Thun: Joy in Python

This implementation is meant as a tool for exploring the programming model and method of Joy. Python seems like a great implementation language for Joy for several reasons.

  • We can lean on the Python immutable types for our basic semantics and types: ints, floats, strings, and tuples, which enforces functional purity.
  • We get garbage collection for free.
  • Compilation via Cython.
  • Python is a “glue language” with loads of libraries which we can wrap in Joy functions.

Read-Eval-Print Loop (REPL)

The main way to interact with the Joy interpreter is through a simple REPL that you start by running the package:

$ python -m joy
Joypy - Copyright © 2017 Simon Forman
This program comes with ABSOLUTELY NO WARRANTY; for details type "warranty".
This is free software, and you are welcome to redistribute it
under certain conditions; type "sharing" for details.
Type "words" to see a list of all words, and "[<name>] help" to print the
docs for a word.


joy? _

The <-top marker points to the top of the (initially empty) stack. You can enter Joy notation at the prompt and a trace of evaluation will be printed followed by the stack and prompt again:

joy? 23 sqr 18 +
       . 23 sqr 18 +
    23 . sqr 18 +
    23 . dup mul 18 +
 23 23 . mul 18 +
   529 . 18 +
529 18 . +
   547 .

547 <-top


The Stack

In Joy, in addition to the types Boolean, integer, float, and string, there is a single sequence type represented by enclosing a sequence of terms in brackets [...]. This sequence type is used to represent both the stack and the expression. It is a cons list made from Python tuples.

Purely Functional Datastructures

Because Joy stacks are made out of Python tuples they are immutable, as are the other Python types we “borrow” for Joy, so all Joy datastructures are purely functional.

The joy() function

An Interpreter

The joy() interpreter function is extrememly simple. It accepts a stack, an expression, and a dictionary, and it iterates through the expression putting values onto the stack and delegating execution to functions which it looks up in the dictionary.

Continuation-Passing Style

One day I thought, What happens if you rewrite Joy to use CPS? I made all the functions accept and return the expression as well as the stack and found that all the combinators could be rewritten to work by modifying the expression rather than making recursive calls to the joy() function.

View function

The joy() function accepts an optional viewer argument that is a function which it calls on each iteration passing the current stack and expression just before evaluation. This can be used for tracing, breakpoints, retrying after exceptions, or interrupting an evaluation and saving to disk or sending over the network to resume later. The stack and expression together contain all the state of the computation at each step.

The TracePrinter.

A viewer records each step of the evaluation of a Joy program. The TracePrinter has a facility for printing out a trace of the evaluation, one line per step. Each step is aligned to the current interpreter position, signified by a period separating the stack on the left from the pending expression (“continuation”) on the right.


The parser is extremely simple. The undocumented re.Scanner class does the tokenizing and then the parser builds the tuple structure out of the tokens. There’s no Abstract Syntax Tree or anything like that.


TODO: Symbols are just a string subclass; used by the parser to represent function names and by the interpreter to look up functions in the dictionary. N.B.: Symbols are not looked up at parse-time. You could define recursive functions, er, recusively, without genrec or other recursion combinators foo == ... foo ... but don’t do that.

Token Regular Expressions

123   1.2   'single quotes'  "double quotes"   function

TBD (look in the :module: joy.parser module.)


joy.parser.text_to_expression('1 2 3 4 5')  # A simple sequence.
(1, (2, (3, (4, (5, ())))))
joy.parser.text_to_expression('[1 2 3] 4 5')  # Three items, the first is a list with three items
((1, (2, (3, ()))), (4, (5, ())))
joy.parser.text_to_expression('1 23 ["four" [-5.0] cons] 8888')  # A mixed bag. cons is
                                                                 # a Symbol, no lookup at
                                                                 # parse-time.  Haiku docs.
(1, (23, (('four', ((-5.0, ()), (cons, ()))), (8888, ()))))
joy.parser.text_to_expression('[][][][][]')  # Five empty lists.
((), ((), ((), ((), ((), ())))))
joy.parser.text_to_expression('[[[[[]]]]]')  # Five nested lists.
((((((), ()), ()), ()), ()), ())


The Joy library of functions (aka commands, or “words” after Forth usage) encapsulates all the actual functionality (no pun intended) of the Joy system. There are simple functions such as addition add (or +, the library module supports aliases), and combinators which provide control-flow and higher-order operations.

