Question

In C++, recursive templates and constant values as template parameters allows to do interesting examples of code generation and compile-time execution, such as the factorial.

Is it possible to do similar things in OCaml, using parametric polymorphism, functors, or other concepts?

Answer 1

The ocaml inteference system uses unification. You can consider it a computational device, and in this case it has a feeling of logic programming. But the possibilities are rather restricted as this was never one of the goals of the type system. As you will see in the page suggested by Jeffrey, type-level computations through unification are actually rather limited (hard to express eg. multiplication). Haskell has a more powerful constraint language, abut again I’m not sure logic programming in the type system is a good way to go.

The other part of the OCaml type system can do type-level computation is in its module and functor language. Functors allow to express type-level computations in a flavor that has been linked to the formal programming language Fω. You could probably encode church numerals at the type level in the module language, but I don’t see what you could do with this, as it is seems quite difficult to retrieve the results in an useful, exploitable form. In particular, I don’t see how to turn that type information back into values usable by your program, as C++ or D do with their compile-time constant computation.

So yes, the type system of OCaml (and most functional language, that would hold of SML, Haskell and Scala as well) has some computational strength, but no, I wouldn’t expect to do particularly useful pre-computation with them; and it’s certainly not standard practice among OCaml programmers. Types are best seen as types, that bring static guarantees about the values they classify.