found 4 overloaded functions named "Exists".

Robert was going to look at this in the AdaCore test suite, but he never
reported back. But in the absence of him reporting that our code here is
unusual, I would have to be 100% against making "exists" a reserved word.
Especially for something that I would use rarely.

...
> !wording
> Add in 2,9 a new keyword
>    exists

2.9 defines "reserved words", not "keywords" (that was the name of the
unreserved identifiers that we dropped last time after substantial opposition).
I've corrected this.

> Add to 3.3 (19) a new constant
>       quantified_expression_parameter

This is written as a syntax item, but in the grammar you give below, this is not
defined. And in the for loop wording that you presumably are borrowing from,
this is a defined term, not a syntax. I've fixed this consistently throughout
the proposal.

> 4.5.8 Quantified expressions

The clause number needs to be 4.5.9, at least given the existing other AIs.
Maybe we'll change that in the future.

>    quantified_expression ::=
>     (quantifier defining_identifier in domain | predicate)
>
>       quantifier ::=  for all | exists
>
>      domain ::=  discrete_subtype_definition | expression
>      predicate ::= boolean_expression

I don't get why these things are indented randomly. The indentation of Ada
syntax is significant. I made them all consistent, but you need to tell me if
that is what you meant.

>    Static Semantics
>
> A quantified expression declares a
> quantified_expression_parameter, whose subtype is defined by the
> domain:

This is a term, no underscores, and, as this is the defining occurrence, it
needs to be surrounded by *stars*.

>    if the domain is a discrete_subtype_definition, this is the subtype
> of the
>     quantified_expression_parameter.
>
>    if the domain is an expression that is a one-dimensional array, the
> subtype
>    of the quantified_expression_parameter is the element type of the
> array
>
>    if the domain is an expression whose value is an instance of a
> container,
>     the subtype of the quantified_expression_parameter is the element
> type of
>     the container.

I think this is supposed to be a bulleted list, but there is no bullets to be
seen. And the second one seems to have a punctuation shortage.

>    Name resolution rules
>
> The expected type of a quantified expression is the predefined type
> Boolean

More missing punctuation.

>    If the domain is an expression, it is expected to be of any type.
>
> Dynamic semantics
>
> The evaluation of a quantified expression assigns to the
> quantified_expression_ parameter each one of the values specified by
> the domain, If the domain is a range, those values are assigned in
> order. In the domain is an array, the values are assigned in order of
> increasing index. If the domain is a container, the values are
> assigned in the order in which container elements are examined in an
> iteration over the container, using the primitives First and  Next.
> The predicate is then evaluated for each value of the quantified_
> expression_parameter. The value of the quantified expression is
> determined as
> follows:
>
> If the quantifier is "for all" the expression is True is the
> evaluation of the predicate yields True for each value of the
> quantified_expression parameter.
> It is false otherwise. Evaluation of the expression stops when all
> values of the domain have been examined, or when the predicate yields
> False for a given value.
>
> If the quantifier is "exists" the expression is True is the evalution
> of the predicate yields True for some value of the
> quantified_expression_parameter.
> It is false otherwise.  Evaluation of the expression stops when all
> values of the domain have been examined, or when the predicate yields
> True for a given value.

Another bulleted list?? "Evalution".

...
> Given that a mapping has a domain and a range, this suggests
> generalizing both of these attributes to be used in quantified
> expressions and in loops, but this is probably too big a change at
> this time.
>
> ed:ALL_AI05 schonberg\$

This looks like your computer's command line prompt. How did it get in your
e-mail?

****************************************************************

From: Ed Schonberg
Sent: Wednesday, February 3, 2010  9:43 PM

>                     Randy, overworked editor.

Thanks for the careful editing. I'll check about the presence of Exists
in our sources.

****************************************************************

From: Randy Brukardt
Sent: Wednesday, February 3, 2010  10:42 PM

For the record, I realized that I had forgotten to actually read most of it (I
was focused on typos). When I went back and did that, I found more typos that I
fixed, and also that you forgot to define the expected type of a "predicate". I
fixed the latter by copying the wording for "condition".

****************************************************************

From: Tucker Taft
Sent: Wednesday, February 3, 2010  10:31 PM

How about "(for'all X in ...)" and "(for'some X in ...)"?
Or "(for-all X in ...)" and "(for-some X in ...)"?
Both of these would allow "some" not to be a reserved word.  I agree with Randy
that "Exists" is simply too common of a name for functions.  I know I have
written "if Exists(X) then ..." many times in various Ada applications.  We
either need a way to have an unreserved keyword, or pick some other less common
word.

