#include<pointer.cvh>
#include<string.h>
#include<stdlib.h>

$input int K;   // growing step
$assume(K > 0);
int N;          // initial length of the array, havoced at main
int * a;        // pointer to the arbitrary array of length N
int l, r;       // l and r, havoed at main

void left() {
  if (l != 0) {
    l--;
    r--;
    a[r] = a[l];
  }
}

void right() {
  if (r < N) {
    a[l] = a[r];
    r++;
    l++;
  }
}

void delete() {
  if (l > 0) {
    l--;
  }
}

void grow() {
  int * b = (int *)malloc(sizeof(int) * (N + K));
  
  memcpy(b, a, sizeof(int) * l);
  memcpy(b+r+K, a+r, sizeof(int) * (N-r));
  r += K;
  N += K;
  free(a);
  a = b;
}

void insert(int x) {
  if (l == r) grow();
  a[l] = x;
  l++;
}

/* ********************** Drivers ******************** */
void left_driver() {
  $assume_push(l <= r && 0 <= l && r < N);

  int pre_text[N-r+l];     // the text content at pre-state

  a = (int *)malloc(sizeof(int) * N);
  memcpy(pre_text, a, l * sizeof(int));
  memcpy(pre_text+l, a+r, (N-r) * sizeof(int));
  // call left:
  left();

  int text[N-r+l];        // the text content at post-state

  memcpy(text, a, l * sizeof(int));
  memcpy(text+l, a+r, (N-r) * sizeof(int));  
  // text content preserves:
  $assert_equals(&text, &pre_text);
  free(a);
  $assume_pop();
}

void right_driver() {
  // assumptions and assertions are identical to left_driver.
  $assume_push(l <= r && 0 <= l && r < N);

  int pre_text[N-r+l];

  a = (int *)malloc(sizeof(int) * N);
  memcpy(pre_text, a, l * sizeof(int));
  memcpy(pre_text+l, a+r, (N-r) * sizeof(int));
  // call right:
  right();

  int text[N-r+l];

  memcpy(text, a, l * sizeof(int));
  memcpy(text+l, a+r, (N-r) * sizeof(int));  
  $assert_equals(&text, &pre_text);
  free(a);
  $assume_pop();
}

void delete_driver() {
  $assume_push(l <= r && 0 <= l && r < N);
  
  int pre_text[N-r+l];    // the text content at pre-state
  int pre_l = l;          // value of l at pre-state

  a = (int *)malloc(sizeof(int) * N);
  memcpy(pre_text, a, l * sizeof(int));
  memcpy(pre_text+l, a+r, (N-r) * sizeof(int));
  // call delete:
  delete();

  int text[N-r+l];         // the text content at post-state
  int numDel = pre_l - l;  // the number of deleted element, either 1 or 0

  memcpy(text, a, l * sizeof(int));
  memcpy(text+l, a+r, (N-r) * sizeof(int));  
  // text content before l - 1 preserves:
  $assert($forall (int i : 0 .. l-2) pre_text[i] == text[i]);
  // text content after l - 1 preserves but shift to left by numDel:
  $assert($forall (int i : l .. (N-r+l-1)) pre_text[i+numDel] == text[i]);
  free(a);
  $assume_pop();
}

void insert_driver() {
  $assume_push(l <= r && 0 <= l && r < N);
  
  int pre_text[N-r+l];  // the text content at pre-state
  int x;                // the arbitrary inserted value

  a = (int *)malloc(sizeof(int) * N);
  $havoc(&x);
  memcpy(pre_text, a, l * sizeof(int));
  memcpy(pre_text+l, a+r, (N-r) * sizeof(int));
  // call delete:
  insert(x);
  
  int text[N-r+l];     // the text content at post-state
  
  memcpy(text, a, l * sizeof(int));
  memcpy(text+l, a+r, (N-r) * sizeof(int));  
  // The text content before l-1 preserves:
  $assert($forall (int i : 0 .. l-2) pre_text[i] == text[i]);
  // The element at l-1 is the inserted one:
  $assert(text[l-1] == x);
  // The text content after l-1 preserves but shift to right by one:
  $assert($forall (int i : l .. (N-r+l-1)) pre_text[i-1] == text[i]);
  free(a);
  $assume_pop();
}

void grow_driver() {
  $assume_push(l <= r && 0 <= l && r < N);

  int pre_text[N-r+l];  // the text content at pre-state

  a = (int *)malloc(sizeof(int) * N);
  memcpy(pre_text, a, l * sizeof(int));
  memcpy(pre_text+l, a+r, (N-r) * sizeof(int));
  // call grow:
  grow();

  int text[N-r+l];     // the text content at post-state

  memcpy(text, a, l * sizeof(int));
  memcpy(text+l, a+r, (N-r) * sizeof(int));
  // the text content is preserved:
  $assert_equals(&text, &pre_text);
  free(a);
  $assume_pop();
}

/* **************** Main: the Entry ************** */

int main() {
  $havoc(&N);
  $assume(N > 0);
  $havoc(&l); 
  $havoc(&r);
  left_driver();
  right_driver();
  delete_driver();
  grow_driver();
  insert_driver();
  return 0;
}