Write You A Scheme, Version 2.0

Posted on November 28, 2016 by Adam Wespiser

A programming language is for thinking about programs, not for expressing programs you’ve already thought of. It should be a pencil, not a pen. Paul Graham


Welcome to Write You a Scheme, Version 2.0. Github repo. You may be familiar with the original Write Yourself a Scheme in 48 hours by Jonathan Tang, and this is a much needed upgraded version. We use as much modern, industry ready Haskell to implement a Scheme that is well on its way to being ready for production. This series will teach how to create a programming language by walking the reader through the components of a Scheme variant Lisp in Haskell. This should take about a weekend of study/programming for a beginner who might have to look up a few new concepts to really internalize the material. The ideal reader has some experience in Haskell, and is eager to see how all the pieces come together in a medium to large sized project.

We won’t have time to go into a lot of detail on things like monad transformers or interpreter theory. Instead, links to further information will be provided when needed. If you are looking for a good Haskell intro, the concepts from Learn You a Haskell for Great Good can be reviewed. Exercism.io has a great collection of Haskell exercises and submission system for getting hands on experience. A great reference while reading this book is What I Wish I Knew When Learning Haskell. Specifically for industry, FP-Complete’s Haskell Syllabus is a great guide. The HaskellWiki has a comprehensive list of resources available for learning Haskell.

This a community project, and if you have improvements, please contact me over Github or on Twitter @wespiser. Better yet, submit a PR! We’ve had to balance language features, tutorial breadth, and level of complexity to provide beginners with a robust but easy to understand implementation. If you have any ideas on how I can better meet these goals, please let us know! We advocate open source languages, although it is possible to use our Scheme to build a vendor-specific language, this article spells out why that is a bad idea. However, if you need an interpreter for commercial purposes, Abstract Definition Interpreters contains the conceptual underpinnings and “invents”, or really “discovers”, the kind of interpreter that can be used.


Here’s the overview of what we will be doing and where we will go:

Why Lisp ?

Although the majority of modern programming follows C/Algo style, Lisp syntax is simple, using the same syntax to represent code and data: the list. This is called homoiconicity, a feature which makes both parsing and evaluation much simpler compared to other languages. Scheme, a dialect of Lisp, is a particularly straight-forward. We won’t strictly follow the Scheme standard for the sake of brevity, but aim to include many useful features. If you are interested in what a fully fledged Scheme looks like, Haskell-Scheme is a fully featured language, in Haskell, and Chicken-Scheme implemented in C. Our Scheme contains the basic elements of these more featured languages.

The Scheme Programming Language is a great book to teach the function of an industrial strength Scheme, and reference to explain language features. Another great book to learn Scheme and interpretation theory is Structure and Interpretation of Computer Programs (SICP), which discusses how to build a meta-circular evaluator in Lisp. Lisp has a history as an educational language, and its simplicity is mostly why we will be continuing the tradition here.

While on the topic of Lisp, the Clojure Programming Language is a modern, functional approach to Lisp targeting the JVM. If you are interested in designing your own Lisp, Clojure is a great example of how you can take Lisp to a modern programming environment. It is probably the most supported modern Lisp community, and is a great source of information and ideas. The other industry relevant to Lisp is EmacsLisp, which is a domain specific language for programmers that don’t know vim! Finally, Read Eval Print Love contains a wonderful and insightful discussion of the Lisp family, and is a great source of additional information for the interested reader!

Why Haskell ?

First off, why not? I love Haskell! Haskell is a purely functional, typed, compiled, and lazy language with many sophisticated and advanced features. With over two decades of research level and industrial development, Haskell is the focus of numerous computer science research projects and implements these ideas with a production worthy compiler. Who cares? Well, these features give the programmer expressive power above and beyond today’s status quo. A set of very powerful and safe abstractions has emerged from its test bed. With great power, comes great responsibility, and there are many complex and under-adopted features that take a while to learn. Fortunately, if you only use a subset of advanced features, Haskell can be an effective production language.

It may be attractive to include advanced type theory extensions and over engineer your project with all the latest advances in type theory. If your background is in academic Haskell research or you have been hacking around in Haskell for years, there is no problem understanding. If you are trying to hire developers to work on your project with you, finding people who can be trained with less cost than the performance gains will be a serious hinderance when proposing your project to weary business type folks. For this reason, we take a conservative approach on what features and abstract concepts are used in this Scheme. When in doubt, we pick the simplest possible abstraction that is needed for functionality, and avoid extra language pragma and type theory extensions at all cost. If you use Haskell for work, your colleague’s job will go a lot easier and less technical debt will emerge.

Project Tool Chain

What you need to run the project is in README.md, and if you are excited to start, skip to Chapter 1!

Haskell is not an island unto itself, and we must manage the libraries required to build the project. I recommend using Ubuntu, version 14.04 or 16.04, (any Linux distribution should work, contact me if you have problems) and the build tool Stack. The library versions are determined for Stack in scheme.cabal, while stack.yaml is the version of Stack’s dependency resolver, and Build.hs is Haskell code for generating documents from these markdown files. More info on stack, here: The README.md contains full instructions on how to build the project source code and documentation, which I encourage you to do. The best way to learn is to modify, break, fix, and finally improve the source code. Two included scripts, build which will monitor for file changes then build upon updates, and run, which will drop you into an interactive REPL, were invaluable in the development of this project. Please feel free to contact with me with any great ideas, modifications, improvements, or vaguely related but interesting concepts. I made this project for you, use it however you please.

What are we going to do?

We are going to make a very basic, but robust, programming language that is both simple to use and highly extendible. You are encouraged to take the language we build and add more functionality. For instance, you could use this language for running jobs on a High Performance Computing Cluster, or analyzing financial data. Language development is really a “killer app” for Haskell, and the approach we take in this tutorial is the basis you’ll need to create a domain specific language for industrial purposes.