In terms of less common words to make reserved, we could use "for_all" and
"there_exists":

(for_all X in ...) and (there_exists X in ...)

****************************************************************

From: Jean-Pierre Rosen
Sent: Thursday, February 4, 2010  3:08 AM

> That's a huge bullet. When we discussed this back in November, I did a
> quicky look at the code of a portion of Janus/Ada (about 25%) and
> found more than 20 parameters and objects named "Exists". I just did a
> look at the public part of Claw and found 4 overloaded functions named "Exists".

Not as pretty as "exists", but wouldn't "is" work (if it does not introduce
syntactic ambiguities):

is X in D | P(x)

****************************************************************

From: John Barnes
Sent: Thursday, February 4, 2010  3:41 AM

I would prefer "for some" rather than "exists".  One problem with exists rather
than there exists is that it seems a bit like a question rather than a
statement.

****************************************************************

From: Edmond Schonberg
Sent: Thursday, February 4, 2010  7:03 AM

I like the symmetry for "for all" and "for some" .  An unreserved keyword is
less of a disturbance than "exists".

****************************************************************

From: Robert Dewar
Sent: Thursday, February 4, 2010  7:12 AM

I agree (significantly more implementation effort, but that's a minor issue in
this case).

****************************************************************

From: Bob Duff
Sent: Thursday, February 4, 2010  7:40 AM

When I read maths texts, I pronounce the upside-down A as "for all" in my head,
and the backwards E as "there exists".  Just "exists" by itself sounds odd to
me.  I think "for some" reads nicely.

I have no objection to unreserved keywords.

****************************************************************

From: Stephen Michell
Sent: Thursday, February 4, 2010  8:15 AM

How about a keyword thereexists, or there_exists. ?

****************************************************************

From: Bob Duff
Sent: Thursday, February 4, 2010  8:30 AM

> I think we have
> to bite the bullet and introduce the keyword "exists".

Unfortunately, there's a predefined function Exists in Ada.Directories!

****************************************************************

From: Steve Baird
Sent: Thursday, February 4, 2010  11:18 AM

> The evaluation of a quantified expression assigns to the
> quantified_expression_parameter each one of the values specified by
> the domain,

I think we need to make clear that no assignment is taking place, at least in
the case of a by-reference type. This is more like the actual-to-formal binding
of a subprogram call - no adjust/finalize calls, no issues with limited types.

Incidentally, I think the proposed wording correctly handles the case where the
domain is empty (result is True for "for-all", False for "for-some"), but I
wonder if AARM clarification of this point would be a good idea.

****************************************************************

From: Edmond Schonberg
Sent: Thursday, February 4, 2010  12:11 PM

> I think we need to make clear that no assignment is taking place, at
> least in the case of a by-reference type.
> This is more like the actual-to-formal binding of a subprogram call -
> no adjust/finalize calls, no issues with limited types.

Good point. Can we say that the parameter is bound to each value in the domain?
in usual parlance, that thing is called the bound variable,  but i did not want
to use "variable" if this is to be treated like a loop_parameter.

> Incidentally, I think the proposed wording correctly handles the case
> where the domain is empty (result is True for "for-all", False for
> "for-some"), but I wonder if AARM clarification of this point would be
> a good idea.

Sure.

****************************************************************

From: Edmond Schonberg
Sent: Monday, February 22, 2010  4:43 PM

[Attached was version /03 of the AI. - Editor]
This is now much simplified because based on AI05-0149 (iterators).
The semantics is sequential because that's what we say about iterators as well.
Instead of the unpalatable "exists" we now have a non- reserved keyword "some" .
The rest seems straightforward.

****************************************************************

From: Randy Brukardt
Sent: Monday, February 22, 2010  6:55 PM

> This is  now much simplified because based on AI05-0149
> (iterators).

I presume you mean AI05-0139-2 here, AI05-0149 is "access subtype conversion and
membership". I changed the AI writeup this way.

****************************************************************

From: Tucker Taft
Sent: Monday, February 22, 2010  5:28 PM

The last line of the "Examples" section
doesn't fly, in my book:

The assertion that a positive number is
composite can be written:

(for some X in 1 .. N / 2 | N mod X /= 0)

-----

I would have expected:

(for some X in 2..N/2 | N mod X = 0)

implies N is composite, while:

(for all X in 2..N/2 | N mod X /= 0)

implies N is prime.

Or am I confused?

