Samuel's Lambda and the Y Combinator

October 8, 2007

So I’m taking “Principles of Programming Languages” at UNO with Dr. Winter. There is a group project, and he is letting me do the project on my own. The project is to make a small imperative (and Turing-complete) language.

Well, as you may or may not know, I’m crazy about functional languages. I love them. So, while I have to write an imperative language for the project, I decided to spend some of the precious free time I have writing a functional one instead. As of now, my language (Samuel’s Lambda, or SL for short) is Turing-complete.

My test for this was that I could calculate the factorial using the most venerable of functional programming tools: the fixed point combinator (a.k.a. the Y combinator).

For my example of recursion, I’ll show you the factorial. What sort of discussion of recursion would this be if I didn’t?

  val y = fn f =>
      (fn g => g g) (fn g => f (fn x => g g x))
  val fac = fn f =>
            fn n =>
               if eq n 0 then 1
               else multiply n (f (subtract n 1))
in y fac 5

When run at the SML/NJ prompt:

- SLParser.evalPrintFile("examples/");
val it = () : unit

It helps that I’m working with a functional language to start with. That makes implementing things such as closures and let nearly trivial. I’m going to add static type checking (sans-inferencing like ML after which the syntax has been modeled) and then I’ll be done with SL. It has been a fun little exercise.

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