Joypy

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. Glue language with loads of libraries.

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.


 <-top

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

joy?

Stacks (aka list, quote, sequence, etc.)

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.

In [1]:
import inspect
import joy.utils.stack


print inspect.getdoc(joy.utils.stack)

When talking about Joy we use the terms "stack", "quote", "sequence",
"list", and others to mean the same thing: a simple linear datatype that
permits certain operations such as iterating and pushing and popping
values from (at least) one end.

There is no "Stack" Python class, instead we use the  `cons list`_, a 
venerable two-tuple recursive sequence datastructure, where the
empty tuple ``()`` is the empty stack and ``(head, rest)`` gives the recursive
form of a stack with one or more items on it::

    stack := () | (item, stack)

Putting some numbers onto a stack::

    ()
    (1, ())
    (2, (1, ()))
    (3, (2, (1, ())))
    ...

Python has very nice "tuple packing and unpacking" in its syntax which
means we can directly "unpack" the expected arguments to a Joy function.

For example::

        def dup((head, tail)):
                return head, (head, tail)

We replace the argument "stack" by the expected structure of the stack,
in this case "(head, tail)", and Python takes care of unpacking the
incoming tuple and assigning values to the names.  (Note that Python
syntax doesn't require parentheses around tuples used in expressions
where they would be redundant.)

Unfortunately, the Sphinx documentation generator, which is used to generate this
web page, doesn't handle tuples in the function parameters.  And in Python 3, this
syntax was removed entirely.  Instead you would have to write::

        def dup(stack):
                head, tail = stack
                return head, (head, tail)


We have two very simple functions, one to build up a stack from a Python
iterable and another to iterate through a stack and yield its items
one-by-one in order.  There are also two functions to generate string representations
of stacks.  They only differ in that one prints the terms in stack from left-to-right while the other prints from right-to-left.  In both functions *internal stacks* are
printed left-to-right.  These functions are written to support :doc:`../pretty`.

.. _cons list: https://en.wikipedia.org/wiki/Cons#Lists

The utility functions maintain order.

The 0th item in the list will be on the top of the stack and vise versa.

In [2]:
joy.utils.stack.list_to_stack([1, 2, 3])
Out[2]:
(1, (2, (3, ())))
In [3]:
list(joy.utils.stack.iter_stack((1, (2, (3, ())))))
Out[3]:
[1, 2, 3]

This requires reversing the sequence (or iterating backwards) otherwise:

In [4]:
stack = ()

for n in [1, 2, 3]:
    stack = n, stack

print stack
print list(joy.utils.stack.iter_stack(stack))

(3, (2, (1, ())))
[3, 2, 1]

Purely Functional Datastructures.

Because Joy lists are made out of Python tuples they are immutable, so all Joy datastructures are purely functional.

The joy() function.

An Interpreter

The joy() 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 it looks up in the dictionary.

Each function is passed the stack, expression, and dictionary and returns them. Whatever the function returns becomes the new stack, expression, and dictionary. (The dictionary is passed to enable e.g. writing words that let you enter new words into the dictionary at runtime, which nothing does yet and may be a bad idea, and the help command.)

In [5]:
import joy.joy

print inspect.getsource(joy.joy.joy)

def joy(stack, expression, dictionary, viewer=None):
	'''Evaluate a Joy expression on a stack.

	This function iterates through a sequence of terms which are either
	literals (strings, numbers, sequences of terms) or function symbols.
	Literals are put onto the stack and functions are looked up in the
	disctionary and executed.

	The viewer is a function that is called with the stack and expression
	on every iteration, its return value is ignored.

	:param stack stack: The stack.
	:param stack expression: The expression to evaluate.
	:param dict dictionary: A ``dict`` mapping names to Joy functions.
	:param function viewer: Optional viewer function.
	:rtype: (stack, (), dictionary)

	'''
	while expression:

		if viewer: viewer(stack, expression)

		term, expression = expression
		if isinstance(term, Symbol):
			term = dictionary[term]
			stack, expression, dictionary = term(stack, expression, dictionary)
		else:
			stack = term, stack

	if viewer: viewer(stack, expression)
	return stack, expression, dictionary

View function

The joy() function accepts a "viewer" 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.