****************************************************************

From: Edmond Schonberg
Sent: Monday, February 22, 2010  8:20 PM

No, you are right, my slip of the finger (was translating from the predicate for
primality, one negation too many)

****************************************************************

From: Steve Baird
Sent: Monday, February 22, 2010  7:02 PM

> The postcondition for a sorting routine on arrays with can be written:
>
> Post => (for all I:T in A'First .. A (T'Pred(A'Last)) | A (I) <= A
> (T'Succ (I)))

Am I right in assuming that you meant
T'Pred (A'Last)
as opposed to
A (T'Pred (A'Last))
?

>    The expected type of a quantified expression is the
>    predefined type Boolean.

I think we want to replace this sentence with something that more closely
follows the rule for a qualified expression. That is, say nothing about the
expected type of a quantified expression (that, after all, is determined by
its context) and instead add a static semantics rule along the lines of
4.7(3.1/3):
The nominal subtype of a quantified_expression is the predefined
type Boolean.

It would seem oddly fitting to have some sort of parallel between quantified
expressions and qualified expressions.

Finally, do we need to state (in the dynamic semantics section) that the
loop_parameter_specification is elaborated? See 5.5(9).

****************************************************************

From: Randy Brukardt
Sent: Monday, February 22, 2010  7:20 PM

Shouldn't the type of the expression be the same as the type of the predicate?
Otherwise you have some weird implicit conversion going on here, which might
require a change of representation (if the encoding of the boolean types is
different).

****************************************************************

From: Edmond Schonberg
Sent: Monday, February 22, 2010  8:24 PM

>Am I right in assuming that you meant
>    T'Pred (A'Last)
>as opposed to
>    A (T'Pred (A'Last))
>?

No, I want  A(A'Last -1),  T is the index type.

...
>It would seem oddly fitting to have some sort of parallel between
>quantified expressions and qualified expressions.

I don't know, I also see quantified expressions as conditions in an
if-statement, for which we do state the expected type. That parallel does not
work for me.

>Finally, do we need to state (in the dynamic semantics section) that
>the loop_parameter_specification is elaborated? See 5.5(9).

Yes.  in particular now that it can include some complex container-valued
expression

****************************************************************

From: Edmond Schonberg
Sent: Monday, February 22, 2010  8:33 PM

>>> The postcondition for a sorting routine on arrays with can be
>>> written:
>>> Post => (for all I:T in A'First .. A (T'Pred(A'Last)) | A (I) <= A
>>> (T'Succ (I)))
>>
>> Am I right in assuming that you meant
>>     T'Pred (A'Last)
>> as opposed to
>>     A (T'Pred (A'Last))
>> ?

Indeed, you are right, this is the range for the index.

****************************************************************

From: Steve Baird
Sent: Monday, February 22, 2010  8:58 PM

> Shouldn't the type of the expression be the same as the type of the
> predicate? Otherwise you have some weird implicit conversion going on
> here, which might require a change of representation (if the encoding
> of the boolean types is different).

The rule you propose would be somewhat more complex to specify and (probably)
somewhat more complex to implement. The only benefit would be slightly more
intuitive semantics in a case that nobody cares about.

I say "slightly" because I have no problem thinking of

(for all I in Some_Range | Some_Derived_Boolean_Type'(Foo (I)))

as being equivalent to a call to a function with body

Temp : Standard.Boolean := True;
begin
for I in Some_Range loop
if Some_Derived_Boolean_Type'(Foo (I)) = False then
Temp := False;
exit;
end if;
end loop;
return Temp;
.

for the rule you suggest. Either way is ok with me.

****************************************************************

From: Steve Baird
Sent: Monday, February 22, 2010  9:41 PM

>> It would seem oddly fitting to have some sort of parallel between
>> quantified expressions and qualified expressions.
>
> I don't know, I also see quantified expressions as conditions in an
> if-statement, for which we do state the expected type. That parallel
> does not work for me.

At the very least we should replace the proposed "is" rule with a "shall be"
rule:
The expected type of a quantified expression shall be the
predefined type Boolean.

Consider a bad construct such as

X : Float := (for all I in ...);

. We do not want to define the expected type of the quantified expression to be
Boolean - that would conflict with the definition of expected type that is
inherited from context (in this case, 3.3.1(4)).

I think (but this would have to be checked - I'm not sure) that the rule I
originally suggested would then follow as a consequence.

Still, an expression whose type is known independently of the context in which
it occurs strikes me as being very similar to a qualified expression and I think
it would be clearest to follow that example.

