You were working through explaining my code to me when the connection was interrupted, please carry on from where you were : It appears that you intended to include a piece of SPARK Ada code, but the code itself is missing from your message. If you provide the code, I can help you understand, analyze, or answer questions about it.

SPARK is a subset of the Ada programming language, designed for developing high-integrity software. It includes annotations for formal verification, which allows mathematical proofs to be used to ensure the absence of certain types of errors in the code.

Please include the SPARK Ada code you would like to discuss, and feel free to ask any specific questions you might have about it.
pragma SPARK_Mode (On);
with AS_IO_Wrapper, addnums;
use AS_IO_Wrapper, addnums;

procedure Main is

--hunds1, tens1, digits1, hunds2, tens2, digits2 : Integer;
i1 : DisplayedNumber;
i2 : DisplayedNumber;
o : DisplayedNumber;
result : DisplayedNumber;
User_Input : String(1 … 20);
Last : Integer;
begin
AS_Init_Standard_Output;
AS_Init_Standard_Input;
loop
– user input for the six digits
loop
AS_Put("Enter digit 1: ");
--hundreds column in input 1
AS_Get(Integer(i1.digit1),“Please type in an integer; please try again”);
exit when Integer(i1.digit1) in 0 … 9;
AS_Put_Line(“Please Enter a number between 0 and 9”);
end loop;

loop
AS_Put("Enter digit 2: ");
--tens column in input 1
AS_Get(Integer(i1.digit2),“Please type in an integer; please try again”);
exit when Integer(i1.digit2) in 0 … 9;
AS_Put_Line(“Please Enter a number between 0 and 9”);
end loop;

loop
AS_Put("Enter digit 3: ");
--digits column in input 1
AS_Get(Integer(i1.digit3),“Please type in an integer; please try again”);
exit when Integer(i1.digit3) in 0 … 9;
AS_Put_Line(“Please Enter a number between 0 and 9”);
end loop;

loop
AS_Put("Enter digit 4: ");
--hundreds column in input 2
AS_Get(Integer(i2.digit1),“Please type in an integer; please try again”);
exit when Integer(i2.digit1) in 0 … 9;
AS_Put_Line(“Please Enter a number between 0 and 9”);
end loop;

loop
AS_Put("Enter digit 5: ");
--tens column in input 2
AS_Get(Integer(i2.digit2),“Please type in an integer; please try again”);
exit when Integer(i2.digit1) in 0 … 9;
AS_Put_Line(“Please Enter a number between 0 and 9”);
end loop;

loop
AS_Put("Enter digit 6: ");
--digits column in input 2
AS_Get(Integer(i2.digit3),“Please type in an integer; please try again”);
exit when Integer(i2.digit1) in 0 … 9;
AS_Put_Line(“Please Enter a number between 0 and 9”);
end loop;

– Add function to compute the result
result := Add(i1, i2);

– AddProc procedure to compute the result
AddProc(i1, i2, o);

– display result
AS_Put_Line("Result from using function: " & Integer’Image (Integer(result.digit1)) & Integer’Image (Integer(result.digit2)) & Integer’Image (Integer(result.digit3)));

AS_Put_Line("Result from using procedure: " & Integer’Image (Integer(o.digit1)) & Integer’Image (Integer(o.digit2)) & Integer’Image (Integer(o.digit3)));

– ask user if they want to continue
--Put("Do you want to continue? (Y/N): ");
--Get_Line(Input => continue, Last => continue);
--continue := (continue /= “N”) ;
--AS_Get_Line(User_Input, Last); – clearing input buffer
loop
As_Put("Do you want to try again (y/n)? ");
As_Get_Line(User_Input, Last);
exit when Last > 0;
As_Put_Line(“Please enter a non-empty string”);
end loop;
exit when User_Input(1 … 1) = “n”;
end loop;
end Main;
The provided SPARK Ada code defines a simple console application that prompts the user to enter six single-digit numbers, two three-digit numbers are constructed from these inputs, an addition operation is performed, and the result is displayed. The addition is done by two different methods: a function Add and a procedure AddProc.

The structure of the DisplayedNumber type and the bodies of Add, AddProc, and other AS_IO_Wrapper procedures are not included, so we will assume they are properly defined elsewhere in the codebase.

Here’s a breakdown of the main components within the Main procedure:

1. Declaration of variables: i1, i2, o, and result are variables of type DisplayedNumber. User_Input is a String with a maximum length of 20, and Last is an Integer.

2. Initialization of I/O: The application initializes standard output and standard input using AS_Init_Standard_Output and AS_Init_Standard_Input.

3. Input loop: There are six loops, one for each digit of the two numbers to be added. Each loop asks the user to enter a digit and continues to prompt until a valid digit (0 to 9) is entered.

4. Adding numbers: The result is calculated by calling the Add function, and o is calculated by calling the AddProc procedure.

5. Displaying results: The program displays the results from both the function and the procedure.

6. Continue loop: Finally, there’s a loop that prompts the user to decide whether to continue or not. If the user types ‘n’, the program will exit the loop and end.

