diff --git a/labcodes/lab2/kern/mm/pmm.c b/labcodes/lab2/kern/mm/pmm.c
index af54731..4cddcbc 100644
--- a/labcodes/lab2/kern/mm/pmm.c
+++ b/labcodes/lab2/kern/mm/pmm.c
@@ -390,7 +390,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -492,7 +492,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -510,7 +510,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -521,8 +521,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -556,7 +556,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab3/kern/mm/pmm.c b/labcodes/lab3/kern/mm/pmm.c
index 77633f2..d397abc 100644
--- a/labcodes/lab3/kern/mm/pmm.c
+++ b/labcodes/lab3/kern/mm/pmm.c
@@ -403,7 +403,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -528,7 +528,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -546,7 +546,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -557,8 +557,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -592,7 +592,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab3/kern/mm/vmm.c b/labcodes/lab3/kern/mm/vmm.c
index 2973e5b..9fa3301 100644
--- a/labcodes/lab3/kern/mm/vmm.c
+++ b/labcodes/lab3/kern/mm/vmm.c
@@ -266,7 +266,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes/lab4/kern/mm/pmm.c b/labcodes/lab4/kern/mm/pmm.c
index 59c70d9..96e49e2 100644
--- a/labcodes/lab4/kern/mm/pmm.c
+++ b/labcodes/lab4/kern/mm/pmm.c
@@ -406,7 +406,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -531,7 +531,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -549,7 +549,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -560,8 +560,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -595,7 +595,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab4/kern/mm/vmm.c b/labcodes/lab4/kern/mm/vmm.c
index 7370361..b402145 100644
--- a/labcodes/lab4/kern/mm/vmm.c
+++ b/labcodes/lab4/kern/mm/vmm.c
@@ -263,7 +263,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes/lab5/kern/mm/pmm.c b/labcodes/lab5/kern/mm/pmm.c
index cb92075..7a2e95d 100644
--- a/labcodes/lab5/kern/mm/pmm.c
+++ b/labcodes/lab5/kern/mm/pmm.c
@@ -406,7 +406,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -625,7 +625,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -643,7 +643,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -654,8 +654,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -689,7 +689,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab5/kern/mm/swap.c b/labcodes/lab5/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes/lab5/kern/mm/swap.c
+++ b/labcodes/lab5/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes/lab5/kern/mm/vmm.c b/labcodes/lab5/kern/mm/vmm.c
index 3727bbb..f2eb426 100644
--- a/labcodes/lab5/kern/mm/vmm.c
+++ b/labcodes/lab5/kern/mm/vmm.c
@@ -353,7 +353,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes/lab6/kern/mm/pmm.c b/labcodes/lab6/kern/mm/pmm.c
index cb92075..7a2e95d 100644
--- a/labcodes/lab6/kern/mm/pmm.c
+++ b/labcodes/lab6/kern/mm/pmm.c
@@ -406,7 +406,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -625,7 +625,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -643,7 +643,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -654,8 +654,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -689,7 +689,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab6/kern/mm/swap.c b/labcodes/lab6/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes/lab6/kern/mm/swap.c
+++ b/labcodes/lab6/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes/lab6/kern/mm/vmm.c b/labcodes/lab6/kern/mm/vmm.c
index 3727bbb..f2eb426 100644
--- a/labcodes/lab6/kern/mm/vmm.c
+++ b/labcodes/lab6/kern/mm/vmm.c
@@ -353,7 +353,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes/lab7/kern/mm/pmm.c b/labcodes/lab7/kern/mm/pmm.c
index cb92075..7a2e95d 100644
--- a/labcodes/lab7/kern/mm/pmm.c
+++ b/labcodes/lab7/kern/mm/pmm.c
@@ -406,7 +406,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -625,7 +625,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -643,7 +643,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -654,8 +654,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -689,7 +689,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab7/kern/mm/swap.c b/labcodes/lab7/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes/lab7/kern/mm/swap.c
+++ b/labcodes/lab7/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes/lab7/kern/mm/vmm.c b/labcodes/lab7/kern/mm/vmm.c
index 6799d1c..ce1a0bb 100644
--- a/labcodes/lab7/kern/mm/vmm.c
+++ b/labcodes/lab7/kern/mm/vmm.c
@@ -353,7 +353,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes/lab8/kern/mm/pmm.c b/labcodes/lab8/kern/mm/pmm.c
index cb92075..7a2e95d 100644
--- a/labcodes/lab8/kern/mm/pmm.c
+++ b/labcodes/lab8/kern/mm/pmm.c
@@ -406,7 +406,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -625,7 +625,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -643,7 +643,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -654,8 +654,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -689,7 +689,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes/lab8/kern/mm/swap.c b/labcodes/lab8/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes/lab8/kern/mm/swap.c
+++ b/labcodes/lab8/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes/lab8/kern/mm/vmm.c b/labcodes/lab8/kern/mm/vmm.c
index 8cf880c..ed3021c 100644
--- a/labcodes/lab8/kern/mm/vmm.c
+++ b/labcodes/lab8/kern/mm/vmm.c
@@ -353,7 +353,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes_answer/lab2_result/kern/mm/pmm.c b/labcodes_answer/lab2_result/kern/mm/pmm.c
index 020d14a..c61e506 100644
--- a/labcodes_answer/lab2_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab2_result/kern/mm/pmm.c