****************************************************************

From: Edmond Schonberg
Sent: Monday, February 22, 2010  9:51 PM

...
>At the very least we should replace the proposed "is" rule with a
>"shall be" rule:
>   The expected type of a quantified expression shall be the
>   predefined type Boolean.

or "any boolean type" as for conditions in if-statements.

...
>Still, an expression whose type is known independently of the context
>in which it occurs strikes me as being very similar to a qualified
>expression and I think it would be clearest to follow that example.

Not sure I follow, this is the same phrasing as for conditions in if-statements,
and those are not qualified expressions. Of course, those conditions are in one
specific context, while quantified expressions are just expressions that can
appear anywhere.  So whatever is clearer.  Still, the expected type of the
predicate must be the same as that of the expression as a whole.

****************************************************************

From: Randy Brukardt
Sent: Monday, February 22, 2010  10:10 PM

>Not sure I follow, this is the same phrasing as for conditions in
>if-statements, and those are not qualified expressions.

Steve is right. An if-statement is a context that *provides* an expected type.
Kinds of expressions are defined to match certain expected types, they don't
have them

>Of course, those conditions are in one specific context, while
>quantified expressions are just expressions that can appear anywhere.
>So whatever is clearer. Still, the expected type of the predicate must
>be the same as that of the expression as a whole.

I had suggested that, and Steve thought it was better that quantified
expressions always returned type Boolean. I don't think it matters that much.
Steve now seems to be suggesting a resolution rule like that of qualified
expressions:

A quantified_expression shall resolve to type Boolean.

But this is a bit different than regular resolution, as it doesn't include
implicit conversions. Not sure that matters in this case (I can't think of a
reason).

An alternative would be to have a legality rule:

The expected type of a quantified_expression shall be a boolean type.

Not sure that works, though, so probably following the model of qualified
expressions is better.

Note that we might want the equivalent of the 4.7(3.1/3) rule, which specifies
the nominal subtype. But since we didn't do that for conditional or case
expressions (and I really don't want to go there!), maybe we don't need it here,
either. (But note that 4.7(3.1/3) has nothing to do with resolution; we
definitely need *some* rule about the resolution of a quantified_expression.)

****************************************************************

From: Steve Baird
Sent: Monday, February 22, 2010  10:21 PM

>> At the very least we should replace the proposed "is" rule with a
>> "shall be" rule:
>>    The expected type of a quantified expression shall be the
>>    predefined type Boolean.
>
> or "any boolean type" as for conditions in if-statements.

That would be fine too.
As I mentioned in an earlier reply to Randy, I prefer your original rule but I don't

...
>> Still, an expression whose type is known independently of the context
>> in which it occurs strikes me as being very similar to a qualified
>> expression and I think it would be clearest to follow that example.
>>
> Not sure I follow, this is the same phrasing as for conditions in
> if-statements, and those are not qualified expressions.

I was just repeating myself, stating that the proposed "shall be"
wording is my second choice; I still prefer
The nominal subtype of a quantified_expression is the predefined
type Boolean.

On the other hand, if we adopt the "any boolean type" rule that you mentioned
above, then the parallel with qualified expressions falls apart (the type of a
quantified expression could no longer be determined independently of its
context). In that case, I think the "shall be" wording would be best.

>  So whatever is clearer.

Agreed. Let's see what others think.

****************************************************************

From: Randy Brukardt
Sent: Monday, February 22, 2010  10:40 PM

> Corrected text follows.

I changed the example again, as you forgot to change 1 to 2 in the loop.
Moreover, everytime I read the leadin "The assertion that a positive number is
composite can be written:" I think the answer is "False" (because "composite"
has a meaning in Ada, and a number is never composite in Ada). I changed it to:

The assertion that a positive number is composite (as opposed to prime) can be
written:

---

You changed the resolution rule to:

The expected type of a quantified expression is any Boolean type.
The predicate in a quantified_expression is expected to be the same type.

This is completely backwards. As Steve says, expected types always come from
context. Moreover, not all expressions have expected types at all (qualified
expressions don't, for instance). So it is dangerous to talk about the expected
type of the expression. (We fought this for conditional_expressions; we
eventually used the rules that () would have if they actually had rules.)

We could use similar rules here:

If a quantified_expression is expected to be of a type T, the expected type for
each *dependent_*expression of the quantified_expression is T. If a
quantified_expression shall resolve to a type T, each dependent_expression shall
resolve to T.

