First impression, could be misinformed, but I'll bite.
Since a hardware circuit is a recursive function that takes a state of the hardware and produces a new state, starting from an initial state (and so is the universe where the initial state was supplied by the Big Bang), you can of course express it straightforwardly as a recursive function, which I think is what they sometimes do:
This is VHDL/Verilog spelled in Haskell (real hardware description languages will not make you spell the old state - leds,mode... - and the new state - leds',mode'... explicitly, which gets annoying for 20 state variables. Of course this could be taken care of by a preprocessor or a macro system, my point isn't that it's verbose but that it's VHDL spelled in Haskell, a bit awkwardly and maybe you can do it less awkwardly but the programming model is the same so calling it Haskell is cheating, kinda.)
This is definitely not what TFA is about - you don't represent the blinking leds as graph reduction, rather, you generate VHDL from VHDL-like Haskell.
This is not to say they aren't doing cool things in this project. If indeed they compile this:
fir coeffs x = dotp coeffs (window x)
where
dotp as bs = sum (zipWith (*) as bs)
...to efficient hardware description code, that's really cool. In general, I think that a sufficiently restricted functional language can compile very nicely to FPGA/hardware (and to DSPs and GPUs etc. etc.) I'm just saying that a general-purpose functional language is better targeted at a CPU, and that a functional language targeting something else is a DSL of sorts.
To me, the inability of these "haskell to hardware" systems to handle general recursion shows that they are fundamentally missing the most important part of the mapping from functional computation to combinational logic plus registers. They don't easily permit the "unrolling" of recursively-written code, so your recursive programs must squirrel away their state between every iteration, even when they could potentially be performed in parallel. In trying to sum a list in parallel in hardware, how do you know how many per-element operations to do at once? This determines the number of gates you'll need, and the buffer size for storing the rest of the list until those gates are free.
One way to get around this is to use termination proofs to bound the size of input data, which is exactly what's done in total functional programming. In total programs, no term is a bottom, so laziness vs. strictness is moot (both give the same answer for all programs with no exceptions or infinite loops in either evaluation strategy). Which is what you would expect since you're modelling hardware which has a clock and will clock out results into its output pins each cycle anyhow.
How can we bridge the mapping? Well, you could write a totality checker which searches for a recursion principle which is well-founded, and use this to bound data/iteration sizes and determine the shape of necessary hardware. Or you could build a theorem-proving language whose constructs enable extraction of these sizing bounds, and have humans write the proof with application of tactics.
What I really think we should be doing is writing specifications (aka, type signatures, per Curry-Howard), which do not themselves impose a particular mode of execution of the program which fulfills the specification, but only completely specify its results (and effects, if in an effectful language), and then do (constrained, by the desirable properties of the resulting programs/hardware designs) searches for proofs of those theorems.
I'm a Haskell fan, so I'll bite: what do you use to program your FPGAs? VHDL or Verilog? Or do you have some other higher level language? I have not found VHDL or Verilog easy to use at all.
Since a hardware circuit is a recursive function that takes a state of the hardware and produces a new state, starting from an initial state (and so is the universe where the initial state was supplied by the Big Bang), you can of course express it straightforwardly as a recursive function, which I think is what they sometimes do:
This is VHDL/Verilog spelled in Haskell (real hardware description languages will not make you spell the old state - leds,mode... - and the new state - leds',mode'... explicitly, which gets annoying for 20 state variables. Of course this could be taken care of by a preprocessor or a macro system, my point isn't that it's verbose but that it's VHDL spelled in Haskell, a bit awkwardly and maybe you can do it less awkwardly but the programming model is the same so calling it Haskell is cheating, kinda.)This is definitely not what TFA is about - you don't represent the blinking leds as graph reduction, rather, you generate VHDL from VHDL-like Haskell.
This is not to say they aren't doing cool things in this project. If indeed they compile this:
...to efficient hardware description code, that's really cool. In general, I think that a sufficiently restricted functional language can compile very nicely to FPGA/hardware (and to DSPs and GPUs etc. etc.) I'm just saying that a general-purpose functional language is better targeted at a CPU, and that a functional language targeting something else is a DSL of sorts.