Continuation-Passing Style

One day I thought, What happens if you rewrite Joy to use CSP? 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.

Parser

In [6]:
import joy.parser

print inspect.getdoc(joy.parser)

This module exports a single function for converting text to a joy
expression as well as a single Symbol class and a single Exception type.

The Symbol string class is used by the interpreter to recognize literals
by the fact that they are not Symbol objects.

A crude grammar::

    joy = term*
    term = int | float | string | '[' joy ']' | symbol

A Joy expression is a sequence of zero or more terms.  A term is a
literal value (integer, float, string, or Joy expression) or a function
symbol.  Function symbols are unquoted strings and cannot contain square
brackets.   Terms must be separated by blanks, which can be omitted
around square brackets.

The parser is extremely simple, the undocumented re.Scanner class does most of the tokenizing work and then you just build the tuple structure out of the tokens. There's no Abstract Syntax Tree or anything like that.

In [7]:
print inspect.getsource(joy.parser._parse)

def _parse(tokens):
	'''
	Return a stack/list expression of the tokens.
	'''
	frame = []
	stack = []
	for tok in tokens:
		if tok == '[':
			stack.append(frame)
			frame = []
			stack[-1].append(frame)
		elif tok == ']':
			try:
				frame = stack.pop()
			except IndexError:
				raise ParseError('Extra closing bracket.')
			frame[-1] = list_to_stack(frame[-1])
		else:
			frame.append(tok)
	if stack:
		raise ParseError('Unclosed bracket.')
	return list_to_stack(frame)

That's pretty much all there is to it.

In [8]:
joy.parser.text_to_expression('1 2 3 4 5')  # A simple sequence.
Out[8]:
(1, (2, (3, (4, (5, ())))))
In [9]:
joy.parser.text_to_expression('[1 2 3] 4 5')  # Three items, the first is a list with three items
Out[9]:
((1, (2, (3, ()))), (4, (5, ())))
In [10]:
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.
Out[10]:
(1, (23, (('four', ((-5.0, ()), (cons, ()))), (8888, ()))))
In [11]:
joy.parser.text_to_expression('[][][][][]')  # Five empty lists.
Out[11]:
((), ((), ((), ((), ((), ())))))
In [12]:
joy.parser.text_to_expression('[[[[[]]]]]')  # Five nested lists.
Out[12]:
((((((), ()), ()), ()), ()), ())

Library

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.

In [13]:
import joy.library

print ' '.join(sorted(joy.library.initialize()))

!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infer infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swons take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •

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

In [14]:
print inspect.getsource(joy.library.dip)

@inscribe
@combinator_effect(_COMB_NUMS(), a1, s1)
@FunctionWrapper
def dip(stack, expression, dictionary):
	'''
	The dip combinator expects a quoted program on the stack and below it
	some item, it hoists the item into the expression and runs the program
	on the rest of the stack.
	::

			 ... x [Q] dip
		-------------------
				 ... Q x

	'''
	(quote, (x, stack)) = stack
	expression = (x, expression)
	return stack, concat(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.

In [15]:
print joy.library.definitions

ii == [dip] dupdip i
of == swap at
product == 1 swap [*] step
flatten == [] swap [concat] step
quoted == [unit] dip
unquoted == [i] dip
enstacken == stack [clear] dip
? == dup truthy
disenstacken == ? [uncons ?] loop pop
dinfrirst == dip infra first
nullary == [stack] dinfrirst
unary == nullary popd
binary == nullary [popop] dip
ternary == unary [popop] dip
pam == [i] map
run == [] swap infra
sqr == dup mul
size == 0 swap [pop ++] step
fork == [i] app2
cleave == fork [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
dupdipd == dup dipd
primrec == [i] genrec
step_zero == 0 roll> step
codireco == cons dip rest cons
make_generator == [codireco] ccons
ifte == [nullary not] dipd branch

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.

In [ ]: