pcf

A one file compiler for PCF to C. It's currently about 275j lines of compiler and 75 lines of extremely boring instances.

What's PCF

PCF is a tiny typed, higher-order functional language. It has 3 main constructs,

1. Natural Numbers

   In PCF there are two constants for natural numbers. Zero and Suc. Zero is pretty self explanatory. Suc e is the successor of a natural number, it's 1 + e in other languages. Finally, when given a natural number you can pattern match on it with ifz.

    ifz e {
       Zero  => ...
     | Suc x => ...
    }
   

   Here the first branch runs if e evaluates to zero and the second branch is run if e evaluates to Suc .... x is bound to the predecessor of e in the successor case.

2. Functions

   PCF has functions. They can close over variables and are higher order. Their pretty much what you would expect from a functional language. The relevant words here are Lam and App. Note that functions must be annotated with their arguments type.

3. General Recursion

   PCF has general recursion (and is thus Turing complete). It provides it in a slightly different way than you might be used to. In PCF you have the expression fix x : t in ... and in the ... x would be bound. The intuition here is that x stands for the whole fix x : t in ... expression. If you're a Haskell person you can just desugar this to fix $ \x : t -> ....

Example

For a quick example of how this all hangs together, here is how you would define plus in PCF

    plus =
      fix rec : nat -> nat -> nat in
        λ m : nat.
        λ n : nat.
          ifz m {
             Zero  => n
           | Suc x => Suc (rec x n)
          }

For this library we'd write this AST as

    let lam x e = Lam Nat $ abstract1 x e
        fix x e = Fix (Arr Nat (Arr Nat Nat)) $ abstract1 x e
        ifz i t x e = Ifz i t (abstract1 x e)
        plus = fix 1 $ lam 2 $ lam 3 $
                 ifz (V 2)
                     (V 3)
                     4 (Suc (App (V 1) (V 4) `App` (V 3)))
    in App (App plus (Suc Zero)) (Suc Zero)

We can then chuck this into the compiler and it will spit out the following C code

    sized_ptr _21(sized_ptr * _30)
    {
        sized_ptr _31 = dec(_30[1]);
        sized_ptr _35 = EMPTY;
        if (isZero(_30[1]))
        {
            _35 = _30[2];
        }
        else
        {
            sized_ptr _32 = apply(_30[0], _31);
            sized_ptr _33 = apply(_32, _30[2]);
            sized_ptr _34 = inc(_33);
            _35 = _34;
        }
        return _35;
    }
    sized_ptr _18(sized_ptr * _36)
    {
        sized_ptr _37 = mkClos(_21, 2, _36[0], _36[1]);
        return _37;
    }
    sized_ptr _16(sized_ptr * _38)
    {
        sized_ptr _39 = mkClos(_18, 1, _38[0]);
        return _39;
    }
    sized_ptr _29(sized_ptr * _40)
    {
        sized_ptr _41 = mkClos(_16, 0);
        sized_ptr _42 = fixedPoint(_41);
        sized_ptr _43 = mkZero();
        sized_ptr _49 = inc(_43);
        sized_ptr _50 = apply(_42, _49);
        sized_ptr _51 = mkZero();
        sized_ptr _56 = inc(_51);
        sized_ptr _57 = apply(_50, _56);
        return _57;
    }
    int main()
    {
        call(_29);
    }

Which when run with preamble.c pasted on top it prints out 2. As you'd hope.