diff --git a/isabelle/Core/Semantics.thy b/isabelle/Core/Semantics.thy
index 1629372f..c003c390 100644
--- a/isabelle/Core/Semantics.thy
+++ b/isabelle/Core/Semantics.thy
@@ -726,34 +726,80 @@ and maxTimeCase :: "Case \<Rightarrow> int" where
 
 subsection "calculateNonAmbiguousInterval" 
 
+text "Helper functions for \<^emph>\<open>calculateNonAmbiguousInterval\<close>"
 fun gtIfNone :: "int option \<Rightarrow> int \<Rightarrow> bool" where
 "gtIfNone None _ = True" |
 "gtIfNone (Some x) y = (x > y)"
 
 fun geIfNone :: "int option \<Rightarrow> int \<Rightarrow> bool" where
 "geIfNone None _ = True" |
-"geIfNone (Some x) y = (x \<ge> y)"
+"geIfNone (Some x) y = (x \<ge> y) "
 
 fun subIfSome :: "int option \<Rightarrow> int \<Rightarrow> int option" where
 "subIfSome None _ = None" |
 "subIfSome (Some x) y = Some (x - y)"
 
 
+text \<open>
+A TimeInterval (startTime, endTime) can be ambiguous wrt a When's timeout if startTime < timeout \<le> endTime
+
+\<close>
+
+text \<open>The \<^emph>\<open>calculateNonAmbiguousInterval\<close> function can help a user to calculate a TimeInterval that
+won't be ambiguous for the next \<^emph>\<open>n\<close> inputs of a contract.\<close>
+
+text \<open>The only Contract constructor that can yield a \<^term>\<open>TEAmbiguousTimeIntervalError\<close> is the \<^term>\<open>When\<close> case. 
+Computing a transaction of a contract that starts in a non quiescent state (\<^term>\<open>Let\<close>, \<^term>\<open>Pay\<close>, \<^term>\<open>If\<close>, \<^term>\<open>Assert\<close>) 
+can end in a \<^term>\<open>TEAmbiguousTimeIntervalError\<close> iff there is a \<^term>\<open>When\<close> case that makes it ambiguous.
+\<close>
+
+text \<open>A TimeInterval expressed as the tuple \<^term>\<open>(startTime \<times> endTime)\<close> can be ambiguous wrt a \<^term>\<open>When\<close>'s timeout
+iff \<^emph>\<open>startTime < timeout \<le> endTime\<close>
+\<close>
+
+text
+\<open> It parameters of \<^emph>\<open>calculateNonAmbiguousInterval\<close> are:
+\<^item> An optional number of Inputs to check. The number of inputs corresponds to the number of "When". 
+If None is passed, it means that we should check for transactions of any number of inputs.
+\<^item> A lower bound (normally the current time).
+\<^item> The Contract to check.
+
+The function returns an Optionally Bound Time Interval, as defined in the \<^emph>\<open>OptBoundTimeInterval.thy\<close> theory.
+In the \<^emph>\<open>TimeRange.thy\<close> theory we prove that computing a transaction with these bounds doesn't end with an ambiguous error. 
+\<close>
+\<comment> \<open>TODO: The intersectInterval can produce an invalid time interval, which would mean that not suitable TimeInterval was found\<close>
 fun calculateNonAmbiguousInterval :: "int option \<Rightarrow> POSIXTime \<Rightarrow> Contract \<Rightarrow> OptBoundTimeInterval"
-where
+  where
+\<comment> \<open>A Close contract can't be ambiguous, so an Unbounded interval is returned \<close>
 "calculateNonAmbiguousInterval _ _ Close = (Unbounded, Unbounded)" |
+\<comment> \<open>A Pay contract isn't ambiguous by itself, so we calculate for the continuation\<close>
 "calculateNonAmbiguousInterval n t (Pay _ _ _ _ c) = calculateNonAmbiguousInterval n t c" |
-"calculateNonAmbiguousInterval n t (If _ ct cf) = intersectInterval (calculateNonAmbiguousInterval n t ct)
+\<comment> \<open>If we branch, we intersect the result of both possibilites. \<close>
+\<comment> \<open>TODO: Note that not knowing which branch can be selected beforehand means that we return a smaller TimeInterval than
+possible. Maybe we could improve this by using the actual Input instead of the number of inputs\<close>
+"calculateNonAmbiguousInterval n t (If _ ct cf) = intersectInterval 
+                                                           (calculateNonAmbiguousInterval n t ct)
                                                            (calculateNonAmbiguousInterval n t cf)" |
-"calculateNonAmbiguousInterval n t (When Nil timeout tcont) =
+\<comment> \<open>We treat the When contract in two parts. The base case (when no actions are available) and a recursive
+case, when we have a particular action \<close>
+"calculateNonAmbiguousInterval n t (When [] timeout tcont) =
   (if t < timeout
+  \<comment> \<open>If the When's timeout is in the future, we can generate a non-ambiguous time interval
+      by restricting the endTime to be strictly lower than the timeout\<close>
    then (Unbounded, Bounded (timeout - 1))
+  \<comment> \<open>If the timeout is in the past, we need to restrict the startTime to be larger or equal than
+     the timeout\<close>
    else intersectInterval (Bounded timeout, Unbounded) (calculateNonAmbiguousInterval n t tcont))" |
-"calculateNonAmbiguousInterval n t (When (Cons (Case _ cont ) tail) timeout tcont) =
+
+"calculateNonAmbiguousInterval n t (When (Case _ cont  # restCases) timeout tcont) =  
   (if gtIfNone n 0
+\<comment> \<open>If n is none (check all) or n > 0 we recursively calculate the intersection for all the continuations\<close>
    then intersectInterval (calculateNonAmbiguousInterval (subIfSome n 1) t cont)
-                         (calculateNonAmbiguousInterval n t (When tail timeout tcont))
-   else calculateNonAmbiguousInterval n t (When tail timeout tcont))" |
+                         (calculateNonAmbiguousInterval n t (When restCases timeout tcont))
+\<comment> \<open>If n \<le> 0 we don't calculate for the current case and we iterate until we reach the base case\<close>  
+\<comment> \<open>TODO: we should be able to change restCases for [] to check the base case directly\<close>
+   else calculateNonAmbiguousInterval n t (When restCases timeout tcont))" |
+\<comment> \<open>A Let or Assert contracts aren't ambiguous by themselves, so we calculate for the continuation\<close>
 "calculateNonAmbiguousInterval n t (Let _ _ c) = calculateNonAmbiguousInterval n t c" |
 "calculateNonAmbiguousInterval n t (Assert _ c) = calculateNonAmbiguousInterval n t c"