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a/docs/sphinx_docs/_build/doctrees/stack.doctree b/docs/sphinx_docs/_build/doctrees/stack.doctree index c335e30..6ce8d34 100644 Binary files a/docs/sphinx_docs/_build/doctrees/stack.doctree and b/docs/sphinx_docs/_build/doctrees/stack.doctree differ diff --git a/docs/sphinx_docs/_build/doctrees/types.doctree b/docs/sphinx_docs/_build/doctrees/types.doctree index b207837..dbb3caf 100644 Binary files a/docs/sphinx_docs/_build/doctrees/types.doctree and b/docs/sphinx_docs/_build/doctrees/types.doctree differ diff --git a/docs/sphinx_docs/_build/html/_modules/index.html b/docs/sphinx_docs/_build/html/_modules/index.html index a09f508..9ee35ef 100644 --- a/docs/sphinx_docs/_build/html/_modules/index.html +++ b/docs/sphinx_docs/_build/html/_modules/index.html @@ -102,7 +102,7 @@
Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/_modules/joy/library.html b/docs/sphinx_docs/_build/html/_modules/joy/library.html index 389391f..da257c6 100644 --- a/docs/sphinx_docs/_build/html/_modules/joy/library.html +++ b/docs/sphinx_docs/_build/html/_modules/joy/library.html @@ -94,7 +94,7 @@ %s ----- end (%s) +---- end ( %s ) ''' @@ -260,15 +260,6 @@ return stack, expression, dictionary -
[docs]@inscribe -@SimpleFunctionWrapper -def parse(stack): - '''Parse the string on the stack to a Joy expression.''' - text, stack = stack - expression = text_to_expression(text) - return expression, stack
- - # @inscribe # @SimpleFunctionWrapper # def infer_(stack): @@ -373,19 +364,18 @@ Use a Boolean value to select one of two items. :: - A B False choice + A B false choice ---------------------- A - A B True choice + A B true choice --------------------- B - Currently Python semantics are used to evaluate the "truthiness" of the - Boolean value (so empty string, zero, etc. are counted as false, etc.) ''' (if_, (then, (else_, stack))) = stack + assert isinstance(if_, bool), repr(if_) return then if if_ else else_, stack @@ -396,12 +386,12 @@ Use a Boolean value to select one of two items from a sequence. :: - [A B] False select + [A B] false select ------------------------ A - [A B] True select + [A B] true select ----------------------- B @@ -625,9 +615,9 @@ Return the tuple (x//y, x%y). Invariant: q * y + r == x. ''' - a, (b, stack) = S - d, m = divmod(a, b) - return d, (m, stack) + y, (x, stack) = S + q, r = divmod(x, y) + return r, (q, stack)
[docs]def sqrt(a): @@ -1482,7 +1472,7 @@
Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0.
diff --git a/docs/sphinx_docs/_build/html/_modules/joy/parser.html b/docs/sphinx_docs/_build/html/_modules/joy/parser.html index 46f58ec..153d3de 100644 --- a/docs/sphinx_docs/_build/html/_modules/joy/parser.html +++ b/docs/sphinx_docs/_build/html/_modules/joy/parser.html @@ -71,6 +71,11 @@ ''' from re import Scanner from .utils.stack import list_to_stack +from .utils.snippets import ( + pat as SNIPPETS, + from_string, + Snippet, + ) BRACKETS = r'\[|\]' @@ -79,6 +84,7 @@ token_scanner = Scanner([ + (SNIPPETS, lambda _, token: from_string(token)), (BRACKETS, lambda _, token: token), (BLANKS, None), (WORDS, lambda _, token: token), @@ -138,20 +144,16 @@ v = frame try: frame = stack.pop() except IndexError: - raise ParseError('Extra closing bracket.') + raise ParseError('Extra closing bracket.') from None frame.append(list_to_stack(v)) - elif tok == 'true': - frame.append(True) - elif tok == 'false': - frame.append(False) + elif tok == 'true': frame.append(True) + elif tok == 'false': frame.append(False) + elif isinstance(tok, Snippet): frame.append(tok) else: - try: - thing = int(tok) - except ValueError: - thing = Symbol(tok) + try: thing = int(tok) + except ValueError: thing = Symbol(tok) frame.append(thing) - if stack: - raise ParseError('Unclosed bracket.') + if stack: raise ParseError('Unclosed bracket.') return list_to_stack(frame) @@ -220,7 +222,7 @@
Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html b/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html index 945bc10..b9fa764 100644 --- a/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html +++ b/docs/sphinx_docs/_build/html/_modules/joy/utils/stack.html @@ -104,6 +104,7 @@ ''' from .errors import NotAListError +from .snippets import Snippet, to_string as snip_to_string
[docs]def list_to_stack(el, stack=()): @@ -162,24 +163,28 @@ return _to_string(expression, iter_stack)
-_JOY_BOOL_LITS = 'false', 'true' +JOY_BOOL_LITERALS = 'false', 'true' def _joy_repr(thing): - if isinstance(thing, bool): - return _JOY_BOOL_LITS[thing] - return repr(thing) + if isinstance(thing, bool): return JOY_BOOL_LITERALS[thing] + if isinstance(thing, Snippet): return snip_to_string(thing) + return repr(thing) def _to_string(stack, f): if not isinstance(stack, tuple): return _joy_repr(stack) if not stack: return '' # shortcut + if isinstance(stack, Snippet): return snip_to_string(stack) return ' '.join(map(_s, f(stack))) _s = lambda s: ( '[%s]' % expression_to_string(s) if isinstance(s, tuple) + and not isinstance(s, Snippet) + # Is it worth making a non-tuple class for Snippet? + # Doing this check on each tuple seems a bit much. else _joy_repr(s) ) @@ -351,7 +356,7 @@
Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/_static/basic.css b/docs/sphinx_docs/_build/html/_static/basic.css index 603f6a8..ac9a52a 100644 --- a/docs/sphinx_docs/_build/html/_static/basic.css +++ b/docs/sphinx_docs/_build/html/_static/basic.css @@ -66,6 +66,10 @@ div.sphinxsidebar ul { list-style: none; } +div.sphinxsidebar li { + padding-bottom: 0.5em; +} + div.sphinxsidebar ul ul, div.sphinxsidebar ul.want-points { margin-left: 20px; diff --git a/docs/sphinx_docs/_build/html/_static/doctools.js b/docs/sphinx_docs/_build/html/_static/doctools.js index 8cbf1b1..e509e48 100644 --- a/docs/sphinx_docs/_build/html/_static/doctools.js +++ b/docs/sphinx_docs/_build/html/_static/doctools.js @@ -4,7 +4,7 @@ * * Sphinx JavaScript utilities for all documentation. * - * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ @@ -264,6 +264,9 @@ var Documentation = { hideSearchWords : function() { $('#searchbox .highlight-link').fadeOut(300); $('span.highlighted').removeClass('highlighted'); + var url = new URL(window.location); + url.searchParams.delete('highlight'); + window.history.replaceState({}, '', url); }, /** diff --git a/docs/sphinx_docs/_build/html/_static/language_data.js b/docs/sphinx_docs/_build/html/_static/language_data.js index 863704b..ebe2f03 100644 --- a/docs/sphinx_docs/_build/html/_static/language_data.js +++ b/docs/sphinx_docs/_build/html/_static/language_data.js @@ -5,7 +5,7 @@ * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. * - * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ diff --git a/docs/sphinx_docs/_build/html/_static/pygments.css b/docs/sphinx_docs/_build/html/_static/pygments.css index f346859..691aeb8 100644 --- a/docs/sphinx_docs/_build/html/_static/pygments.css +++ b/docs/sphinx_docs/_build/html/_static/pygments.css @@ -1,7 +1,7 @@ -pre { line-height: 125%; margin: 0; } -td.linenos pre { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; } -span.linenos { color: #000000; background-color: #f0f0f0; padding-left: 5px; padding-right: 5px; } -td.linenos pre.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } +pre { line-height: 125%; } +td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } +span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } +td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } .highlight .hll { background-color: #ffffcc } .highlight { background: #eeffcc; } diff --git a/docs/sphinx_docs/_build/html/_static/searchtools.js b/docs/sphinx_docs/_build/html/_static/searchtools.js index 002e9c4..2d77859 100644 --- a/docs/sphinx_docs/_build/html/_static/searchtools.js +++ b/docs/sphinx_docs/_build/html/_static/searchtools.js @@ -4,7 +4,7 @@ * * Sphinx JavaScript utilities for the full-text search. * - * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ diff --git a/docs/sphinx_docs/_build/html/genindex.html b/docs/sphinx_docs/_build/html/genindex.html index ce6c14b..f1bedb1 100644 --- a/docs/sphinx_docs/_build/html/genindex.html +++ b/docs/sphinx_docs/_build/html/genindex.html @@ -326,8 +326,6 @@

P

    -
  • parse() (in module joy.library) -
  • ParseError
  • pick() (in module joy.utils.stack) @@ -570,7 +568,7 @@
    Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/index.html b/docs/sphinx_docs/_build/html/index.html index a8eb5af..ca81a00 100644 --- a/docs/sphinx_docs/_build/html/index.html +++ b/docs/sphinx_docs/_build/html/index.html @@ -256,7 +256,7 @@ interesting aspects. It’s quite a treasure trove.


    Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/joy.html b/docs/sphinx_docs/_build/html/joy.html index 4a5a08e..20854d5 100644 --- a/docs/sphinx_docs/_build/html/joy.html +++ b/docs/sphinx_docs/_build/html/joy.html @@ -191,7 +191,7 @@ on every iteration, its return value is ignored.


    Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/lib.html b/docs/sphinx_docs/_build/html/lib.html index 03f9a10..1e59f3a 100644 --- a/docs/sphinx_docs/_build/html/lib.html +++ b/docs/sphinx_docs/_build/html/lib.html @@ -1333,7 +1333,7 @@ soley of containers, without strings or numbers or anything else.)


    Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/. - Created using Sphinx 4.3.0. + Created using Sphinx 4.4.0. diff --git a/docs/sphinx_docs/_build/html/library.html b/docs/sphinx_docs/_build/html/library.html index 1325405..63e7a53 100644 --- a/docs/sphinx_docs/_build/html/library.html +++ b/docs/sphinx_docs/_build/html/library.html @@ -150,18 +150,16 @@ program.

    joy.library.choice(stack)[source]

    Use a Boolean value to select one of two items.

    -
       A B False choice
+
       A B false choice
 ----------------------
    A
 
 
-   A B True choice
+   A B true choice
 ---------------------
      B
 
    
 
    
-
    Currently Python semantics are used to evaluate the “truthiness” of the
-Boolean value (so empty string, zero, etc. are counted as false, etc.)
    @@ -449,7 +447,7 @@ with the list as its stack. Does not affect the rest of the stack.

    -joy.library.inscribe(function, d={'!=': <function ne>, '%': <function mod>, '&': <function and_>, '*': <function mul>, '+': <function add>, '++': <function succ>, '-': <function sub>, '--': <function pred>, '/': <function floordiv>, '//': <function floordiv>, '/floor': <function floordiv>, '<': <function lt>, '<<': <function lshift>, '<=': <function le>, '<>': <function ne>, '=': <function eq>, '>': <function gt>, '>=': <function ge>, '>>': <function rshift>, '^': <function xor>, '_Tree_add_Ee': <function _Tree_add_Ee>, '_Tree_delete_R0': <function _Tree_delete_R0>, '_Tree_delete_clear_stuff': <function _Tree_delete_clear_stuff>, '_Tree_get_E': <function _Tree_get_E>, 'abs': <function abs>, 'add': <function add>, 'and': <function and_>, 'app1': <function app1>, 'app2': <function app2>, 'app3': <function app3>, 'at': <function getitem>, 'b': <function b>, 'bool': <function bool>, 'branch': <function branch>, 'ccons': <function ccons>, 'choice': <function choice>, 'clear': <function clear>, 'cmp': <function cmp_>, 'concat': <function concat_>, 'cond': <function cond>, 'cons': <function cons>, 'dip': <function dip>, 'dipd': <function dipd>, 'dipdd': <function dipdd>, 'disenstacken': <function disenstacken>, 'div': <function floordiv>, 'divmod': <function divmod_>, 'drop': <function drop>, 'dup': <function dup>, 'dupd': <function dupd>, 'dupdd': <function dupdd>, 'dupdip': <function dupdip>, 'eq': <function eq>, 'first': <function first>, 'first_two': <function first_two>, 'floor': <function floor>, 'floordiv': <function floordiv>, 'fourth': <function fourth>, 'gcd2': <function gcd2>, 'ge': <function ge>, 'genrec': <function genrec>, 'getitem': <function getitem>, 'gt': <function gt>, 'help': <function help_>, 'i': <function i>, 'id': <function id_>, 'ifte': <function ifte>, 'ii': <function ii>, 'infra': <function infra>, 'inscribe': <function inscribe_>, 'le': <function le>, 'loop': <function loop>, 'lshift': <function lshift>, 'lt': <function lt>, 'map': <function map_>, 'max': <function max_>, 'min': <function min_>, 'mod': <function mod>, 'modulus': <function mod>, 'mul': <function mul>, 'ne': <function ne>, 'neg': <function neg>, 'not': <function not_>, 'or': <function or_>, 'over': <function over>, 'parse': <function parse>, 'pick': <function getitem>, 'pm': <function pm>, 'pop': <function pop>, 'popd': <function popd>, 'popdd': <function popdd>, 'popop': <function popop>, 'popopd': <function popopd>, 'popopdd': <function popopdd>, 'pow': <function pow>, 'pred': <function pred>, 'primrec': <function primrec>, 'rem': <function mod>, 'remainder': <function mod>, 'remove': <function remove>, 'rest': <function rest>, 'reverse': <function reverse>, 'roll<': <function rolldown>, 'roll>': <function rollup>, 'rolldown': <function rolldown>, 'rollup': <function rollup>, 'round': <function round>, 'rrest': <function rrest>, 'rshift': <function rshift>, 'second': <function second>, 'select': <function select>, 'sharing': <function sharing>, 'shunt': <function shunt>, 'sort': <function sort_>, 'sqrt': <function sqrt>, 'stack': <function stack>, 'step': <function step>, 'stuncons': <function stuncons>, 'stununcons': <function stununcons>, 'sub': <function sub>, 'succ': <function succ>, 'sum': <function sum_>, 'swaack': <function swaack>, 'swap': <function swap>, 'swons': <function swons>, 'take': <function take>, 'third': <function third>, 'times': <function times>, 'truthy': <function bool>, 'tuck': <function tuck>, 'uncons': <function uncons>, 'unique': <function unique>, 'unit': <function unit>, 'unswons': <function unswons>, 'void': <function void>, 'warranty': <function warranty>, 'words': <function words>, 'x': <function x>, 'xor': <function xor>, 'zip': <function zip_>, '•': <function id_>})[source]
    +joy.library.inscribe(function, d={'!=': <function ne>, '%': <function mod>, '&': <function and_>, '*': <function mul>, '+': <function add>, '++': <function succ>, '-': <function sub>, '--': <function pred>, '/': <function floordiv>, '//': <function floordiv>, '/floor': <function floordiv>, '<': <function lt>, '<<': <function lshift>, '<=': <function le>, '<>': <function ne>, '=': <function eq>, '>': <function gt>, '>=': <function ge>, '>>': <function rshift>, '^': <function xor>, '_Tree_add_Ee': <function _Tree_add_Ee>, '_Tree_delete_R0': <function _Tree_delete_R0>, '_Tree_delete_clear_stuff': <function _Tree_delete_clear_stuff>, '_Tree_get_E': <function _Tree_get_E>, 'abs': <function abs>, 'add': <function add>, 'and': <function and_>, 'app1': <function app1>, 'app2': <function app2>, 'app3': <function app3>, 'at': <function getitem>, 'b': <function b>, 'bool': <function bool>, 'branch': <function branch>, 'ccons': <function ccons>, 'choice': <function choice>, 'clear': <function clear>, 'cmp': <function cmp_>, 'concat': <function concat_>, 'cond': <function cond>, 'cons': <function cons>, 'dip': <function dip>, 'dipd': <function dipd>, 'dipdd': <function dipdd>, 'disenstacken': <function disenstacken>, 'div': <function floordiv>, 'divmod': <function divmod_>, 'drop': <function drop>, 'dup': <function dup>, 'dupd': <function dupd>, 'dupdd': <function dupdd>, 'dupdip': <function dupdip>, 'eq': <function eq>, 'first': <function first>, 'first_two': <function first_two>, 'floor': <function floor>, 'floordiv': <function floordiv>, 'fourth': <function fourth>, 'gcd2': <function gcd2>, 'ge': <function ge>, 'genrec': <function genrec>, 'getitem': <function getitem>, 'gt': <function gt>, 'help': <function help_>, 'i': <function i>, 'id': <function id_>, 'ifte': <function ifte>, 'ii': <function ii>, 'infra': <function infra>, 'inscribe': <function inscribe_>, 'le': <function le>, 'loop': <function loop>, 'lshift': <function lshift>, 'lt': <function lt>, 'map': <function map_>, 'max': <function max_>, 'min': <function min_>, 'mod': <function mod>, 'modulus': <function mod>, 'mul': <function mul>, 'ne': <function ne>, 'neg': <function neg>, 'not': <function not_>, 'or': <function or_>, 'over': <function over>, 'pick': <function getitem>, 'pm': <function pm>, 'pop': <function pop>, 'popd': <function popd>, 'popdd': <function popdd>, 'popop': <function popop>, 'popopd': <function popopd>, 'popopdd': <function popopdd>, 'pow': <function pow>, 'pred': <function pred>, 'primrec': <function primrec>, 'rem': <function mod>, 'remainder': <function mod>, 'remove': <function remove>, 'rest': <function rest>, 'reverse': <function reverse>, 'roll<': <function rolldown>, 'roll>': <function rollup>, 'rolldown': <function rolldown>, 'rollup': <function rollup>, 'round': <function round>, 'rrest': <function rrest>, 'rshift': <function rshift>, 'second': <function second>, 'select': <function select>, 'sharing': <function sharing>, 'shunt': <function shunt>, 'sort': <function sort_>, 'sqrt': <function sqrt>, 'stack': <function stack>, 'step': <function step>, 'stuncons': <function stuncons>, 'stununcons': <function stununcons>, 'sub': <function sub>, 'succ': <function succ>, 'sum': <function sum_>, 'swaack': <function swaack>, 'swap': <function swap>, 'swons': <function swons>, 'take': <function take>, 'third': <function third>, 'times': <function times>, 'truthy': <function bool>, 'tuck': <function tuck>, 'uncons': <function uncons>, 'unique': <function unique>, 'unit': <function unit>, 'unswons': <function unswons>, 'void': <function void>, 'warranty': <function warranty>, 'words': <function words>, 'x': <function x>, 'xor': <function xor>, 'zip': <function zip_>, '•': <function id_>})[source]

    A decorator to inscribe functions into the default dictionary.

