bedrock2: A Coq repository from Programming Languages and Verification Group at MIT CSAIL - Programming Languages and Verification Group at MIT CSAIL

A work-in-progress language and compiler for verified low-level programming

This repository containts ongoing work on a low-level systems programming language. One piece of the puzzle is a verified compiler targeting RISC-V. The source language itself is also equipped with a simple program logic for proving correctness of the source programs. It is not ready yet, at least for most uses.

This project has similar goals as bedrock, but uses a different design. No code is shared between bedrock and bedrock2.

Current Features

The source language is a "C-like" language. It is an imperative language with expressions. Currently, the only data type is word (32-bit or 64-bit), and the memory is a partial map from words to bytes.

Non-features

It is a design decision to not support the following features:

Function pointers
Recursive functions (we might add them later, but we always want to prove that we don't run out of stack space)
Non-terminating programs (except for the top-level event loop)

Build

You'll need Coq. We try to support the latest released version as well as master. If unsure which version to pick, it's best to check the build log of the continuous integration server.

In case you didn't clone with --recursive, use make clone_all to clone the git submodules.

Then simply run make or make -j or make -jN where N is the number of cores to use. This will invoke the Makefiles of each subproject in the correct order, and also pass the -j switch to the recursive make.

Project Overview

This repository is an umbrella repository integrating several sub-projects, allowing us to prove end-to-end theorems describing the I/O behavior of a pipelined processor executing a program written in the bedrock2 language, verified with our program logic, and compiled with our compiler.

There are the following sub-projects:

coqutil: Coq library for tactics, basic definitions, sets, maps
riscv-coq: RISC-V specification in Coq
bedrock2/bedrock2: The bedrock2 language, a simple C-like programming language with a program logic and a few verified sample programs
bedrock2/compiler: A very simple compiler from the bedrock2 language to bare metal, position independent RISC-V machine code
kami: Provides a 4-stage pipelined RISC-V processor
bedrock2/processor: Proves that the hardware-centric RISC-V specification of Kami matches the software-centric specification of riscv-coq
bedrock2/end2end: Combines all the projects into an end-to-end theorem about a concrete program, the IoT lightbulb demo.

The Kami processor can be extracted to bluespec, which can be compiled to Verilog, and run on an FPGA.

The project dependency structure looks as follows (right depends on left):

         bedrock2
       /          \
coqutil            compiler
       \          /         \
         riscv-coq           end2end
                  \         /
                   processor
                  /
              kami

The IoT lightbulb demo

In the above picture, the FPGA at the bottom left is running the Kami processor, which executes a program proven correct using the bedrock2 program logic and compiled to bytes using the bedrock2 compiler. Through a set of blue wires (using SPI), the FPGA is connected to an ethernet card (which we do not verify), and through a red & black wire, it is connected to a power relay which can turn on and off a lightbulb.

Code Overview

Throughout the compiler, we use (big-step) omnisemantics, i.e. judgments of the form exec c s P, meaning "if we execude command c from starting state s, all possible final states satisfy the postcondition P, and none of the (nondeterministic) execution branches will fail.

Here's a list of files that might be interesting to step through in your IDE:

The big-step omnisemantics of the bedrock2 language are in bedrock2.Semantics. You might also want to look at compiler.FlatImp, a flattened version of it, written down in more traditional syntax.
bedrock2.WeakestPrecondition contains the verification condition generator used by the program logic.
bedrock2Examples.swap is a small program logic proof.
bedrock2.WeakestPreconditionProperties.sound_cmd is not interesting, but confirms that the weakest precondition generator agrees with the bigstep omnisemantics formulation.
compilerExamples.MMIO shows how to instantiate external calls (which are kept abstract throughout the compiler) with memory-mapped I/O (MMIO).
To see how we connect omnisemantics to the traditional small-step semantics of Kami, you might want to start at processor.KamiRiscv.riscv_to_kamiImplProcessor, then look at processor.KamiRiscvStep.kamiStep_sound, and compiler.CompilerInvariant.compiler_invariant_proofs proves the assumptions made by processor.KamiRiscv.riscv_to_kamiImplProcessor, by using a "low level invariant" ll_inv, defined in compiler.ToplevelLoop, which says, "the current RISC-V state is a finite numer of steps away from a good state, where good state means a RISC-V state that is related to a bedrock2 state that can be observed at the end of an iteration of the toplevel event loop". Note that this "finite number of steps" might be different for each nondeterministic execution branch, so we can't just state it as exists numberOfSteps, .... Instead, we use riscv.Utility.runsToNonDet.runsTo (that we write as ◊ in papers).
The semantics of each RISC-V instruction is defined in terms of the primitives given in riscv.Spec.Machine.RiscvProgram.
The function that executes a RISC-V instruction from the basic I extension is in riscv.Spec.ExecuteI, but since it has been translated from Haskell and Coq's beautify option is broken, the Coq code is not very readable, so you have to read ExecuteI.hs from the Haskell spec instead, or import the MonadNotations and do Print ExecuteI.execute inside Coq to read it.
To see how we instaniate this generic RiscvProgram monad with small-step omnisemantics, you can look at riscv.Platform.MinimalMMIO.

Compiler Overview

Here are the names of the languages and the compiler phases between them (see compiler.Pipeline for more details):

Syntax.cmd
  ↓ FlattenExpr
FlatImp.stmt string
  ↓ RegAlloc
FlatImp.stmt Z
  ↓ Spilling
FlatImp.stmt Z
  ↓ FlatToRiscv
list Instruction
  ↓ instrencode
list byte

The compiler provides two interfaces:

1) The "more traditional" interface:

Input:

list of bedrock2 functions
name of "main"

Output:

Compiled functions as list of instructions
Relative position of main function

Correctness theorem: compiler.Pipeline.compiler_correct:

If all high-level executions satisfy post, running the compiled functions from a "good" initial RISC-V machine leads only to machines whose memory and I/O trace satisfy post.

2) The event loop interface: