$//$ Define the Colour enum

datatype Colour $=$ Red $|$ White $|$ Blue

$//$ Method: FlagSort

method FlagSort$($flag: array$)$ returns $($white: int, blue: int$)$

modifies flag

ensures white blue flag.Length

ensures

i :: i $$ white $==>$ flag$[$i$]==$ Red

ensures forall i :: white i $$ blue $==>$ flag$[$i$]==$ White

ensures forall i :: blue i $$ flag.Length $==>$ flag$[$i$]==$ Blue

$\{$

var r :$=0$; $//$ End of red section

var w :$=0$; $//$ End of white section

var b :$=$ flag.Length; $//$ Start of blue section

var i :$=0$;

$//$ Initialize invariants

while i $$ b

invariant r w i b flag.Length

invariant forall j :: j $$ r $==>$ flag$[$j$]==$ Red

invariant forall j :: r j $$ w $==>$ flag$[$j$]==$ White

invariant forall j :: b j $$ flag.Length $==>$ flag$[$j$]==$ Blue

invariant forall j :: w j $$ b $==>$ flag$[$j$]!=$ Red && flag$[$j$]!=$ White

$\{$

if flag$[$i$]==$ Red $\{$

$//$ Swap current element with end of Red section

flag$[$i$],$ flag$[$r$]$ :$=$ flag$[$r$],$ flag$[$i$]$;

r :$=$ r $+1$;

w :$=$ w $+1$;

i :$=$ i $+1$;

$\}$ else if flag$[$i$]==$ White $\{$

$//$ Extend White section

w :$=$ w $+1$;

i :$=$ i $+1$;

$\}$ else $\{//$ Blue

$//$ Swap current element with start of Blue section

b :$=$ b $-1$;

flag$[$i$],$ flag$[$b$]$ :$=$ flag$[$b$],$ flag$[$i$]$;

$//$ Do not increment $`$i$`$ here, as the new element at $`$i$`$ must be re$-$evaluated

$\}$

$\}$

white :$=$ w;

blue :$=$ b;

$\}$

$//$ Method: FlagSortx

method FlagSortx$($flag: array$)$

modifies flag

ensures isSorted$($flag$)$

$\{$

var $\_,\_$ :$=$ FlagSort$($flag$)$;

$\}$

$//$ Predicate: isSorted

predicate isSorted$($flag: array$)$

reads flag

$\{$

forall i :: i $$ flag.Length $-1==>($

$($flag$[$i$]==$ Red $==>$ flag$[$i $+1]$ in $\{$Red$,$ White, Blue$\})$ &&

$($flag$[$i$]==$ White $==>$ flag$[$i $+1]$ in $\{$White$,$ Blue$\})$ &&

$($flag$[$i$]==$ Blue $==>$ flag$[$i $+1]==$ Blue$)$

$)$

$\}$

$//$ Validator for FlagSortx

method ValidateFlagSortx$($flag: array$)$

modifies flag

ensures isSorted$($flag$)$

$\{$

FlagSortx$($flag$)$;

assert isSorted$($flag$)$;

$\}$

this is my code and this is the error I$\text{'}$m getting;

The task involves solving a sorting problem with coloured balls using a modified version of the Dijkstra strategy:

$1.$ Create a function that sorts an array of coloured balls into the following order: $**$unsorted balls first$**,$ followed by $**$red balls$**,$ then $**$white balls$**,$ and finally $**$blue balls$**.$ This function should return two values: the end position of the white section and the start position of the blue section.

$2.$ Modify the sorting function so that it no longer returns any values and directly sorts the array. Then, verify that this function works correctly and does not corrupt the array.

For verification:

$-$ Create a check $($a predicate$)$ that ensures the array is sorted in the order: $**$red balls$**,**$white balls$**,$ and $**$blue balls$**.$ The check should not directly compare the data but confirm the correct arrangement of colours.