# pcf

A one file compiler for PCF

Latest on Hackage: | 0.1.0.1 |

This package is not currently in any snapshots. If you're interested in using it, we recommend adding it to Stackage Nightly. Doing so will make builds more reliable, and allow stackage.org to host generated Haddocks.

**Danny Gratzer**

**jozefg@cmu.edu**

## pcf

A one file compiler for PCF to C. It's currently about 275 lines of compiler and 75 lines of extremely boring instances. The compiler is fully explained in this blog post.

## What's PCF

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

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.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.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

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