Thun/docs/0._This_Implementation_of_Joy_in_Python.ipynb

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.

Documentation of Stack Module

The utility functions maintain order.

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

In [1]:

from joy.utils.stack import iter_stack, list_to_stack

In [2]:

list_to_stack([1, 2, 3])

Out [2]:

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

In [3]:

list(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(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.)

Documentation of Joy Module

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 [5]:

from joy.parser import text_to_expression

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.

A simple sequence.

In [6]:

text_to_expression('1 2 3 4 5')

Out [6]:

(1, (2, (3, (4, (5, ())))))

Three items, the first is a list with three items

In [7]:

text_to_expression('[1 2 3] 4 5')

Out [7]:

((1, (2, (3, ()))), (4, (5, ())))

A mixed bag.

In [8]:

text_to_expression('1 23 ["four" [-5.0] cons] 8888')

Out [8]:

(1, (23, (("four", ((-5.0, ()), (cons, ()))), (8888, ()))))

Five empty lists.

In [9]:

text_to_expression('[][][][][]')

Out [9]:

((), ((), ((), ((), ((), ())))))

Five nested lists.

In [10]:

text_to_expression('[[[[[]]]]]')

Out [10]:

((((((), ()), ()), ()), ()), ())

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 [11]:

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 div divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd gcd2 ge genrec getitem gt help i id ifte ii 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 swoncat swons tailrec take ternary third times 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 [12]:

import inspect

In [13]:

print(inspect.getdoc(joy.library.dip))

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

The code (I was using inspect.getsource() here to automatically print the souce but it was not as nice-looking that way due to lack of syntax highlighting and the docstring being too long for the width of the element and wrapping in an ungainly way. SO now, instead, I'm just including it as a Python cell in the notebook):

In [14]:

def dip(stack, expression, dictionary):
    try:
        (quote, (x, stack)) = stack
    except ValueError:
        raise StackUnderflowError('Not enough values on stack.')
    return stack, concat(quote, (x, 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.

(Note that the embedded joy.library.definitions is going away in favor of a def.txt file that would be read in at start-time. See Ticket: thun-der#7)

In [15]:

print(joy.library.definitions)

? == dup truthy
*fraction == [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
*fraction0 == concat [[swap] dip * [*] dip] infra
anamorphism == [pop []] swap [dip swons] genrec
average == [sum 1.0 *] [size] cleave /
binary == nullary [popop] dip
cleave == fork [popd] dip
codireco == cons dip rest cons
dinfrirst == dip infra first
unstack == ? [uncons ?] loop pop
down_to_zero == [0 >] [dup --] while
dupdipd == dup dipd
enstacken == stack [clear] dip
flatten == [] swap [concat] step
fork == [i] app2
gcd == 1 [tuck modulus dup 0 >] loop pop
ifte == [nullary not] dipd branch
ii == [dip] dupdip i
least_fraction == dup [gcd] infra [div] concat map
make_generator == [codireco] ccons
nullary == [stack] dinfrirst
of == swap at
pam == [i] map
tailrec == [i] genrec
product == 1 swap [*] step
quoted == [unit] dip
range == [0 <=] [1 - dup] anamorphism
range_to_zero == unit [down_to_zero] infra
run == [] swap infra
size == 0 swap [pop ++] step
sqr == dup mul
step_zero == 0 roll> step
swoncat == swap concat
tailrec == [i] genrec
ternary == unary [popop] dip
unary == nullary popd
unquoted == [i] dip
while == swap [nullary] cons dup dipd concat loop

Currently, there's no function to add new definitions to the dictionary from "within" Joy code itself. (Actually there is, it's called inscribe, but don't use it, eh? :) 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.