TLDR; do you know of any general purpose languages that can also compile a function to some representation of AND/OR gates (or NAND gates, or whatever)?
Edit: actually any algebra/formal-logical system is also fine (not just boolean algebra).
Yes, a A LOT of additional info is needed, like defining how input/output is defined, and I am interested in how those would be specified. I’m not interested in printing an actual circuit, just the boolean-logic level. And I’m mostly asking because I feel like most compilers can’t generate a clean/mathematical representation from their AST. There’s AST to IR, there’s hard-coded optimizations on the IR, and then there’s hard-coded mappings from the IR to assembly, but at no point (AFAIK) is the code turned into a algebraic/logical system where something like De Morgan’s Law can be applied. And that seems really sad to me.
So you could say my real question is: what compilers have a strong logical/algebraic internal representation of their own AST?
Maybe something like Haskell or Prolog do this. The Wolfram Language almost certainly does but it’s closed source.
You will need a hardware description language (HDL). Verilog and VHDL are two very established ones but they are tricky. A newcomer is Bluespec, which is now open source so if you wanna go down that rabbit hole, I’d recommend this one.
Sorry, I meant a general language rather than one that is described as a “hardware description language”. I went ahead and edited the post to be more clear about that.
Thanks for the info though as others might still be interested in it!
The most low level languages, such as C, compiles down to CPU instructions, which still is way above logic gates. The CPU in turn reads the instructions and controls the computer to in a way “simulate” what could be described as a boolean expression – at every CPU clock cycle. The next cycle the permutation of all control signals and computer compinents will be different. I highly doubt any programming language implementation has an IR that resembles what you are looking for, including mathematica. The closest you get is probably HDLs but then you need to do all the mathing yourself
And with so much stuff being built ontop of C (or at minimum LLVM) I was afraid that would be the case.
I was kinda hoping there would be some hacky compiler that could take a C function like:
short doStuff(short a, short b) { short c = a * b; short d = c + a; return d; } /* A more realistic example would be something like AES/DES/DEA */- Create boolean inputs for the bits in
aandb, and an boolean outputs forc - Have mappings/templates for converting multiply and add into boolean logic expressions
- Simplify/compress/optimize the expressions
- Print out some kind of expression or maybe graph representation of the logic gates and connections
I can highly recommend you have a look at some HDL languages, eg Verilog can look roughly like your example and synthesizes down to logic elements
Cool I’ll give them I shot! I’ll admit I haven’t heard great things about typical HDL langs, so I haven’t looked into them much
Another way could be to run that through a compiler with optimization activated, and then decompile the resulting binary back to code. But if you want to optimize hot code then usually mathematical reduction is seldomly wherein the problem lies
I don’t know about math reduction not being the bottle neck. If I was custom optimizing hot code then yeah, cache hit optimization is huge, but I’m thinking of generic optimizations on hot code that only the compiler looks at. Beyond out-of-order-execution and SIMD kind of algebraic shuffling. For example, I want to be confident that the compiler would transform something like
for each in range(x) x += x
into
x*=x+1And based on stuff like this (which is shockingly recent IMO) I don’t think modern compilers can even find that shortcut right now. Which is kinda sad when you think about it.
If x=65536, any non-algebraic optimizaiton would be vastly inferior. And sure an experienced dev wouldn’t make this kind of mistake, but I bet half the code running on the average computer wasnt written by experienced devs. And its not like its an either-or situation, we can do both optimization steps.
- Create boolean inputs for the bits in
Another newcomer is Amaranth HDL which might be more approachable and transpiles to VHDL
Another problem I see is that for some machine instructions, the boolean output would be absolutely massive (not to mention redundant). Take something like a fetch from RAM for example - which happens at least once on every machine instruction. The binary description would be huge, especially if you include every “false” check.
If you haven’t seen it, I highly recommend Ben Eater’s Breadboard Computer series. His videos take you from logic gates up to a simple functioning computer.
If you could create/find a C compiler for this simple-as-possible computer, then in theory you could use these videos to get the full boolean logic of each instruction. Not something I would do, but I think that would be the easiest way to do it.
This is a really good point. If a complicated pure function is straightforward-ly converted into a boolean expression; at some point the the best way to simplify it would be making a Turing machine INSIDE the expression itself.
I was mostly thinking of small scale functions or sections of really hot/real-time code. Maybe using it for analysis for potential new/helpful instructions for an assembly language or as a foundation for highly advanced bit-level optimizations like the inverse square root hack for Quake (but automated and generic).
I’ll check out that link! In my undergrad one of the classes had us make our own machine language starting from logic gates, muxers, building registers, memory, adders, ALU’s, etc all the way up to a our own custom assembly language. It was probably the most helpful class in my entire undergraduate.