    @@ -498,12 +496,6 @@ new list with the results in place of the program and original list.

    Given a list find the minimum.

    -
    -
    -joy.library.parse(stack)[source]
    -

    Parse the string on the stack to a Joy expression.

    -
    -
    joy.library.pm(stack)[source]
    @@ -580,12 +572,12 @@ empty or the item isn’t in the list then the list is unchanged.

    joy.library.select(stack)[source]

    Use a Boolean value to select one of two items from a sequence.

    -
       [A B] False select
+
       [A B] false select
 ------------------------
     A
 
 
-   [A B] True select
+   [A B] true select
 -----------------------
       B
 
    
@@ -748,7 +740,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.ccons(stack)[source]
    
-
    (a2 a1 [...1] -- [a2 a1 ...1])
+
    (a2 a1 [...1] -- [a2 a1 ...1])
 
    
 
    
 
    
@@ -756,7 +748,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.cons(stack)[source]
    
-
    (a1 [...0] -- [a1 ...0])
+
    (a1 [...0] -- [a1 ...0])
 
    
 
    
 
    
@@ -788,7 +780,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.first(stack)[source]
    
-
    ([a1 ...1] -- a1)
+
    ([a1 ...1] -- a1)
 
    
 
    
 
    
@@ -796,7 +788,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.first_two(stack)[source]
    
-
    ([a1 a2 ...1] -- a1 a2)
+
    ([a1 a2 ...1] -- a1 a2)
 
    
 
    
 
    
@@ -804,7 +796,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.fourth(stack)[source]
    
-
    ([a1 a2 a3 a4 ...1] -- a4)
+
    ([a1 a2 a3 a4 ...1] -- a4)
 
    
 
    
 
    
@@ -868,7 +860,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.rest(stack)[source]
    
-
    ([a1 ...0] -- [...0])
+
    ([a1 ...0] -- [...0])
 
    
 
    
 
    
@@ -892,7 +884,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.rrest(stack)[source]
    
-
    ([a1 a2 ...1] -- [...1])
+
    ([a1 a2 ...1] -- [...1])
 
    
 
    
 
    
@@ -900,7 +892,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.second(stack)[source]
    
-
    ([a1 a2 ...1] -- a2)
+
    ([a1 a2 ...1] -- a2)
 
    
 
    
 
    
@@ -932,7 +924,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.swaack(stack)[source]
    
-
    ([...1] -- [...0])
+
    ([...1] -- [...0])
 
    
 
    
 
    
@@ -948,7 +940,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.swons(stack)[source]
    
-
    ([...1] a1 -- [a1 ...1])
+
    ([...1] a1 -- [a1 ...1])
 
    
 
    
 
    
@@ -956,7 +948,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.third(stack)[source]
    
-
    ([a1 a2 a3 ...1] -- a3)
+
    ([a1 a2 a3 ...1] -- a3)
 
    
 
    
 
    
@@ -972,7 +964,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.uncons(stack)[source]
    
-
    ([a1 ...0] -- a1 [...0])
+
    ([a1 ...0] -- a1 [...0])
 
    
 
    
 
    
@@ -988,7 +980,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
    
 
    
 joy.utils.generated_library.unswons(stack)[source]
    
-
    ([a1 ...1] -- [...1] a1)
+
    ([a1 ...1] -- [...1] a1)
 
    
 
    
 
    
@@ -1066,7 +1058,7 @@ from each list.  The smallest list sets the length of the result list.
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Categorical.html b/docs/sphinx_docs/_build/html/notebooks/Categorical.html
index 420e11c..7b2020f 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Categorical.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Categorical.html
@@ -80,6 +80,7 @@
 
  • Treating Trees II: treestep
    • 
 
  • Using x to Generate Values
    • 
 
  • Newton’s method
    • 
+
  • Square Spiral Example Joy Code
    • 
 
  • Traversing Datastructures with Zippers
    • 
 
  • The Blissful Elegance of Typing Joy
    • 
 
  • Type Checking
    • 
@@ -130,7 +131,7 @@
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
    diff --git a/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html b/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html index 34e24eb..fc0fd9c 100644 --- a/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html +++ b/docs/sphinx_docs/_build/html/notebooks/Derivatives_of_Regular_Expressions.html @@ -96,15 +96,15 @@ R∘λ = λ∘R = R

    Implementation

    -
    from functools import partial as curry
-from itertools import product
+
    from functools import partial as curry
+from itertools import product
 
    
 
    
 
    
 
    ϕ and λ
    
 
    The empty set and the set of just the empty string.
    
-
    phi = frozenset()   # ϕ
-y = frozenset({''}) # λ
+
    phi = frozenset()   # ϕ
+y = frozenset({''}) # λ
 
    
 
    
 
    
@@ -115,7 +115,7 @@ illustrate the algorithm and because you can represent any other
 alphabet with two symbols (if you had to.)
    
 
    I chose the names O and l (uppercase “o” and lowercase “L”) to
 look like 0 and 1 (zero and one) respectively.
    
-
    syms = O, l = frozenset({'0'}), frozenset({'1'})
+
    syms = O, l = frozenset({'0'}), frozenset({'1'})
    @@ -133,7 +133,7 @@ expression is one of:

    Where R and S stand for regular expressions.

    -
    AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split()  # Tags are just strings.
+
    AND, CONS, KSTAR, NOT, OR = 'and cons * not or'.split()  # Tags are just strings.
 
    
 
    
 
    Because they are formed of frozenset, tuple and str objects
@@ -141,36 +141,36 @@ only, these datastructures are immutable.
    
 
 
    
 
    String Representation of RE Datastructures
    
-
    def stringy(re):
-    '''
-    Return a nice string repr for a regular expression datastructure.
-    '''
-    if re == I: return '.'
-    if re in syms: return next(iter(re))
-    if re == y: return '^'
-    if re == phi: return 'X'
+
    def stringy(re):
+    '''
+    Return a nice string repr for a regular expression datastructure.
+    '''
+    if re == I: return '.'
+    if re in syms: return next(iter(re))
+    if re == y: return '^'
+    if re == phi: return 'X'
 
-    assert isinstance(re, tuple), repr(re)
-    tag = re[0]
+    assert isinstance(re, tuple), repr(re)
+    tag = re[0]
 
-    if tag == KSTAR:
-        body = stringy(re[1])
-        if not body: return body
-        if len(body) > 1: return '(' + body + ")*"
-        return body + '*'
+    if tag == KSTAR:
+        body = stringy(re[1])
+        if not body: return body
+        if len(body) > 1: return '(' + body + ")*"
+        return body + '*'
 
-    if tag == NOT:
-        body = stringy(re[1])
-        if not body: return body
-        if len(body) > 1: return '(' + body + ")'"
-        return body + "'"
+    if tag == NOT:
+        body = stringy(re[1])
+        if not body: return body
+        if len(body) > 1: return '(' + body + ")'"
+        return body + "'"
 
-    r, s = stringy(re[1]), stringy(re[2])
-    if tag == CONS: return r + s
-    if tag == OR:   return '%s | %s' % (r, s)
-    if tag == AND:  return '(%s) & (%s)' % (r, s)
+    r, s = stringy(re[1]), stringy(re[2])
+    if tag == CONS: return r + s
+    if tag == OR:   return '%s | %s' % (r, s)
+    if tag == AND:  return '(%s) & (%s)' % (r, s)
 
-    raise ValueError
+    raise ValueError
 
    
 
    
 
    
@@ -180,10 +180,10 @@ only, these datastructures are immutable.
    
 
    I = (0|1)*
 
    
 
    
-
    I = (KSTAR, (OR, O, l))
+
    I = (KSTAR, (OR, O, l))
 
    
 
    
-
    print stringy(I)
+
    print stringy(I)
 
    
 
    
 
    .
@@ -193,57 +193,57 @@ only, these datastructures are immutable.
    
 
    
 
    (.111.) & (.01 + 11*)'
    
 
    The example expression from Brzozowski:
    
-
    (.111.) & (.01 + 11*)'
+
    (.111.) & (.01 + 11*)'
    a    &  (b  +  c)'
 
    
 
    
 
    Note that it contains one of everything.
    
-
    a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I))))
-b = (CONS, I, (CONS, O, l))
-c = (CONS, l, (KSTAR, l))
-it = (AND, a, (NOT, (OR, b, c)))
+
    a = (CONS, I, (CONS, l, (CONS, l, (CONS, l, I))))
+b = (CONS, I, (CONS, O, l))
+c = (CONS, l, (KSTAR, l))
+it = (AND, a, (NOT, (OR, b, c)))
 
    
 
    
-
    print stringy(it)
+
    print stringy(it)
 
    
 
    
-
    (.111.) & ((.01 | 11*)')
+
    (.111.) & ((.01 | 11*)')
 
    
 
    
 
    
 
    
 
    nully()
    
 
    Let’s get that auxiliary predicate function δ out of the way.
    
-
    def nully(R):
-    '''
-    δ - Return λ if λ ⊆ R otherwise ϕ.
-    '''
+
    def nully(R):
+    '''
+    δ - Return λ if λ ⊆ R otherwise ϕ.
+    '''
 
-    # δ(a) → ϕ
-    # δ(ϕ) → ϕ
-    if R in syms or R == phi:
-        return phi
+    # δ(a) → ϕ
+    # δ(ϕ) → ϕ
+    if R in syms or R == phi:
+        return phi
 
-    # δ(λ) → λ
-    if R == y:
-        return y
+    # δ(λ) → λ
+    if R == y:
+        return y
 
-    tag = R[0]
+    tag = R[0]
 
-    # δ(R*) → λ
-    if tag == KSTAR:
-        return y
+    # δ(R*) → λ
+    if tag == KSTAR:
+        return y
 
-    # δ(¬R) δ(R)≟ϕ → λ
-    # δ(¬R) δ(R)≟λ → ϕ
-    if tag == NOT:
-        return phi if nully(R[1]) else y
+    # δ(¬R) δ(R)≟ϕ → λ
+    # δ(¬R) δ(R)≟λ → ϕ
+    if tag == NOT:
+        return phi if nully(R[1]) else y
 
-    # δ(R∘S) → δ(R) ∧ δ(S)
-    # δ(R ∧ S) → δ(R) ∧ δ(S)
-    # δ(R ∨ S) → δ(R) ∨ δ(S)
-    r, s = nully(R[1]), nully(R[2])
-    return r & s if tag in {AND, CONS} else r | s
+    # δ(R∘S) → δ(R) ∧ δ(S)
+    # δ(R ∧ S) → δ(R) ∧ δ(S)
+    # δ(R ∨ S) → δ(R) ∨ δ(S)
+    r, s = nully(R[1]), nully(R[2])
+    return r & s if tag in {AND, CONS} else r | s
 
    
 
    
 
    
@@ -252,71 +252,71 @@ only, these datastructures are immutable.
    
 
    This is the straightforward version with no “compaction”. It works fine,
 but does waaaay too much work because the expressions grow each
 derivation.
    
-
    def D(symbol):
+
    def D(symbol):
 
-    def derv(R):
+    def derv(R):
 
-        # ∂a(a) → λ
-        if R == {symbol}:
-            return y
+        # ∂a(a) → λ
+        if R == {symbol}:
+            return y
 
-        # ∂a(λ) → ϕ
-        # ∂a(ϕ) → ϕ
-        # ∂a(¬a) → ϕ
-        if R == y or R == phi or R in syms:
-            return phi
+        # ∂a(λ) → ϕ
+        # ∂a(ϕ) → ϕ
+        # ∂a(¬a) → ϕ
+        if R == y or R == phi or R in syms:
+            return phi
 
-        tag = R[0]
+        tag = R[0]
 
-        # ∂a(R*) → ∂a(R)∘R*
-        if tag == KSTAR:
-            return (CONS, derv(R[1]), R)
+        # ∂a(R*) → ∂a(R)∘R*
+        if tag == KSTAR:
+            return (CONS, derv(R[1]), R)
 
-        # ∂a(¬R) → ¬∂a(R)
-        if tag == NOT:
-            return (NOT, derv(R[1]))
+        # ∂a(¬R) → ¬∂a(R)
+        if tag == NOT:
+            return (NOT, derv(R[1]))
 
-        r, s = R[1:]
+        r, s = R[1:]
 
-        # ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
-        if tag == CONS:
-            A = (CONS, derv(r), s)  # A = ∂a(R)∘S
-            # A ∨ δ(R) ∘ ∂a(S)
-            # A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)
-            # A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A
-            return (OR, A, derv(s)) if nully(r) else A
+        # ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
+        if tag == CONS:
+            A = (CONS, derv(r), s)  # A = ∂a(R)∘S
+            # A ∨ δ(R) ∘ ∂a(S)
+            # A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)
+            # A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A
+            return (OR, A, derv(s)) if nully(r) else A
 
-        # ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
-        # ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
-        return (tag, derv(r), derv(s))
+        # ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
+        # ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
+        return (tag, derv(r), derv(s))
 
-    return derv
+    return derv
 
    
 
    
 
 
    
 
    Compaction Rules
    
-
    def _compaction_rule(relation, one, zero, a, b):
-    return (
-        b if a == one else  # R*1 = 1*R = R
-        a if b == one else
-        zero if a == zero or b == zero else  # R*0 = 0*R = 0
-        (relation, a, b)
-        )
+
    def _compaction_rule(relation, one, zero, a, b):
+    return (
+        b if a == one else  # R*1 = 1*R = R
+        a if b == one else
+        zero if a == zero or b == zero else  # R*0 = 0*R = 0
+        (relation, a, b)
+        )
 
    
 
    
 
    An elegant symmetry.
    
-
    # R ∧ I = I ∧ R = R
-# R ∧ ϕ = ϕ ∧ R = ϕ
-_and = curry(_compaction_rule, AND, I, phi)
+
    # R ∧ I = I ∧ R = R
+# R ∧ ϕ = ϕ ∧ R = ϕ
+_and = curry(_compaction_rule, AND, I, phi)
 
-# R ∨ ϕ = ϕ ∨ R = R
-# R ∨ I = I ∨ R = I
-_or = curry(_compaction_rule, OR, phi, I)
+# R ∨ ϕ = ϕ ∨ R = R
+# R ∨ I = I ∨ R = I
+_or = curry(_compaction_rule, OR, phi, I)
 
-# R∘λ = λ∘R = R
-# R∘ϕ = ϕ∘R = ϕ
-_cons = curry(_compaction_rule, CONS, y, phi)
+# R∘λ = λ∘R = R
+# R∘ϕ = ϕ∘R = ϕ
+_cons = curry(_compaction_rule, CONS, y, phi)
 
    
 
    
 
    
@@ -325,21 +325,21 @@ derivation.
    
 
    We can save re-processing by remembering results we have already
 computed. RE datastructures are immutable and the derv() functions
 are pure so this is fine.
    
-
    class Memo(object):
+
    class Memo(object):
 
-    def __init__(self, f):
-        self.f = f
-        self.calls = self.hits = 0
-        self.mem = {}
+    def __init__(self, f):
+        self.f = f
+        self.calls = self.hits = 0
+        self.mem = {}
 
-    def __call__(self, key):
-        self.calls += 1
-        try:
-            result = self.mem[key]
-            self.hits += 1
-        except KeyError:
-            result = self.mem[key] = self.f(key)
-        return result
+    def __call__(self, key):
+        self.calls += 1
+        try:
+            result = self.mem[key]
+            self.hits += 1
+        except KeyError:
+            result = self.mem[key] = self.f(key)
+        return result
 
    
 
    
 
@@ -347,47 +347,47 @@ are pure so this is fine.
    
