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README
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 explanation.md
.
What's PCF
PCF is a tiny typed, higherorder functional language. It has 3 main constructs,
Natural Numbers
In PCF there are two constants for natural numbers.
Zero
andSuc
.Zero
is pretty self explanatory.Suc e
is the successor of a natural number, it's1 + e
in other languages. Finally, when given a natural number you can pattern match on it withifz
.ifz e { Zero => ...  Suc x => ... }
Here the first branch runs if
e
evaluates to zero and the second branch is run ife
evaluates toSuc ...
.x
is bound to the predecessor ofe
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.