Many of the functions are defined in Python, like dip:

print inspect.getsource(joy.library.dip)
def dip(stack, expression, dictionary):
  (quote, (x, stack)) = stack
  expression = x, expression
  return stack, pushback(quote, expression), dictionary

Some functions are defined in equations in terms of other functions. When the interpreter executes a definition function that function just pushes its body expression onto the pending expression (the continuation) and returns control to the interpreter.

print joy.library.definitions
second == rest first
third == rest rest first
product == 1 swap [*] step
swons == swap cons
swoncat == swap concat
flatten == [] swap [concat] step
unit == [] cons
quoted == [unit] dip
unquoted == [i] dip
enstacken == stack [clear] dip
disenstacken == ? [uncons ?] loop pop
? == dup truthy
dinfrirst == dip infra first
nullary == [stack] dinfrirst
unary == [stack [pop] dip] dinfrirst
binary == [stack [popop] dip] dinfrirst
ternary == [stack [popop pop] dip] dinfrirst
pam == [i] map
run == [] swap infra
sqr == dup mul
size == 0 swap [pop ++] step
cleave == [i] app2 [popd] dip
average == [sum 1.0 ] [size] cleave /
gcd == 1 [tuck modulus dup 0 >] loop pop
least_fraction == dup [gcd] infra [div] concat map
*fraction == [uncons] dip uncons [swap] dip concat [] infra [*] dip cons
fraction0 == concat [[swap] dip * [] dip] infra
down_to_zero == [0 >] [dup --] while
range_to_zero == unit [down_to_zero] infra
anamorphism == [pop []] swap [dip swons] genrec
range == [0 <=] [1 - dup] anamorphism
while == swap [nullary] cons dup dipd concat loop
dudipd == dup dipd
primrec == [i] genrec

Currently, there’s no function to add new definitions to the dictionary from “within” Joy code itself. Adding new definitions remains a meta-interpreter action. You have to do it yourself, in Python, and wash your hands afterward.

It would be simple enough to define one, but it would open the door to name binding and break the idea that all state is captured in the stack and expression. There’s an implicit standard dictionary that defines the actual semantics of the syntactic stack and expression datastructures (which only contain symbols, not the actual functions. Pickle some and see for yourself.)

“There should be only one.”

Which brings me to talking about one of my hopes and dreams for this notation: “There should be only one.” What I mean is that there should be one universal standard dictionary of commands, and all bespoke work done in a UI for purposes takes place by direct interaction and macros. There would be a Grand Refactoring biannually (two years, not six months, that’s semi-annually) where any new definitions factored out of the usage and macros of the previous time, along with new algorithms and such, were entered into the dictionary and posted to e.g. IPFS.

Code should not burgeon wildly, as it does today. The variety of code should map more-or-less to the well-factored variety of human computably-solvable problems. There shouldn’t be dozens of chat apps, JS frameworks, programming languages. It’s a waste of time, a fractal “thundering herd” attack on human mentality.

Literary Code Library

If you read over the other notebooks you’ll see that developing code in Joy is a lot like doing simple mathematics, and the descriptions of the code resemble math papers. The code also works the first time, no bugs. If you have any experience programming at all, you are probably skeptical, as I was, but it seems to work: deriving code mathematically seems to lead to fewer errors.

But my point now is that this great ratio of textual explanation to wind up with code that consists of a few equations and could fit on an index card is highly desirable. Less code has fewer errors. The structure of Joy engenders a kind of thinking that seems to be very effective for developing structured processes.

There seems to be an elegance and power to the notation.