be-strict | use strict ' on the top of js files | Runtime Evironment library

I was thinking about how I could save myself from undefinition, and one idea I had was to enumerate all possible sources of partiality. At least I would know what of to beware. I found three yet:

1. Incomplete pattern matches or guards.
2. Recursion. (Optionally excluding structural recursion on algebraic types.)
3. If a function is unsafe, any use of that function infects the user code. (Should I be saying "partiality is transitive"?)

I have heard of other ways to obtain a logical contradiction, for instance by using negative types, but I am not sure if anything of that sort applies to Haskell. There are many logical paradoxes out there, and some of them can be encoded in Haskell, but may it be true that any logical paradox requires the use of recursion, and is therefore covered by the point 2 above?

For instance, if it were proven that a Haskell expression free of recursion can always be evaluated to normal form, then the three points I give would be a complete list. I fuzzily remember seeing something like a proof of this in one of Simon Peyton Jones's books, but that was written like 30 years ago, so even if I remember correctly and it used to apply to a prototype Haskell back then, it may be false today, seeing how many a language extension we have. Possibly some of them enable other ways to undefine a program?

And then, if it were so easy to detect expressions that cannot be partial, why do we not do that? How easier would life be!