And then we'd need a legality rule:

The type of a quantified_expresion shall be a boolean type.

Alternatively, we could follow Steve's suggestion. However, that is unfortunate
as the only place the type (as opposed to the subtype, and we just added that
very recently) of a qualified_expression is defined is in the informal
introductory text. (Ignore my previous message on this subject.) So there isn't
a good example to copy.

Aside: We didn't try to identify the type of a conditional expression, much less
the subtype. So what is the completeness rule for a case statement? Consider:

case (if Func then 1 else 2) is
when 1 => null;
when 2 => null;
end case;

Is an others required or not?? Same applies to a case_expression. (Darn, I'm
thinking like Steve now.)

****************************************************************

From: Bob Duff
Sent: Tuesday, February 23, 2010  7:33 PM

> Steve is right. An if-statement is a context that *provides* an
> expected type. Kinds of expressions are defined to match certain
> expected types, they don't have them

I don't "get" this tempest in a tea pot.  Just define the doggone result type!

The expected type for the predicate is "any boolean type".
The type of a quantified_expression is Boolean.
Word it that way: end of story, no?
I don't get what various folks are arguing about (just wording?).

There's no need to define "expected type" for quantified_expression; indeed that
makes no sense, as Randy explains above.  Expected types go down, result types
go up (assuming you draw trees with roots at the top and leaves at the bottom,
like all right-thinking computer scientists do).

Maybe I'm missing something...

By the way, there's a bit of a notational problem here:

quantified_expression ::= (for quantifier loop_parameter_specification | predicate)
quantifier         ::= all | some
predicate          ::= boolean_expression

There's an ambiguity about what "|" means (and it threw me for a loop at
first!).

"1.1.4 Method of Description and Syntax Notation" contains this kludge:

12      * A vertical line separates alternative items unless it occurs
immediately after an opening curly bracket, in which case it stands for
itself:

13        constraint ::= scalar_constraint | composite_constraint
discrete_choice_list ::= discrete_choice {| discrete_choice}

Sigh.  Oh what a tangled web we weave, when first we practise to kludge.
Apologies to Scott, whose version rhymes better, but my version is apt.

I shall refrain from suggesting that "such" and "that" should be keywords,
reserved or otherwise.

****************************************************************

From: Edmond Schonberg
Sent: Wednesday, February 24, 2010  1:17 PM

> By the way, there's a bit of a notational problem here:
>
>    quantified_expression ::= (for quantifier
> loop_parameter_specification | predicate)
>       quantifier         ::= all | some
>       predicate          ::= boolean_expression
>
> There's an ambiguity about what "|" means (and it threw me for a loop
> at first!).

Yes, sorry for the sloppy notation.  The vertical bar should be in quotes...
or else we choose a different separator:  colon and right-arrow have been
proposed:

for all X in S :  P (X)

or

for all X in S => P (X)

Slight preference for colon in this context, but that would conflict with the
new iterator syntax, where we could say:

for all X : T of C : P (X)

which is definitely confusing.  So right arrow may be the obvious choice.

****************************************************************

From: Bob Duff
Sent: Wednesday, February 24, 2010  1:39 PM

> Yes, sorry for the sloppy notation.  The vertical bar should be in
> quotes...

The first one.

> or else we choose a different separator:  colon and right-arrow have
> been proposed:
>
>        for all X in S :  P (X)
>
> or
>
>      for all X in S => P (X)
>
> Slight preference for colon in this context, but that would conflict
> with the new iterator syntax, where we could say:
>
>     for all X : T of C : P (X)
>
> which is definitely confusing.  So right arrow may be the obvious
> choice.

Well, I hate for our inability to say "|" in our meta-language drive the actual
syntax.

Anyway, I agree ":" is confusing.  I could live with either "=>" or "|".

Maybe we should change "1.1.4 Method of Description and Syntax Notation"
to say that "|" (with the quotes) stands for a vertical line, and change the
syntax for discrete_choice_list, discriminant_association,
component_choice_list, and exception_handler to quote the thing?

(If I ran the circus, all literal terminals would be quoted.)

****************************************************************

From: Gary Dismukes
Sent: Wednesday, February 24, 2010  1:55 PM

> Yes, sorry for the sloppy notation.  The vertical bar should be in
> quotes...
> or else we choose a different separator:  colon and right-arrow have
> been proposed:

Just because there's a notational issue with the syntax doesn't mean we should
change to a different separator.  Let's please stick with the vertical bar and
resolve the syntax notation issue somehow.

****************************************************************

From: Tucker Taft
Sent: Wednesday, February 24, 2010  2:04 PM

I agree.  "|" seems preferable to other separators.

In other places where we use "|" in the syntax (e.g. 4.3.1 record aggregates),
the distinction seems to be merely one of the font (which is admittedly pretty
subtle).

****************************************************************

From: Edmond Schonberg
Sent: Wednesday, February 24, 2010  2:05 PM

> Just because there's a notational issue with the syntax doesn't mean
> we should change to a different separator.  Let's please stick with
> the vertical bar and resolve the syntax notation issue somehow.

I wasn't suggesting the other possible separators just because of the notational
issue. I've heard objections (on aesthetic grounds) about the use of the
vertical bar here (from John in particular), and other had suggested  => as more
meaningful.

****************************************************************

From: Randy Brukardt
Sent: Wednesday, February 24, 2010  7:59 PM

> I agree.  "|" seems preferable to other separators.
>
> In other places where we use "|" in the syntax (e.g. 4.3.1 record
> aggregates), the distinction seems to be merely one of the font (which

All such cases follow "{", and the wording that Bob pointed out covers that
explicitly. This is the first time | is used to separate something other than a
list, so now we have a problem. No solution comes to mind. (One also wonders
about the inconsistency of using a list separator in a non-list context. I'd
solve the problem by not bothering with this feature, but I'm not expecting that
solution to fly. :-)

****************************************************************

From: Steve Baird
Sent: Wednesday, February 24, 2010  1:26 PM

> I don't get what various folks are arguing about (just wording?).

Pretty much.

There is a more-than-just-wording question about a corner case which nobody
seems to feel strongly about, but which needs to be resolved one way or the
other:

If the predicate expression is of a derived boolean type, is
the type of the quantified expression Standard.Boolean or is
it the derived boolean type?

I argued that if we choose Standard.Boolean, then a quantified expression is a
lot like a qualified expression in the sense that its type can be determined
independently of its context.

This suggested to me that we should therefore use the wording for qualified
expressions as a model.

Unfortunately, this introduced confusion because, as Randy pointed out, the
wording for qualified expressions isn't really right. It hasn't changed for many
years and there have been no complaints about it, but doesn't explicitly define
the type of a qualified expression. It does define the nominal subtype, but
Randy says that "4.7(3.1/3) has nothing to do with resolution,".

So something like
The type of a quantified_expression is the predefined
type Boolean.
is probably needed.

If we go the other way on the derived-boolean-type corner-case question, then of
course things are different.

****************************************************************

From: Edmond Schonberg
Sent: Wednesday, February 24, 2010  1:42 PM

> So something like
>  The type of a quantified_expression is the predefined  type Boolean.
> is probably needed.

That's certainly the simplest. I see zero advantage in saying "any boolean
type" here (or elsewhere for that matter...).

****************************************************************

From: Bob Duff
Sent: Wednesday, February 24, 2010  1:44 PM

>     If the predicate expression is of a derived boolean type, is
>     the type of the quantified expression Standard.Boolean or is
>     it the derived boolean type?

I see.  The correct answer is "Who cares?", but I agree we need to decide one
way or 'tother.

...
> So something like
>    The type of a quantified_expression is the predefined
>    type Boolean.
> is probably needed.

OK with me.  It does mean that Interfaces.Fortran.Logical gets implicitly
converted to Boolean, which involves a change of representation.  Problem?

****************************************************************

From: Tucker Taft
Sent: Wednesday, February 24, 2010  1:57 PM

I think I disagree with saying it is the predefined type Boolean, on language
consistency grounds. Standard.Boolean appears essentially nowhere in the name
resolutions rules, so why introduce it here?

Since conditions are allowed to be of any boolean type, then I would say the
expected type for the predicate expression is "any boolean type", and the type
of the quantified expression is the same as that of the predicate expression.
In fact, if you define "predicate" as:

predicate ::= condition

in RM 5.3 to have an expected type of "any boolean type."

****************************************************************

From: Bob Duff
Sent: Wednesday, February 24, 2010  2:15 PM

> I think I disagree with saying it is the predefined type Boolean, on
> language consistency grounds.
> Standard.Boolean appears essentially nowhere in the name resolutions
> rules, so why introduce it here?

I think I agree with Tucker here.

> Since conditions are allowed to be of any boolean type, then I would
> say the expected type for the predicate expression is "any boolean
> type", ...

Yes, definitely -- that's the way everything else works, so should be easiest to
implement.  That's what I suggested before.

>...and the type of the quantified
> expression is the same as that of the predicate  expression.

Yes, I've changed my mind, and now agree it should not be hardwired to Boolean.
I actually think this is easier to implement, because you don't have to
implicitly convert from Derived_Boolean to Boolean (which could require a change
of representation).

>...In fact, if you define "predicate" as:
>
>    predicate ::= condition
>
> then I think much of this happens for free, since "condition" is
> already defined in RM 5.3 to have an expected type of "any boolean
> type."

Good idea.  This covers the expected type of the predicate.
We still need to say that the type of the quant_exp is that of the predicate.

****************************************************************

From: Bob Duff
Sent: Wednesday, February 24, 2010  2:18 PM

> That's certainly the simplest.  I see zero advantage in saying "any
> boolean type"  here (or elsewhere for that matter...).

Perhaps, but we already do so elsewhere, so it's simplest to do likewise here.

Anyway, it's kind of convenient to be able to use if statements on type
Interfaces.Fortran.Logical.

****************************************************************

From: Tucker Taft
Sent: Wednesday, February 24, 2010  2:55 PM

Is this Bob Duff I or Bob Duff II?
I thought you just sent out a note agreeing the predicate should be expected
to be of any boolean type, and the quantified expression should be that same type.

Implicit converting to Standard.Boolean
seems of little value, and if someone has gone to the effort of using a
non-standard boolean type, they would presumably be annoyed that all of the
logical operations preserve their non-standard boolean type *except* quantified
expressions.

****************************************************************

From: Randy Brukardt
Sent: Wednesday, February 24, 2010  3:05 PM

Some of Bob's messages got delivered out of order because they were briefly
delayed in the spam filter. That might account for the confusion.

****************************************************************

From: Edmond Schonberg
Sent: Wednesday, February 24, 2010  3:14 PM

> Implicit converting to Standard.Boolean seems of little value, and if someone
> has gone to the effort of using a non-standard boolean type, they would
> presumably be annoyed that all of the logical operations preserve their
> non-standard boolean type *except* quantified expressions.

the argument about Fortran.Logical seems compelling, so I agree that these
should be treated like other conditions. "Any boolean type"is fine.

****************************************************************

From: Steve Baird
Sent: Wednesday, February 24, 2010  3:29 PM

> I see.  The correct answer is "Who cares?", but I agree we need to
> decide one way or 'tother.

Agreed.

>> So something like
>>    The type of a quantified_expression is the predefined
>>    type Boolean.
>> is probably needed.
>
> OK with me.  It does mean that Interfaces.Fortran.Logical gets
> implicitly converted to Boolean, which involves a change of
> representation.  Problem?

I don't see it as a problem, although it sounds like it doesn't matter whether
it is a problem or not because folks seem to be leaning towards the "use the
type of the predicate" approach (which is fine with me).

One could even argue that there isn't any change of representation (or at least
it is well camouflaged) if you choose to think of a quantified expression as I
described it in an earlier message:

> ... I have no problem thinking of
>
>     (for all I in Some_Range | Some_Derived_Boolean_Type'(Foo (I)))
>
> as being equivalent to a call to a function with body
>
>     Temp : Standard.Boolean := True;
>   begin
>     for I in Some_Range loop
>        if Some_Derived_Boolean_Type'(Foo (I)) = False then
>           Temp := False;
>           exit;
>        end if;
>     end loop;
>     return Temp;

****************************************************************

From: Bob Duff
Sent: Wednesday, February 24, 2010  3:35 PM

> Is this Bob Duff I or Bob Duff II?
> I thought you just sent out a note agreeing the predicate should be
> expected to be of any boolean type, and the quantified expression
> should be that same type.

I think you read my e-mails in the opposite order I sent them.

I changed my mind.  My current opinion agrees with yours.
Reasons:  Easier to implement.  Better for the user of derived types (not many
of those, but we do have Logical).

****************************************************************

From: Bob Duff
Sent: Wednesday, February 24, 2010  8:19 PM

> All such cases follow "{", and the wording that Bob pointed out covers
> that explicitly. This is the first time | is used to separate
> something other than a list, so now we have a problem.

Right.

>...No solution comes to mind.

I suggested one.  Quote the | and say so in section 2.whatever.

>... (One also
> wonders about the inconsistency of using a list separator in a
>non-list  context.

I'm happy with either "=>" or "|".  I don't understand why Gary adamantly
prefers the latter.  Shrug.

>... I'd solve the problem by not bothering with this feature, but I'm
>not expecting that solution to fly. :-)

Well, it's easy to implement (my main concern)...

****************************************************************

From: Jean-Pierre Rosen
Sent: Thursday, February 25, 2010  3:53 AM

> Since conditions are allowed to be of any boolean type, then I would
> say the expected type for the predicate expression is "any boolean
> type",
Agreed, and the argument for Logical is important for this one.

> and the type of the quantified
> expression is the same as that of the predicate expression.
I don't see any reason why the result type of the quantified expression should
be the same as the type of the predicate. After all, if I write:

L : Fortran.Logical;

...

if L = True then

The type of "=" is Boolean, not logical. I see the predicate as a kind of
"extended" equality. Why should it be different?

****************************************************************

From: Tucker Taft
Sent: Thursday, February 25, 2010  8:10 AM

Really?  I see it as an extended "and then" or "or else".

****************************************************************

From: Jean-Pierre Rosen
Sent: Thursday, February 25, 2010  8:23 AM

Interesting. To me, it answers the question: "Is it true that all Foos verify
this condition?" rather than an "and then" between the evaluation of all the
conditions.

****************************************************************

From: Edmond Schonberg
Sent: Thursday, February 25, 2010  8:32 AM

The dynamic semantics makes it clear that the evaluation is short-circuited
(stop when counterexample is found) so this is definitely a sequence of "and
then" between conditions.

****************************************************************

From: Jean-Pierre Rosen
Sent: Thursday, February 25, 2010  8:49 AM

Sure - and nobody even thought of not stopping as soon as the result is known.
But that it is implementation. From a user's point of view, I would say that
this is a predicate. The same way you ask "is X equal to 1?" you would ask "are
all elements of Tab equal to 1?". All comparison operators return boolean...

****************************************************************

From: Bob Duff
Sent: Thursday, February 25, 2010  9:15 AM

I don't see that, because "are all elements of Tab equal to 1?" would be:

(for all I in Some_Range | Foo (I) = 1)

and that will return Boolean under either rule we're arguing about, because "Foo
(I) = 1" is Boolean.  The only issue would be if the predicate were actually of
type Logical (or some other derived type).  For example, if you have an array A
of Logical, and say:

(for all I in Some_Range | A (I))

It seems to me the result should be Logical.

You are arguing for Steve's point of view, here:

> ... I have no problem thinking of
>
>     (for all I in Some_Range | Some_Derived_Boolean_Type'(Foo (I)))
>
> as being equivalent to a call to a function with body
>
>     Temp : Standard.Boolean := True;
>   begin
>     for I in Some_Range loop
>        if Some_Derived_Boolean_Type'(Foo (I)) = False then
>           Temp := False;
>           exit;
>        end if;
>     end loop;
>     return Temp;

But Steve's code could just as well be:

>     Temp : Some_Derived_Boolean_Type := True;  <<<<<
>   begin
>     for I in Some_Range loop
>        if not Some_Derived_Boolean_Type'(Foo (I)) then  <<<<<
>           Temp := False;
>           exit;
>        end if;
>     end loop;
>     return Temp;

(Modified lines marked <<<<<.)

I find the latter more intuitive, because I always write "if not Blah"
rather than "if Blah = False".

****************************************************************

From: Edmond Schonberg
Sent: Thursday, February 25, 2010  8:18 AM

The update of AI-0176 seems incomplete. The version I sent a few days ago uses
the new iterator forms, and the non-reserved keyword "for some" not "exists".

****************************************************************

From: Randy Brukardt
Sent: Thursday, February 25, 2010  12:02 PM

Not sure what you are looking at. The version posted on the web (version /04)
has all of those changes.

****************************************************************

From: Edmond Schonberg
Sent: Thursday, February 25, 2010  7:15 PM

Looking at the one on the web. The productions (under 4.5.9) are old, they
mention "exists" and do not mention the new iterator forms (using
loop_parameter_specification).

[Editor's Note: Version /05 fixes these errors.]

****************************************************************

From: Yannick Moy
Sent: Friday, May 21, 2010  2:47 AM

Looking at AI05-0176-1/06 2010-04-12 on Quantified expressions, I found a few typos:

In !problem, I found 2 typos:

the property A(I) <= A (I+1) obtains
^^^^^^^ (holds)

to indicate that all elemnts X satisfy
^^^^^^^ (elements)

In !proposal, I found 1 typo:

that verify whether all (resp. al least one)
^^ (at)

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