 
    With “Compaction”
    
 
    This version uses the rules above to perform compaction. It keeps the
 expressions from growing too large.
    
-
    def D_compaction(symbol):
+
    def D_compaction(symbol):
 
-    @Memo
-    def derv(R):
+    @Memo
+    def derv(R):
 
-        # ∂a(a) → λ
-        if R == {symbol}:
-            return y
+        # ∂a(a) → λ
+        if R == {symbol}:
+            return y
 
-        # ∂a(λ) → ϕ
-        # ∂a(ϕ) → ϕ
-        # ∂a(¬a) → ϕ
-        if R == y or R == phi or R in syms:
-            return phi
+        # ∂a(λ) → ϕ
+        # ∂a(ϕ) → ϕ
+        # ∂a(¬a) → ϕ
+        if R == y or R == phi or R in syms:
+            return phi
 
-        tag = R[0]
+        tag = R[0]
 
-        # ∂a(R*) → ∂a(R)∘R*
-        if tag == KSTAR:
-            return _cons(derv(R[1]), R)
+        # ∂a(R*) → ∂a(R)∘R*
+        if tag == KSTAR:
+            return _cons(derv(R[1]), R)
 
-        # ∂a(¬R) → ¬∂a(R)
-        if tag == NOT:
-            return (NOT, derv(R[1]))
+        # ∂a(¬R) → ¬∂a(R)
+        if tag == NOT:
+            return (NOT, derv(R[1]))
 
-        r, s = R[1:]
+        r, s = R[1:]
 
-        # ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
-        if tag == CONS:
-            A = _cons(derv(r), s)  # A = ∂a(r)∘s
-            # A ∨ δ(R) ∘ ∂a(S)
-            # A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)
-            # A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A
-            return _or(A, derv(s)) if nully(r) else A
+        # ∂a(R∘S) → ∂a(R)∘S ∨ δ(R)∘∂a(S)
+        if tag == CONS:
+            A = _cons(derv(r), s)  # A = ∂a(r)∘s
+            # A ∨ δ(R) ∘ ∂a(S)
+            # A ∨  λ   ∘ ∂a(S) → A ∨ ∂a(S)
+            # A ∨  ϕ   ∘ ∂a(S) → A ∨ ϕ → A
+            return _or(A, derv(s)) if nully(r) else A
 
-        # ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
-        # ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
-        dr, ds = derv(r), derv(s)
-        return _and(dr, ds) if tag == AND else _or(dr, ds)
+        # ∂a(R ∧ S) → ∂a(R) ∧ ∂a(S)
+        # ∂a(R ∨ S) → ∂a(R) ∨ ∂a(S)
+        dr, ds = derv(r), derv(s)
+        return _and(dr, ds) if tag == AND else _or(dr, ds)
 
-    return derv
+    return derv
 
    
 
    
 
@@ -395,59 +395,59 @@ expressions from growing too large.
    
 
    
 
    Let’s try it out…
    
 
    (FIXME: redo.)
    
-
    o, z = D_compaction('0'), D_compaction('1')
-REs = set()
-N = 5
-names = list(product(*(N * [(0, 1)])))
-dervs = list(product(*(N * [(o, z)])))
-for name, ds in zip(names, dervs):
-    R = it
-    ds = list(ds)
-    while ds:
-        R = ds.pop()(R)
-        if R == phi or R == I:
-            break
-        REs.add(R)
+
    o, z = D_compaction('0'), D_compaction('1')
+REs = set()
+N = 5
+names = list(product(*(N * [(0, 1)])))
+dervs = list(product(*(N * [(o, z)])))
+for name, ds in zip(names, dervs):
+    R = it
+    ds = list(ds)
+    while ds:
+        R = ds.pop()(R)
+        if R == phi or R == I:
+            break
+        REs.add(R)
 
-print stringy(it) ; print
-print o.hits, '/', o.calls
-print z.hits, '/', z.calls
-print
-for s in sorted(map(stringy, REs), key=lambda n: (len(n), n)):
-    print s
+print stringy(it) ; print
+print o.hits, '/', o.calls
+print z.hits, '/', z.calls
+print
+for s in sorted(map(stringy, REs), key=lambda n: (len(n), n)):
+    print s
 
    
 
    
-
    (.111.) & ((.01 | 11*)')
+
    (.111.) & ((.01 | 11*)')
 
 92 / 122
 92 / 122
 
-(.01)'
-(.01 | 1)'
-(.01 | ^)'
-(.01 | 1*)'
-(.111.) & ((.01 | 1)')
-(.111. | 11.) & ((.01 | ^)')
-(.111. | 11. | 1.) & ((.01)')
-(.111. | 11.) & ((.01 | 1*)')
-(.111. | 11. | 1.) & ((.01 | 1*)')
+(.01)'
+(.01 | 1)'
+(.01 | ^)'
+(.01 | 1*)'
+(.111.) & ((.01 | 1)')
+(.111. | 11.) & ((.01 | ^)')
+(.111. | 11. | 1.) & ((.01)')
+(.111. | 11.) & ((.01 | 1*)')
+(.111. | 11. | 1.) & ((.01 | 1*)')
 
    
 
    
 
    Should match:
    
-
    (.111.) & ((.01 | 11*)')
+
    (.111.) & ((.01 | 11*)')
 
 92 / 122
 92 / 122
 
-(.01     )'
-(.01 | 1 )'
-(.01 | ^ )'
-(.01 | 1*)'
-(.111.)            & ((.01 | 1 )')
-(.111. | 11.)      & ((.01 | ^ )')
-(.111. | 11.)      & ((.01 | 1*)')
-(.111. | 11. | 1.) & ((.01     )')
-(.111. | 11. | 1.) & ((.01 | 1*)')
+(.01     )'
+(.01 | 1 )'
+(.01 | ^ )'
+(.01 | 1*)'
+(.111.)            & ((.01 | 1 )')
+(.111. | 11.)      & ((.01 | ^ )')
+(.111. | 11.)      & ((.01 | 1*)')
+(.111. | 11. | 1.) & ((.01     )')
+(.111. | 11. | 1.) & ((.01 | 1*)')
 
    
 
    
 
    
@@ -495,7 +495,7 @@ for now.
    
 
    State Machine
    
 
    We can drive the regular expressions to flesh out the underlying state
 machine transition table.
    
-
    .111. & (.01 + 11*)'
+
    .111. & (.01 + 11*)'
 
    
 
    
 
    Says, “Three or more 1’s and not ending in 01 nor composed of all 1’s.”
    
@@ -540,60 +540,60 @@ a --1--> ∂1(a)
 
    
 
    And so on, each new unique RE is a new state in the FSM table.
    
 
    Here are the derived REs at each state:
    
-
    a = (.111.) & ((.01 | 11*)')
-b = (.111.) & ((.01 | 1)')
-c = (.111. | 11.) & ((.01 | 1*)')
-d = (.111. | 11.) & ((.01 | ^)')
-e = (.111. | 11. | 1.) & ((.01 | 1*)')
-f = (.111. | 11. | 1.) & ((.01)')
-g = (.01 | 1*)'
-h = (.01)'
-i = (.01 | 1)'
-j = (.01 | ^)'
+
    a = (.111.) & ((.01 | 11*)')
+b = (.111.) & ((.01 | 1)')
+c = (.111. | 11.) & ((.01 | 1*)')
+d = (.111. | 11.) & ((.01 | ^)')
+e = (.111. | 11. | 1.) & ((.01 | 1*)')
+f = (.111. | 11. | 1.) & ((.01)')
+g = (.01 | 1*)'
+h = (.01)'
+i = (.01 | 1)'
+j = (.01 | ^)'
 
    
 
    
 
    You can see the one-way nature of the g state and the hij “trap”
 in the way that the .111. on the left-hand side of the &
 disappears once it has been matched.
    
-
    from collections import defaultdict
-from pprint import pprint
-from string import ascii_lowercase
+
    from collections import defaultdict
+from pprint import pprint
+from string import ascii_lowercase
 
    
 
    
-
    d0, d1 = D_compaction('0'), D_compaction('1')
+
    d0, d1 = D_compaction('0'), D_compaction('1')
 
    
 
    
 
 
    
 
    explore()
    
-
    def explore(re):
+
    def explore(re):
 
-    # Don't have more than 26 states...
-    names = defaultdict(iter(ascii_lowercase).next)
+    # Don't have more than 26 states...
+    names = defaultdict(iter(ascii_lowercase).next)
 
-    table, accepting = dict(), set()
+    table, accepting = dict(), set()
 
-    to_check = {re}
-    while to_check:
+    to_check = {re}
+    while to_check:
 
-        re = to_check.pop()
-        state_name = names[re]
+        re = to_check.pop()
+        state_name = names[re]
 
-        if (state_name, 0) in table:
-            continue
+        if (state_name, 0) in table:
+            continue
 
-        if nully(re):
-            accepting.add(state_name)
+        if nully(re):
+            accepting.add(state_name)
 
-        o, i = d0(re), d1(re)
-        table[state_name, 0] = names[o] ; to_check.add(o)
-        table[state_name, 1] = names[i] ; to_check.add(i)
+        o, i = d0(re), d1(re)
+        table[state_name, 0] = names[o] ; to_check.add(o)
+        table[state_name, 1] = names[i] ; to_check.add(i)
 
-    return table, accepting
+    return table, accepting
 
    
 
    
-
    table, accepting = explore(it)
-table
+
    table, accepting = explore(it)
+table
 
    
 
    
 
    {('a', 0): 'b',
@@ -618,7 +618,7 @@ disappears once it has been matched.
    
  ('j', 1): 'h'}
 
    
 
    
-
    accepting
+
    accepting
 
    
 
    
 
    {'h', 'i'}
@@ -629,31 +629,31 @@ disappears once it has been matched.
    
 
    Generate Diagram
    
 
    Once we have the FSM table and the set of accepting states we can
 generate the diagram above.
    
-
    _template = '''\
-digraph finite_state_machine {
-  rankdir=LR;
-  size="8,5"
-  node [shape = doublecircle]; %s;
-  node [shape = circle];
-%s
-}
-'''
+
    _template = '''\
+digraph finite_state_machine {
+  rankdir=LR;
+  size="8,5"
+  node [shape = doublecircle]; %s;
+  node [shape = circle];
+%s
+}
+'''
 
-def link(fr, nm, label):
-    return '  %s -> %s [ label = "%s" ];' % (fr, nm, label)
+def link(fr, nm, label):
+    return '  %s -> %s [ label = "%s" ];' % (fr, nm, label)
 
 
-def make_graph(table, accepting):
-    return _template % (
-        ' '.join(accepting),
-        '\n'.join(
-          link(from_, to, char)
-          for (from_, char), (to) in sorted(table.iteritems())
-          )
-        )
+def make_graph(table, accepting):
+    return _template % (
+        ' '.join(accepting),
+        '\n'.join(
+          link(from_, to, char)
+          for (from_, char), (to) in sorted(table.iteritems())
+          )
+        )
 
    
 
    
-
    print make_graph(table, accepting)
+
    print make_graph(table, accepting)
 
    
 
    
 
    digraph finite_state_machine {
@@ -699,14 +699,14 @@ hard-code the information in the table into a little patch of branches.
    
 
    Trampoline Function
    
 
    Python has no GOTO statement but we can fake it with a “trampoline”
 function.
    
-
    def trampoline(input_, jump_from, accepting):
-    I = iter(input_)
-    while True:
-        try:
-            bounce_to = jump_from(I)
-        except StopIteration:
-            return jump_from in accepting
-        jump_from = bounce_to
+
    def trampoline(input_, jump_from, accepting):
+    I = iter(input_)
+    while True:
+        try:
+            bounce_to = jump_from(I)
+        except StopIteration:
+            return jump_from in accepting
+        jump_from = bounce_to
 
    
 
    
 
    
@@ -714,17 +714,17 @@ function.
    
 
    Stream Functions
    
 
    Little helpers to process the iterator of our data (a “stream” of “1”
 and “0” characters, not bits.)
    
-
    getch = lambda I: int(next(I))
+
    getch = lambda I: int(next(I))
 
 
-def _1(I):
-    '''Loop on ones.'''
-    while getch(I): pass
+def _1(I):
+    '''Loop on ones.'''
+    while getch(I): pass
 
 
-def _0(I):
-    '''Loop on zeros.'''
-    while not getch(I): pass
+def _0(I):
+    '''Loop on zeros.'''
+    while not getch(I): pass
 
    
 
    
 
@@ -735,28 +735,28 @@ and “0” characters, not bits.)
    
 code. (You have to imagine that these are GOTO statements in C or
 branches in assembly and that the state names are branch destination
 labels.)
    
-
    a = lambda I: c if getch(I) else b
-b = lambda I: _0(I) or d
-c = lambda I: e if getch(I) else b
-d = lambda I: f if getch(I) else b
-e = lambda I: g if getch(I) else b
-f = lambda I: h if getch(I) else b
-g = lambda I: _1(I) or i
-h = lambda I: _1(I) or i
-i = lambda I: _0(I) or j
-j = lambda I: h if getch(I) else i
+
    a = lambda I: c if getch(I) else b
+b = lambda I: _0(I) or d
+c = lambda I: e if getch(I) else b
+d = lambda I: f if getch(I) else b
+e = lambda I: g if getch(I) else b
+f = lambda I: h if getch(I) else b
+g = lambda I: _1(I) or i
+h = lambda I: _1(I) or i
+i = lambda I: _0(I) or j
+j = lambda I: h if getch(I) else i
 
    
 
    
 
    Note that the implementations of h and g are identical ergo
 h = g and we could eliminate one in the code but h is an
 accepting state and g isn’t.
    
-
    def acceptable(input_):
-    return trampoline(input_, a, {h, i})
+
    def acceptable(input_):
+    return trampoline(input_, a, {h, i})
 
    
 
    
-
    for n in range(2**5):
-    s = bin(n)[2:]
-    print '%05s' % s, acceptable(s)
+
    for n in range(2**5):
+    s = bin(n)[2:]
+    print '%05s' % s, acceptable(s)
 
    
 
    
 
        0 False
@@ -928,7 +928,7 @@ derivative-with-respect-to-N of some other state/RE:
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Developing.html b/docs/sphinx_docs/_build/html/notebooks/Developing.html
index 164db0d..6a2808e 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Developing.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Developing.html
@@ -13,7 +13,7 @@
     
     
     
-    
+    
     
     
     
@@ -113,7 +113,7 @@ these differences to the counter one-by-one in a loop.
    
 go we need a function that will accept the sum, the counter, and the
 next term to add, and that adds the term to the counter and a copy of
 the counter to the running sum. This function will do that:
    
-
    PE1.1 == + [+] dupdip
+
    PE1.1 == + [+] dupdip
 
    
 
    
 
    define('PE1.1 == + [+] dupdip')
@@ -122,10 +122,10 @@ the counter to the running sum. This function will do that:
    
 
    V('0 0 3 PE1.1')
 
    
 
    
-
            . 0 0 3 PE1.1
-      0 . 0 3 PE1.1
-    0 0 . 3 PE1.1
-  0 0 3 . PE1.1
+
            . 0 0 3 PE1.1
+      0 . 0 3 PE1.1
+    0 0 . 3 PE1.1
+  0 0 3 . PE1.1
   0 0 3 . + [+] dupdip
     0 3 . [+] dupdip
 0 3 [+] . dupdip
@@ -137,73 +137,73 @@ the counter to the running sum. This function will do that:
    
 
    V('0 0 [3 2 1 3 1 2 3] [PE1.1] step')
 
    
 
