Is there a largest class of halting programs?

The halting problem says that a Turing machine cannot decide if another Turing machine halts.

However, we know that it is possible to determine if some programs halt. For example, FORTRAN DO statements are simple to formally verify. FORTRAN is however not Turing complete.

What is the largest subset or class of halting programs that can be decided?
Is there a class of such languages?

This blog entry
seems to hint at the fact that since the compiler optimized the code by eleminating the while(1) loop, Fermat's last theorem is disproved by a compiler.

There is no largest class of programs which have a decidable halting problem. If $L$ is such a class and $P \notin L$, then the class $L \cup \{P\}$ also has a decidable halting problem (why?). (This works since the class of all programs does not have a decidable halting problem.)

Responding to Raphael's comment, there is also no largest class of programs, up to finitely many exceptions, with a decidable halting problem. For each program $P$, let $L(P)$ be some infinite decidable set of programs equivalent to $P$ (for Turing machines, we can add dummy unreachable states, for example). Let $L$ be a class with decidable halting problem. I claim that there must be some $P$ such that $L(P) \cap L = \emptyset$. Otherwise, we could decide the halting problem for an arbitrary program $P$ by enumerating $L(P)$. Given a program $P$ such that $L(P) \cap L = \emptyset$, we can obtain a decider for $L \cup L(P)$, so that $L$ has infinitely many exceptions.

StackExchange Computer Science Q#24627, answer score: 6