How is this any different from compiling C to assembly? Why would higher level languages create unsynthesizable circuits? You trust the C compiler to create the proper instructions for your target architecture then I don't see why the same can't be done with a Haskell DSL that compiles to Verilog.
From memory, in several HDLs like VHDL and Verilog, a "boolean" value can have up to 8 or so different values (true, false, undefined, hi, lo (different from true and false apparently) plus a few more).
My experience with Verilog is that it's very easy to write things which look fine, you can simulate and then fail in hardware; the semantics are just wrong in the languages.
Higher level languages inevitably come with built in semantics that the programmer takes for granted, but can't be synthesized directly to hardware. In C, it's the function call stack. In Haskell it's higher order types and recursive data structures (and more). You could in theory create some runtime package that you'd compile to hardware for your program to be synthesized to, or "run on".....but then you'd just be making a straight up computer, wouldn't you. ;-)
None of these things are relevant in most HDLs implemented as DSLs in high level languages. The point of most of the HDL work in Haskell (for example Lava, and Bluespec) is to provide primitives to talk about hardware and to use a sane language as a way to manipulate them to build larger specifications. It is embarrassing that people use tools that allow you to write un-synthesizable code.
A computer is a much simpler abstraction and much less leaky than a circuit model.
Yes, in theory a computer could get a high level description of a circuit, and turn it into a very efficient hardware implementation. In practice our computers are not good enough - the same way they were not good enough for compiling high level languages at the 70's, and people wrote assembly by hand.