    
-
                                . 0 0 [3 2 1 3 1 2 3] [PE1.1] step
-                          0 . 0 [3 2 1 3 1 2 3] [PE1.1] step
-                        0 0 . [3 2 1 3 1 2 3] [PE1.1] step
-        0 0 [3 2 1 3 1 2 3] . [PE1.1] step
-0 0 [3 2 1 3 1 2 3] [PE1.1] . step
-              0 0 3 [PE1.1] . i [2 1 3 1 2 3] [PE1.1] step
-                      0 0 3 . PE1.1 [2 1 3 1 2 3] [PE1.1] step
-                      0 0 3 . + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
-                        0 3 . [+] dupdip [2 1 3 1 2 3] [PE1.1] step
-                    0 3 [+] . dupdip [2 1 3 1 2 3] [PE1.1] step
-                        0 3 . + 3 [2 1 3 1 2 3] [PE1.1] step
-                          3 . 3 [2 1 3 1 2 3] [PE1.1] step
-                        3 3 . [2 1 3 1 2 3] [PE1.1] step
-          3 3 [2 1 3 1 2 3] . [PE1.1] step
-  3 3 [2 1 3 1 2 3] [PE1.1] . step
-              3 3 2 [PE1.1] . i [1 3 1 2 3] [PE1.1] step
-                      3 3 2 . PE1.1 [1 3 1 2 3] [PE1.1] step
-                      3 3 2 . + [+] dupdip [1 3 1 2 3] [PE1.1] step
-                        3 5 . [+] dupdip [1 3 1 2 3] [PE1.1] step
-                    3 5 [+] . dupdip [1 3 1 2 3] [PE1.1] step
-                        3 5 . + 5 [1 3 1 2 3] [PE1.1] step
-                          8 . 5 [1 3 1 2 3] [PE1.1] step
-                        8 5 . [1 3 1 2 3] [PE1.1] step
-            8 5 [1 3 1 2 3] . [PE1.1] step
-    8 5 [1 3 1 2 3] [PE1.1] . step
-              8 5 1 [PE1.1] . i [3 1 2 3] [PE1.1] step
-                      8 5 1 . PE1.1 [3 1 2 3] [PE1.1] step
-                      8 5 1 . + [+] dupdip [3 1 2 3] [PE1.1] step
-                        8 6 . [+] dupdip [3 1 2 3] [PE1.1] step
-                    8 6 [+] . dupdip [3 1 2 3] [PE1.1] step
-                        8 6 . + 6 [3 1 2 3] [PE1.1] step
-                         14 . 6 [3 1 2 3] [PE1.1] step
-                       14 6 . [3 1 2 3] [PE1.1] step
-             14 6 [3 1 2 3] . [PE1.1] step
-     14 6 [3 1 2 3] [PE1.1] . step
-             14 6 3 [PE1.1] . i [1 2 3] [PE1.1] step
-                     14 6 3 . PE1.1 [1 2 3] [PE1.1] step
-                     14 6 3 . + [+] dupdip [1 2 3] [PE1.1] step
-                       14 9 . [+] dupdip [1 2 3] [PE1.1] step
-                   14 9 [+] . dupdip [1 2 3] [PE1.1] step
-                       14 9 . + 9 [1 2 3] [PE1.1] step
-                         23 . 9 [1 2 3] [PE1.1] step
-                       23 9 . [1 2 3] [PE1.1] step
-               23 9 [1 2 3] . [PE1.1] step
-       23 9 [1 2 3] [PE1.1] . step
-             23 9 1 [PE1.1] . i [2 3] [PE1.1] step
-                     23 9 1 . PE1.1 [2 3] [PE1.1] step
-                     23 9 1 . + [+] dupdip [2 3] [PE1.1] step
-                      23 10 . [+] dupdip [2 3] [PE1.1] step
-                  23 10 [+] . dupdip [2 3] [PE1.1] step
-                      23 10 . + 10 [2 3] [PE1.1] step
-                         33 . 10 [2 3] [PE1.1] step
-                      33 10 . [2 3] [PE1.1] step
-                33 10 [2 3] . [PE1.1] step
-        33 10 [2 3] [PE1.1] . step
-            33 10 2 [PE1.1] . i [3] [PE1.1] step
-                    33 10 2 . PE1.1 [3] [PE1.1] step
-                    33 10 2 . + [+] dupdip [3] [PE1.1] step
-                      33 12 . [+] dupdip [3] [PE1.1] step
-                  33 12 [+] . dupdip [3] [PE1.1] step
-                      33 12 . + 12 [3] [PE1.1] step
-                         45 . 12 [3] [PE1.1] step
-                      45 12 . [3] [PE1.1] step
-                  45 12 [3] . [PE1.1] step
-          45 12 [3] [PE1.1] . step
-            45 12 3 [PE1.1] . i
-                    45 12 3 . PE1.1
+
                                . 0 0 [3 2 1 3 1 2 3] [PE1.1] step
+                          0 . 0 [3 2 1 3 1 2 3] [PE1.1] step
+                        0 0 . [3 2 1 3 1 2 3] [PE1.1] step
+        0 0 [3 2 1 3 1 2 3] . [PE1.1] step
+0 0 [3 2 1 3 1 2 3] [PE1.1] . step
+              0 0 3 [PE1.1] . i [2 1 3 1 2 3] [PE1.1] step
+                      0 0 3 . PE1.1 [2 1 3 1 2 3] [PE1.1] step
+                      0 0 3 . + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
+                        0 3 . [+] dupdip [2 1 3 1 2 3] [PE1.1] step
+                    0 3 [+] . dupdip [2 1 3 1 2 3] [PE1.1] step
+                        0 3 . + 3 [2 1 3 1 2 3] [PE1.1] step
+                          3 . 3 [2 1 3 1 2 3] [PE1.1] step
+                        3 3 . [2 1 3 1 2 3] [PE1.1] step
+          3 3 [2 1 3 1 2 3] . [PE1.1] step
+  3 3 [2 1 3 1 2 3] [PE1.1] . step
+              3 3 2 [PE1.1] . i [1 3 1 2 3] [PE1.1] step
+                      3 3 2 . PE1.1 [1 3 1 2 3] [PE1.1] step
+                      3 3 2 . + [+] dupdip [1 3 1 2 3] [PE1.1] step
+                        3 5 . [+] dupdip [1 3 1 2 3] [PE1.1] step
+                    3 5 [+] . dupdip [1 3 1 2 3] [PE1.1] step
+                        3 5 . + 5 [1 3 1 2 3] [PE1.1] step
+                          8 . 5 [1 3 1 2 3] [PE1.1] step
+                        8 5 . [1 3 1 2 3] [PE1.1] step
+            8 5 [1 3 1 2 3] . [PE1.1] step
+    8 5 [1 3 1 2 3] [PE1.1] . step
+              8 5 1 [PE1.1] . i [3 1 2 3] [PE1.1] step
+                      8 5 1 . PE1.1 [3 1 2 3] [PE1.1] step
+                      8 5 1 . + [+] dupdip [3 1 2 3] [PE1.1] step
+                        8 6 . [+] dupdip [3 1 2 3] [PE1.1] step
+                    8 6 [+] . dupdip [3 1 2 3] [PE1.1] step
+                        8 6 . + 6 [3 1 2 3] [PE1.1] step
+                         14 . 6 [3 1 2 3] [PE1.1] step
+                       14 6 . [3 1 2 3] [PE1.1] step
+             14 6 [3 1 2 3] . [PE1.1] step
+     14 6 [3 1 2 3] [PE1.1] . step
+             14 6 3 [PE1.1] . i [1 2 3] [PE1.1] step
+                     14 6 3 . PE1.1 [1 2 3] [PE1.1] step
+                     14 6 3 . + [+] dupdip [1 2 3] [PE1.1] step
+                       14 9 . [+] dupdip [1 2 3] [PE1.1] step
+                   14 9 [+] . dupdip [1 2 3] [PE1.1] step
+                       14 9 . + 9 [1 2 3] [PE1.1] step
+                         23 . 9 [1 2 3] [PE1.1] step
+                       23 9 . [1 2 3] [PE1.1] step
+               23 9 [1 2 3] . [PE1.1] step
+       23 9 [1 2 3] [PE1.1] . step
+             23 9 1 [PE1.1] . i [2 3] [PE1.1] step
+                     23 9 1 . PE1.1 [2 3] [PE1.1] step
+                     23 9 1 . + [+] dupdip [2 3] [PE1.1] step
+                      23 10 . [+] dupdip [2 3] [PE1.1] step
+                  23 10 [+] . dupdip [2 3] [PE1.1] step
+                      23 10 . + 10 [2 3] [PE1.1] step
+                         33 . 10 [2 3] [PE1.1] step
+                      33 10 . [2 3] [PE1.1] step
+                33 10 [2 3] . [PE1.1] step
+        33 10 [2 3] [PE1.1] . step
+            33 10 2 [PE1.1] . i [3] [PE1.1] step
+                    33 10 2 . PE1.1 [3] [PE1.1] step
+                    33 10 2 . + [+] dupdip [3] [PE1.1] step
+                      33 12 . [+] dupdip [3] [PE1.1] step
+                  33 12 [+] . dupdip [3] [PE1.1] step
+                      33 12 . + 12 [3] [PE1.1] step
+                         45 . 12 [3] [PE1.1] step
+                      45 12 . [3] [PE1.1] step
+                  45 12 [3] . [PE1.1] step
+          45 12 [3] [PE1.1] . step
+            45 12 3 [PE1.1] . i
+                    45 12 3 . PE1.1
                     45 12 3 . + [+] dupdip
                       45 15 . [+] dupdip
                   45 15 [+] . dupdip
@@ -279,15 +279,15 @@ integer terms from the list.
    
 
    V('0 0 14811 PE1.2')
 
    
 
    
-
                          . 0 0 14811 PE1.2
-                    0 . 0 14811 PE1.2
-                  0 0 . 14811 PE1.2
-            0 0 14811 . PE1.2
-            0 0 14811 . [3 & PE1.1] dupdip 2 >>
-0 0 14811 [3 & PE1.1] . dupdip 2 >>
-            0 0 14811 . 3 & PE1.1 14811 2 >>
-          0 0 14811 3 . & PE1.1 14811 2 >>
-                0 0 3 . PE1.1 14811 2 >>
+
                          . 0 0 14811 PE1.2
+                    0 . 0 14811 PE1.2
+                  0 0 . 14811 PE1.2
+            0 0 14811 . PE1.2
+            0 0 14811 . [3 & PE1.1] dupdip 2 >>
+0 0 14811 [3 & PE1.1] . dupdip 2 >>
+            0 0 14811 . 3 & PE1.1 14811 2 >>
+          0 0 14811 3 . & PE1.1 14811 2 >>
+                0 0 3 . PE1.1 14811 2 >>
                 0 0 3 . + [+] dupdip 14811 2 >>
                   0 3 . [+] dupdip 14811 2 >>
               0 3 [+] . dupdip 14811 2 >>
@@ -302,15 +302,15 @@ integer terms from the list.
    
 
    V('3 3 3702 PE1.2')
 
    
 
    
-
                         . 3 3 3702 PE1.2
-                   3 . 3 3702 PE1.2
-                 3 3 . 3702 PE1.2
-            3 3 3702 . PE1.2
-            3 3 3702 . [3 & PE1.1] dupdip 2 >>
-3 3 3702 [3 & PE1.1] . dupdip 2 >>
-            3 3 3702 . 3 & PE1.1 3702 2 >>
-          3 3 3702 3 . & PE1.1 3702 2 >>
-               3 3 2 . PE1.1 3702 2 >>
+
                         . 3 3 3702 PE1.2
+                   3 . 3 3702 PE1.2
+                 3 3 . 3702 PE1.2
+            3 3 3702 . PE1.2
+            3 3 3702 . [3 & PE1.1] dupdip 2 >>
+3 3 3702 [3 & PE1.1] . dupdip 2 >>
+            3 3 3702 . 3 & PE1.1 3702 2 >>
+          3 3 3702 3 . & PE1.1 3702 2 >>
+               3 3 2 . PE1.1 3702 2 >>
                3 3 2 . + [+] dupdip 3702 2 >>
                  3 5 . [+] dupdip 3702 2 >>
              3 5 [+] . dupdip 3702 2 >>
@@ -325,127 +325,127 @@ integer terms from the list.
    
 
    V('0 0 14811 7 [PE1.2] times pop')
 
    
 
