pqnelson / ml

A Study in Implementing Functional Programming Languages

This is an exploration of various ways to implement an ML/Haskell-like functional programming language. From scratch. In C. With an emphasis on proving correctness of the implementation.

A generic functional programming language can be decomposed into several levels based on abstraction:

• High level: this is what you program in, when you learn Haskell/OCaml/Standard ML
• Intermediate level: this is a reduced version of the programming language, types are filled in, some optimizations are made, and so on. It's still human readable at this point.
• Low Level: This is where the code is compiled into something resembling either assembly language or (binary) bytecode, specifically designed to run on a sort of virtual machine historically called an "abstract machine".

The compilation pipeline looks like:

ML.compile :: [ML.Expr] -> [CoreML.Expr]
CoreML.compile :: (AbstractMachine a) => [CoreML.Expr] -> [ByteCode a]

compile :: (AbstractMachine a) => [ML.Expr] -> [ByteCode a]
compile = CoreML.compile . ML.compile -- compile ML to bytecode

eval :: (AbstractMachine a, [ByteCode a]) -> (AbstractMachine a, [ByteCode a])

The low level abstract machine is the bit worth studying, where there are actual substantive differences. Want a lazy language? It's done in the abstract machine. Want to meddle with the garbage collector? Look in the abstract machine. Native array support? Tinker with the abstract machine.

Lacking creativity, I'll generically refer to the "high level" language as "ML" for "MetaLanguage", the intermediate level language as "Core-ML", and the low level abstract machines...well, there are many possibilities! This is more a study in functional programming language implementation, so I hope to provide a number of abstract machine implementations.

ML

We are trying to implement a pure functional programming language. The exact definition and criteria for a functional language to be "pure" varies, unfortunately, it seems "safe" to say: "A functional language is 'pure' if all evaluation strategies (call-by-name, call-by-value, call-by-need) produce 'the same results'."

(For more on pure functional languages, see Amr Sabry's "What is Purely Functional Language?" J. Functional Programming 8, no.1 (1993): 1–22, doi:10.1017/S0956796897002943.)

Generic features one should expect:

• Functions are first class values
• Static typing via type inference
• Statically scoped
• Polymorphic types
• Type system includes support for Algebraic Data Types
• Garbage Collections

Game plan for "Proving Correctness"

I'm hoping to use the ACSL annotations for "Hoare-triples in C". This is how we'll prove correctness.

We will use Twelf to prove the metatheory of the language is correct. This is inspired from previous work in the field, specifically:

• Robert Harper and Daniel R. Licata, "Mechanizing Metatheory in a Logical Framework." Eprint

"Mechanizing the metatheory" will prove the specification is correct using Twelf, and ACSL will prove our implementation adheres to the specification. (The skeptical reader may ask, "Isn't using Twelf to prove the correctness of the specification simply punting the problem? It'd be as correct as the Twelf implementation program, which may be buggy..." True, but Twelf proofs can be checked "by hand", if needed.)

Repository Layout

• includes/ - All the header files
• src/ - All the C code
• target/ - All intermediate files that occur in the compilation process live here.
• test/ - Unit tests live here.
• test-results/ - XML output from running unit tests reside here.
• twelf/ - Holds all the Twelf spec files

FAQ

Why are you doing this?

I need a functional programming language whose implementation has been "proven correct".

What License are you using?

MIT License for all the code.