Update HOME_EXAM.md

HOME_EXAM.md

@@ -443,10 +443,16 @@ Let statements works in a similiar way.
 
 ##### Functioncall
 ```math
-\frac{}{};
+\frac{(<e_1,σ> → n_1 ... <e_i,σ> → n_i) → σ(arg1 := n_1, ..., argi := n_i))}{<c,σ> → (x,σ')}; \text{where x is the return value}
 ```
 
 ```rust
+    fn a(x: i32) -> () {
+        x = x + 1;
+    }
+    fn main() -> () {
+        a(5+2);
+    }
 ```
 
 #### Showcase step by step
@@ -555,7 +561,7 @@ fn b() -> bool {
 
 ##### Conditional command
 ```math
-\frac{<e,σ> → \text{ bool } <c0,σ> → t}{<\text{ if e then } c0 \text{ else } c1,σ> → t}, where t = type of last statement
+\frac{<e,σ> → \text{ bool } <c0,σ> → t}{<\text{ if e then } c0 \text{ else } c1,σ> → t}, \text{ where t = type of last statement }
 ```
 
 For the if statement to go through the type checker need the expression, e, be a boolean.
@@ -586,10 +592,22 @@ The example above is valid for the type checker due to it only checking that the
 
 ##### Functioncall
 ```math
-\frac{}{};
+\frac{(<e_1,σ> → t1 ... <e_i,σ> → ti)}{<c,σ> → t_res}, \text{ where t_res = return type of function }
 ```
+Each expression evaluating to the same type as the arguments connected to the function.
+
 
 ```rust
+    fn a(x: i32) -> bool {
+        x < 5;
+    }
+    fn b(x: bool, y: i32) -> () {
+        x = x + 1;
+    }
+    fn main() -> () {
+        a(5+2); // Valid
+        b(true, 5 < 7); //Invalid for type checker
+    }
 ```
 
 #### Coverage