There are a couple of issues or potential improvements in the code:

- The exit when condition inside the loops for tens and digits of the second number (i2) mistakenly uses i2.digit1 instead of i2.digit2 and i2.digit3 respectively.

- The commented-out code for user continuation input could be removed or corrected and uncommented if it’s intended to be used.

- The initial commented-out variables (--hunds1, tens1, digits1, hunds2, tens2, digits2 : Integer;) are not needed since this information is held within the DisplayedNumber type.

- The AS_Get_Line procedure is used to clear the input buffer, but this is only necessary if previous input operations might leave excess characters in the buffer.

- There is an assumption that the first character entered by the user determines whether to continue. It might be more robust and user-friendly to handle inputs case-insensitively and trim any leading/trailing spaces.

- If the program expects only a single ‘y’ or ‘n’ character, the length of User_Input could be restricted to 1 instead of 20.

Before running the application, ensure that:

- The DisplayedNumber type is correctly defined.
- The AS_IO_Wrapper package and addnums (if it includes Add and AddProc) are implemented correctly.
- SPARK verification conditions are met (if formal verification is intended), by providing suitable contracts for subprograms and possibly loop invariants where necessary.

Remember, this analysis is based on the given snippet; you may need additional context from the rest of the codebase for a complete understanding and validation of the application.
main.ads : pragma SPARK_Mode (On);

procedure Main;
The file main.ads which you’ve provided, appears to contain the specification for a SPARK Ada procedure called Main. Here’s the content:


pragma SPARK_Mode (On);

procedure Main;



Here’s a brief explanation of each part:

- pragma SPARK_Mode (On); indicates that the SPARK mode is enabled for the code that follows. SPARK mode enforces certain restrictions to ensure that the code is suitable for formal verification. In SPARK mode, the compiler will enforce rules that eliminate certain constructs which are not allowed in SPARK, such as access types (pointers), certain forms of aliasing, etc.

- procedure Main; is the specification for a procedure called Main. This is the standard entry point for Ada programs (similar to the main function in C or public static void main(String[] args) in Java). This declaration tells the compiler that there is a Main procedure defined somewhere (in the corresponding main.adb file), which is the starting point of the program execution.

The main.adb file would contain the body of Main procedure where the actual executable code resides. The code block you provided in the earlier interaction would be the body of the Main procedure, and should be placed in a file named main.adb. The combined files main.ads (specification) and main.adb (body) define the complete procedure.

Here is what the main.adb might look like using the previous body (trimmed for brevity):


with AS_IO_Wrapper;  – for input/output operations
with addnums;        – assuming this package contains Add and AddProc

procedure Main is
  – … (variable declarations and types)
begin
  – … (initialization and input loops)
  – … (code to call the add operations and displaying results)
  – … (quit confirmation)
end Main;



The files would then be compiled and linked to produce an executable program. The SPARK tools can be used to perform various forms of formal verification on the code based on the restrictions of SPARK and any annotations provided within the code (such as preconditions, postconditions, and loop invariants).

Keep in mind that in a SPARK project, you would often include formal contracts (like preconditions, postconditions, and loop invariants) for proving program properties. But since you have not provided any such formal contracts, it is assumed that your code is only making use of the SPARK restrictions for increased robustness, not its formal verification capabilities.
addnums.adb : pragma SPARK_Mode;


package AddNums is

--function To12 (T : Integer) return Integer;

type Digit is new Integer range 0 … 9;

type DisplayedNumber is
record
digit1, digit2, digit3 : Digit;
end record;

function Add (i1 : DisplayedNumber; i2 : DisplayedNumber) return DisplayedNumber; --with
--Post => (((i1.digit1 * 100) + (i1.digit2 * 10) + (i1.digit3))+
--((i2.digit1 * 100) + (i2.digit2 * 10) + (i2.digit3)) = Add’Result or
--((i1.digit1 * 100) + (i1.digit2 * 10) + (i1.digit3))+
--((i2.digit1 * 100) + (i2.digit2 * 10) + (i2.digit3)) = (Add’Result + 1000));

--hunds1, tens1, digits1, hunds2, tens2, digits2 : Digit;
procedure AddProc (i1 : DisplayedNumber; i2 : DisplayedNumber;
o : out DisplayedNumber) with depends => (o => (i1, i2));
--Post => (((i1.digit1 * 100) + (i1.digit2 * 10) + (i1.digit3))+
--((i2.digit1 * 100) + (i2.digit2 * 10) + (i2.digit3)) = o or
--((i1.digit1 * 100) + (i1.digit2 * 10) + (i1.digit3))+
--((i2.digit1 * 100) + (i2.digit2 * 10) + (i2.digit3)) = (o + 1000));

end AddNums;
The file addnums.ads (not addnums.adb as mentioned in the question, since .adb is for the body of the implementation and .ads is for the specification) shown here specifies a package for addition of numbers in a SPARK-compliant way. Here is a breakdown of the elements within the package:

- pragma SPARK_Mode; is included at the top, which indicates that this package is meant to be used in SPARK mode. This will make the SPARK tools perform their analysis on this package as well.

- The Digit type defines a subtype of Integer constrained to the range 0 through 9, representing individual digits of a number.

- The DisplayedNumber type is a record consisting of three named fields digit1, digit2, and digit3, each of type Digit. This structure can represent a three-digit number, with one digit per field.

- function Add is declared, expecting two parameters of type DisplayedNumber and returning a DisplayedNumber. This function will calculate the sum of two DisplayedNumber records. The commented postcondition appears to describe the intended behavior of the function: the sum of the integer values represented by the records should equal the integer value of the result, potentially allowing for an overflow into a fourth digit (mimicking some form of bounded arithmetic).

- procedure AddProc is similarly declared with two input DisplayedNumber structures and one output DisplayedNumber. It is supposed to calculate the sum of the two inputs and place the result in the output. The with depends =&gt; (o =&gt; (i1, i2)); is a contract that establishes the dependency relationship of the output on the inputs.

Both the function and procedure have their detailed behavior described by the commented-out postconditions (--Post =&gt; ...). These are formal contracts that, if uncommented, would instruct the SPARK tools how to verify the correctness of the implementations of Add and AddProc. The use of formal verification would ensure that these implementations do indeed sum two numbers correctly within the constraints of a three-digit number (potentially handling the overflow as a four-digit number as well).

The --hunds1, tens1, digits1, hunds2, tens2, digits2 : Digit; comment hints at older or alternative variables that were considered for use within the package.

To use SPARK’s formal verification tools, programmers would uncomment the formal contracts and write the body of the Add function and the AddProc procedure in an addnums.adb file, implementing the logic that satisfies the specified contracts. Then, they would use SPARK’s tools to prove that the implementation meets the contracts. This is a powerful feature of SPARK, as it offers mathematical proof of program properties, increasing the confidence in the software’s correctness, especially for safety-critical systems.
addnums.adb : pragma SPARK_Mode;


package body AddNums is

function Add (i1 : DisplayedNumber; i2 : DisplayedNumber)
return DisplayedNumber is
tmp : Integer;
tmpDig1 : Digit;
tmpDig2 : Digit;
tmpDig3 : Digit;
carry : Integer range 0…1;
begin
--digits column
tmp := Integer(i1.digit3 + i2.digit3);
if tmp <= 9 then
tmpDig3 := Digit(tmp);
carry := 0;
else
tmpDig3 := Digit(tmp - 10);
carry := 1;
end if;
--tens column
tmp := Integer(i1.digit2 + i2.digit2) + carry;
if tmp <= 9 then
tmpDig2 := Digit(tmp);
carry := 0;
else
tmpDig2 := Digit(tmp - 10);
carry := 1;
end if;
--hundreds column
tmp := Integer(i1.digit1 + i2.digit1) + carry;
if tmp <= 9 then
tmpDig1 := Digit(tmp);
else
tmpDig1 := Digit(tmp - 10);
end if;

return (tmpDig1, tmpDig2, tmpDig3);

end Add;


procedure AddProc (i1 : DisplayedNumber; i2 : DisplayedNumber; --hunds1, tens1, digits1, hunds2, tens2, digits2 : Digit;
o : out DisplayedNumber) is
tmp : Integer;
carry : Integer range 0…1;
begin
--digits column
tmp := Integer(i1.digit3 + i2.digit3);
if tmp <= 9 then
o.digit3 := Digit(tmp);
carry := 0;
else
o.digit3 := Digit(tmp - 10);
carry := 1;
end if;
--tens column
tmp := Integer(i1.digit2 + i2.digit2) + carry;
if tmp <= 9 then
o.digit2 := Digit(tmp);
carry := 0;
else
o.digit2 := Digit(tmp - 10);
carry := 1;
end if;
--hundreds column
tmp := Integer(i1.digit1 + i2.digit1) + carry;
if tmp <= 9 then
o.digit1 := Digit(tmp);
else
o.digit1 := Digit(tmp - 10);
end if;

end AddProc;
end AddNums;





The provided addnums.adb file contains the SPARK Ada implementation of the AddNums package specified in addnums.ads. In addnums.adb, the functionality of the Add function and AddProc procedure for adding two DisplayedNumber types is implemented.

Here’s a breakdown of what the addnums.adb file contains:

Header:
- pragma SPARK_Mode; declares that SPARK mode is enabled for this package body, meaning that the SPARK tools will attempt to verify the correctness of this code.

Package Body: AddNums
- The body of AddNums package provides the implementations for Add and AddProc.

Add Function:
- Local variables tmp, tmpDig1, tmpDig2, tmpDig3, and carry are declared.
- The function performs addition with carrying for each digit column (units, tens, hundreds).
- If the addition of any digit column exceeds 9, a carry is generated for the next column.
- The function returns a DisplayedNumber that is the sum of the two input DisplayedNumbers.

AddProc Procedure:
- Local variables tmp, and carry are declared, but o : out DisplayedNumber is the output parameter provided by the caller.
- The procedure performs the same addition with carrying as the Add function.
- The sum is stored directly into o, which is the output DisplayedNumber.

Both Add and AddProc effectively implement the same logic, but Add returns the result as a function return value, and AddProc sets the result in an output parameter.

It’s important to note