diff --git a/lib/miniFun/TypeChecker.ml b/lib/miniFun/TypeChecker.ml
index 9fcfa30..2bfcdec 100644
--- a/lib/miniFun/TypeChecker.ml
+++ b/lib/miniFun/TypeChecker.ml
@@ -9,30 +9,48 @@ let rec evaluate_type (program: t_exp) (context: ftype VariableMap.t) : (ftype,
   match program with
     Integer _ -> Ok IntegerType
   | Boolean _ -> Ok BooleanType
-  | Variable x -> (
+  | Variable x -> ( (* check for the type in the context *)
       match VariableMap.find_opt x context with
-        None -> Error (`AbsentAssignment ("The variable " ^ x ^ " is not defined."))
+        None -> Error (`AbsentAssignment
+                         ("The variable " ^ x ^ " is not defined."))
       | Some t -> Ok t
     )
   | Function (xs, typef, fbody) -> (
+      (* first check that the function has the right specified type then check
+         that the number of inputs are the right number, finally eval the type
+         of the body using the bindings for the inputs *)
       match typef with
         FunctionType (tin, tout) -> (
           if List.length xs <> List.length tin then
-            Error (`WrongTypeSpecification "Type specification for function has wrong arity.")
+            Error (`WrongTypeSpecification
+                     ("Type specification for function has wrong arity."))
           else
-            let context1 = List.fold_left2 (fun acc x t -> VariableMap.add x t acc) context xs tin in
+            let context1 = List.fold_left2
+                (fun acc x t -> VariableMap.add x t acc)
+                context
+                xs
+                tin
+            in
             let* typefbody = evaluate_type fbody context1 in
-            match (typefbody = tout) with
-              (false) -> Error (`WrongTypeSpecification "Function does not return specified type.")
-            | (true) -> Ok typef
+            if (typefbody = tout) then
+              Ok typef
+            else
+              Error (`WrongTypeSpecification
+                       ("Function does not return specified type."))
         )
-      | _ -> Error (`WrongTypeSpecification "Specification of function is not a function type.")
+      | _ -> Error (`WrongTypeSpecification
+                      ("Specification of function is not a function type."))
     )
   | Application (f, xs) -> (
+      (* check that the type is actually a function, then checks that the
+         supplied inputs are of the right type, returns the return type if all
+         inputs are supplied, otherwise a function from the remaining inputs to
+         the output types *)
       let* evalf = evaluate_type f context in
       match evalf with
         FunctionType (tin, tout) -> (
-          let rec helper params typeparams =
+          let rec helper (params: t_exp list) (typeparams: ftype list) =
+            (* consumes until params are exausted *)
             match (params, typeparams) with
               ([], _) -> Ok typeparams
             | (_, []) -> Error (`WrongArity ("Function application has arity " ^
@@ -72,8 +90,10 @@ let rec evaluate_type (program: t_exp) (context: ftype VariableMap.t) : (ftype,
       let* typez = evaluate_type z context in
       match typex, typey, typez with
       | (IntegerType, IntegerType, IntegerType) -> Ok IntegerType
-      | (IntegerType, IntegerType, _) -> Error (`WrongType "Third term is not an integer.")
-      | (IntegerType, _, _) -> Error (`WrongType "Second term is not an integer.")
+      | (IntegerType, IntegerType, _) -> Error (`WrongType ("Third term is " ^
+                                                            "not an integer."))
+      | (IntegerType, _, _) -> Error (`WrongType
+                                        ("Second term is not an integer."))
       | (_, _, _) -> Error (`WrongType "First term is not an integer.")
     )
   | Rand (x) -> (
@@ -123,26 +143,37 @@ let rec evaluate_type (program: t_exp) (context: ftype VariableMap.t) : (ftype,
       | (_, _, _) -> Error (`WrongType "If guard is not a boolean.")
     )
   | LetIn (x, xval, rest) ->
+    (* bind the type to the variable name in the context *)
     let* typex = evaluate_type xval context in
     evaluate_type rest (VariableMap.add x typex context)
   | LetFun (f, xs, typef, fbody, rest) ->
+    (* like with the function type, but also add f itself to the bindings *)
     match typef with
       FunctionType (tin, tout) -> (
         if List.length xs <> List.length tin then
           Error (`WrongArity "Type specification for function has wrong arity.")
         else
           let context1 = VariableMap.add f typef context in
-          let context2 = List.fold_left2 (fun acc x t -> VariableMap.add x t acc) context1 xs tin in
+          let context2 = List.fold_left2
+              (fun acc x t -> VariableMap.add x t acc)
+              context1
+              xs
+              tin
+          in
           let* typefbody = evaluate_type fbody context2 in
           let* typerest = evaluate_type rest context1 in
           match (typefbody = tout, typerest) with
-            (false, _) -> Error (`WrongTypeSpecification "Function does not return specified type.")
+            (false, _) -> Error (`WrongTypeSpecification
+                                   "Function does not return specified type.")
           | (true, t) -> Ok t
       )
-    | _ -> Error (`WrongTypeSpecification "Specification of function is not a function type.")
+    | _ -> Error (`WrongTypeSpecification
+                    "Specification of function is not a function type.")
 
 let typecheck (program: t_exp) : (ftype, error) result =
   let* typeprogram = evaluate_type program VariableMap.empty in
   match typeprogram with
-    FunctionType ([IntegerType], IntegerType) -> Ok (FunctionType ([IntegerType], IntegerType))
+    FunctionType ([IntegerType], IntegerType) -> (
+      Ok (FunctionType ([IntegerType], IntegerType))
+    )
   | _ -> Error (`WrongType "Program is not a function from int to int.")