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An FPGA-based SKI calculus evaluator written in Cλash/Haskell


Blog post:

HaSKI is my attempt at building a reasonably simple hardware-based evaluator for the dead-simple, turing-complete SKI combinator calculus.

I decided to do this project using a Haskell-to-hardware compiler called Cλash because I don't like most HDLs.

The SKI calculus is defined by three terms (S, K, and I), but these terms don't have any side effects, so it's hard to make a pure SKI program do anything interesting. Therefore, I added an L (for "Literal") term, which is just like I except that it causes the evaluator to emit a 32-bit value when evaluated.

For demonstration purposes, I use these 32-bit values to encode characters, so that the evaluator can print things.


  • Haskell/ contains Haskell/Cλash code.
    • Compile.hs compiles SKI programs to HaSKI binary machine code (as .hex files).
    • Hardware.hs contains topEntity, which is the final generated circuit.
    • Main.hs contains some utilities for simulating the CPU. Mostly used for debugging.
    • Model/ contains a pure Haskell "demo" evaluator. It's very simple.
      • Model.hs contains SKI term definitions.
      • Parser.hs contains a simple parser.
      • Programs.hs contains example programs.
      • StackMachine.hs contains the evaluator.
    • Hardware/ contains the Cλash code that can actually target hardware.
      • CPU.hs ties together memory and evaluator logic.
      • Defs.hs contains some useful type definitions.
      • MMU.hs contains memory logic.
      • Model.hs contains type definitions for basic building blocks (SKI terms and pointers).
      • StackMachine.hs contains the core evaluator logic.
      • MemoryEmulator/ contains some RAM simulation logic.
        • RAM.hs contains a RAM device implemented using block RAM.
        • Default.hs contains default pseudo-RAM contents for a few programs.
      • Sim/ contains evaluator simulation logic. This simulates at a higher level than the hardware simulation, so is easier for debugging.
        • Compile.hs contains code for compiling SKI programs (as strings) into various forms (including HaSKI machine code).
        • Harness.hs contains code for running the evaluator on programs.
        • Memory.hs contains code for simulating a memory device.
  • HDL/ contains low-level hardware simulation code.

The model evaluator

Because it's many times simpler, I've included a Haskell (not Cλash) SKI calculus evaluator that isn't compilable to hardware. It's in Haskell/Model/. To use it, run

ghci Model/Programs.hs
evaluate hello4
evaluate $ parse "K(Ia)b"

I suggest you read this first to understand what the evaluator is doing.

The hardware evaluator

The hardware evaluator does the same thing as the model evaluator, but it can be implemented in hardware. This means that the only RAM is that which is manually controlled over a data bus, which means we have no stack, no heap, no garbage collection, etc. Therefore, we have to be a lot more explicit about all the evaluator's possible states, which means the code gets a lot more complicated.


Using the code in Haskell/Hardware/Sim/, we can simulate the hardware by compiling it to a binary. That's one of the great things about Cλash; it's all just Haskell (plus some extensions), so we can compile it to a program just like normal Haskell code.

To generate and run a binary,

clash Main.hs

Looking at the contents of Main.hs, you can see that it does the following:

  • Compile the program "hello4" (which emits hello_world! four times)
  • Compiles and formats the program into memory
  • Prints the compiled program
  • Runs the evaluator with the memory containing the compiled "hello4"
  • Prints the character representation of all outputs

You can also simulate the hardware directly, but this is a bit uglier because the outputs are raw bits. To do this,

clash --interactive Hardware.hs
sampleN 1000 topEntity


To generate a circuit description, run

clash --verilog Hardware.hs

The circuit description will be placed in verilog/Hardware. Hardware_topEntity.v is the file containing the top-level circuit description.

Cλash can also generate other HDLs, like SystemVerilog or VHDL.

Note that, for purposes of making this project more "plug-and-play", I used block RAM instead of connecting to an external RAM module. This limits RAM to a few hundred kilobits on my cheap FGPA board. It shouldn't be too hard to implement real RAM hardware for your FPGA board, though. See ramHardware in Haskell/Hardware.hs.

The default RAM contents are specified in Haskell/Hardware/MemoryEmulator/Default.hs.

After generating Verilog code, you can use it to replace Hardware_*.v in HDL/. Then, you can simulate it with iverilog by running

make cpu

This prints a . if there is no output that cycle, a character if there is output that cycle, and stops when the CPU halts (runs out of code to execute).

The default program outputs hello_world! four times and then stops.


Cλash/Haskell FPGA-based SKI calculus evaluator



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