Yep, that&#x27;s called the &quot;halting problem&quot;, and I hear it&#x27;s very hard to solve :)<p>Here&#x27;s how I generally see it. Writing large software is hard (and a software composed of multiple components is large software, even if you decide using the network stack when calling some functions is a good idea ;)). &quot;Type&quot; people (and I&#x27;m certainly for some kinds of static types, I just don&#x27;t think that they&#x27;re the solution to everything) would tell you that types help restrict your computation in such a way that reasoning about it is easier. To that I say, but I want to do something specific which it&#x27;s pretty annoying in PFP, and they answer, just do it a different way, to which I say, if I can do it differently, so can the compiler on my behalf. In short, I don&#x27;t think that explicit types (i.e. those that can be defined in the language you use) are stronger than implicit types (i.e. anything that a verifier can prove about your program), and at least in theory, they are both &quot;the same&quot; (though, see another comment here on what I think about two things being the same in a mathematical sense). We should use whatever is easier for our minds to grasp.<p>The more essential problem -- although I don&#x27;t know if it&#x27;s more interesting or less interesting -- is what exactly do we want to do in our programs? If we require a Turing complete model, then no matter how many types -- explicit or implicit -- we throw at the problem, we just won&#x27;t be able to formally prove properties we might care about. Some people, however, claim that we don&#x27;t really need Turing completeness, and if we don&#x27;t, that might open a whole new world of possibilities. But once we start restricting the computational model, the representation we use -- say, PFP or imperative -- might become much more important, each being able to compute things that the other cannot (we know that lambda calculus and Turing machines both compute the same functions, but once we restrict each in some arbitrary ways, it gets harder to find equivalences between restrictions in the PFP model and those in the imperative model).<p>Finally, I think that the notions of what it means &quot;to reason about&quot; or even what it means to be correct (and certainly how important it is to be correct) are themselves vague and require answers from empirical psychological&#x2F;sociological&#x2F;economic research than from math.