A tour of Factor: 1

Getting your feet wet with concatenative programming

Posted by Andrea Ferretti on May 23, 2016

A panoramic tour of Factor

This series is a repost from A panoramic tour of Factor. I will split the original tutorial in more manageable chunks, but the content will stay mostly the same.

Factor is a mature, dynamically typed language based on the concatenative paradigm. Getting started with Factor can be daunting since the concatenative paradigm is different from most mainstream languages. This tutorial will guide you through the basics of Factor so you can appreciate its simplicity and power.

I assume you are an experienced programmer familiar with a functional language, and I’ll assume you understand concepts like folding, higher-order functions, and currying.

Even though Factor is a niche language, it is mature and has a comprehensive standard library covering tasks from JSON serialization to socket programming and HTML templating. It runs in its own optimized VM with very high performance for a dynamically typed language. It also has a flexible object system, a FFI to C, and asynchronous I/O that works a bit like Node.js, but with a much simpler model for cooperative multithreading.

You may wonder why you should care enough about Factor to read this tutorial. Factor has a few significant advantages over other languages, most arising from the fact that it has essentially no syntax:

  • refactoring is very easy, leading to short and meaningful function definitions;
  • it is extremely succinct, letting the programmer concentrate on what is important instead of boilerplate;
  • it has powerful metaprogramming capabilities, exceeding even those of LISPs;
  • it is ideal to create DSLs;
  • it integrates easily with powerful tools.

Before you start this tutorial, download a copy of Factor so you can follow along with the examples in the listener (the Factor REPL).

I assume you are using Mac OS X or some distribution of Linux, but everything should work the same on other systems, provided you adjust the file paths in the examples.

The first section gives some motivation for the rather peculiar model of computation of concatenative languages, but feel free to skip it if you want to get your feet wet and return to it after some hands on practice with Factor.

Concatenative languages

Factor is a concatenative programming language in the spirit of Forth. What does this even mean?

To understand concatenative programming, imagine a world where every value is a function, and the only operation allowed is function composition. Since function composition is so pervasive, it is implicit, and functions can be literally juxtaposed in order to compose them. So if f and g are two functions, their composition is just f g (unlike in mathematical notation, functions are read from left to right, so this means first execute f, then execute g).

This requires some explanation, since we know functions often have multiple inputs and outputs, and it is not always the case that the output of f matches the input of g. For instance, g may need access to values computed by earlier functions. But the only thing that g can see is the output of f, so the output of f is the whole state of the world as far as g is concerned. To make this work, functions have to thread the global state, passing it to each other.

There are various ways this global state can be encoded. The most naive would use a hashmap that maps variable names to their values. This turns out to be too flexible: if every function can access any piece of global state, there is little control on what functions can do, little encapsulation, and ultimately programs become an unstructured mess of routines mutating global variables.

It works well in practice to represent the state of the world as a stack. Functions can only refer to the topmost element of the stack, so that elements below it are effectively out of scope. If a few primitives are given to manipulate a few elements on the stack (e.g., swap, that exchanges the top two elements on the stack), then it becomes possible to refer to values down the stack, but the farther the value is down the stack, the harder it becomes to refer to it.

So, functions are encouraged to stay small and only refer to the top two or three elements on the stack. In a sense, there is no distinction between local and global variables, but values can be more or less local depending on their distance from the top of the stack.

Notice that if every function takes the state of the whole world and returns the next state, its input is never used anymore. So, even though it is convenient to think of pure functions as receiving a stack as input and outputting a stack, the semantics of the language can be implemented more efficiently by mutating a single stack.

This leaves concatenative languages like Factor in a strange position: they are both extremely functional - only allowing composition of simpler functions into more complex ones - and largely imperative - describing operations on a mutable stack.

Playing with the stack

Let us start looking what Factor actually feels like. Our first words will be literals, like 3, 12.58 or "Chuck Norris". Literals can be thought as functions that push themselves on the stack. Try writing 5 in the listener and then press enter to confirm. You will see that the stack, initially empty, now looks like


You can enter more that one number, separated by spaces, like 7 3 1, and get


(the interface shows the top of the stack on the bottom). What about operations? If you write +, you will run the + function, which pops the two topmost elements and pushes their sum, leaving us with


You can put additional inputs in a single line, so for instance - * will leave the single number 15 on the stack (do you see why?).

The function . (a period or a dot) prints the item at the top of the stack, while popping it out of the stack, leaving the stack empty.

