README

L: A Small Untyped Lambda Calculus Reduction Machine

L is a simple untyped lambda calculus reduction machine. It reads
expressions and then reduces them.

The current implementation is essentially driven by a primitive
REPL. While I'll write more detailed documentation as I get more time,
a quick sample of how to interact with the machine follows:

First let us enter some definitions into the REPL:

:Zero = L a b . b;
:Succ = L n f x. f (n f x);

Now that the machine knows what these elements are, we can start
combining them:

:One = :Succ :Zero;

Note that the REPL will respond with `:One = :Succ :Zero'. This is
because the actual evaluation has not occurred yet. You can view the
raw un-computed value stored in `:One' by simply typing `:One' in the
REPL.

To actually reduce `:One' you have to use the EVAL operator, which is
essentially a pair of square braces. You can 

  i. Display the computed value, by entering:
             [:One];
 ii. Update the value stored in the identifier:
             :One = [:One];
iii. Store the computed value elsewhere:
             :AnotherOne = [:One];

Please note that you could have simply done a `:One = [:Succ :Zero]'
in the first place.

As another example, let us calculate 3!.

First, the foundations:

 L > :Zero = L a b . b;
 L > :Succ = L n f x. f (n f x);
 L > :Pred = L n f x . n (L g h . h (g f)) (L u . x) (L u . u);
 L > :One = :Succ :Zero;
 L > :Three = :Succ (:Succ (:Succ :Zero));
 L > :Mult = L m n f. n (m f);

Then the conditionals:

 L > :IfThenElse = L a b c . a b c;
 L > :True = L a b . a;
 L > :False = L a b . b;
 L > :IsZero = L a . a (L t . :False) :True;

The factorial function is the fixed-point solution of this equations:

 L > :FactorialEqn = L f n . :IfThenElse (:IsZero n) :One (:Mult n (f
 ... (:Pred n)));

The combinator to solve the above fixed-point equation.

 L > :YCombinator = L f.(L x.f (x x)) (L x.f (x x));

The factorial function:

 L > :ActualFactorial = :YCombinator :FactorialEqn;

Then the solution:

 L > [:ActualFactorial :Three]

to give the final solution.

L still has a lot of issues; specifically, things like the lack of
proper error handling and poor file management are being worked on.