Version 1.12 of ai12s/ai12-0312-1.txt

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!standard 5.5.2(2/3)          19-10-06 AI12-0312-1/07
!class presentation 19-02-07
!status work item 19-02-07
!status received 19-02-07
!priority Low
!difficulty Easy
!subject Examples for Ada 2020
!summary
Additional examples are added, and existing ones improved.
!question
Some new parts of the Standard have few or no examples, while others have too many examples (see 4.3.5). We need a more consistent use of examples, right? (Yes.)
!response
(See Summary.)
!wording
Append after 3.5.2(11) [or perhaps 13.4(14) instead?]
-- See 3.5.2 [if placed in 13.4] for Roman_Digit use ('I' => 1,
'V' => 5, 'X' => 10, 'L' => 50, 'C' => 100, 'D' => 500, 'M' => 1000);
Modify 3.10.1(23)
My_Car, Your_Car, Next_Car : Car_Name := new Car; -- see 4.8 [George]{Casey} : Person_Name := new Person(M);
...
[George]{Casey}.Vehicle := Your_Car;
[Author's note: George was changed to Casey, because a more unisex name was asked for in the comments against the example for 4.5.7(21/3), and googling famous people named Casey produces about an even mix of the sexes. Chris produced mostly male for example, and Pat was also heavily male oriented]
Append after 4.2.1(9.d/5):
Examples
subtype Roman_Character is Character with Static_Predicate => Roman_Character in 'I' | 'V' | 'X' | 'L' | 'C' | 'D' | 'M';
Max_Roman_Number : constant := 3_999; -- MMMCMXCIX
subtype Roman_Number is Positive range 1 .. Max_Roman_Number with String_Literal => To_Roman_Number;
function To_Roman_Number (S : String) return Roman_Number with Pre => S'Length > 0 and then (for all Char of S => Char in Roman_Character);
function To_Roman_Number (S : String) return Roman_Number is (declare R : constant array (Integer range <>) of Integer := (for D in S'range => Roman_Digit'Enum_Rep (Roman_Digit'Value (S (D..D)))) -- See 3.5.2 [(and 13.4 ???)] begin [for I in R'range => (if I < R'Last and then R(I) < R(I + 1) then -1 else 1) * R(I))] 'Reduce("+", 0) );
X : Roman_Number := "III" * "IV" * "XII"; -- 144 ( i.e. CXLIV)
Append after 4.3.3(47/5):
Empty_Matrix : constant Matrix := []; -- A matrix without elements
Delete paragraph 4.3.5(86/5-87-5). [Already show example of empty container aggregate]
Delete paragraph 4.3.5(97/5). [Alternate form example shown above]
Delete paragraphs 4.3.5(99/5 - 100/5). [Already show example of empty container aggregate]
Delete paragraphs 4.3.5(105/5 - 106/5). [Example is not that different from others]
Append after 4.5.7(22.a/5):
Examples
Put_Line ("Casey is " & (if Casey.Sex = M then "Male" else "Female")); -- See 3.10.1
function Card_Color (Card : Suit) return Color is -- See 3.5.2
(case Card is
when Clubs | Spades => Black, when Hearts | Diamonds => Red);
Modify after 4.5.8 (13/3)
pragma Assert (for some X in 2 .. N {when X * X <= N}[/ 2] => N mod X = 0); -- See iterator_filter in 5.5
Append after 4.5.10 (53/5):
A parallel reduction expression used to calculate the mean of the elements of a two dimensional array of subtype Matrix (see 3.6) that are greater than 100.0:
type Accumulator is record Sum : Real; -- See 3.5.7 Count : Integer; end record;
function Accumulate (L, R : Accumulator) return Accumulator is (Sum => L.Sum + R.Sum, Count => L.Count + R.Count);
function Average_of_Values_Greater_Than_100 (M : Matrix) return Real is (declare Acc : constant Accumulator := [parallel for Val of M when Val > 100.0 => (Val, 1)] 'Reduce(Accumulate, (Sum => 0, Count => 0)); begin Acc.Sum / Real(Acc.Count));
Modify 5.5(22/5): "Example{s} of [a] parallel loop{s}: "
Add after 5.5(23/5):
Example of a parallel loop with a chunk specification
declare subtype Chunk_Number is Natural range 1 .. 8;
Partial_Sum, Partial_Max : array (Chunk_Number) of Natural := (others => 0); Partial_Min : array (Chunk_Number) of Natural := (others => Natural'Last); begin parallel (Chunk in Chunk_Number) for I in Grid'range(1) loop declare True_Count : constant Natural := [for J in Grid'range(2) => (if Grid (I, J) then 1 else 0)]'Reduce("+",0); begin Partial_Sum (Chunk) := @ + True_Count; Partial_Min (Chunk) := Natural'Min(@, True_Count); Partial_Max (Chunk) := Natural'Max(@, True_Count); end; end loop;
Put_Line("Total=" & Partial_Sum'Reduce("+", 0) & ", Min=" & Partial_Min'Reduce(Natural'Min, Natural'Last) & ", Max=" & Partial_Max'Reduce(Natural'Max, 0)); end;
For an example of an iterator_filter, see 4.5.8
Append after 6.1.1(42/3):
6 For an example of the use of these aspects and attributes, see the Streams Subsystem definitions in 13.13.1.
Append after 6.1.2(50.b/5):
NOTES
For an example of the use of these aspects, see the Vector container definition in A.18.2.
Append after 7.3.2(24.a/3):
Examples
-- A work scheduler where only urgent work can be scheduled for weekends
with See_RM_3_5_1; use See_RM_3_5_1;
package Work_Orders is
-- See 3.5.1 for type declarations of Level, Day, and Weekday
type Work_Order is private with Type_Invariant => Day_Scheduled (Work_Order) in Weekday or else Priority (Work_Order) = Urgent;
function Schedule_Work (Urgency : in Level; To_Occur : in Day) return Work_Order with Pre => Urgency = Urgent or else To_Occur in Weekday;
function Day_Scheduled (Order : in Work_Order) return Day;
function Priority (Order : in Work_Order) return Level;
procedure Change_Priority (Order : in out Work_Order; New_Priority : in Level; Changed : out Boolean) with Post => Changed = (Day_Scheduled(Order) in Weekday or else Priority(Order) = Urgent); private
type Work_Order is record Scheduled : Day; Urgency : Level; end record;
end Work_Orders;
package body Work_Orders is
function Schedule_Work (Urgency : in Level; To_Occur : in Day) return Work_Order is (Scheduled => To_Occur, Urgency => Urgency);
function Day_Scheduled (Order : in Work_Order) return Day is (Order.Scheduled); function Priority (Order : in Work_Order) return Level is (Order.Urgency); procedure Change_Priority (Order : in out Work_Order; New_Priority : in Level; Changed : out Boolean) is begin -- Ensure type invariant is not violated if Order.Urgency = Urgent or else (Order.Scheduled in Weekday) then Changed := True; Order.Urgency := New_Priority; else Changed := False; end if; end Change_Priority;
end Work_Orders;
Append after 7.3.3(9.a/5):
NOTES
For an example of the use of this aspect, see the Vector container definition in A.18.2.
Append after 11.3(7):
For an example of a raise expression, see the Streams Subsytem definitions in 13.13.1.
Append after 13.4(14)
For an example of the use of 'Enum_Rep, see 4.2.1
Modify B.3(78/3): --Calling the C Library Function{s} strcpy{, and printf} with Interfaces.C; procedure Test is
package C renames Interfaces.C; use type C.char_array; -- Call <string.h>strcpy: -- C definition of strcpy: char *strcpy(char *s1, const char *s2); -- This function copies the string pointed to by s2 (including the terminating null character) -- into the array pointed to by s1. If copying takes place between objects that overlap, -- the behavior is undefined. The strcpy function returns the value of s1.
Append after B.3(78/3):
-- Call <sdtio.h>printf: -- C definition of printf: int printf ( const char * format, ... ); -- This function writes the C string pointed by format to the standard -- output (stdout). If format includes format specifiers (subsequences -- beginning with %), the additional arguments following format are -- formatted and inserted in the resulting string replacing their -- respective specifiers. If the number of arguments does not match -- the number of format specifiers, or if the types of the arguments -- do not match the corresponding format specifier, the behaviour is -- undefined. On success, the printf function returns the total -- number of characters written to the standard output. If a writing -- error occurs, a negative number is returned.
-- Note: since the C function's return value is of no interest, the Ada interface is a procedure
procedure Printf (Format : in C.char_array)
with Import => True, Convention => C_Variadic_1, External_Name => "printf";
Append after B.3(83):
Printf("The String=%s, Length=%d", Chars1, Chars1'Length);
!discussion
A survey of the RM found that there were no examples in the defining sections for:
- Conditional Expressions (4.5.7) - Reduction Expressions using a Combiner (4.5.10) - Pre and Post conditions (6.1.1) - Global Aspect (6.1.2) - Type Invariants (7.3.2) - Default Initial Conditions (7.3.3) - raise expressions and Predicate_Failure (11.3) - Image Attributes (4.10) - Variadic C functions (B.3) - User Defined Literals (4.2.1) - Explicit Chunk definition for parallel loops (5.5) - implicit subtype mark in object renames (8.5.1) - null array aggregates (4.3.3)
The 'Image attribute has existed since Ada 83, but improved in Ada 202x, however it doesn't seem that an example is necessary.
Similarly, there is an existing example for object renames, with an explicit subtype mark. It seems to not be worthwhile to add another example where the subtype mark is implicit.
!ASIS
None needed.
!ACATS test
No ACATS tests needed.
!appendix

From: Brad Moore
Sent: Friday, February 22, 2019  5:45 PM

I managed to get an initial draft of this AI, possibly just under or over
the deadline.

So far, Jeff and Ed have not seen this or have had a chance to comment on
it, yet they are listed as being involved in the homework assignment.

Had I finished this earlier, I would have sent it an initial draft out to
them, but since it is this close to the deadline, I figured it would be
better to just send this out to the group, in case we want to discuss it at
the meeting.

In the meantime, it would be great if Jeff and/or Ed could review with an eye
to;

1) Did I miss some features that need examples?
2) Are the examples I have satisfactory, or could be improved upon?
3) Did I reduce the container aggregate examples sufficiently, or perhaps cut off
   too much?
4) Do you have additional examples that you'd like to see added?

Some of the features are actually Ada 2005 features, such as type invariants.
However, since the goal of this work is to make the RM more consistent in the
examples department, this seemed like a good idea to provide a few extra
examples.

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

From: Brad Moore
Sent: Friday, February 22, 2019  6:04 PM

A minor correction to the User Defined Literal example:


     function To_Date (Value : String) return Date is
        (declare
            Integer_String : constant String := Integer'Image (Integer'Value (Value));
         begin
           (Day => Integer'Value(Integer_String (Integer_String'Last-5 .. Integer_String'Last-4)),
            Year => Integer'Value (Integer_String (Integer_String'Last - 3 .. Integer_String'Last)),
            Month => Month_Name'Val (Integer'Value(Integer_String (Integer_String'First .. Integer_String'Last - 6))-1)));

In determining the Month component, I needed to subtract 1 before applying 'Val on the Month_Name enumeration.
Also, I believe I was missing a semicolon on the declaration of Integer_String in the declare expression.
The above has these corrections.

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

From: Randy Brukardt
Sent: Friday, February 22, 2019  9:32 PM

> I managed to get an initial draft of this AI, possibly just under or
> over the deadline.

This message was time-stamped at 5:45 CST, so you were 45 minutes late. As
always, I ask that people that might be late send me a heads-up. It didn't
matter today, as processing the draft of the hour for AI12-0191-1 took
forever.

> Some of the features are actually Ada 2005 features, such as type invariants.

Type invariants are an Ada 2012 feature. Not that that matters to your point...

> A minor correction to the User Defined Literal example:

Correction applied.

>     function To_Date (Value : String) return Date is
>       (declare
>            Integer_String : constant String := Integer'Image (Integer'Value (Value));
>         begin
>           (Day => Integer'Value(Integer_String (Integer_String'Last-5 .. Integer_String'Last-4)),
>            Year => Integer'Value (Integer_String (Integer_String'Last - 3 .. Integer_String'Last)),
>            Month => Month_Name'Val (Integer'Value(Integer_String
> (Integer_String'First .. Integer_String'Last - 6))-1)));

Some of these lines are too long to put in the RM as-is. It would help to break
them to be shorter, so I don't have to guess where to do it.

>!wording
>
>delete paragraphs 4.3.5 (86/5 - 86/5)       [Already show example of empty container aggregate]

You have a range with one paragraph in it; I suspect that you meant something
else.

>Append after 4.5.7 (21/3)
...
>Value : constant Natural := (case
>type Roman_Digit is ('I', 'V', 'X', 'L', 'C', 'D', 'M');

There is something wrong with this! I haven't previously encountered the
"case type expression"! :-)

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

From: Brad Moore
Sent: Friday, February 22, 2019  10:23 PM

>> I managed to get an initial draft of this AI, possibly just under or
>> over the deadline.
>
> This message was time-stamped at 5:45 CST, so you were 45 minutes
> late. As always, I ask that people that might be late send me a
> heads-up. It didn't matter today, as processing the draft of the hour
> for AI12-0191-1 took forever.

Whew! Glad to hear it made it under the door even if only by luck....

...
>>     function To_Date (Value : String) return Date is
>>       (declare
>>            Integer_String : constant String := Integer'Image
> (Integer'Value (Value));
>>         begin
>>           (Day => Integer'Value(Integer_String (Integer_String'Last-5 ..
> Integer_String'Last-4)),
>>            Year => Integer'Value (Integer_String (Integer_String'Last
>> - 3
> .. Integer_String'Last)),
>>            Month => Month_Name'Val (Integer'Value(Integer_String
> (Integer_String'First .. Integer_String'Last - 6))-1)));
>
> Some of these lines are too long to put in the RM as-is. It would help
> to break them to be shorter, so I don't have to guess where to do it.

I found it helped to shorten some of the variable names. Here is what I have currently.

   function To_Date (Value : String) return Date is
     declare S : constant String := Integer'Image (Integer'Value (Value)); begin
       (Day => Integer'Value (S (S'Last-5 .. S'Last-4)),
        Year => Integer'Value (S (S'Last-3 .. S'Last)),
        Month => Month_Name'Val (Integer'Value (S (S'First .. S'Last-6))-1));

One question. I wasn't sure if I need an extra set of parens around the
expression function, or can the parens used for the aggregate object suffice?
If not, you'll need to add those.

Also not sure if style here warrants putting the declare and begin on the same
line, but I quite like the new look of this example.

>>!wording
>>
>>delete paragraphs 4.3.5 (86/5 - 86/5)       [Already show example of empty
> container aggregate]
>
> You have a range with one paragraph in it; I suspect that you meant
> something else.

I meant (86/5 - 87/5)

>>Append after 4.5.7 (21/3)
> ...
>>Value : constant Natural := (case
>>type Roman_Digit is ('I', 'V', 'X', 'L', 'C', 'D', 'M');
>
> There is something wrong with this! I haven't previously encountered the
> "case type expression"! :-)

These two lines are garbage and should be deleted....

"Value : constant Natural := (case
type Roman_Digit is ('I', 'V', 'X', 'L', 'C', 'D', 'M');"

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

From: Randy Brukardt
Sent: Friday, February 22, 2019  10:59 PM

...
> Whew! Glad to hear it made it under the door even if only by luck....

...but not with this message. :-)

...
> > Some of these lines are too long to put in the RM as-is. It would
> > help to break them to be shorter, so I don't have to guess where to do it.
> >
>
> I found it helped to shorten some of the variable names. Here is what
> I have currently.
>
>    function To_Date (Value : String) return Date is
>      declare S : constant String := Integer'Image (Integer'Value
> (Value));
begin
>        (Day => Integer'Value (S (S'Last-5 .. S'Last-4)),
>         Year => Integer'Value (S (S'Last-3 .. S'Last)),
>         Month => Month_Name'Val (Integer'Value (S (S'First ..
S'Last-6))-1));
>
> One question. I wasn't sure if I need an extra set of parens around
> the expression function, or can the parens used for the aggregate
> object suffice? If not, you'll need to add those.

This example doesn't have any parens at all (needed around the declare
expression), so that's a problem. And putting the declare/declaration/begin
on the same line isn't the recommended style, and it's probably too long
anyway (only room for roughly 70 characters on a line in an example,
including the indenting white space), so let's not do that.

> Also not sure if style here warrants putting the declare and begin on
> the same line, but I quite like the new look of this example.

See above.

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

From: Jeff Cousins
Sent: Monday, February 22, 2019  2:27 PM

Presumably "delete paragraphs (86/5 – 86/5)" should be "Delete paragraphs (86/5 – 87/5)".

"Add after 5.5 (23/5)" It would help to begin with a comment of explanation,
e.g. that it is an example of explicit chunk definition.

"Append after 11.3 (7)" I can only see one example in 13.13.1; if so, this
should be in singular.

"Append after B.3 (78/3)" It would help to begin with a comment of explanation,
e.g. that it is an example of a variadic C function.

"Append after 4.5.7 (21/3)" Is the last line simply spurious, partly cut and
pasted from 3.5.2?

Also, could all these be put in RM order?

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

From: Brad Moore
Sent: Monday, March 7, 2019  5:18 PM

Here are some relatively minor updates to AI12-0312-1

This addresses editorial comments raised by Randy and Jeff on my previous
submission.

[This is version /02 of the AI - Editor.]

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

From: Brad Moore
Sent: Friday, March 22, 2019  2:32 PM

Here is a minor update to AI12-0312-1

[This is version /03 of the AI - Editor.]

Steve Baird had commented that it would be good to have an example of a parallel
reduction expression with a combiner.

Thanks also to Steve for suggesting an example, which I incorporated.

I extended the example to use an iterator filter, which makes the example more
practical, as otherwise one could just do an integer reduction / A'Length to get
a mean.

The example is:

Append after 4.5.10 (53/5)

     A parallel reduction expression that outputs the mean of the
     elements with even values for an array:

     type Accumulator is record
        Sum : Integer; Addends : Natural;
     end;=

     function Combine (L, R : Accumulator) return Accumulator is
        (Sum => L.Sum + R.Sum, Addends => L.Addends + R.Addends);

     function Reduce (A : Accumulator; Addend : Integer) is
        (Sum => A.Sum + Addend, Addends => A.Addends + 1);

     function Mean (A : Accumulator) return Integer is (A.Sum / A.Addends);

     Put_Line("The mean of the even values of A is" &
              Mean ([for Val of A when (A mod 2) = 0 => Val]
                      'Parallel_Reduce(Reduce,
                                       (Sum => 0, Addends => 0),
                                       Combine)));

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

From: Jean-Pierre Rosen
Sent: Saturday, March 23, 2019  6:49 PM

There are several glitches in the example that caused me quite a hard time
understanding it...

1)
                Mean ([for Val of A when (A mod 2) = 0 => Val]

   "A mod 2" should be "Val mod 2", right?

2)
In the above, A is some array whose declaration is not shown, while everywhere
else, A is the accumulator. Please use a different name (and possibly show the
declaration).

3)
It took me quite a time to spot the difference between "addend" and "addends".
Using "count" instead of "addends" would help a lot...

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

From: Brad Moore
Sent: Sunday, March 24, 2019  2:20 PM

> There are several glitches in the example that caused me quite a hard
> time understanding it...
>
> 1)
>                Mean ([for Val of A when (A mod 2) = 0 => Val]
> "A mod 2" should be "Val mod 2", right?

Thanks for catching this, Steve Baird also caught this.

He also noted there was an extraneous "=" after the declaration of the
Accumulator type.

>
> 2)
> In the above, A is some array whose declaration is not shown, while
> everywhere else, A is the accumulator. Please use a different name (and
> possibly show the declaration).

The example was placed immediately after the following one in the RM, (4.5.10
53/5)

Calculate the sum of elements of an array of integers:

A'Reduce("+",0)  -- See 4.3.3.

If you follow that reference you find the declaration of A, which is;

type Table    is array(1 .. 10) of Integer;

A : Table := (7, 9, 5, 1, 3, 2, 4, 8, 6, 0);

That being said, this array is too small to likely be worth processing with a
parallel reduction expression, so I think the example needs to hint at
processing a much larger array.

I decided to rework this example, to operate on the Matrix type defined in the
RM, which is an unconstrained array type of real. By making the example an
expression function, where the matrix is passed as a parameter, that will allow
a potentially very large array to be processed, without having to declare the
array in the RM. Since the type of the sum is now Real, instead of Integer, the
iterator filter should be something like filtering out all values <= 100.0,
rather than even numbers, which is probably a more realistic filter anyway.

There also were a couple of other glitches in the AI, which I noticed, making a
better case for submitting an new update, which I have done below.

- The Accumulator type is missing "record" after end, i.e. "end record;"
- The function Reduce doesn't specify what it is returning
- The expression function, To_Date for an earlier example in the AI Appended
  after 4.2.1(10/5) has the first opening paren after the declare of the
  declare expression, instead of before.
- In the discussion section there are some comments about missing aspect
  examples ('Global and 'Stable_Properties) that have since been added to
  the RM draft, so those comments are no longer needed. It also needs to
  mention that we were missing an example of a reduction expression
  using a Combiner.

> 3)
> It took me quite a time to spot the difference between "addend" and
> "addends". Using "count" instead of "addends" would help a lot...

I agree that is pretty subtle, but I also find Count is perhaps too vague,
and doesn't describe what we are counting. So I would use Addend_Count instead,
which seems to address your comment, as well as my own.

Here is a new version of the AI after these updates.

Note that I got rid of the Mean function, since the new expression function
incorporates the mean. I also used a declare expression in the expression
function which does the parallel reduction.

