PLAI - Rudimentary Interpreters

I’ve just finished the second section of PLAI, Rudimentary Interpreters.

It revolves around a basic interpreter for arithmetic expressions. The idea was presented from chapter I actually. The difference is that chapter I introduces the syntax for this languages, which is more or less Scheme with curly brackets instead of braces. For example, {+ 1 2} represents the addition operation between the numbers 1 and 2. The second chapter though, deals with the semantics of the language; introduces concepts such as identifiers, scope and functions. All in a progressive manner, building new concepts on top of existing ones.

A little digression. PLAI uses a dialect of Scheme as its languages, and while I like Scheme, this language that they use, called PLAI Scheme, is actually quite ugly to my eyes. The reason is that it’s some sort of typed Scheme, in that it has algebraic data types and means of destructuring such data into its variants. In fact, it looks a lot like Haskell, so what I did was to write all the supporting code in Haskell. I started with PLAI Scheme in chapter one, but chapter two was all Haskell. The little disadvantage is that in Haskell I don’t have a read function that takes valid Scheme code and returns a corresponding Scheme data structure. So I had to write the parser myself, but it was no big deal for two reasons. First of all, the syntax for this arithmetic language is quite simple, and secondly, Haskell has really powerful libraries for parsing. For convenience I’ve used Parsec, as I already have some experience with it, but there lots of other parsing libraries (I’ve heard some of them are even better than Parsec). To end this digression, all the Haskell code I wrote for this chapter is available in my Github repo. I hope I’ll write another blog post with details about its implementation.

Now, back to the book.

The chapter starts by exploring the concept of identifiers and ways of supporting them in a language by means of substitution. These identifiers resemble normal variables that we all know, except for one thing, they can’t be reassigned a new values. So they’re actually constants, not variables. It then goes on describing what happens when there are overlapping identifiers names, whether it’s a good thing and how to implement it correctly. But it’s not a book that gives you the correct solution from the first shot. It makes you write a program with mistakes, then provides some examples that won’t work with the respective program, at which point the whole theory behind the concepts begins. The reason is very simple, the author wants the readers to judge based on a concrete program instead of some abstract concepts.

I won’t go into details about substitution, as it is a pretty complex subject and would provide no information that it’s not in the book. There’s one thing that I want to mention though. One section of chapter three asks whether names are necessary for identifiers. It appears that someone called Nicolaas de Bruijn said they’re not, and instead, he used numbers. This appears to be employed in compiler construction. Maybe I’ll talk in detail about substitution in a future post.

After substitution, the language is enriched with functions. These are quite simple conceptually, as they take a single argument and return a value that is always numeric, but it’s a good start for observing the issues that arise when combining substitution and functions.

After substitution and functions, the author introduces deferred substitution as a means of improving the performance of the interpreter. Instead of passing through the whole program for each identifier that dictates a substitution, the interpreter is now storing these identifiers and their values in a data structure that is queried on a per need basis, i.e., whenever a new scope is found that uses a free identifier.

The last part of this second section of the book deals with first-class functions, i.e., functions that ca be used as any other value in the language. They can be returned from functions, or passed to functions. Also, in the moment functions as first-class values meet deferred substitution, the concept of closure emerges.

In short, that’s what section two of PLAI touches. If you want more details, then start reading the book. I had a lot of fun implementing this little language in Haskell. Although small, it encompasses a lot of advanced programming concepts unavailable in other languages (PHP for example, which is what I do for a living).