Update HOME_EXAM.md

HOME_EXAM.md

@@ -199,6 +199,9 @@ Showcase of EBNF:
         if (c > 0) {
             true
         } 
+        else {
+            false
+        }
     }
     
     fn main() {
@@ -374,7 +377,7 @@ let a = 2;
 
 ### Assign expression
 ```math
-\frac{<e, σ> → n}{<mv = e,σ> → σ'[mv=n]}
+\frac{<e, σ> → n}{<e, σ> → σ'[mv=n]}
 ```
 Where the expression also can be a boolean or function.
 
@@ -408,7 +411,7 @@ else {
 ```
 
 ``` rust
-let a = 0;
+let mut a = 0;
 while a < 10 {
     // something that should loop 10 times
     a = a + 1;
@@ -435,6 +438,9 @@ fn func(x:i32, y:i32) -> i32 {
         if (c > 0) {
             true
         } 
+        else {
+            false
+        }
     }
     
     fn main() {
@@ -454,6 +460,7 @@ fn func(x:i32, y:i32) -> i32 {
 - →, evaluates
 - c, command
 - v, variable
+- mv, mutable variable
 - e, expression
 - t, type
 
@@ -518,7 +525,7 @@ false < 2; // Type missmatch
 ```
 
 ```math
-\frac{<e,σ> → \&text{mut } t}{<*e,σ> → \text{mut} t}
+\frac{<e,σ> → \&\text{mut } t}{<*e,σ> → \text{mut} t}
 ```
 
 ```math
@@ -537,20 +544,23 @@ let d:bool = *b; // <-- Type missmatch
 \frac{<f(e), σ> → t}{<f, σ> → \text{ret } t}
 ```
 
+```math
+\frac{<e_1, σ> → <t_1, σ^1> ... <e_n, σ^{n-1}> → <t_n, σ^n> <f_{call}, σ^n[p_1=t_1, ..., p_n=t_n]> → <t_{res}, σ'>}{<f(e_1, ..., e_n), σ> → <f_t, σ'>}
+```
+
 ``` rust
-fn func() -> i32 {
-    1+3
+fn example1() -> i32 {
+    1+3     // This is okay return type
 }
 
-fn main() {
-    let a = func();
-    let b:bool = a(); // Type missmatch
+fn example2() -> i32 {
+    true    // This is a type missmatch with what type is expected to return
 }
 ```
 
 ### Let expression
 ```math
-\frac{<e, σ> → t, σ'}{<v := e,σ> → σ'[v:=n]}
+\frac{<e, σ> → t}{<{/text{let } v = e,σ> →  <(), σ[v=t]>}
 ```
 ``` rust
 let a:i32 = 1;
@@ -598,13 +608,13 @@ else {
 ```
 
 ``` rust
-let a = 0;
+let mut a = 0;
 while a < 10 {
     // something that should loop 10 times
     a = a + 1;
 }
 
-let a = 0;
+let mut a = 0;
 while a * 10 { // Type missmatch
     // something that should loop 10 times
     a = a + 1;