@@ -402,7 +402,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -512,7 +512,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -530,7 +530,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -541,8 +541,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -576,7 +576,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab3_result/kern/mm/pmm.c b/labcodes_answer/lab3_result/kern/mm/pmm.c
index fcb862e..379f1a4 100644
--- a/labcodes_answer/lab3_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab3_result/kern/mm/pmm.c
@@ -415,7 +415,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -548,7 +548,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -566,7 +566,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -577,8 +577,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -612,7 +612,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab3_result/kern/mm/vmm.c b/labcodes_answer/lab3_result/kern/mm/vmm.c
index 33228ee..33065c5 100644
--- a/labcodes_answer/lab3_result/kern/mm/vmm.c
+++ b/labcodes_answer/lab3_result/kern/mm/vmm.c
@@ -266,7 +266,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes_answer/lab4_result/kern/mm/pmm.c b/labcodes_answer/lab4_result/kern/mm/pmm.c
index b597c5d..ac4efd6 100644
--- a/labcodes_answer/lab4_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab4_result/kern/mm/pmm.c
@@ -418,7 +418,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -551,7 +551,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -569,7 +569,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -580,8 +580,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -615,7 +615,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab4_result/kern/mm/vmm.c b/labcodes_answer/lab4_result/kern/mm/vmm.c
index af221e3..5881a83 100644
--- a/labcodes_answer/lab4_result/kern/mm/vmm.c
+++ b/labcodes_answer/lab4_result/kern/mm/vmm.c
@@ -267,7 +267,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes_answer/lab5_result/kern/mm/pmm.c b/labcodes_answer/lab5_result/kern/mm/pmm.c
index cf9fa77..b3d8aa1 100644
--- a/labcodes_answer/lab5_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab5_result/kern/mm/pmm.c
@@ -418,7 +418,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -651,7 +651,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -669,7 +669,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -680,8 +680,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -715,7 +715,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab5_result/kern/mm/swap.c b/labcodes_answer/lab5_result/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes_answer/lab5_result/kern/mm/swap.c
+++ b/labcodes_answer/lab5_result/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes_answer/lab5_result/kern/mm/vmm.c b/labcodes_answer/lab5_result/kern/mm/vmm.c
index 4f4aaed..b54a8ae 100644
--- a/labcodes_answer/lab5_result/kern/mm/vmm.c
+++ b/labcodes_answer/lab5_result/kern/mm/vmm.c
@@ -357,7 +357,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes_answer/lab6_result/kern/mm/pmm.c b/labcodes_answer/lab6_result/kern/mm/pmm.c
index cf9fa77..b3d8aa1 100644
--- a/labcodes_answer/lab6_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab6_result/kern/mm/pmm.c
@@ -418,7 +418,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -651,7 +651,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -669,7 +669,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -680,8 +680,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -715,7 +715,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab6_result/kern/mm/swap.c b/labcodes_answer/lab6_result/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes_answer/lab6_result/kern/mm/swap.c
+++ b/labcodes_answer/lab6_result/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes_answer/lab6_result/kern/mm/vmm.c b/labcodes_answer/lab6_result/kern/mm/vmm.c
index 37d0ee6..877b033 100644
--- a/labcodes_answer/lab6_result/kern/mm/vmm.c
+++ b/labcodes_answer/lab6_result/kern/mm/vmm.c
@@ -357,7 +357,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes_answer/lab7_result/kern/mm/pmm.c b/labcodes_answer/lab7_result/kern/mm/pmm.c
index cf9fa77..b3d8aa1 100644
--- a/labcodes_answer/lab7_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab7_result/kern/mm/pmm.c
@@ -418,7 +418,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -651,7 +651,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -669,7 +669,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -680,8 +680,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -715,7 +715,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab7_result/kern/mm/swap.c b/labcodes_answer/lab7_result/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes_answer/lab7_result/kern/mm/swap.c
+++ b/labcodes_answer/lab7_result/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes_answer/lab7_result/kern/mm/vmm.c b/labcodes_answer/lab7_result/kern/mm/vmm.c
index 4802f65..04f514d 100644
--- a/labcodes_answer/lab7_result/kern/mm/vmm.c
+++ b/labcodes_answer/lab7_result/kern/mm/vmm.c
@@ -357,7 +357,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;
diff --git a/labcodes_answer/lab8_result/kern/mm/pmm.c b/labcodes_answer/lab8_result/kern/mm/pmm.c
index cf9fa77..b3d8aa1 100644
--- a/labcodes_answer/lab8_result/kern/mm/pmm.c
+++ b/labcodes_answer/lab8_result/kern/mm/pmm.c
@@ -418,7 +418,7 @@ get_page(pde_t *pgdir, uintptr_t la, pte_t **ptep_store) {
         *ptep_store = ptep;
     }
     if (ptep != NULL && *ptep & PTE_P) {
-        return pa2page(*ptep);
+        return pte2page(*ptep);
     }
     return NULL;
 }
@@ -651,7 +651,7 @@ check_pgdir(void) {
 