Here is the updated example for the AI


     A parallel reduction expression used to calculate the mean of the
     elements of a two dimensional array of subtype Matrix (see 3.6) that
     are greater than 100.0:

   type Accumulator is record
      Sum          : Real; -- See 3.5.7
      Addend_Count : Integer;
   end record;

   function Combine (L, R : Accumulator) return Accumulator is
     (Sum => L.Sum + R.Sum,
      Addend_Count => L.Addend_Count + R.Addend_Count);

   function Reduce (A : Accumulator; Addend : Real) return Accumulator is
     (Sum => A.Sum + Addend, Addend_Count => A.Addend_Count + 1);

   function Average_of_Values_Greater_Than_100 (M : Matrix) return Real is
     (declare Acc : constant Accumulator :=
        [for Val of M when Val > 100.0 => Val]
          'Parallel_Reduce(Reduce, (Sum => 0, Addends => 0), Combine);
      begin
        Acc.Sum / Real(Acc.Addend_Count));


And here is the full updated AI, which the changes described above;

[This is version /04 of the AI - Editor.]

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

From: Brad Moore
Sent: Thursday, June 20, 2019  12:59 AM

In Warsaw, for AI12-0312-1 Examples for Ada 2020,

I had an example for user defined literals involving specifying dates as
integers using underscores to separate the fields.

This generally was not liked, (for example Erhard commented that one could
create an aggregate assignment for this, which is safer, which is a good point).
So since then I have conjured up another example, that I think is an
improvement.

This example uses the Roman numeral types in the RM to allow one to express
values for an integer type, using roman numeral strings.

I think this means, one would be able to write expressions such as;

  X : Roman_Number := "III" * "IV" * "XII";   --  = 144 or "CXLIV", when 'Image is applied

As I am thinking the compiler will deduce from the context that all values
are of the same type, and thus should be converted to integer Roman_Number
values before applying the operations.

Does that sound right?

In any case, the example code I have is an interesting example in that it
uses a lot of newer features.
  - Static Subtype Predicates
  - Dynamic Subtype Predicate
  - User Defined String Literals
  - Quantified Expression
  - Expression Functions
  - Declare Expressions
  - Conditional Expressions
  - Reduction Expressions
  - Case Expressions
  - Array Aggregate with an iterator expression
  - When clause on an iterator expression
  - User defined 'Image
  - Preconditions

So I am curious to see if others think this is an appropriate example, or if
someone might suggest a better idea.

The user defined literal going from Roman Numerals to Integer was surprisingly
simple with the new features.
Going the other way round, with 'Image was surprisingly more difficult than
expected, but we could drop off the 'Image easily enough from the example.

   type Roman_Digit is ('I', 'V', 'X', 'L', 'C', 'D', 'M');    -- From RM 3.5.2 (11)

   type Roman      is array(Positive range <>) of Roman_Digit;  -- From RM 3.6 (26)

   subtype Roman_Character is Character
     with Static_Predicate =>
       Roman_Character in 'I' | 'V' | 'X' | 'L' | 'C' | 'D' | 'M';

   subtype Roman_String is String with   -- Not really needed for this example
     Dynamic_Predicate =>
       (for all Char of Roman_String => Char in Roman_Character);

   subtype Roman_Number is Positive range 1 .. 1_000   -- Subtype with user-defined string literal
      with String_Literal => To_Roman_Number;
   for Roman_Number'Put_Image use Image;

   function To_Roman_Number (S : String) return Roman_Number
     with Pre => (for all Char of S => Char in Roman_Character);

   function To_Roman_Number (S : String) return Roman_Number is
     (declare R : constant array (Integer range <>) of Roman_Number :=
        (for D of S =>
             (case D is
                 when 'I' => 1,
                 when 'V' => 5,
                 when 'X' => 10,
                 when 'L' => 50,
                 when 'C' => 100,
                 when 'D' => 500,
                 when 'M' => 1000))
      begin
        [for I in R'Range =>
          (if I < R'Last and then R(I) < R(I + 1) then -1 else 1) * R(I))]
            'Reduce("+", 0)
     );

   procedure Image
     (Arg : Integer;
      Stream : not null access Ada.Streams.Root_Stream_Type'Class)
      with Pre => (Arg <= 1000);

   procedure Image
     (Arg : Integer;
      Stream : not null access Ada.Streams.Root_Stream_Type'Class)
   is
      Lookup : constant array (Roman_Digit) of Roman_Number :=
        ('I' => 1, 'V' => 5, 'X' => 10, 'L' => 50, 'C' => 100, 'D' => 500,
         'M' => 1000);

      procedure Convert (Value : Natural)
      is
         Above : constant Roman_Digit :=
            [for I in Lookup'Range when Lookup (I) >= Value => I]
             'Reduce(Roman_Digit'Min, Roman_Digit'Last);
      begin
         if Value = 0 then
            return;
         elsif Value = 1 then
            Roman_Digit'Write (Stream, 'I');
         elsif Value = Lookup (Above) then
            Roman_Digit'Write (Stream, Above);
            Convert (Value - Lookup (Above));
         elsif Roman_Digit'Pos(Above) rem 2 = 0 and then Value >= Lookup (Above) -
           Lookup (Roman_Digit'Pred(Roman_Digit'Pred (Above))) then
            Roman_Digit'Write (Stream,
                               Roman_Digit'Pred(Roman_Digit'Pred (Above)));
            Roman_Digit'Write (Stream, Above);
            Convert
              (Value - (Lookup (Above) -
                 Lookup (Roman_Digit'Pred(Roman_Digit'Pred (Above)))));
         elsif Value /= Lookup (Above) and then
           Roman_Digit'Pos(Above) rem 2 = 1 and then Value >= Lookup (Above) -
           Lookup (Roman_Digit'Pred (Above))
         then
            Roman_Digit'Write (Stream,
                               Roman_Digit'Pred (Above));
            Roman_Digit'Write (Stream, Above);
            Convert
              (Value - (Lookup (Above) -
                 Lookup (Roman_Digit'Pred (Above))));
         else
            Roman_Digit'Write (Stream, Roman_Digit'Pred(Above));
            Convert (Value - Lookup (Roman_Digit'Pred (Above)));
         end if;
      end Convert;
   begin
      Convert (Arg);
   end Image;

  X : Roman_Integer := "III" * "IV" * "XII"; -- 144 ( i.e. CXLIV)

...
   --  Outputs  "Answer is 144 ( CXLIV )"
   Put_Line ("Answer is" & Integer'Image(X)
             & " ( " & Roman_Number'Image(X) & " )");


I also have a working version of this, using Ada 2012 syntax, and one of my
Stream Buffer class in case anyone is interested.

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

From: Tucker Taft
Sent: Thursday, June 20, 2019  7:36 AM

Interesting.  Implementation is too long for the manual, but we could put
just the specs in the manual.  Might be clearer if you called the routine
"Put_Image" rather than "Image".  Might make a good ACATS test.

> I think this means, one would be able to write expressions such as;
>
>  X : Roman_Number := "III" * "IV" * "XII";   --  = 144 or "CXLIV", when 'Image is applied
>
> As I am thinking the compiler will deduce from the context that all
> values are of the same type, and thus should be converted to integer
> Roman_Number values before applying the operations.
>
> Does that sound right?
> ...

