Thought 1 - but doesn't that mean you immediately run up against the halting problem? Surely we could create a type representing Program, and a function 'halts'. No compiler is going to be able to tell us which programs halt.
Thought 2 - Aha, is this the reason why the language isn't turing complete, so we KNOW that we never run into that difficulty? In other words, the language is constrained somewhat so that we can do these dependent types, because we can then guarantee there's always some calculation the compiler can do ahead of time to ensure all cases will work.
You are correct in the sense that the language isn't Turing complete to guarantee that the language is strongly terminating. The language being strongly terminating means that 1) there is a Normal Form for the type of an expression and 2) the number of steps to reach Normal Form is finite. All programs definable in Epigram have a normal form (i.e. result) and this normal form (result) is reachable in finite time. Therefore hanging and infinite loops are impossible.
However, these aspects are unrelated to the fact that Epigram is dependently typed. We could easily implement a Turing complete dependently typed language or implement a non-dependently typed language which is not Turing complete.
I'm not entirely sure what the problem is you are thinking of in thought 1. Could you elaborate?
Thought 2 - Aha, is this the reason why the language isn't turing complete, so we KNOW that we never run into that difficulty? In other words, the language is constrained somewhat so that we can do these dependent types, because we can then guarantee there's always some calculation the compiler can do ahead of time to ensure all cases will work.