     pte_t *ptep;
     assert((ptep = get_pte(boot_pgdir, 0x0, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert(page_ref(p1) == 1);
 
     ptep = &((pte_t *)KADDR(PDE_ADDR(boot_pgdir[0])))[1];
@@ -669,7 +669,7 @@ check_pgdir(void) {
     assert(page_ref(p1) == 2);
     assert(page_ref(p2) == 0);
     assert((ptep = get_pte(boot_pgdir, PGSIZE, 0)) != NULL);
-    assert(pa2page(*ptep) == p1);
+    assert(pte2page(*ptep) == p1);
     assert((*ptep & PTE_U) == 0);
 
     page_remove(boot_pgdir, 0x0);
@@ -680,8 +680,8 @@ check_pgdir(void) {
     assert(page_ref(p1) == 0);
     assert(page_ref(p2) == 0);
 
-    assert(page_ref(pa2page(boot_pgdir[0])) == 1);
-    free_page(pa2page(boot_pgdir[0]));
+    assert(page_ref(pde2page(boot_pgdir[0])) == 1);
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_pgdir() succeeded!\n");
@@ -715,7 +715,7 @@ check_boot_pgdir(void) {
     assert(strlen((const char *)0x100) == 0);
 
     free_page(p);
-    free_page(pa2page(PDE_ADDR(boot_pgdir[0])));
+    free_page(pde2page(boot_pgdir[0]));
     boot_pgdir[0] = 0;
 
     cprintf("check_boot_pgdir() succeeded!\n");
diff --git a/labcodes_answer/lab8_result/kern/mm/swap.c b/labcodes_answer/lab8_result/kern/mm/swap.c
index d2b5952..704ec18 100644
--- a/labcodes_answer/lab8_result/kern/mm/swap.c
+++ b/labcodes_answer/lab8_result/kern/mm/swap.c
@@ -262,7 +262,7 @@ check_swap(void)
      } 
 
      //free_page(pte2page(*temp_ptep));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
      pgdir[0] = 0;
      mm->pgdir = NULL;
      mm_destroy(mm);
diff --git a/labcodes_answer/lab8_result/kern/mm/vmm.c b/labcodes_answer/lab8_result/kern/mm/vmm.c
index 9f37163..9b12b3f 100644
--- a/labcodes_answer/lab8_result/kern/mm/vmm.c
+++ b/labcodes_answer/lab8_result/kern/mm/vmm.c
@@ -357,7 +357,7 @@ check_pgfault(void) {
     assert(sum == 0);
 
     page_remove(pgdir, ROUNDDOWN(addr, PGSIZE));
-    free_page(pa2page(pgdir[0]));
+    free_page(pde2page(pgdir[0]));
     pgdir[0] = 0;
 
     mm->pgdir = NULL;