I have to think a bit about the overload resolution here.  I am unsure whether
the multiplication will work as you wrote it.  Normally we require exactly one
expected type for string literals, unlike for numeric literals.  There is no
"universal" type for string literals.  But since you provided an expected
type of Roman_Number it is probably fine.

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

From: Erhard Ploedereder
Sent: Thursday, June 20, 2019  10:58 AM

Cute example, much better than the old one, ....

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

From: Brad Moore
Sent: Thursday, June 20, 2019  7:58 AM

I've made a few minor fixes to this. In particular, the user-defined Image
function needed to write to the stream as characters, not Roman Digits.

Since Tullio privately mentioned an interest in seeing the Ada 2012 version,
I might as well send out the update with the fix as well as the working Ada
2012 version to the group. Please see the attached tar file which contains
both. [Not available here, see source below - Editor.]

The Ada 202x version is in main_202x.adb, and the Ada 2012 version is in
main.adb.

The Ada 2012 version is actually a hybrid between Ada 2012 and Ada 202x, as
it incorporates some 202x features that have already been implemented in
GNAT, such as @, and array aggregate with iterators.

The project file should compile with the latest GNAT community edition,
released this month (or in May)

For those not wanting to fiddle with untarring files, here are the relevant
bits from the updated 202x version....

  type Roman_Digit is ('I', 'V', 'X', 'L', 'C', 'D', 'M');

   subtype Roman_Character is Character
     with Static_Predicate =>
       Roman_Character in 'I' | 'V' | 'X' | 'L' | 'C' | 'D' | 'M';

   subtype Roman_String is String with
     Dynamic_Predicate =>
       (for all Char of Roman_String => Char in Roman_Character);

   subtype Roman_Number is Positive range 1 .. 1_000
      with String_Literal => To_Roman_Number;
   for Roman_Number'Put_Image use Image;

   function To_Roman_Number (S : String) return Roman_Number
     with Pre => (for all Char of S => Char in Roman_Character);

   function To_Roman_Number (S : String) return Roman_Number is
     (declare R : constant array (Integer range <>) of Integer :=
        (for D of S =>
             (case D is
                 when 'I' => 1,
                 when 'V' => 5,
                 when 'X' => 10,
                 when 'L' => 50,
                 when 'C' => 100,
                 when 'D' => 500,
                 when 'M' => 1000))
      begin
        [for I in R'Range =>
          (if I < R'Last and then R(I) < R(I + 1) then -1 else 1) * R(I))]
            'Reduce("+", 0)
     );

   procedure Image
     (Arg : Integer;
      Stream : not null access Ada.Streams.Root_Stream_Type'Class)
      with Pre => (Arg <= 1000);

   procedure Image
     (Arg : Integer;
      Stream : not null access Ada.Streams.Root_Stream_Type'Class)
   is
      Lookup : constant array (Roman_Digit) of Roman_Number :=
        ('I' => 1, 'V' => 5, 'X' => 10, 'L' => 50, 'C' => 100, 'D' => 500,
         'M' => 1000);

      procedure Convert (Value : Natural)
      is
         function To_Char (D : Roman_Digit) return Roman_Character is
           (case D is
               when 'I' => 'I',
               when 'V' => 'V',
               when 'X' => 'X',
               when 'L' => 'L',
               when 'C' => 'C',
               when 'D' => 'D',
               when 'M' => 'M');

         Above : constant Roman_Digit :=
            [for I in Lookup'Range when Lookup (I) >= Value => I]
             'Reduce(Roman_Digit'Min, Roman_Digit'Last);
      begin --  Convert
         if Value = 0 then
            return;
         elsif Value = 1 then
            Character'Write (Stream, 'I');
         elsif Value = Lookup (Above) then
            Character'Write (Stream, To_Char (Above));
            Convert (Value - Lookup (Above));
         elsif Roman_Digit'Pos (Above) rem 2 = 0
           and then Value >= Lookup (Above) -
           Lookup (Roman_Digit'Pred (Roman_Digit'Pred (Above)))
         then
            Character'Write
              (Stream,
               To_Char (Roman_Digit'Pred (Roman_Digit'Pred (Above))));
            Character'Write (Stream, To_Char (Above));
            Convert
              (Value - (Lookup (Above) -
                 Lookup (Roman_Digit'Pred (Roman_Digit'Pred (Above)))));
         elsif Value /= Lookup (Above) and then
           Roman_Digit'Pos (Above) rem 2 = 1 and then Value >= Lookup (Above) -
           Lookup (Roman_Digit'Pred (Above))
         then
            Character'Write (Stream, To_Char (Roman_Digit'Pred (Above)));
            Character'Write (Stream, To_Char (Above));
            Convert
              (Value - (Lookup (Above) -
                 Lookup (Roman_Digit'Pred (Above))));
         else
            Character'Write (Stream, To_Char (Roman_Digit'Pred (Above)));
            Convert (Value - Lookup (Roman_Digit'Pred (Above)));
         end if;
      end Convert;
   begin --  Image
      Convert (Arg);
   end Image;

  X : Roman_Number := "III" * "IV" * "XII"; -- 144 ( i.e. CXLIV)

...
   --  Outputs  "Answer is 144 ( CXLIV )
   Put_Line ("Answer is" & Integer'Image(X)
             & " ( " & Roman_Number'Image(X) & " )");

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

From: Randy Brukardt
Sent: Thursday, June 20, 2019  11:36 AM

> Interesting.  Implementation is too long for the manual, but we could
> put just the specs in the manual.

I think it is OK if all of the stuff unrelated to user-defined literals is
left out (that is, all of the Image stuff). Perhaps that fits in the Image
section to show a redefinition, but it definitely doesn't belong in a
user-defined literal example.

I'd also leave out the unused Roman_String, especially as one could also
declare a string type thusly:
    type Other_Roman_String is array (Positive range <>) of Roman_Character;

Do you use Roman_Character for anything in this example?

> Might be clearer
> if you called the routine "Put_Image" rather than "Image".

Agreed. Why confuse the usage (usually a routine "Image" returns a String).

> Might make a good ACATS test.

Well, no, because it uses a kitchen sink of features and would cover
objectives from multiple sections. We try to make ACATS tests that
mostly use basic stuff outside of the tested feature so that the tests
are useable for staged implementations (no one can implement everything at
once).

I suppose it could make *two* ACATS tests (one for user-defined literals, and
one for user-defined image), but I'd probably suggest getting rid of the
preconditions and predicates in that case (replacing them with regular code)
- those things aren't under test here.

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

From: Randy Brukardt
Sent: Wednesday, July 24, 2019  8:44 PM

Jeff had the following comments on your AI that didn't get discussed in Warsaw
as Jeff misplaced his notes. These ought to be addressed in the next draft
along with the things noted in the minutes:

	4.3.5(86/5 - 86/5) should be 4.3.5(86/5 - 87/5)

	11.3 (7) There is only one raise expression in 13.13.1 so this should say
        "for an example of a raise expression..."

	B.3(78/3) needs a comment saying what it is about:

	-- Example of a variadic C function

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

From: Brad Moore
Sent: Saturday, September 28, 2019  6:20 PM

In the minutes from last meeting, I was asked to see if I could simplify
the Reduction Expression example for 4.5.10 (53/5), possibly by using a set
container.

The example currently in the AI is;

   type Accumulator is record
      Sum          : Real; -- See 3.5.7
      Addend_Count : Integer;
   end record;

   function Combine (L, R : Accumulator) return Accumulator is
     (Sum => L.Sum + R.Sum,
      Addend_Count => L.Addend_Count + R.Addend_Count);

   function Reduce (A : Accumulator; Addend : Real) return Accumulator is
     (Sum => A.Sum + Addend, Addend_Count => A.Addend_Count + 1);

   function Average_of_Values_Greater_Than_100 (M : Matrix) return Real is
     (declare Acc : constant Accumulator :=
        [parallel for Val of M when Val > 100.0 => Val]
          'Reduce(Reduce, (Sum => 0, Addend_Count => 0), Combine);
      begin
        Acc.Sum / Real(Acc.Addend_Count));


I have given thought to using a container such as a set, but so far, have not
arrived at anything sensible.

However, I do think the example can be simplified, without using containers.

We can eliminate the need for a separate combiner function by having the
map/reduce part of the value_sequence produce an Accumulator object rather
than a real value as an input to the reduction. The count part of the
accumulator is 1, which gets tallied up by the reducer.

If we do that, then the example becomes;

  type Accumulator is record
      Sum   : Real; -- See 3.5.7
      Count : Integer;
   end record;

   function Reduce (L, R : Accumulator) return Accumulator is
     (Sum   => L.Sum   + R.Sum,
      Count => L.Count + R.Count);

   function Average_of_Values_Greater_Than_100 (M : Matrix) return Real is
     (declare Acc : constant Accumulator :=
        [parallel for Val of M when Val > 100.0 => (Val, 1)]
          'Reduce(Reduce, (Sum => 0, Count => 0));
      begin
        Acc.Sum / Real(Acc.Count));

It this enough of a simplification for this example? I looks pretty simple to
me.

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

From: Jean-Pierre Rosen
Sent: Sunday, September 29, 2019  12:15 AM

> It this enough of a simplification for this example? I looks pretty simple to me.

Much better; I'd rather call the function Reducer (or something else) to avoid the
"'Reduce(Reduce"

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

From: Edmond Schonberg
Sent: Sunday, September 29, 2019  8:17 AM

Second. For greater clarity I would suggest the name “Accumulate” for that function.

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

From: Brad Moore
Sent: Sunday, September 29, 2019  11:33 AM

I agree with both comments, and ultimately went with Eds suggestion.

I am now wondering though, whether we need the combiner field for parallel
reduction at all?

The combiner field (the third parameter to a reduction attribute is only
needed for parallel reductions, when the types of the parameters to the
reducer function are different types. For non-parallel reduction, there is no
need to combine results from different threads of execution.

This example shows that it can be possible to simplify the expression to a
form that doesn't need the combiner, by using the map/reduce part of the value
sequence to make both parameters of the reduction the same type.

Another motivating example that was used for justifying the combiner is a
concatenation example.

Consider:

function Accumulate(Result : in String; Letter : in Character) return String is
   (Result & Letter);

Alphabet : constant String :=
   [parallel for Letter in 'A' .. 'Z' => Letter]'Reduce(Accumulate, "", "&");

Admittedly, this is not a practical parallelism example, but it does illustrate my point.

Again, the combiner can be eliminated here, and this can all be replaced with;

Alphabet : constant String :=
   [parallel for Letter in 'A' .. 'Z' => String'(1 => Letter)]'Reduce("&", "");


It is at least worthwhile to consider if eliminating the combiner from the syntax would
"guide" programmers to  write simpler, more readable code, which is one of the features
I generally like about Ada.

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

From: Randy Brukardt
Sent: Monday, September 30, 2019  8:24 PM

...
> I am now wondering though, whether we need the combiner field for
> parallel reduction at all?
...
> This example shows that it can be possible to simplify the expression
> to a form that doesn't need the combiner, by using the map/reduce part
> of the value sequence to make both parameters of the reduction the
> same type.

Didn't we consider that when we designed this feature? Didn't we decide that
the performance impact of eliminating the combiner would be unacceptable?
After all, the only reason for parallelizing something is to improve the
performance, and if doing that requires making a lot of expensive copies
then that doesn't make much sense. I'm certain that we discussed this at
least once and probably more than once. I'd suggest going back through
the mail/minutes on this topic (AI12-0242-1 & AI12-0262-1) to see what we
discussed about it in the past (rather than reopening a discussion that we've
had in the past).

IMHO, this feature is complex enough without forcing people to jump through
hoops to figure out how to encode the parameters as both the same type. Just
because something is *possible* doesn't mean that we ought to make the *only*
way. And I'm pretty sure we had examples that didn't work well without
allowing the parameters to be of different types (which then requires a
combiner).

>It is at least worthwhile to consider if eliminating the combiner from
>the syntax would "guide" programmers to write simpler, more readable
>code, which is one of the features I generally like about Ada.

There's no reduction code that will ever qualify as "simpler" or "readable".
The idea itself is a brain-bender for most - I'd guess that most of us will
have to write out the expansion of any such expression to figure out what's
going on. (There are some of course who find such things "natural", but
they're weird. ;-)

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

From: Brad Moore
Sent: Sunday, September 29, 2019  7:58 PM

Here is my homework for the upcoming ARG meeting, which addresses all
comments captured in the Warsaw meeting. [This is version /05 of the AI -
Editor.]

Also, I do have recollection of having addressed Jeff's comments a long time
ago, so I was curious to find out why his early comments were not incorporated
into the version we were looking at in Warsaw.

It turns out that on March 7th, 2019, I sent out an update which addressed
Jeff's comments. However, that version of the AI did not seem to properly
make it into the system.

There is a version 1.4 of the AI, which corresponds to Mar 8th, which seems
like it should be the version that corresponds to my sent email, but it
doesn't have the changes that I sent out.

Anyway, I hope I now have addressed Jeff's comments in this new version of
the AI.

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

From: Jean-Pierre Rosen
Sent: Monday, September 30, 2019  12:04 AM

Suggestion:

             (case D is
                 when 'I' => 1,
                 when 'V' => 5,
                 when 'X' => 10,
                 when 'L' => 50,
                 when 'C' => 100,
                 when 'D' => 500,
                 when 'M' => 1000,
                 when others => raise Program_Error with "Impossible"))

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

From: Jeff Cousins
Sent: Monday, September 30, 2019  2:41 PM

Thanks Brad.

Some of the paragraph numbers seem odd places to give the examples:

6.1.1(41/3) (actually now up to 41/5) is in Implementation Permissions,
6.1.2(42/5) is in the middle of Legality Rules.

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

From: Randy Brukardt
Sent: Monday, September 30, 2019  4:27 PM

The paragraph numbers in "new" clauses, like 6.1.2, change every time there is
a change to those clauses, so they have to be rechecked with every version.
Also, we have a meta-rule allowing paragraph numbers of non-normative material
to change, so if there are additions near the end of a clause, the paragraph
numbers of examples may change.

Which is a long-winded way of saying that Brad probably had the right paragraph
numbers when he wrote the AI, but they've probably changed since. It would be
hard to keep up.

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

From: Randy Brukardt
Sent: Monday, September 30, 2019  9:01 PM

>Here is my homework for the upcoming ARG meeting...

I fixed up some of the "Modify" and "Append" headers to have the correct form.

You have:

>Modify A.18.2(8/5):
>
>type Vector is tagged private
>      with Constant_Indexing => Constant_Reference,
>           Variable_Indexing => Reference,
>           Default_Iterator  => Iterate,
>           Iterator_Element  => Element_Type,
>           Iterator_View     => Stable.Vector,
>           Aggregate         => (Empty          => Empty,
>                                 Add_Unnamed    => Append_One,
>                                 New_Indexed    => New_Vector,
>                                 Assign_Indexed => Replace_Element),
>           Stable_Properties => (Length, Capacity,
>                                 Tampering_With_Cursors_Prohibited,
>                                 Tampering_With_Elements_Prohibited),
>           Default_Initial_Condition =>
>              Length (Vector) = 0 and then
>              (not Tampering_With_Cursors_Prohibited (Vector)) and then
>              (not Tampering_With_Elements_Prohibited (Vector)){,
>           Type_Invariant => Length (Vector) <= Capacity (Vector)};

That is, adding a Type_Invariant to the containers.

This would be a normative change, so it doesn't belong in an AI about examples.
If we're going to do this, it will have to be in some other AI.

I presume that you added this change based on Tucker's comment from the
meeting:

   Tucker suggests that we could imagine a type invariant on the containers
   that Length(V) <= Capacity(V).

This followed some discussion about shortcomings in the example you had. I
believe he was suggesting a different example that you could use, not a change
to the container's contracts. "we could imagine" doesn't sound to me to be a
directive to change the actual container's definition.

Note that there's nothing really wrong with adding this to the containers
other than the work required (both for me and for implementers). But it is
already reflected in various postconditions where it could be relevant, so
it seems like it would primarily be redundant (you only found a single
postcondition that it would make redundant).

>Modify A.18.6(16.7/5):
> procedure Assign (Target : in out Map; Source : in Map)
>      with Pre  => (if Tampering_With_Cursors_Prohibited (Target)
>                    then raise Program_Error),
>           Post => Length (Source) = Length (Target) [and then
>                   Capacity (Target) >= Length (Source)];
>
>[Author's note: This is a bug in the RM. Ordered maps do not have a Capacity
>function!]

I've fixed this, an obvious cut-and-paste error. No need to mention it
anywhere (few of the container contract things are written out anywhere other
than the RM and we can fix mistakes accordingly, at least until we publish a
new Standard).

I note that I concluded when contracting containers that it would have been a
lot easier had all of the containers had a Capacity of some sort. (I also
concluded that we needed a different cross-cut than the way the Sets/Maps are
organized -- probably, there should have been a set of operations that exist
in all six of the "normal" containers defined separately [there are about
30 or so], and then all of the other operations defined individually. That
would save a lot of text. Too late to do any of that, of course, it would
mainly be churn now and it would change all of the clause numbers.)

>Modify A.18.20(5/3):
>  type List (Capacity : Count_Type) is tagged private{,
>     with Type_Invariant => Length (List) <= List.Capacity};

This doesn't work as you wrote it, as the lead-in text says that this is only
describing the discriminant. Moreover, all of these are wrong anyway as they
seem to imply that this is the complete declaration, when this is only the
first line. That is, the existing example text (for all of the bounded forms)
should end with "..." and not ";", thus:

  type List (Capacity : Count_Type) is tagged private...

as they already have 6 or more aspects specified after them. There's no intent
that this declaration change any of those aspects unless there is text
elsewhere to do that. (Note that the Bounded_Vectors have text to omit the
capacity from the stable properties.)

>[Author's question: I presume that we only need to describe type invariants
>for bounded containers where the unbounded forms do not already have such a
>type invariant?

Surely (if we do this at all).

>Also, presuming that in unbounded forms it's OK to use
>non- object prefix form (for consistency, and not need to redefine to
>use prefix form for bounded containers even though that is required
>because Capacity is a discriminant, not a primitive operation? ...

??? Bounded_Vectors, Bounded_Hashed_Maps, and Bounded_Hashed_Sets all still
have a function Capacity. So it's certainly OK to call it! Map.Capacity is
the discriminant, Capacity (Map) is the function. (There's a preference for
components, else there would have been a nasty incompatibility and the
possibility of "losing" access to components because of an inherited
primitive.)

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

From: Brad Moore
Sent: Tuesday, October 1, 2019  8:29 AM

> ...
>> This example shows that it can be possible to simplify the expression
>> to a form that doesn't need the combiner, by using the map/reduce
>> part of the value sequence to make both parameters of the reduction
>> the same type.
>
> Didn't we consider that when we designed this feature? Didn't we
> decide that the performance impact of eliminating the combiner would be unacceptable?
> After all, the only reason for parallelizing something is to improve
> the performance, and if doing that requires making a lot of expensive
> copies then that doesn't make much sense. I'm certain that we
> discussed this at least once and probably more than once. I'd suggest
> going back through the mail/minutes on this topic (AI12-0242-1 &
> AI12-0262-1) to see what we discussed about it in the past (rather
> than reopening a discussion that we've had in the past).

The example I was simplifying was originally intended to be an example showing
the use of a combiner. Once I found that that example is better written
without a combiner, I was struggling to find an example that needed a
combiner. Most reducing problems dont.

However, I think I have found an example that would likely also be good to
include as an example in the RM.

That is,

Finding the set of prime numbers within some large range of integers.

I am thinking of using a Set container for this problem.

I will try to write up an example for this, and probably send out another
version of the AI, with the additional example, as well as other correction
suggested I've received so far.

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

From: Brad Moore
Sent: Tuesday, October 1, 2019  4:34 PM

Here is a minor update to my AI. [This is version /06 - Editor.]

I applied J.P's suggestion to raise Program_Error with "Impossible", if a
Character is found in the String parameter that does not satisfy the
precondition.

I fixed up the paragraph numbers to match the current draft RM

I removed adding type invariants to all the containers, because Randy suggests
if we want to do that, that should be a different AI.

I added a reduction example that uses a combiner function. (The prime number
example)


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

From: Ed Schonberg
Sent: Thursday, October 3, 2019  5:15 PM

The new examples are expressive, but the primes constructor using Reduce is
incomplete (Is_Prime is incomplete) and both hard to read and much more
inefficient than known algorithms. Of course, the good ones are sieves that are
intrinsically sequential. I would prefer the following, as an example of
iterator filters:

 primes :=
     (for I in 2 .. N
          when (for all J in 2 ..I => J * J <= I and then I mod J /= 0) =>  I));

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

From: Ed Schonberg
Sent: Friday, October 4, 2019  10:15 AM

Steve pointed out that the quantified expression as written is bound to fail,
and in fact the upper bound should also be handled by means of a filter,
so the proper code is:

    primes :=  (for I in 2 .. N when
         (for all J in 2 ..I when J * J <= I => I mod J /= 0)
            => I);

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

From: Brad Moore
Sent: Friday, October 4, 2019  10:52 AM

I found the same problem with the logic when I tried to implement this in
Ada 2012.

I agree that is a nice tidy way to express the primes, but I disagree that it
is more efficient.

In fact, I have implemented (in Ada 2012 this logic), as well as using an
Is_Prime function, and the execution times are pretty much equivalent.

But when I apply parallelism, as in my example, using the Paraffin libraries,
I see that I get about 4 times faster results on my quadcore computer.