If we write everything on one line, our program so far looks like

5 7 3 1 + - * .

which shows Factor’s peculiar way of doing arithmetic by putting the arguments first and the operator last - a convention which is called Reverse Polish Notation (RPN). Notice that RPN requires no parenthesis, unlike the polish notation of Lisps where the operator comes first, and RPN requires no precedence rules, unlike the infix notation used in most programming languages and in everyday arithmetic. For instance in any Lisp, the same computation would be written

(* 5 (- 7 (+ 3 1)))

and in familiar infix notation

(7 - (3 + 1)) * 5

Also notice that we have been able to split our computation onto many lines or combine it onto fewer lines rather arbitrarily, and that each line made sense in itself.

Defining our first word

We will now define our first function. Factor has slightly odd naming of functions: since functions are read from left to right, they are simply called words, and this is what we’ll call them from now on. Modules in Factor define words in terms of previous words and these sets of words are then called vocabularies.

Suppose we want to compute the factorial. To start with a concrete example, we’ll compute the factorial of 10, so we start by writing 10 on the stack. Now, the factorial is the product of the numbers from 1 to 10, so we should produce such a list of numbers first.

The word to produce a range is called [a,b] (tokenization is trivial in Factor because words are always separated by spaces, so this allows you to use any combination of non-whitespace characters as the name of a word; there are no semantics to the [, the , and the ] in [a,b] since it is just a token like foo or bar).

The range we want starts with 1, so we can use the simpler word [1,b] that assumes the range starts at 1 and only expects the value at the top of the range to be on the stack. If you write [1,b] in the listener, Factor will prompt you with a choice, because the word [1,b] is not imported by default. Factor is able to suggest you import the math.ranges vocabulary, so choose that option and proceed.

You should now have on your stack a rather opaque structure which looks like

T{ range f 1 10 1 }

This is because our range functions are lazy and only create the range when we attempt to use it. To confirm that we actually created the list of numbers from 1 to 10, we convert the lazy response on the stack into an array using the word >array. Enter that word and your stack should now look like

{ 1 2 3 4 5 6 7 8 9 10 }

which is promising!

Next, we want to take the product of those numbers. In many functional languages, this could be done with a function called reduce or fold. Let’s look for one. Pressing F1 in the listener will open a contextual help system, where you can search for reduce. It turns out that reduce is actually the word we are looking for, but at this point it may not be obvious how to use it.

Try writing 1 [ * ] reduce and look at the output: it is indeed the factorial of 10. Now, reduce usually takes three arguments: a sequence (and we had one on the stack), a starting value (this is the 1 we put on the stack next) and a binary operation. This must certainly be the *, but what about those square brackets around the *?

If we had written just *, Factor would have tried to apply multiplication to the topmost two elements on the stack, which is not what we wanted. What we need is a way to get a word onto the stack without applying it. Keeping to our textual metaphor, this mechanism is called quotation. To quote one or more words, you just surround them by [ and ] (leaving spaces!). What you get is akin to an anonymous function in other languages.

Let’s type the word drop into the listener to empty the stack, and try writing what we have done so far in a single line: 10 [1,b] 1 [ * ] reduce. This will leave 3628800 on the stack as expected.

We now want to define a word for factorial that can be used whenever we want a factorial. We will call our word fact (although ! is customarily used as the symbol for factorial, in Factor ! is the word used for comments). To define it, we first need to use the word :. Then we put the name of the word being defined, then the stack effects and finally the body, ending with the ; word:

: fact ( n -- n! ) [1,b] 1 [ * ] reduce ;

What are stack effects? In our case it is the ( n -- n! ). Stack effects are how you document the inputs from the stack and outputs to the stack for your word. You can use any identifier to name the stack elements - here we use n. Factor will perform a consistency check that the number of inputs and outputs you specify agrees with what the body does.

If you try to write

: fact ( m n -- n! ) [1,b] 1 [ * ] reduce ;

Factor will signal an error that the 2 inputs (m and n) are not consistent with the body of the word. To restore the previous correct definition press Ctrl+P two times to get back to the previous input and then enter it.

We can think at the stack effects in definitions both as a documentation tool and as a very simple type system, which nevertheless does catch a few errors.

In any case, you have succesfully defined your first word: if you write 10 fact in the listener you can prove it.

Notice that the 1 [ * ] reduce part of the definition sort of makes sense on its own, being the product of a sequence. The nice thing about a concatenative language is that we can just factor this part out and write

: prod ( {x1,...,xn} -- x1*...*xn ) 1 [ * ] reduce ;
: fact ( n -- n! ) [1,b] prod ;

Our definitions have become simpler and there was no need to pass parameters, rename local variables, or do anything else that would have been necessary to refactor our function in most languages.

Of course, Factor already has a word for the factorial (actually there is a whole math.factorials vocabulary, including many variants of the usual factorial) and a word for the product (product in the sequences vocabulary), but as it often happens introductory examples overlap with the standard library.

In the next post we will start to look at some basic words called combinators that are used as fundamental building blocks for more complex operations.

Until then!