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HOME_EXAM_Type_check_part3.md

+### Assignment
+Given the type $`\tau`$, variable $`x`$ and value $`n`$
+
+```math
+\frac{\Gamma \ \vdash \ x \ : \ \tau \quad \Gamma \ \vdash \ n \ : \ \tau}{\lang x := n, \sigma \rang \ \Darr \ \Gamma \ \vdash x \ : \ \tau}
+```
+
+### **let** assignment
+```math
+\frac{\Gamma \ \vdash \ n \ : \ \tau}{\lang \text{let} \  x \ : \ \tau \ := \ n, \sigma \rang \ \Darr \ \Gamma \ \vdash x \ : \ \tau}
+```
+
+### **while** statement
+The condition, $`b`$, of the while statement  
+
+```math
+\frac{}{\Gamma \ \vdash b \ : \ bool}
+```
+
+### **if/elseif** statement
+The conditions, $`b_i`$, of the if- and elseif-statements
+
+```math
+\frac{}{\Gamma \ \vdash b_i \ : \ bool}
+```
+
+### Functions
+Given the function $`p`$ with the type of its return type
+
+```math
+\frac{\Gamma \ \vdash p \ : \ \tau \quad \lang p, \sigma \rang \ \Darr \ n}{\Gamma \ \vdash n \ : \ \tau}
+```
+
+#### Parameters and arguments
+Given a function with parameters $`p1, \dotsb, p_i`$ and arguments $`a1, \dotsb, a_i`$ then for every parameter and argument
+
+```math
+\frac{\Gamma \ \vdash p_i \ : \ \tau}{\Gamma \ \vdash a_i \ : \ \tau}
+```
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