The source code follows, as well as the output showing the execution times:

with Ada.Command_Line;
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Containers.Ordered_Sets; use Ada;
with Ada.Real_Time;
with Ada.Float_Text_IO; use Ada.Float_Text_IO;
with Paraffin.Loops.Generic_Work_Seeking_Functional_Reduction;

procedure Find_All_Primes is

   Start : constant Integer :=
     (if Command_Line.Argument_Count >= 1 then
         Integer'Value (Command_Line.Argument (1)) else 2);

   N : constant Integer :=
     (if Command_Line.Argument_Count >= 2 then
         Integer'Value (Command_Line.Argument (2)) else 1_000_000);

   package Integer_Sets is new
     Ada.Containers.Ordered_Sets (Element_Type => Integer);

   Start_Time : Real_Time.Time;
   Elapsed    : Duration;
   use type Real_Time.Time;

begin

   --  Should be Equivalent to Ed's example
   declare
      --        Primes : Integer_Sets.Set :=
      --          (for I in Start .. N
      --              when (for all J in 2 ..I =>
      --                        J * J <= I and then I mod J /= 0) =>  I));
      Primes : Integer_Sets.Set;
   begin
      Start_Time := Real_Time.Clock;

      for I in Start .. N loop
         Inner_Loop :
         for J in 2 .. I loop
            if I mod J = 0 then
               goto Next_I;
            end if;
            exit Inner_Loop when J * J > I;
         end loop Inner_Loop;
         Primes.Include (I);
         <<Next_I>>
      end loop;

      Elapsed := Real_Time.To_Duration (Real_Time.Clock - Start_Time);

      Put_Line ("Eds approach: " &
                  Containers.Count_Type'Image (Primes.Length) &
                  " primes found");

      Put ("Elapsed = ");

      Float_Text_IO.Put (Item => Float (Elapsed),
                         Fore => 2,
                         Aft  => 2,
                         Exp  => 0);
      New_Line;

   end;

   -- Should be equivalent to my example, but using sequential processing
   declare


      function Is_Prime (Number : Integer) return Boolean is
      begin
         for J in 2 .. Number loop
            if Number mod J = 0 then
               return False;
            end if;
            exit when J * J > Number;
         end loop;

         return True;

      end Is_Prime;


      Primes : Integer_Sets.Set;
   begin
      Start_Time := Real_Time.Clock;

      for I in 1 .. N loop
         if Is_Prime (I) then
            Primes.Include (I);
         end if;
      end loop;

      Elapsed := Real_Time.To_Duration (Real_Time.Clock - Start_Time);

      Put_Line ("Brad's approach sequentially: " &
                  Containers.Count_Type'Image (Primes.Length) &
                  " primes found");

      Put ("Elapsed = ");

      Float_Text_IO.Put (Item => Float (Elapsed),
                         Fore => 2,
                         Aft  => 2,
                         Exp  => 0);
      New_Line;
   end;

   -- Should be equivalent to my example, but using parallel processing
   declare

      subtype Iteration is Integer range Start .. N;

      package Integer_Loops is new
        Paraffin.Loops.Generic_Work_Seeking_Functional_Reduction
          (Loop_Index     => Iteration,
           Result_Type    => Integer_Sets.Set,
           Reducer        => Integer_Sets.Union,
           Identity       => Integer_Sets.Empty_Set);

      function Is_Prime (Number : Integer) return Boolean is
      begin
         for J in 2 .. Number loop
            if Number mod J = 0 then
               return False;
            end if;
            exit when J * J > Number;
         end loop;

         return True;

      end Is_Prime;

      procedure Process (Start, Finish : Iteration;
                         Result : in out Integer_Sets.Set) is
      begin
         for I in Start .. Finish loop
            if Is_Prime (I) then
               Result.Include (I);
            end if;
         end loop;
      end Process;

      Start_Time : Real_Time.Time := Real_Time.Clock;

      Primes : Integer_Sets.Set :=
        Integer_Loops.Parallel_Loop (Process => Process'Access);

   begin

      Elapsed := Real_Time.To_Duration (Real_Time.Clock - Start_Time);

      Put_Line ("Brad's approach in parallel: " &
                  Containers.Count_Type'Image (Primes.Length) & " primes found");

      Put ("Elapsed = ");

      Float_Text_IO.Put (Item => Float (Elapsed),
                         Fore => 2,
                         Aft  => 2,
                         Exp  => 0);
      New_Line;
   end;

   --  All_Primes := [for I in 1 .. 2_000_000 => I]'Reduce(Integer_Sets.Include, [], Integer_Sets.Union);

end Find_All_Primes;


Output:

Eds approach:  348513 primes found
Elapsed = 13.01
Brad's approach sequentially:  348513 primes found
Elapsed = 12.88
Brad's approach in parallel:  348513 primes found
Elapsed =  4.49

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

From: Brad Moore
Sent: Friday, October 4, 2019  11:03 AM

Also, I should mention, the inputs to the program that provided the results below were:

./find_all_primes 1 5_000_000


And the Is_Prime function if we wanted to include it in full in the RM could
be written as;

     function Is_Prime (Number : Integer) return Boolean is
        (for all J in 2 ..Number when J * J <= Number => Number mod J /= 0);

Which still provides the same filter example, and perhaps is a bit more
readable due to being a simpler expression.

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

From: Tucker Taft
Sent: Friday, October 4, 2019  11:16 AM

This does seem simpler and easier to understand.

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

From: Tucker Taft
Sent: Friday, October 4, 2019  11:27 AM

By the way, whenever I have seen something written like this, the high bound
has always been N/2 rather than N since we know Floor(Sqrt(N)) <= Floor(N/2),
presuming N > 1.  So perhaps:

   function Is_Prime (Number : Integer) return Boolean is
      (Number >= 2 and then
         (for all J in 2 .. Number/2 when J * J <= Number => Number mod J /= 0));

With your original Is_Prime(1) = True ;-)

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

From: Ed Schonberg
Sent: Friday, October 4, 2019   2:56 PM

> And the Is_Prime function if we wanted to include it in full in the RM
> could be written as;
>
>     function Is_Prime (Number : Integer) return Boolean is
>        (for all J in 2 ..Number when J * J <= Number => Number mod J
> /= 0);
>
> Which still provides the same filter example, and perhaps is a bit
> more readable due to being a simpler expression.

the parallel code is a nice example. but in terms of performance this is still
quadratic in the number of divisions. The standard sieve is not easily
parallelizable but it's linear and only uses additions.  by the way, can the
quantified expression be marked parallel?

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

From: Tucker Taft
Sent: Friday, October 4, 2019  7:39 PM

We have not proposed allowing "parallel" in a quantified expression, though a
quantified expression is essentially a special case of a reduction (universal
is a reduction over "and" with identity "True" while existential is a
reduction over "or" with identity "False"), so it would certainly make sense
to allow "parallel."  I have argued in the past that these constructs are
simple enough and self-contained enough that the compiler could probably
decide on its own whether a parallel evaluation would be safe and would
produce any savings.  But since that argument didn't "fly" for explicit
reduction expressions, it seems like it probably wouldn't fly for these
"implicit" reductions.

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

From: Brad Moore
Sent: Sunday, October 6, 2019  1:32 PM

Here is an update to the RM Examples, which hopefully addresses all comments
from yesterday. [This is version /07 of the AI - Editor.]

I removed the example with of a reduction expression with a combiner function,
as we said we wanted to create a new AI to include such an example, once we
come up with one.

I changed the Roman numeral conversion example to make use of the existing
Roman_Digit type. I also defined an enumeration rep clause for that, and use
the 'Enum_Rep attribute to do the conversion.

Also the Work_Order example we reworked so that it could actually compile.

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

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