Indeed, but you can compile a lot into h/w. For example, you can compile recursive and higher-order functions and ground-type mutable state. You can also have a type system that tells you at compile time whether your program can be compiled or not.

Here are some entry points to the Verity/GOS project:

* Paper describing the theory: Dan R. Ghica, Alex I. Smith, Satnam Singh: Geometry of Synthesis IV: Compiling affine recursion into static hardware. ICFP 2011: 221-233

* Compiler from Verity to HDL: www.veritygos.org