Scheme Syntax

Lisp is a list processing language, and is old enough to join the AARP with a very storied history. Scheme is a fully specified Lisp implementation, though we will take many liberties for the sake of simplicity. For Scheme, this means every expression is a list with a prefix operator. This is known as an S-Expression. Whenever a S-Expression is encountered, it is evaluated in the same way, minus a handful of special forms. Data is also represented as an S-Expression, and there is no syntactical difference between code and data. This minimalism is what Scheme is well known for!

Scheme semantics

Similar to Haskell, Scheme is a functional programming language. Everything in our Scheme is an object, for instance numbers, strings, functions, variables, and booleans. This is our Haskell type, LispVal. These objects are stored in a single environment, EnvCtx which is queried to resolve the value of an evaluated variable. In Scheme, no object is ever destroyed, and we won’t need garbage collection. However, the scope of a variable is limited to its lexical context. Further, arguments in scheme are passed by value, so when a function is called, all of its arguments are evaluated before being passed into the function. Contrast this to Haskell, where evaluation is lazy, and values are not computed until they are needed, which is known as “call by need”.

The environment to find and store variables is the same to find primitive functions, so when (file? "tmp") is evaluated, file? is a variable with a corresponding value (a function) in the environment. This approach is a system called Lisp-1, contrasted to Common Lisp’s Lisp-2 system, where functions and variables have different environments.

Scheme Type System

Scheme is a dynamic language, like Python, Ruby, Perl, or as contrasted with a static language like C++ or Java. Dynamic languages are easy to use and simple to implement, but allow for some preventable errors that would be impossible in a static language. For an example from our Scheme, (+ 'a' 1) is valid syntax wildly open to interpretation at runtime. (Try it on the REPL!)

If you are interested in building a typed language in Haskell, this guide shows how type inference makes language engineering significantly more complex. Dynamic languages are not all doom and gloom: they give the user tremendous flexibility. The R Programming Language is an excellent example of a dynamic language that excels at statistical computing by giving the user incredible flexibility and choice over how to implement ideas.

A concept called Dynamic Dispatch allows functions to be determined, at runtime, by the types of the arguments passed in, so (+ 1 1) and (+ "a" "b") could use different versions of the + function. This is a key feature in dynamically typed programming languages, and we will be implementing this feature in our Scheme.


We are building an interpreted language, an alternative to compiling to assembly language, LLVM or using a virtual machine like Java’s JVM. This means that we have a program that actively runs to evaluate a program written in our Scheme. This approach yields slower performance due to the higher memory and processor overhead, but we will be able to finish the project in a single weekend.

For the motivated, Lisp In Small Pieces walks you through over 30 interpreted and 2 compiled versions of Scheme, written in Scheme. You can find the program code here. If you want to write a language with performance in mind, you’ll want to use an LLVM backend. I warn you: there be dragons!

On Type System Complexity, Cautionary Tale

Type systems are extremely complex to build, and balancing programming productivity versus performance gains is difficult. For instance, Guy Steele has worked on successful languages like Common Lisp and Java, but spent most of the 8 years building Fortress getting the type system right. Steele cited issues with the complexity of the type system when winding down development on Fortress.

Although type systems are complex, it’s theoretically possible to create a type system so advanced that programs can have provable properties and abstractions as powerful as those in mathematics. This is far beyond the scope of this tutorial, and the majority of production code written is done in a dynamic language. However, If you’re a novice, then this tutorial is a great way to get involved in a very exciting movement that will shape the way of things to come for industry programming. For now, the best we get is an industrial language that, if it compiles, it runs, and this language is Haskell. Finally, Types and Programming Languages by Benjamin C. Pierce is the place to learn the theory and implementation of type systems.

Scheme Examples, Operational Semantics

To get a feel for our Scheme, here is the evaluation of some functions and their arguments. Keep in mind that we must build the abstractions that are capable of evaluating these forms. Both the right and left hand side of the form are represented with LispVal.

List Processing

There are three primitive functions for manipulating lists in our Scheme. We will implement them later as part of the standard library and discuss the tradeoffs.
car(car '(1 2 3)) => 1
cdr(cdr '(1 2 3)) => (2 3)
cons(cons 1 '(2 3)) => (1 2 3)


Mathematical functions can take 2 or more arguments.
(* 60 9) => 540
(+ 10 30 2) => 42


quote is a special form that delays evaluation on its argument.
(quote (1 2 3 4)) => (1 2 3 4)
'(1 2 3 4) => (1 2 3 4)

Conditional Statements

The if statement acts like it does in any language.
(if (< 4 5) #f 42) => #f

Lambdas & Anonymous functions

lambda is used to create an anonymous function.
((lambda (y) (+ y 2)) 40) => 42

Let Statements

let takes two arguments. Its first is a paired list of variables and values. These variables are set to corresponding values, which are then in scope for the evaluation of the second argument.
(let (x 42) x) => 42
(let (x 2 y 40) (+ x y)) => 42


begin evaluates a series of one or more S-Expressions in order. S-Expressions can modify the environment using define, then subsequent expressions may access the modified environment. Further, when running a Scheme program, its S-Expressions are essentially wrapped in a single begin function. More on this when we go over Eval.hs.
(begin (define x 413000) (define y (+ x 281)) (+ x y)) => 826281

The Rest

Although Scheme is a minimal language, this list of functions is not complete. There are two files that contain the rest of the internally defined functions: special forms in Eval.hs, and the primitives in Prim.hs. For a full Scheme specification, see The R5RS Specification. It’s not the most modern, but its complete enough to work.

[Understanding Check]

Next: Introduction to our implementing Scheme