> it is a weaker kind of functional in the sense that given the same inputs it will return the same outputs - it has no state,

I'm trying to imagine what paucity of knowledge about a CPU you can have to say something like "no state." Registers? The program counter? The megabytes of caches? You've got to be stretching the definition of "state" beyond recognition. Each CPU has at least a few dozen, up to a few hundred, fuses covering everything from PLL tuning values to the vendor string.

CPU's are not deterministic, in the sense that given the same inputs it will return the same outputs. Have you never powercycled a system to have it come up when no "state" was changed? A single degree difference can cause transitions to different power states. A PLL might not lock on the same cycle. Electrical systems are ugly nightmares and it's just speaking to the quality of the abstractions that have been presented to you that you think otherwise.

> and even memory access is just a function to set or read from an address and those functions never fail, never throw null pointer exceptions, etc. Do you disagree that a circuit is more an example of data-flow paradigm than an example of the state-machine paradigm?

I'm not sure how to answer this. Everything's built as a series of state machines. Crack open a PRM and see state machines explicitly drawn out with all their transition arcs. If we're talking about generic "circuits," take a look at something like the PCIe LTSSM. PCIe is all about shoveling data from point to point, pretty dataflow-oriented, but it's behavior is specified as a combination of state machines.

> For a CPU to take the next step and decide what work to do at each clock cycle it needs only its inputs - it need not inspect the previous work it did in order to decide what to do next - it simply reads the next opcode the user wants to execute, and does it. That means it is referentially transparent. Which means it's tons more functional than C.

You're not talking about a "CPU" here. You're talking about the abstraction that a CPU provides about how it's assembly instructions will be interpreted. Normally it's not really an issue, people blur that all the time, but you're using statements about the abstraction to talk about the concrete. Map instead of the territory.

If CPU's were implemented in the fashion you describe they'd be incredibly slow. They HAVE to consider what they did before, what they're doing next, and how it all relates to the current instruction. There are prefetch blocks that just watch traffic, completely unaware of the actual instruction stream, just looking for patterns and optimistically pulling things into the cache. There's a ton of state just to keep up the illusion that things are happening sequentially, instruction by instructions, instead of out-of-order as possible to keep execution units humming.

> I will grant you though that I was wrong that CPUs never have bugs, they do and I appreciate your opening my eyes to that. Lots of interesting reading ahead of me. Let me ask you, then. Do you think CPUs have so few bugs just because of more stringent testing, or because of referential transparency and the fact that they a CPU is not a state machine like a C program is?

CPU's have so few bugs because of more stringent testing. There is no functional magic happening. It's just hard work by a lot of talented people. Please respect their effort.