    
-
                          . 0 0 14811 7 [PE1.2] times pop
-                    0 . 0 14811 7 [PE1.2] times pop
-                  0 0 . 14811 7 [PE1.2] times pop
-            0 0 14811 . 7 [PE1.2] times pop
-          0 0 14811 7 . [PE1.2] times pop
-  0 0 14811 7 [PE1.2] . times pop
-    0 0 14811 [PE1.2] . i 6 [PE1.2] times pop
-            0 0 14811 . PE1.2 6 [PE1.2] times pop
-            0 0 14811 . [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
-0 0 14811 [3 & PE1.1] . dupdip 2 >> 6 [PE1.2] times pop
-            0 0 14811 . 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
-          0 0 14811 3 . & PE1.1 14811 2 >> 6 [PE1.2] times pop
-                0 0 3 . PE1.1 14811 2 >> 6 [PE1.2] times pop
-                0 0 3 . + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
-                  0 3 . [+] dupdip 14811 2 >> 6 [PE1.2] times pop
-              0 3 [+] . dupdip 14811 2 >> 6 [PE1.2] times pop
-                  0 3 . + 3 14811 2 >> 6 [PE1.2] times pop
-                    3 . 3 14811 2 >> 6 [PE1.2] times pop
-                  3 3 . 14811 2 >> 6 [PE1.2] times pop
-            3 3 14811 . 2 >> 6 [PE1.2] times pop
-          3 3 14811 2 . >> 6 [PE1.2] times pop
-             3 3 3702 . 6 [PE1.2] times pop
-           3 3 3702 6 . [PE1.2] times pop
-   3 3 3702 6 [PE1.2] . times pop
-     3 3 3702 [PE1.2] . i 5 [PE1.2] times pop
-             3 3 3702 . PE1.2 5 [PE1.2] times pop
-             3 3 3702 . [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
- 3 3 3702 [3 & PE1.1] . dupdip 2 >> 5 [PE1.2] times pop
-             3 3 3702 . 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
-           3 3 3702 3 . & PE1.1 3702 2 >> 5 [PE1.2] times pop
-                3 3 2 . PE1.1 3702 2 >> 5 [PE1.2] times pop
-                3 3 2 . + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
-                  3 5 . [+] dupdip 3702 2 >> 5 [PE1.2] times pop
-              3 5 [+] . dupdip 3702 2 >> 5 [PE1.2] times pop
-                  3 5 . + 5 3702 2 >> 5 [PE1.2] times pop
-                    8 . 5 3702 2 >> 5 [PE1.2] times pop
-                  8 5 . 3702 2 >> 5 [PE1.2] times pop
-             8 5 3702 . 2 >> 5 [PE1.2] times pop
-           8 5 3702 2 . >> 5 [PE1.2] times pop
-              8 5 925 . 5 [PE1.2] times pop
-            8 5 925 5 . [PE1.2] times pop
-    8 5 925 5 [PE1.2] . times pop
-      8 5 925 [PE1.2] . i 4 [PE1.2] times pop
-              8 5 925 . PE1.2 4 [PE1.2] times pop
-              8 5 925 . [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
-  8 5 925 [3 & PE1.1] . dupdip 2 >> 4 [PE1.2] times pop
-              8 5 925 . 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
-            8 5 925 3 . & PE1.1 925 2 >> 4 [PE1.2] times pop
-                8 5 1 . PE1.1 925 2 >> 4 [PE1.2] times pop
-                8 5 1 . + [+] dupdip 925 2 >> 4 [PE1.2] times pop
-                  8 6 . [+] dupdip 925 2 >> 4 [PE1.2] times pop
-              8 6 [+] . dupdip 925 2 >> 4 [PE1.2] times pop
-                  8 6 . + 6 925 2 >> 4 [PE1.2] times pop
-                   14 . 6 925 2 >> 4 [PE1.2] times pop
-                 14 6 . 925 2 >> 4 [PE1.2] times pop
-             14 6 925 . 2 >> 4 [PE1.2] times pop
-           14 6 925 2 . >> 4 [PE1.2] times pop
-             14 6 231 . 4 [PE1.2] times pop
-           14 6 231 4 . [PE1.2] times pop
-   14 6 231 4 [PE1.2] . times pop
-     14 6 231 [PE1.2] . i 3 [PE1.2] times pop
-             14 6 231 . PE1.2 3 [PE1.2] times pop
-             14 6 231 . [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
- 14 6 231 [3 & PE1.1] . dupdip 2 >> 3 [PE1.2] times pop
-             14 6 231 . 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
-           14 6 231 3 . & PE1.1 231 2 >> 3 [PE1.2] times pop
-               14 6 3 . PE1.1 231 2 >> 3 [PE1.2] times pop
-               14 6 3 . + [+] dupdip 231 2 >> 3 [PE1.2] times pop
-                 14 9 . [+] dupdip 231 2 >> 3 [PE1.2] times pop
-             14 9 [+] . dupdip 231 2 >> 3 [PE1.2] times pop
-                 14 9 . + 9 231 2 >> 3 [PE1.2] times pop
-                   23 . 9 231 2 >> 3 [PE1.2] times pop
-                 23 9 . 231 2 >> 3 [PE1.2] times pop
-             23 9 231 . 2 >> 3 [PE1.2] times pop
-           23 9 231 2 . >> 3 [PE1.2] times pop
-              23 9 57 . 3 [PE1.2] times pop
-            23 9 57 3 . [PE1.2] times pop
-    23 9 57 3 [PE1.2] . times pop
-      23 9 57 [PE1.2] . i 2 [PE1.2] times pop
-              23 9 57 . PE1.2 2 [PE1.2] times pop
-              23 9 57 . [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
-  23 9 57 [3 & PE1.1] . dupdip 2 >> 2 [PE1.2] times pop
-              23 9 57 . 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
-            23 9 57 3 . & PE1.1 57 2 >> 2 [PE1.2] times pop
-               23 9 1 . PE1.1 57 2 >> 2 [PE1.2] times pop
-               23 9 1 . + [+] dupdip 57 2 >> 2 [PE1.2] times pop
-                23 10 . [+] dupdip 57 2 >> 2 [PE1.2] times pop
-            23 10 [+] . dupdip 57 2 >> 2 [PE1.2] times pop
-                23 10 . + 10 57 2 >> 2 [PE1.2] times pop
-                   33 . 10 57 2 >> 2 [PE1.2] times pop
-                33 10 . 57 2 >> 2 [PE1.2] times pop
-             33 10 57 . 2 >> 2 [PE1.2] times pop
-           33 10 57 2 . >> 2 [PE1.2] times pop
-             33 10 14 . 2 [PE1.2] times pop
-           33 10 14 2 . [PE1.2] times pop
-   33 10 14 2 [PE1.2] . times pop
-     33 10 14 [PE1.2] . i 1 [PE1.2] times pop
-             33 10 14 . PE1.2 1 [PE1.2] times pop
-             33 10 14 . [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
- 33 10 14 [3 & PE1.1] . dupdip 2 >> 1 [PE1.2] times pop
-             33 10 14 . 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
-           33 10 14 3 . & PE1.1 14 2 >> 1 [PE1.2] times pop
-              33 10 2 . PE1.1 14 2 >> 1 [PE1.2] times pop
-              33 10 2 . + [+] dupdip 14 2 >> 1 [PE1.2] times pop
-                33 12 . [+] dupdip 14 2 >> 1 [PE1.2] times pop
-            33 12 [+] . dupdip 14 2 >> 1 [PE1.2] times pop
-                33 12 . + 12 14 2 >> 1 [PE1.2] times pop
-                   45 . 12 14 2 >> 1 [PE1.2] times pop
-                45 12 . 14 2 >> 1 [PE1.2] times pop
-             45 12 14 . 2 >> 1 [PE1.2] times pop
-           45 12 14 2 . >> 1 [PE1.2] times pop
-              45 12 3 . 1 [PE1.2] times pop
-            45 12 3 1 . [PE1.2] times pop
-    45 12 3 1 [PE1.2] . times pop
-      45 12 3 [PE1.2] . i pop
-              45 12 3 . PE1.2 pop
-              45 12 3 . [3 & PE1.1] dupdip 2 >> pop
-  45 12 3 [3 & PE1.1] . dupdip 2 >> pop
-              45 12 3 . 3 & PE1.1 3 2 >> pop
-            45 12 3 3 . & PE1.1 3 2 >> pop
-              45 12 3 . PE1.1 3 2 >> pop
+
                          . 0 0 14811 7 [PE1.2] times pop
+                    0 . 0 14811 7 [PE1.2] times pop
+                  0 0 . 14811 7 [PE1.2] times pop
+            0 0 14811 . 7 [PE1.2] times pop
+          0 0 14811 7 . [PE1.2] times pop
+  0 0 14811 7 [PE1.2] . times pop
+    0 0 14811 [PE1.2] . i 6 [PE1.2] times pop
+            0 0 14811 . PE1.2 6 [PE1.2] times pop
+            0 0 14811 . [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
+0 0 14811 [3 & PE1.1] . dupdip 2 >> 6 [PE1.2] times pop
+            0 0 14811 . 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
+          0 0 14811 3 . & PE1.1 14811 2 >> 6 [PE1.2] times pop
+                0 0 3 . PE1.1 14811 2 >> 6 [PE1.2] times pop
+                0 0 3 . + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
+                  0 3 . [+] dupdip 14811 2 >> 6 [PE1.2] times pop
+              0 3 [+] . dupdip 14811 2 >> 6 [PE1.2] times pop
+                  0 3 . + 3 14811 2 >> 6 [PE1.2] times pop
+                    3 . 3 14811 2 >> 6 [PE1.2] times pop
+                  3 3 . 14811 2 >> 6 [PE1.2] times pop
+            3 3 14811 . 2 >> 6 [PE1.2] times pop
+          3 3 14811 2 . >> 6 [PE1.2] times pop
+             3 3 3702 . 6 [PE1.2] times pop
+           3 3 3702 6 . [PE1.2] times pop
+   3 3 3702 6 [PE1.2] . times pop
+     3 3 3702 [PE1.2] . i 5 [PE1.2] times pop
+             3 3 3702 . PE1.2 5 [PE1.2] times pop
+             3 3 3702 . [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
+ 3 3 3702 [3 & PE1.1] . dupdip 2 >> 5 [PE1.2] times pop
+             3 3 3702 . 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
+           3 3 3702 3 . & PE1.1 3702 2 >> 5 [PE1.2] times pop
+                3 3 2 . PE1.1 3702 2 >> 5 [PE1.2] times pop
+                3 3 2 . + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
+                  3 5 . [+] dupdip 3702 2 >> 5 [PE1.2] times pop
+              3 5 [+] . dupdip 3702 2 >> 5 [PE1.2] times pop
+                  3 5 . + 5 3702 2 >> 5 [PE1.2] times pop
+                    8 . 5 3702 2 >> 5 [PE1.2] times pop
+                  8 5 . 3702 2 >> 5 [PE1.2] times pop
+             8 5 3702 . 2 >> 5 [PE1.2] times pop
+           8 5 3702 2 . >> 5 [PE1.2] times pop
+              8 5 925 . 5 [PE1.2] times pop
+            8 5 925 5 . [PE1.2] times pop
+    8 5 925 5 [PE1.2] . times pop
+      8 5 925 [PE1.2] . i 4 [PE1.2] times pop
+              8 5 925 . PE1.2 4 [PE1.2] times pop
+              8 5 925 . [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
+  8 5 925 [3 & PE1.1] . dupdip 2 >> 4 [PE1.2] times pop
+              8 5 925 . 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
+            8 5 925 3 . & PE1.1 925 2 >> 4 [PE1.2] times pop
+                8 5 1 . PE1.1 925 2 >> 4 [PE1.2] times pop
+                8 5 1 . + [+] dupdip 925 2 >> 4 [PE1.2] times pop
+                  8 6 . [+] dupdip 925 2 >> 4 [PE1.2] times pop
+              8 6 [+] . dupdip 925 2 >> 4 [PE1.2] times pop
+                  8 6 . + 6 925 2 >> 4 [PE1.2] times pop
+                   14 . 6 925 2 >> 4 [PE1.2] times pop
+                 14 6 . 925 2 >> 4 [PE1.2] times pop
+             14 6 925 . 2 >> 4 [PE1.2] times pop
+           14 6 925 2 . >> 4 [PE1.2] times pop
+             14 6 231 . 4 [PE1.2] times pop
+           14 6 231 4 . [PE1.2] times pop
+   14 6 231 4 [PE1.2] . times pop
+     14 6 231 [PE1.2] . i 3 [PE1.2] times pop
+             14 6 231 . PE1.2 3 [PE1.2] times pop
+             14 6 231 . [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
+ 14 6 231 [3 & PE1.1] . dupdip 2 >> 3 [PE1.2] times pop
+             14 6 231 . 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
+           14 6 231 3 . & PE1.1 231 2 >> 3 [PE1.2] times pop
+               14 6 3 . PE1.1 231 2 >> 3 [PE1.2] times pop
+               14 6 3 . + [+] dupdip 231 2 >> 3 [PE1.2] times pop
+                 14 9 . [+] dupdip 231 2 >> 3 [PE1.2] times pop
+             14 9 [+] . dupdip 231 2 >> 3 [PE1.2] times pop
+                 14 9 . + 9 231 2 >> 3 [PE1.2] times pop
+                   23 . 9 231 2 >> 3 [PE1.2] times pop
+                 23 9 . 231 2 >> 3 [PE1.2] times pop
+             23 9 231 . 2 >> 3 [PE1.2] times pop
+           23 9 231 2 . >> 3 [PE1.2] times pop
+              23 9 57 . 3 [PE1.2] times pop
+            23 9 57 3 . [PE1.2] times pop
+    23 9 57 3 [PE1.2] . times pop
+      23 9 57 [PE1.2] . i 2 [PE1.2] times pop
+              23 9 57 . PE1.2 2 [PE1.2] times pop
+              23 9 57 . [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
+  23 9 57 [3 & PE1.1] . dupdip 2 >> 2 [PE1.2] times pop
+              23 9 57 . 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
+            23 9 57 3 . & PE1.1 57 2 >> 2 [PE1.2] times pop
+               23 9 1 . PE1.1 57 2 >> 2 [PE1.2] times pop
+               23 9 1 . + [+] dupdip 57 2 >> 2 [PE1.2] times pop
+                23 10 . [+] dupdip 57 2 >> 2 [PE1.2] times pop
+            23 10 [+] . dupdip 57 2 >> 2 [PE1.2] times pop
+                23 10 . + 10 57 2 >> 2 [PE1.2] times pop
+                   33 . 10 57 2 >> 2 [PE1.2] times pop
+                33 10 . 57 2 >> 2 [PE1.2] times pop
+             33 10 57 . 2 >> 2 [PE1.2] times pop
+           33 10 57 2 . >> 2 [PE1.2] times pop
+             33 10 14 . 2 [PE1.2] times pop
+           33 10 14 2 . [PE1.2] times pop
+   33 10 14 2 [PE1.2] . times pop
+     33 10 14 [PE1.2] . i 1 [PE1.2] times pop
+             33 10 14 . PE1.2 1 [PE1.2] times pop
+             33 10 14 . [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
+ 33 10 14 [3 & PE1.1] . dupdip 2 >> 1 [PE1.2] times pop
+             33 10 14 . 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
+           33 10 14 3 . & PE1.1 14 2 >> 1 [PE1.2] times pop
+              33 10 2 . PE1.1 14 2 >> 1 [PE1.2] times pop
+              33 10 2 . + [+] dupdip 14 2 >> 1 [PE1.2] times pop
+                33 12 . [+] dupdip 14 2 >> 1 [PE1.2] times pop
+            33 12 [+] . dupdip 14 2 >> 1 [PE1.2] times pop
+                33 12 . + 12 14 2 >> 1 [PE1.2] times pop
+                   45 . 12 14 2 >> 1 [PE1.2] times pop
+                45 12 . 14 2 >> 1 [PE1.2] times pop
+             45 12 14 . 2 >> 1 [PE1.2] times pop
+           45 12 14 2 . >> 1 [PE1.2] times pop
+              45 12 3 . 1 [PE1.2] times pop
+            45 12 3 1 . [PE1.2] times pop
+    45 12 3 1 [PE1.2] . times pop
+      45 12 3 [PE1.2] . i pop
+              45 12 3 . PE1.2 pop
+              45 12 3 . [3 & PE1.1] dupdip 2 >> pop
+  45 12 3 [3 & PE1.1] . dupdip 2 >> pop
+              45 12 3 . 3 & PE1.1 3 2 >> pop
+            45 12 3 3 . & PE1.1 3 2 >> pop
+              45 12 3 . PE1.1 3 2 >> pop
               45 12 3 . + [+] dupdip 3 2 >> pop
                 45 15 . [+] dupdip 3 2 >> pop
             45 15 [+] . dupdip 3 2 >> pop
@@ -471,10 +471,10 @@ integer terms from the list.
    
 
 
    
 
    Let’s refactor
    
-
      14811 7 [PE1.2] times pop
-  14811 4 [PE1.2] times pop
-  14811 n [PE1.2] times pop
-n 14811 swap [PE1.2] times pop
+
      14811 7 [PE1.2] times pop
+  14811 4 [PE1.2] times pop
+  14811 n [PE1.2] times pop
+n 14811 swap [PE1.2] times pop
 
    
 
    
 
    define('PE1.3 == 14811 swap [PE1.2] times pop')
@@ -493,10 +493,10 @@ integer terms from the list.
    
 
    Here’s our joy program all in one place. It doesn’t make so much sense,
 but if you have read through the above description of how it was derived
 I hope it’s clear.
    
-
    PE1.1 == + [+] dupdip
-PE1.2 == [3 & PE1.1] dupdip 2 >>
-PE1.3 == 14811 swap [PE1.2] times pop
-PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop
+
    PE1.1 == + [+] dupdip
+PE1.2 == [3 & PE1.1] dupdip 2 >>
+PE1.3 == 14811 swap [PE1.2] times pop
+PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop
 
    
 
    
 
    
@@ -697,6 +697,7 @@ is just:
    
 
  • Treating Trees II: treestep
    • 
 
  • Using x to Generate Values
    • 
 
  • Newton’s method
    • 
+
  • Square Spiral Example Joy Code
    • 
 
  • Traversing Datastructures with Zippers
    • 
 
  • The Blissful Elegance of Typing Joy
    • 
 
  • Type Checking
    • 
@@ -747,7 +748,7 @@ is just:
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html b/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html
index 938d607..166daab 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Generator_Programs.html
@@ -36,7 +36,7 @@
   
    
 
    Using x to Generate Values
    
 
    Cf. jp-reprod.html
    
-
    from notebook_preamble import J, V, define
+
    from notebook_preamble import J, V, define
 
    
 
    
 
    Consider the x combinator:
    
@@ -76,7 +76,7 @@ function C
    
 
    
 
    Let’s try it:
    
-
    V('[0 swap [dup ++] dip rest cons] x')
+
    V('[0 swap [dup ++] dip rest cons] x')
 
    
 
    
 
                                               . [0 swap [dup ++] dip rest cons] x
@@ -95,7 +95,7 @@ function C
 
    After one application of x the quoted program contains 1 and
 0 is below it on the stack.
    
-
    J('[0 swap [dup ++] dip rest cons] x x x x x pop')
+
    J('[0 swap [dup ++] dip rest cons] x x x x x pop')
 
    
 
    
 
    0 1 2 3 4
@@ -103,10 +103,10 @@ function C
 
    
 
    direco
    
-
    define('direco == dip rest cons')
+
    define('direco == dip rest cons')
 
    
 
    
-
    V('[0 swap [dup ++] direco] x')
+
    V('[0 swap [dup ++] direco] x')
 
    
 
    
 
                                        . [0 swap [dup ++] direco] x
@@ -147,17 +147,17 @@ our quoted program:
    
 G == [direco] cons [swap] swoncat cons
 
    
 
    
-
    define('G == [direco] cons [swap] swoncat cons')
+
    define('G == [direco] cons [swap] swoncat cons')
 
    
 
    
 
    Let’s try it out:
    
-
    J('0 [dup ++] G')
+
    J('0 [dup ++] G')
 
    
 
    
 
    [0 swap [dup ++] direco]
 
    
 
    
-
    J('0 [dup ++] G x x x pop')
+
    J('0 [dup ++] G x x x pop')
 
    
 
    
 
    0 1 2
@@ -165,7 +165,7 @@ our quoted program:
    
 
    
 
    
 
    Powers of 2
    
-
    J('1 [dup 1 <<] G x x x x x x x x x pop')
+
    J('1 [dup 1 <<] G x x x x x x x x x pop')
 
    
 
    
 
    1 2 4 8 16 32 64 128 256
@@ -176,7 +176,7 @@ our quoted program:
    
 
    [x] times
    
 
    If we have one of these quoted programs we can drive it using times
 with the x combinator.
    
-
    J('23 [dup ++] G 5 [x] times')
+
    J('23 [dup ++] G 5 [x] times')
 
    
 
    
 
    23 24 25 26 27 [28 swap [dup ++] direco]
@@ -200,14 +200,14 @@ int:
    
 
    
 
    And pick them off by masking with 3 (binary 11) and then shifting the
 int right two bits.
    
-
    define('PE1.1 == dup [3 &] dip 2 >>')
+
    define('PE1.1 == dup [3 &] dip 2 >>')
 
    
 
    
-
    V('14811 PE1.1')
+
    V('14811 PE1.1')
 
    
 
    
-
                      . 14811 PE1.1
-            14811 . PE1.1
+
                      . 14811 PE1.1
+            14811 . PE1.1
             14811 . dup [3 &] dip 2 >>
       14811 14811 . [3 &] dip 2 >>
 14811 14811 [3 &] . dip 2 >>
@@ -220,36 +220,36 @@ int right two bits.
    
 
    
 
    
 
    If we plug 14811 and [PE1.1] into our generator form…
    
-
    J('14811 [PE1.1] G')
+
    J('14811 [PE1.1] G')
 
    
 
    
-
    [14811 swap [PE1.1] direco]
+
    [14811 swap [PE1.1] direco]
 
    
 
    
 
    …we get a generator that works for seven cycles before it reaches zero:
    
-
    J('[14811 swap [PE1.1] direco] 7 [x] times')
+
    J('[14811 swap [PE1.1] direco] 7 [x] times')
 
    
 
    
-
    3 2 1 3 1 2 3 [0 swap [PE1.1] direco]
+
    3 2 1 3 1 2 3 [0 swap [PE1.1] direco]
 
    
 
    
 
    
 
    Reset at Zero
    
 
    We need a function that checks if the int has reached zero and resets it
 if so.
    
-
    define('PE1.1.check == dup [pop 14811] [] branch')
+
    define('PE1.1.check == dup [pop 14811] [] branch')
 
    
 
    
-
    J('14811 [PE1.1.check PE1.1] G')
+
    J('14811 [PE1.1.check PE1.1] G')
 
    
 
    
-
    [14811 swap [PE1.1.check PE1.1] direco]
+
    [14811 swap [PE1.1.check PE1.1] direco]
 
    
 
    
-
    J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times')
+
    J('[14811 swap [PE1.1.check PE1.1] direco] 21 [x] times')
 
    
 
    
-
    3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 [0 swap [PE1.1.check PE1.1] direco]
+
    3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 [0 swap [PE1.1.check PE1.1] direco]
 
    
 
    
 
    (It would be more efficient to reset the int every seven cycles but
@@ -262,20 +262,20 @@ say.)
    
 
    In the PE1 problem we are asked to sum all the multiples of three and
 five less than 1000. It’s worked out that we need to use all seven
 numbers sixty-six times and then four more.
    
-
    J('7 66 * 4 +')
+
    J('7 66 * 4 +')
 
    
 
    
 
    466
 
    
 
    
 
    If we drive our generator 466 times and sum the stack we get 999.
    
-
    J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times')
+
    J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times')
 
    
 
    
-
    3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco]
+
    3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 1 2 3 3 2 1 3 [57 swap [PE1.1.check PE1.1] direco]
 
    
 
    
-
    J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
+
    J('[14811 swap [PE1.1.check PE1.1] direco] 466 [x] times pop enstacken sum')
 
    
 
    
 
    999
@@ -285,11 +285,11 @@ numbers sixty-six times and then four more.
    
 
    
 
    
 
    Project Euler Problem One
    
-
    define('PE1.2 == + dup [+] dip')
+
    define('PE1.2 == + dup [+] dip')
 
    
 
    
 
    Now we can add PE1.2 to the quoted program given to G.
    
-
    J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop')
+
    J('0 0 0 [PE1.1.check PE1.1] G 466 [x [PE1.2] dip] times popop')
 
    
 
    
 
    233168
@@ -351,13 +351,13 @@ numbers sixty-six times and then four more.
    
 fib_gen == [1 1 F]
 
    
 
    
-
    define('fib == + [popdd over] cons infra uncons')
+
    define('fib == + [popdd over] cons infra uncons')
 
    
 
    
-
    define('fib_gen == [1 1 fib]')
+
    define('fib_gen == [1 1 fib]')
 
    
 
    
-
    J('fib_gen 10 [x] times')
+
    J('fib_gen 10 [x] times')
 
    
 
    
 
    1 2 3 5 8 13 21 34 55 89 [144 89 fib]
@@ -373,21 +373,21 @@ not exceed four million, find the sum of the even-valued terms.
    
 
    Now that we have a generator for the Fibonacci sequence, we need a
 function that adds a term in the sequence to a sum if it is even, and
 pops it otherwise.
    
-
    define('PE2.1 == dup 2 % [+] [pop] branch')
+
    define('PE2.1 == dup 2 % [+] [pop] branch')
 
    
 
    
 
    And a predicate function that detects when the terms in the series
 “exceed four million”.
    
-
    define('>4M == 4000000 >')
+
    define('>4M == 4000000 >')
 
    
 
    
 
    Now it’s straightforward to define PE2 as a recursive function that
 generates terms in the Fibonacci sequence until they exceed four million
 and sums the even ones.
    
-
    define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')
+
    define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')
 
    
 
    
-
    J('PE2')
+
    J('PE2')
 
    
 
    
 
    4613732
@@ -400,8 +400,8 @@ and sums the even ones.
    
 even == dup 2 %
 >4M == 4000000 >
 
-PE2.1 == even [+] [pop] branch
-PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec
+PE2.1 == even [+] [pop] branch
+PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec
 
    
 
    
 
    
@@ -418,23 +418,23 @@ and sums the even ones.
    
 
    
 
    
 
    Every third term is even.
    
-
    J('[1 0 fib] x x x')  # To start the sequence with 1 1 2 3 instead of 1 2 3.
+
    J('[1 0 fib] x x x')  # To start the sequence with 1 1 2 3 instead of 1 2 3.
 
    
 
    
 
    1 1 2 [3 2 fib]
 
    
 
    
 
    Drive the generator three times and popop the two odd terms.
    
-
    J('[1 0 fib] x x x [popop] dipd')
+
    J('[1 0 fib] x x x [popop] dipd')
 
    
 
    
 
    2 [3 2 fib]
 
    
 
    
-
    define('PE2.2 == x x x [popop] dipd')
+
    define('PE2.2 == x x x [popop] dipd')
 
    
 
    
-
    J('[1 0 fib] 10 [PE2.2] times')
+
    J('[1 0 fib] 10 [PE2.2] times')
 
    
 
    
 
    2 8 34 144 610 2584 10946 46368 196418 832040 [1346269 832040 fib]
@@ -442,7 +442,7 @@ and sums the even ones.
    
 
    
 
    Replace x with our new driver function PE2.2 and start our
 fib generator at 1 0.
    
-
    J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
+
    J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
 
    
 
    
 
    4613732
@@ -457,10 +457,10 @@ modifications to the default 
 
    
 
    An Interesting Variation
    
-
    define('codireco == cons dip rest cons')
+
    define('codireco == cons dip rest cons')
 
    
 
    
-
    V('[0 [dup ++] codireco] x')
+
    V('[0 [dup ++] codireco] x')
 
    
 
    
 
                                     . [0 [dup ++] codireco] x
@@ -479,10 +479,10 @@ modifications to the default 0 [1 [dup ++] codireco] .
 
    
 
    
-
    define('G == [codireco] cons cons')
+
    define('G == [codireco] cons cons')
 
    
 
    
-
    J('230 [dup ++] G 5 [x] times pop')
+
    J('230 [dup ++] G 5 [x] times pop')
 
    
 
    
 
    230 231 232 233 234
@@ -577,7 +577,7 @@ modifications to the default 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Intro.html b/docs/sphinx_docs/_build/html/notebooks/Intro.html
index 658704d..d56d9e0 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Intro.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Intro.html
@@ -369,7 +369,7 @@ developing structured processes.
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html b/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
index 4a8ff3a..5d23612 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Newton-Raphson.html
@@ -13,7 +13,7 @@
     
     
     
-    
+    
     
     
     
@@ -40,7 +40,7 @@
 to write a function that can compute the square root of a number.
    
 
    Cf. “Why Functional Programming Matters” by John
 Hughes
    
-
    from notebook_preamble import J, V, define
+
    from notebook_preamble import J, V, define
 
    
 
    
 
    
@@ -92,10 +92,10 @@ function we’re writing. If we let 1 be the initial approximation:
    
 1   [dup 23 over / + 2 /]                    make_generator
 
    
 
    
-
    define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
+
    define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
 
    
 
    
-
    J('23 gsra')
+
    J('23 gsra')
 
    
 
    
 
    [1 [dup 23 over / + 2 /] codireco]
@@ -103,7 +103,7 @@ function we’re writing. If we let 1 be the initial approximation:
    
 
    
 
    Let’s drive the generator a few time (with the x combinator) and
 square the approximation to see how well it works…
    
-
    J('23 gsra 6 [x popd] times first sqr')
+
    J('23 gsra 6 [x popd] times first sqr')
 
    
 
    
 
    23.0000000001585
@@ -145,7 +145,7 @@ generated already and epsilon ε is handy on the stack…
    
 (abs(a-b)<=ε)
 
    
 
    
-
    define('_within_P [first - abs] dip <=')
+
    define('_within_P [first - abs] dip <=')
 
    
 
    
 
    
@@ -157,7 +157,7 @@ generated already and epsilon ε is handy on the stack…
    
    b
 
    
 
    
-
    define('_within_B roll< popop first')
+
    define('_within_B roll< popop first')
 
    
 
    
 
    
@@ -182,7 +182,7 @@ generated already and epsilon ε is handy on the stack…
    
 b [c G] ε within
 
    
 
    
-
    define('_within_R [popd x] dip')
+
    define('_within_R [popd x] dip')
 
    
 
    
 
    
@@ -194,33 +194,33 @@ generated already and epsilon ε is handy on the stack…
    
 a [b G] ε ...
 
    
 
    
-
    define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
-define('sqrt gsra within')
+
    define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
+define('sqrt gsra within')
 
    
 
    
 
    Try it out…
    
-
    J('36 sqrt')
+
    J('36 sqrt')
 
    
 
    
 
    6.0
 
    
 
    
-
    J('23 sqrt')
+
    J('23 sqrt')
 
    
 
    
 
    4.795831523312719
 
    
 
    
 
    Check it.
    
-
    4.795831523312719**2
+
    4.795831523312719**2
 
    
 
    
 
    22.999999999999996
 
    
 
    
-
    from math import sqrt
+
    from math import sqrt
 
-sqrt(23)
+sqrt(23)
 
    
 
    
 
    4.795831523312719
@@ -316,7 +316,7 @@ generated already and epsilon ε is handy on the stack…
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html b/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html
index 65498ab..797a302 100644
--- a/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html
+++ b/docs/sphinx_docs/_build/html/notebooks/NoUpdates.html
@@ -93,6 +93,7 @@
 
  • Treating Trees II: treestep
    • 
 
  • Using x to Generate Values
    • 
 
  • Newton’s method
    • 
+
  • Square Spiral Example Joy Code
    • 
 
  • Traversing Datastructures with Zippers
    • 
 
  • The Blissful Elegance of Typing Joy
    • 
 
  • Type Checking
    • 
@@ -143,7 +144,7 @@
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html b/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
index 05fa302..6d63e16 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Ordered_Binary_Trees.html
@@ -63,7 +63,7 @@ the Sufficiently Smart Compiler can be modified to use an optimized
 implementation under the hood. (Where does the “type” come from? It has
 a contingent existence predicated on the disciplined use of these
 functions on otherwise undistinguished Joy datastructures.)
    
-
    from notebook_preamble import D, J, V, define, DefinitionWrapper
+
    from notebook_preamble import D, J, V, define, DefinitionWrapper
 
    
 
    
 
    
@@ -100,10 +100,10 @@ functions on otherwise undistinguished Joy datastructures.)
    
 
    Tree-new == swap [[] []] cons cons
 
    
 
    
-
    define('Tree-new == swap [[] []] cons cons')
+
    define('Tree-new == swap [[] []] cons cons')
 
    
 
    
-
    J('"v" "k" Tree-new')
+
    J('"v" "k" Tree-new')
 
    
 
    
 
    ['k' 'v' [] []]
@@ -159,10 +159,10 @@ comparison operator:
    
 P   == pop roll> pop first
 
    
 
    
-
    define('P == pop roll> pop first')
+
    define('P == pop roll> pop first')
 
    
 
    
-
    J('["old_key" 23 [] []] 17 "new_key" ["..."] P')
+
    J('["old_key" 23 [] []] 17 "new_key" ["..."] P')
 
    
 
    
 
    'new_key' 'old_key'
@@ -217,10 +217,10 @@ stack:
    
 
    T == cons cons [dipdd] cons infra
 
    
 
    
-
    define('T == cons cons [dipdd] cons infra')
+
    define('T == cons cons [dipdd] cons infra')
 
    
 
    
-
    J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T')
+
    J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] T')
 
    
 
    
 
    ['old_k' 'old_value' 'left' 'Tree-add' 'new_key' 'new_value' 'right']
@@ -234,7 +234,7 @@ stack:
    
 [key_n value_n left right] value key [Tree-add] [P <] [Te] [Ee] ifte
 
    
 
    
-
    define('E == [P <] [Te] [Ee] ifte')
+
    define('E == [P <] [Te] [Ee] ifte')
 
    
 
    
 
    In this case Te works that same as T but on the left child tree
@@ -243,10 +243,10 @@ instead of the right, so the only difference is that it must use
 
    Te == cons cons [dipd] cons infra
 
    
 
    
-
    define('Te == cons cons [dipd] cons infra')
+
    define('Te == cons cons [dipd] cons infra')
 
    
 
    
-
    J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te')
+
    J('["old_k" "old_value" "left" "right"] "new_value" "new_key" ["Tree-add"] Te')
 
    
 
    
 
    ['old_k' 'old_value' 'Tree-add' 'new_key' 'new_value' 'left' 'right']
@@ -274,10 +274,10 @@ instead of the right, so the only difference is that it must use
               [key new_value left right]
 
    
 
    
-
    define('Ee == pop swap roll< rest rest cons cons')
+
    define('Ee == pop swap roll< rest rest cons cons')
 
    
 
    
-
    J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee')
+
    J('["k" "old_value" "left" "right"] "new_value" "k" ["Tree-add"] Ee')
 
    
 
    
 
    ['k' 'new_value' 'left' 'right']
@@ -302,43 +302,43 @@ instead of the right, so the only difference is that it must use
 Tree-add == [popop not] [[pop] dipd Tree-new] [] [R] genrec
 
    
 
    
-
    define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec')
+
    define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [[P >] [T] [E] ifte] genrec')
 
    
 
    
 
    
 
    
 
    Examples
    
-
    J('[] 23 "b" Tree-add')  # Initial
+
    J('[] 23 "b" Tree-add')  # Initial
 
    
 
    
 
    ['b' 23 [] []]
 
    
 
    
-
    J('["b" 23 [] []] 88 "c" Tree-add')  # Greater than
+
    J('["b" 23 [] []] 88 "c" Tree-add')  # Greater than
 
    
 
    
 
    ['b' 23 [] ['c' 88 [] []]]
 
    
 
    
-
    J('["b" 23 [] []] 88 "a" Tree-add')  # Less than
+
    J('["b" 23 [] []] 88 "a" Tree-add')  # Less than
 
    
 
    
 
    ['b' 23 ['a' 88 [] []] []]
 
    
 
    
-
    J('["b" 23 [] []] 88 "b" Tree-add')  # Equal to
+
    J('["b" 23 [] []] 88 "b" Tree-add')  # Equal to
 
    
 
    
 
    ['b' 88 [] []]
 
    
 
    
-
    J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add')  # Series.
+
    J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add')  # Series.
 
    
 
    
 
    ['b' 23 ['a' 88 [] []] ['c' 44 [] []]]
 
    
 
    
-
    J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step')
+
    J('[] [[23 "b"] [88 "a"] [44 "c"]] [i Tree-add] step')
 
    
 
    
 
    ['b' 23 ['a' 88 [] []] ['c' 44 [] []]]
@@ -365,19 +365,19 @@ values:
    
                 L
 
    
 
    
-
    J("1 0 ['G'] ['E'] ['L'] cmp")
+
    J("1 0 ['G'] ['E'] ['L'] cmp")
 
    
 
    
 
    'G'
 
    
 
    
-
    J("1 1 ['G'] ['E'] ['L'] cmp")
+
    J("1 1 ['G'] ['E'] ['L'] cmp")
 
    
 
    
 
    'E'
 
    
 
    
-
    J("0 1 ['G'] ['E'] ['L'] cmp")
+
    J("0 1 ['G'] ['E'] ['L'] cmp")
 
    
 
    
 
    'L'
@@ -414,7 +414,7 @@ node key (by throwing everything else away):
    
 
    P == over [popop popop first] nullary
 
    
 
    
-
    define('P == over [popop popop first] nullary')
+
    define('P == over [popop popop first] nullary')
 
    
 
    
 
    Using cmp to simplify our code above at
@@ -434,10 +434,10 @@ to understand:
    
 
    Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec
 
    
 
    
-
    define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec')
+
    define('Tree-add == [popop not] [[pop] dipd Tree-new] [] [P [T] [Ee] [Te] cmp] genrec')
 
    
 
    
-
    J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add')  # Still works.
+
    J('[] 23 "b" Tree-add 88 "a" Tree-add 44 "c" Tree-add')  # Still works.
 
    
 
    
 
    ['b' 23 ['a' 88 [] []] ['c' 44 [] []]]
@@ -545,22 +545,22 @@ with an interesting situation:
    
 
    Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec
 
    
 
    
-
    define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec')
+
    define('Tree-iter == [not] [pop] roll< [dupdip rest rest] cons [step] genrec')
 
    
 
    
 
    
 
    
 
    Examples
    
-
    J('[] [foo] Tree-iter')  #  It doesn't matter what F is as it won't be used.
+
    J('[] [foo] Tree-iter')  #  It doesn't matter what F is as it won't be used.
 
    
 
    
-
    J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter")
+
    J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [first] Tree-iter")
 
    
 
    
 
    'b' 'a' 'c'
 
    
 
    
-
    J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter")
+
    J("['b' 23 ['a' 88 [] []] ['c' 44 [] []]] [second] Tree-iter")
 
    
 
    
 
    23 88 44
@@ -575,16 +575,16 @@ to e.g. 0 and ignoring them. It’s set-like in that duplicate items added
 to it will only occur once within it, and we can query it in
 :math:`O(log_2 N) <https://en.wikipedia.org/wiki/Binary_search_tree#cite_note-2>`__
 time.
    
-
    J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step')
+
    J('[] [3 9 5 2 8 6 7 8 4] [0 swap Tree-add] step')
 
    
 
    
 
    [3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]]
 
    
 
    
-
    define('to_set == [] swap [0 swap Tree-add] step')
+
    define('to_set == [] swap [0 swap Tree-add] step')
 
    
 
    
-
    J('[3 9 5 2 8 6 7 8 4] to_set')
+
    J('[3 9 5 2 8 6 7 8 4] to_set')
 
    
 
    
 
    [3 0 [2 0 [] []] [9 0 [5 0 [4 0 [] []] [8 0 [6 0 [] [7 0 [] []]] []]] []]]
@@ -592,10 +592,10 @@ time.
    
 
    
 
    And with that we can write a little program unique to remove
 duplicate items from a list.
    
-
    define('unique == [to_set [first] Tree-iter] cons run')
+
    define('unique == [to_set [first] Tree-iter] cons run')
 
    
 
    
-
    J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique')  # Filter duplicate items.
+
    J('[3 9 3 5 2 9 8 8 8 6 2 7 8 4 3] unique')  # Filter duplicate items.
 
    
 
    
 
    [7 6 8 4 5 9 2 3]
@@ -679,23 +679,23 @@ right side:
    
 
    
 
    
 
    Now we can sort sequences.
    
-
    #define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')
+
    #define('Tree-iter-order == [not] [pop] [dup third] [[cons dip] dupdip [[first] dupdip] dip [rest rest rest first] dip i] genrec')
 
 
-DefinitionWrapper.add_definitions('''
+DefinitionWrapper.add_definitions('''
 
-fourth == rest rest rest first
+fourth == rest rest rest first
 
-proc_left == [cons dip] dupdip
-proc_current == [[first] dupdip] dip
-proc_right == [fourth] dip i
+proc_left == [cons dip] dupdip
+proc_current == [[first] dupdip] dip
+proc_right == [fourth] dip i
 
-Tree-iter-order == [not] [pop] [dup third] [proc_left proc_current proc_right] genrec
+Tree-iter-order == [not] [pop] [dup third] [proc_left proc_current proc_right] genrec
 
-''', D)
+''', D)
 
    
 
    
-
    J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order')
+
    J('[3 9 5 2 8 6 7 8 4] to_set Tree-iter-order')
 
    
 
    
 
    2 3 4 5 6 7 8 9
@@ -835,54 +835,54 @@ because there’s no value to discard.
    
 Tree-get == [pop not] swap [] [P [T>] [E] [T<] cmp] genrec
 
    
 
    
-
    # I don't want to deal with name conflicts with the above so I'm inlining everything here.
-# The original Joy system has "hide" which is a meta-command which allows you to use named
-# definitions that are only in scope for a given definition.  I don't want to implement
-# that (yet) so...
+
    # I don't want to deal with name conflicts with the above so I'm inlining everything here.
+# The original Joy system has "hide" which is a meta-command which allows you to use named
+# definitions that are only in scope for a given definition.  I don't want to implement
+# that (yet) so...
 
 
-define('''
-Tree-get == [pop not] swap [] [
-  over [pop popop first] nullary
-  [[fourth] dipd i]
-  [popop second]
-  [[third] dipd i]
-  cmp
-  ] genrec
-''')
+define('''
+Tree-get == [pop not] swap [] [
+  over [pop popop first] nullary
+  [[fourth] dipd i]
+  [popop second]
+  [[third] dipd i]
+  cmp
+  ] genrec
+''')
 
    
 
    
-
    J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get')
+
    J('["gary" 23 [] []] "mike" [popd " not in tree" +] Tree-get')
 
    
 
    
 
    'mike not in tree'
 
    
 
    
-
    J('["gary" 23 [] []] "gary" [popop "err"] Tree-get')
+
    J('["gary" 23 [] []] "gary" [popop "err"] Tree-get')
 
    
 
    
 
    23
 
    
 
    
-
    J('''
+
    J('''
 
-    [] [[0 'a'] [1 'b'] [2 'c']] [i Tree-add] step
+    [] [[0 'a'] [1 'b'] [2 'c']] [i Tree-add] step
 
-    'c' [popop 'not found'] Tree-get
+    'c' [popop 'not found'] Tree-get
 
-''')
+''')
 
    
 
    
 
    2
 
    
 
    
-
    J('''
+
    J('''
 
-    [] [[0 'a'] [1 'b'] [2 'c']] [i Tree-add] step
+    [] [[0 'a'] [1 'b'] [2 'c']] [i Tree-add] step
 
-    'd' [popop 'not found'] Tree-get
+    'd' [popop 'not found'] Tree-get
 
-''')
+''')
 
    
 
    
 
    'not found'
@@ -1160,11 +1160,11 @@ E == [
 W == dup W.rightmost W.unpack over
 E.clear_stuff == roll> popop rest
 E.delete == cons dipd
-E.0 == E.clear_stuff [W] dip E.delete swap
+E.0 == E.clear_stuff [W] dip E.delete swap
 E == [
     [[pop third not] pop fourth]
     [[pop fourth not] pop third]
-    [[E.0] cons infra]
+    [[E.0] cons infra]
 ] cond
 T> == [dipd] cons infra
 T< == [dipdd] cons infra
@@ -1175,61 +1175,61 @@ E == [
 
    
 
    By the standards of the code I’ve written so far, this is a huge Joy
 program.
    
-
    DefinitionWrapper.add_definitions('''
-first_two == uncons uncons pop
-fourth == rest rest rest first
-?fourth == [] [fourth] [] ifte
-W.rightmost == [?fourth] [fourth] while
-E.clear_stuff == roll> popop rest
-E.delete == cons dipd
-W == dup W.rightmost first_two over
-E.0 == E.clear_stuff [W] dip E.delete swap
-E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond
-T> == [dipd] cons infra
-T< == [dipdd] cons infra
-R0 == over first swap dup
-R1 == cons roll> [T>] [E] [T<] cmp
-Tree-Delete == [pop not] [pop] [R0] [R1] genrec
-''', D)
+
    DefinitionWrapper.add_definitions('''
+first_two == uncons uncons pop
+fourth == rest rest rest first
+?fourth == [] [fourth] [] ifte
+W.rightmost == [?fourth] [fourth] while
+E.clear_stuff == roll> popop rest
+E.delete == cons dipd
+W == dup W.rightmost first_two over
+E.0 == E.clear_stuff [W] dip E.delete swap
+E == [[[pop third not] pop fourth] [[pop fourth not] pop third] [[E.0] cons infra]] cond
+T> == [dipd] cons infra
+T< == [dipdd] cons infra
+R0 == over first swap dup
+R1 == cons roll> [T>] [E] [T<] cmp
+Tree-Delete == [pop not] [pop] [R0] [R1] genrec
+''', D)
 
    
 
    
-
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ")
+
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'c' Tree-Delete ")
 
    
 
    
 
    ['a' 23 [] ['b' 88 [] []]]
 
    
 
    
-
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ")
+
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'b' Tree-Delete ")
 
    
 
    
 
    ['a' 23 [] ['c' 44 [] []]]
 
    
 
    
-
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ")
+
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'a' Tree-Delete ")
 
    
 
    
 
    ['b' 88 [] ['c' 44 [] []]]
 
    
 
    
-
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ")
+
    J("['a' 23 [] ['b' 88 [] ['c' 44 [] []]]] 'der' Tree-Delete ")
 
    
 
    
 
    ['a' 23 [] ['b' 88 [] ['c' 44 [] []]]]
 
    
 
    
-
    J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step')
+
    J('[] [4 2 3 1 6 7 5 ] [0 swap Tree-add] step')
 
    
 
    
 
    [4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]]
 
    
 
    
-
    J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ")
+
    J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 3 Tree-Delete ")
 
    
 
    
 
    [4 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]]
 
    
 
    
-
    J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ")
+
    J("[4 0 [2 0 [1 0 [] []] [3 0 [] []]] [6 0 [5 0 [] []] [7 0 [] []]]] 4 Tree-Delete ")
 
    
 
    
 
    [3 0 [2 0 [1 0 [] []] []] [6 0 [5 0 [] []] [7 0 [] []]]]
@@ -1373,7 +1373,7 @@ Tree-delete == [pop not] [pop] [_Tree_delete_R0] [_Tree_delete_R1] genrec
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Quadratic.html b/docs/sphinx_docs/_build/html/notebooks/Quadratic.html
index 4c2d7c8..86fe364 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Quadratic.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Quadratic.html
@@ -13,7 +13,7 @@
     
     
     
-    
+    
     
     
     
@@ -34,7 +34,7 @@
 
           
    
             
-  
    from notebook_preamble import J, V, define
+  
    from notebook_preamble import J, V, define
 
    
 
    
 
    
@@ -100,11 +100,11 @@ the variables:
    
 
    
 
    The three arguments are to the left, so we can “chop off” everything to
 the right and say it’s the definition of the quadratic function:
    
-
    define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
+
    define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
 
    
 
    
 
    Let’s try it out:
    
-
    J('3 1 1 quadratic')
+
    J('3 1 1 quadratic')
 
    
 
    
 
    -0.3819660112501051 -2.618033988749895
@@ -114,7 +114,7 @@ the right and say it’s the definition of the dip and dipd combinators building the main program
 by incorporating the values on the stack. Then that program runs and you
 get the results. This is pretty typical of Joy code.
    
-
    V('-5 1 4 quadratic')
+
    V('-5 1 4 quadratic')
 
    
 
    
 
                                                       . -5 1 4 quadratic
@@ -253,7 +253,7 @@ get the results. This is pretty typical of Joy code.
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html b/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
index d143e1a..385778c 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Recursion_Combinators.html
@@ -33,7 +33,7 @@
 
           
    
             
-  
    from notebook_preamble import D, DefinitionWrapper, J, V, define
+  
    from notebook_preamble import D, DefinitionWrapper, J, V, define
 
    
 
    
 
    
@@ -101,18 +101,18 @@ cons list”.

It may be helpful to see this function implemented in imperative Python code.

-
def hylomorphism(c, F, P, G):
-    '''Return a hylomorphism function H.'''
+
def hylomorphism(c, F, P, G):
+    '''Return a hylomorphism function H.'''
 
-    def H(a):
-        if P(a):
-            result = c
-        else:
-            b, aa = G(a)
-            result = F(b, H(aa))  # b is stored in the stack frame during recursive call to H().
-        return result
+    def H(a):
+        if P(a):
+            result = c
+        else:
+            b, aa = G(a)
+            result = F(b, H(aa))  # b is stored in the stack frame during recursive call to H().
+        return result
 
-    return H
+    return H
 

 

 
Cf. “Bananas, Lenses, & Barbed
@@ -185,7 +185,7 @@ the left so we have a definition for 
 
hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
 

 

-
define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec')
+
define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec')
 

 

 

@@ -200,17 +200,17 @@ of all positive integers less than that one. (In this case the types
 
  • [G] is [-- dup]
    • 
 
  • [F] is [+]
    • 
 
-
    define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
+
    define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
 
    
 
    
 
    Let’s try it:
    
-
    J('5 triangular_number')
+
    J('5 triangular_number')
 
    
 
    
 
    10
 
    
 
    
-
    J('[0 1 2 3 4 5 6] [triangular_number] map')
+
    J('[0 1 2 3 4 5 6] [triangular_number] map')
 
    
 
    
 
    [0 0 1 3 6 10 15]
@@ -372,10 +372,10 @@ values.
    
    == [0 <=] [pop []] [-- dup] [dip swons] genrec
 
    
 
    
-
    define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
+
    define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
 
    
 
    
-
    J('5 range')
+
    J('5 range')
 
    
 
    
 
    [4 3 2 1 0]
@@ -388,10 +388,10 @@ values.
    
    == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec
 
    
 
    
-
    define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
+
    define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
 
    
 
    
-
    J('5 range_reverse')
+
    J('5 range_reverse')
 
    
 
    
 
    [0 1 2 3 4]
@@ -404,10 +404,10 @@ values.
    
    == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec
 
    
 
    
-
    define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
+
    define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
 
    
 
    
-
    J('5 ranger')
+
    J('5 ranger')
 
    
 
    
 
    [5 4 3 2 1]
@@ -420,10 +420,10 @@ values.
    
    == [] swap [0 <=] [pop] [[swons] dupdip --] primrec
 
    
 
    
-
    define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
+
    define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
 
    
 
    
-
    J('5 ranger_reverse')
+
    J('5 ranger_reverse')
 
    
 
    
 
    [1 2 3 4 5]
@@ -444,17 +444,17 @@ and makes some new value.
    
 
    C == [not] c [uncons swap] [F] hylomorphism
 
    
 
    
-
    define('swuncons == uncons swap')  # Awkward name.
+
    define('swuncons == uncons swap')  # Awkward name.
 
    
 
    
 
    An example of a catamorphism is the sum function.
    
 
    sum == [not] 0 [swuncons] [+] hylomorphism
 
    
 
    
-
    define('sum == [not] 0 [swuncons] [+] hylomorphism')
+
    define('sum == [not] 0 [swuncons] [+] hylomorphism')
 
    
 
    
-
    J('[5 4 3 2 1] sum')
+
    J('[5 4 3 2 1] sum')
 
    
 
    
 
    15
@@ -464,7 +464,7 @@ and makes some new value.
    
 
    The step combinator
    
 
    The step combinator will usually be better to use than
 catamorphism.
    
-
    J('[step] help')
+
    J('[step] help')
 
    
 
    
 
    Run a quoted program on each item in a sequence.
@@ -488,10 +488,10 @@ and makes some new value.
    
 on top of the stack.
 
    
 
    
-
    define('sum == 0 swap [+] step')
+
    define('sum == 0 swap [+] step')
 
    
 
    
-
    J('[5 4 3 2 1] sum')
+
    J('[5 4 3 2 1] sum')
 
    
 
    
 
    15
@@ -512,10 +512,10 @@ and makes some new value.
    
 P == 1 <=
 
    
 
    
-
    define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
+
    define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
 
    
 
    
-
    J('5 factorial')
+
    J('5 factorial')
 
    
 
    
 
    120
@@ -544,10 +544,10 @@ pattern H2P == not
 
    
 
    
-
    define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
+
    define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
 
    
 
    
-
    J('[1 2 3] tails')
+
    J('[1 2 3] tails')
 
    
 
    
 
    [[] [3] [2 3]]
@@ -675,7 +675,7 @@ Wire”
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Replacing.html b/docs/sphinx_docs/_build/html/notebooks/Replacing.html
index 01108aa..f1fcbbc 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Replacing.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Replacing.html
@@ -42,12 +42,12 @@ we can implement e.g. a function that adds new functions to the
 dictionary. However, there’s no function that does that. Adding a new
 function to the dictionary is a meta-interpreter action, you have to do
 it in Python, not Joy.
    
-
    from notebook_preamble import D, J, V
+
    from notebook_preamble import D, J, V
 
    
 
    
 
    
 
    A long trace
    
-
    V('[23 18] average')
+
    V('[23 18] average')
 
    
 
    
 
                                      . [23 18] average
@@ -105,30 +105,30 @@ it in Python, not Joy.
    
 
    An efficient sum function is already in the library. But for
 size we can use a “compiled” version hand-written in Python to speed
 up evaluation and make the trace more readable.
    
-
    from joy.library import SimpleFunctionWrapper
-from joy.utils.stack import iter_stack
+
    from joy.library import SimpleFunctionWrapper
+from joy.utils.stack import iter_stack
 
 
-@SimpleFunctionWrapper
-def size(stack):
-    '''Return the size of the sequence on the stack.'''
-    sequence, stack = stack
-    n = 0
-    for _ in iter_stack(sequence):
-        n += 1
-    return n, stack
+@SimpleFunctionWrapper
+def size(stack):
+    '''Return the size of the sequence on the stack.'''
+    sequence, stack = stack
+    n = 0
+    for _ in iter_stack(sequence):
+        n += 1
+    return n, stack
 
    
 
    
 
    Now we replace the old version in the dictionary with the new version,
 and re-evaluate the expression.
    
-
    D['size'] = size
+
    D['size'] = size
 
    
 
    
 
    
 
    
 
    A shorter trace
    
 
    You can see that size now executes in a single step.
    
-
    V('[23 18] average')
+
    V('[23 18] average')
 
    
 
    
 
                                      . [23 18] average
@@ -251,7 +251,7 @@ and re-evaluate the expression.
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html b/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html
index 474d0b8..a6033ad 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Square_Spiral.html
@@ -33,7 +33,7 @@
 
           
    
             
-  
    from notebook_preamble import J, V, define
+  
    from notebook_preamble import J, V, define
 
    
 
    
 
    
@@ -99,8 +99,8 @@ to apply abs
 that each accept two quoted predicate programs, run the first, and
 conditionally run the second only if required (to compute the final
 Boolean value). They run their predicate arguments nullary.
    
-
    define('&& [nullary] cons [nullary [0]] dip branch')
-define('|| [nullary] cons [nullary] dip [1] branch')
+
    define('&& [nullary] cons [nullary [0]] dip branch')
+define('|| [nullary] cons [nullary] dip [1] branch')
 
    
 
    
 
    Given those, we can define x != y || x >= 0 as:
    
@@ -143,7 +143,7 @@ legible.
    
 
    
 
    
 
    “Not Negative”
    
-
    define('!- 0 >=')
+
    define('!- 0 >=')
 
    
 
    
 
    
@@ -169,29 +169,29 @@ of ifte
    
 
    
-
    define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
+
    define('spiral_next [[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte')
 
    
 
    
 
    Let’s try it out:
    
-
    J('0 0 spiral_next')
+
    J('0 0 spiral_next')
 
    
 
    
 
    1 0
 
    
 
    
-
    J('1 0 spiral_next')
+
    J('1 0 spiral_next')
 
    
 
    
 
    1 -1
 
    
 
    
-
    J('1 -1 spiral_next')
+
    J('1 -1 spiral_next')
 
    
 
    
 
    0 -1
 
    
 
    
-
    J('0 -1 spiral_next')
+
    J('0 -1 spiral_next')
 
    
 
    
 
    -1 -1
@@ -240,7 +240,7 @@ From:
    
            [x' y']
 
    
 
    
-
    J('[0 0] [spiral_next] infra')
+
    J('[0 0] [spiral_next] infra')
 
    
 
    
 
    [0 1]
@@ -262,7 +262,7 @@ us out of the value and stepper function:
    
 
    
 
    
 
    Here it is in action:
    
-
    J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
+
    J('[0 0] [dup [spiral_next] infra] make_generator x x x x pop')
 
    
 
    
 
    [0 0] [0 1] [-1 1] [-1 0]
@@ -290,13 +290,13 @@ pairs, where the next pair in the series can be generated at any time by
 using the x combinator on the generator (which is just a quoted
 expression containing a copy of the current pair and the “stepper
 function” to generate the next pair from that.)
    
-
    define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
-define('_spn_T [!-] [[++]] [[--]] ifte dip')
-define('_spn_E [pop !-] [--] [++] ifte')
-define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
+
    define('_spn_P [[abs] ii <=] [[<>] [pop !-] ||] &&')
+define('_spn_T [!-] [[++]] [[--]] ifte dip')
+define('_spn_E [pop !-] [--] [++] ifte')
+define('spiral_next _spn_P [_spn_E] [_spn_T] branch')
 
    
 
    
-
    V('23 18 spiral_next')
+
    V('23 18 spiral_next')
 
    
 
    
 
                                                                   . 23 18 spiral_next
@@ -456,7 +456,7 @@ function” to generate the next pair from that.)
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html b/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html
index b2ae3a1..3be8e1e 100644
--- a/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html
+++ b/docs/sphinx_docs/_build/html/notebooks/The_Four_Operations.html
@@ -404,7 +404,7 @@ evaluation, yeah?)
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Treestep.html b/docs/sphinx_docs/_build/html/notebooks/Treestep.html
index 5c37053..f5d8d63 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Treestep.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Treestep.html
@@ -125,13 +125,13 @@ the desired outcome.
    
 
    
 
    
 
    Extract a couple of auxiliary definitions:
    
-
    TS.0 == [[not] swap] dip
-TS.1 == [dip] cons [uncons] swoncat
+
    TS.0 == [[not] swap] dip
+TS.1 == [dip] cons [uncons] swoncat
 
    
 
    
-
    [B] [N] TS.1 TS.0 [map C]                         genrec
-[B] [N]           [map C]         [TS.1 TS.0] dip genrec
-[B] [N] [C]         [map] swoncat [TS.1 TS.0] dip genrec
+
    [B] [N] TS.1 TS.0 [map C]                         genrec
+[B] [N]           [map C]         [TS.1 TS.0] dip genrec
+[B] [N] [C]         [map] swoncat [TS.1 TS.0] dip genrec
 
    
 
    
 
    The givens are all to the left so we have our definition.
    
@@ -148,17 +148,17 @@ the desired outcome.
    
 
    
 
    
 
    Define treestep
    
-
    from notebook_preamble import D, J, V, define, DefinitionWrapper
+
    from notebook_preamble import D, J, V, define, DefinitionWrapper
 
    
 
    
-
    DefinitionWrapper.add_definitions('''
+
    DefinitionWrapper.add_definitions('''
 
-    _treestep_0 == [[not] swap] dip
-    _treestep_1 == [dip] cons [uncons] swoncat
-    treegrind == [_treestep_1 _treestep_0] dip genrec
-    treestep == [map] swoncat treegrind
+    _treestep_0 == [[not] swap] dip
+    _treestep_1 == [dip] cons [uncons] swoncat
+    treegrind == [_treestep_1 _treestep_0] dip genrec
+    treestep == [map] swoncat treegrind
 
-''', D)
+''', D)
 
    
 
    
 
    
@@ -169,7 +169,7 @@ all nodes in a tree with this function:
    
 
    sumtree == [pop 0] [] [sum +] treestep
 
    
 
    
-
    define('sumtree == [pop 0] [] [sum +] treestep')
+
    define('sumtree == [pop 0] [] [sum +] treestep')
 
    
 
    
 
    Running this function on an empty tree value gives zero:
    
@@ -178,7 +178,7 @@ all nodes in a tree with this function:
    
            0
 
    
 
    
-
    J('[] sumtree')  # Empty tree.
+
    J('[] sumtree')  # Empty tree.
 
    
 
    
 
    0
@@ -192,61 +192,61 @@ all nodes in a tree with this function:
    
 n+m
 
    
 
    
-
    J('[23] sumtree')  # No child trees.
+
    J('[23] sumtree')  # No child trees.
 
    
 
    
 
    23
 
    
 
    
-
    J('[23 []] sumtree')  # Child tree, empty.
+
    J('[23 []] sumtree')  # Child tree, empty.
 
    
 
    
 
    23
 
    
 
    
-
    J('[23 [2 [4]] [3]] sumtree')  # Non-empty child trees.
+
    J('[23 [2 [4]] [3]] sumtree')  # Non-empty child trees.
 
    
 
    
 
    32
 
    
 
    
-
    J('[23 [2 [8] [9]] [3] [4 []]] sumtree')  # Etc...
+
    J('[23 [2 [8] [9]] [3] [4 []]] sumtree')  # Etc...
 
    
 
    
 
    49
 
    
 
    
-
    J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep')  # Alternate "spelling".
+
    J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep')  # Alternate "spelling".
 
    
 
    
 
    49
 
    
 
    
-
    J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep')  # Replace each node.
+
    J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep')  # Replace each node.
 
    
 
    
 
    [23 [23 [23] [23]] [23] [23 []]]
 
    
 
    
-
    J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep')
+
    J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep')
 
    
 
    
 
    [1 [1 [1] [1]] [1] [1 []]]
 
    
 
    
-
    J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree')
+
    J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree')
 
    
 
    
 
    6
 
    
 
    
-
    J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep')  # Combine replace and sum into one function.
+
    J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep')  # Combine replace and sum into one function.
 
    
 
    
 
    6
 
    
 
    
-
    J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep')  # Combine replace and sum into one function.
+
    J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep')  # Combine replace and sum into one function.
 
    
 
    
 
    3
@@ -277,7 +277,7 @@ all nodes in a tree with this function:
    
 
    
 
    
 
    This doesn’t quite work:
    
-
    J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep')
+
    J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep')
 
    
 
    
 
    3 'B' 'B'
@@ -299,7 +299,7 @@ depositing our results directly on the stack.
    
 
    [] [first] [flatten cons] treestep
 
    
 
    
-
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [first] [flatten cons] treestep')
+
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [first] [flatten cons] treestep')
 
    
 
    
 
    [3 2 9 5 4 8 6 7]
@@ -322,7 +322,7 @@ depositing our results directly on the stack.
    
 
    [] [i roll< swons concat] [first] treestep
 
    
 
    
-
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [uncons pop] [i roll< swons concat] treestep')
+
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [uncons pop] [i roll< swons concat] treestep')
 
    
 
    
 
    [2 3 4 5 6 7 8 9]
@@ -343,7 +343,7 @@ non-empty node is:
    
 
    [key value] N [left right] [K] C
 
    
 
    
-
    J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind')
+
    J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind')
 
    
 
    
 
    ['key' 'value'] 'N' [['left'] ['right']] [[not] ['B'] [uncons ['N'] dip] ['C'] genrec] 'C'
@@ -353,21 +353,21 @@ non-empty node is:
    
 
    
 
    treegrind with step
    
 
    Iteration through the nodes
    
-
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] ["N"] [step] treegrind')
+
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] ["N"] [step] treegrind')
 
    
 
    
 
    [3 0] 'N' [2 0] 'N' [9 0] 'N' [5 0] 'N' [4 0] 'N' [8 0] 'N' [6 0] 'N' [7 0] 'N'
 
    
 
    
 
    Sum the nodes’ keys.
    
-
    J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] [first +] [step] treegrind')
+
    J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [pop] [first +] [step] treegrind')
 
    
 
    
 
    44
 
    
 
    
 
    Rebuild the tree using map (imitating treestep.)
    
-
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [[100 +] infra] [map cons] treegrind')
+
    J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]]   [] [[100 +] infra] [map cons] treegrind')
 
    
 
    
 
    [[103 0] [[102 0] [] []] [[109 0] [[105 0] [[104 0] [] []] [[108 0] [[106 0] [] [[107 0] [] []]] []]] []]]
@@ -449,37 +449,37 @@ equal):
    
 
    
 
    
 
    To me, that seems simpler than the genrec version.
    
-
    DefinitionWrapper.add_definitions('''
+
    DefinitionWrapper.add_definitions('''
 
-    T> == pop [first] dip i
-    T< == pop [second] dip i
-    E == roll> popop first
-    P == roll< [roll< uncons swap] dip
+    T> == pop [first] dip i
+    T< == pop [second] dip i
+    E == roll> popop first
+    P == roll< [roll< uncons swap] dip
 
-    Tree-get == [P [T>] [E] [T<] cmp] treegrind
+    Tree-get == [P [T>] [E] [T<] cmp] treegrind
 
-''', D)
+''', D)
 
    
 
    
-
    J('''\
+
    J('''\
 
-[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
+[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
 
-[] [5] Tree-get
+[] [5] Tree-get
 
-''')
+''')
 
    
 
    
 
    15
 
    
 
    
-
    J('''\
+
    J('''\
 
-[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
+[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
 
-[pop "nope"] [25] Tree-get
+[pop "nope"] [25] Tree-get
 
-''')
+''')
 
    
 
    
 
    'nope'
@@ -574,7 +574,7 @@ equal):
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html b/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
index 142a672..09ebb68 100644
--- a/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
+++ b/docs/sphinx_docs/_build/html/notebooks/TypeChecking.html
@@ -35,33 +35,33 @@
             
   
    
 
    Type Checking
    
-
    import logging, sys
+
    import logging, sys
 
-logging.basicConfig(
-  format='%(message)s',
-  stream=sys.stdout,
-  level=logging.INFO,
-  )
+logging.basicConfig(
+  format='%(message)s',
+  stream=sys.stdout,
+  level=logging.INFO,
+  )
 
    
 
    
-
    from joy.utils.types import (
-    doc_from_stack_effect,
-    infer,
-    reify,
-    unify,
-    FUNCTIONS,
-    JoyTypeError,
-)
+
    from joy.utils.types import (
+    doc_from_stack_effect,
+    infer,
+    reify,
+    unify,
+    FUNCTIONS,
+    JoyTypeError,
+)
 
    
 
    
-
    D = FUNCTIONS.copy()
-del D['product']
-globals().update(D)
+
    D = FUNCTIONS.copy()
+del D['product']
+globals().update(D)
 
    
 
    
 
    
 
    An Example
    
-
    fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
+
    fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
 
    
 
    
 
    25 (--) ∘ pop swap rolldown rrest ccons
@@ -72,32 +72,32 @@
 40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
 
    
 
    
-
    print doc_from_stack_effect(fi, fo)
+
    print doc_from_stack_effect(fi, fo)
 
    
 
    
-
    ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
+
    ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1])
 
    
 
    
-
    from joy.parser import text_to_expression
-from joy.utils.stack import stack_to_string
+
    from joy.parser import text_to_expression
+from joy.utils.stack import stack_to_string
 
    
 
    
-
    e = text_to_expression('0 1 2 [3 4]')  # reverse order
-print stack_to_string(e)
+
    e = text_to_expression('0 1 2 [3 4]')  # reverse order
+print stack_to_string(e)
 
    
 
    
 
    [3 4] 2 1 0
 
    
 
    
-
    u = unify(e, fi)[0]
-u
+
    u = unify(e, fi)[0]
+u
 
    
 
    
 
    {a1: 0, a2: 1, a3: 2, a4: 3, a5: 4, s2: (), s1: ()}
 
    
 
    
-
    g = reify(u, (fi, fo))
-print doc_from_stack_effect(*g)
+
    g = reify(u, (fi, fo))
+print doc_from_stack_effect(*g)
 
    
 
    
 
    (... [3 4 ] 2 1 0 -- ... [1 2 ])
@@ -106,18 +106,18 @@
 
    
 
    
 
    Unification Works “in Reverse”
    
-
    e = text_to_expression('[2 3]')
+
    e = text_to_expression('[2 3]')
 
    
 
    
-
    u = unify(e, fo)[0]  # output side, not input side
-u
+
    u = unify(e, fo)[0]  # output side, not input side
+u
 
    
 
    
 
    {a2: 2, a3: 3, s2: (), s1: ()}
 
    
 
    
-
    g = reify(u, (fi, fo))
-print doc_from_stack_effect(*g)
+
    g = reify(u, (fi, fo))
+print doc_from_stack_effect(*g)
 
    
 
    
 
    (... [a4 a5 ] 3 2 a1 -- ... [2 3 ])
@@ -126,7 +126,7 @@
 
    
 
    
 
    Failing a Check
    
-
    fi, fo = infer(dup, mul)[0]
+
    fi, fo = infer(dup, mul)[0]
 
    
 
    
 
    25 (--) ∘ dup mul
@@ -135,17 +135,17 @@
 31 (i1 -- i2) ∘
 
    
 
    
-
    e = text_to_expression('"two"')
-print stack_to_string(e)
+
    e = text_to_expression('"two"')
+print stack_to_string(e)
 
    
 
    
 
    'two'
 
    
 
    
-
    try:
-    unify(e, fi)
-except JoyTypeError, err:
-    print err
+
    try:
+    unify(e, fi)
+except JoyTypeError, err:
+    print err
 
    
 
    
 
    Cannot unify 'two' and f1.
@@ -240,7 +240,7 @@
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Types.html b/docs/sphinx_docs/_build/html/notebooks/Types.html
index 2330787..8a5b149 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Types.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Types.html
@@ -182,8 +182,8 @@ terms in the forms:
    
 
    
 
    Compiling pop∘swap∘roll<
    
 
    The simplest way to “compile” this function would be something like:
    
-
    def poswrd(s, e, d):
-    return rolldown(*swap(*pop(s, e, d)))
+
    def poswrd(s, e, d):
+    return rolldown(*swap(*pop(s, e, d)))
 
    
 
    
 
    However, internally this function would still be allocating tuples
@@ -193,9 +193,9 @@ terms in the forms:
    
 
    
 
    
 
    We should be able to directly write out a Python function like:
    
-
    def poswrd(stack):
-    (_, (a, (b, (c, stack)))) = stack
-    return (c, (b, (a, stack)))
+
    def poswrd(stack):
+    (_, (a, (b, (c, stack)))) = stack
+    return (c, (b, (a, stack)))
 
    
 
    
 
    This eliminates the internal work of the first version. Because this
@@ -243,14 +243,14 @@ available index number for the right-side stack effect comment):
    
 
    
 
    
 
    Re-label (the tails of the lists on each side each get their own label):
    
-
    ([4 .0.] 2 3 0 -- 3 2 [.0.]) ([5 .1.] -- [.1.])
+
    ([4 .0.] 2 3 0 -- 3 2 [.0.]) ([5 .1.] -- [.1.])
 
    
 
    
 
    Unify and update (note the opening square brackets have been omited in
 the substitution dict, this is deliberate and I’ll explain below):
    
-
    ([4 .0.]   2 3 0 -- 3 2 [.0.]  ) ([5 .1.] -- [.1.])
-                                                    w/ { .0.] : 5 .1.] }
-([4 5 .1.] 2 3 0 -- 3 2 [5 .1.]) ([5 .1.] -- [.1.])
+
    ([4 .0.]   2 3 0 -- 3 2 [.0.]  ) ([5 .1.] -- [.1.])
+                                                    w/ { .0.] : 5 .1.] }
+([4 5 .1.] 2 3 0 -- 3 2 [5 .1.]) ([5 .1.] -- [.1.])
 
    
 
    
 
    How do we find .0.] in [4 .0.] and replace it with 5 .1.]
@@ -258,15 +258,15 @@ getting the result 
 underlying structure of the Joy list is a cons-list in Python it’s
 actually pretty easy. I’ll explain below.
    
 
    Next we unify and find our two terms are the same already: [5 .1.]:
    
-
    ([4 5 .1.] 2 3 0 -- 3 2 [5 .1.]) ([5 .1.] -- [.1.])
+
    ([4 5 .1.] 2 3 0 -- 3 2 [5 .1.]) ([5 .1.] -- [.1.])
 
    
 
    
 
    Giving us:
    
-
    ([4 5 .1.] 2 3 0 -- 3 2) (-- [.1.])
+
    ([4 5 .1.] 2 3 0 -- 3 2) (-- [.1.])
 
    
 
    
 
    From here we apply the first rule and get:
    
-
    ([4 5 .1.] 2 3 0 -- 3 2 [.1.])
+
    ([4 5 .1.] 2 3 0 -- 3 2 [.1.])
 
    
 
    
 
    Cleaning up the labels:
    
@@ -281,19 +281,19 @@ actually pretty easy. I’ll explain below.
    
 
    
 
    
 
    Re-label:
    
-
    ([4 5 .1.] 2 3 1 -- 3 2 [.1.]) (6 [.2.] -- [6 .2.])
+
    ([4 5 .1.] 2 3 1 -- 3 2 [.1.]) (6 [.2.] -- [6 .2.])
 
    
 
    
 
    Unify:
    
-
    ([4 5 .1.] 2 3 1 -- 3 2 [.1.]) (6 [.2.] -- [6 .2.])
-                                                     w/ { .1.] : .2.] }
-([4 5 .2.] 2 3 1 -- 3 2      ) (6       -- [6 .2.])
+
    ([4 5 .1.] 2 3 1 -- 3 2 [.1.]) (6 [.2.] -- [6 .2.])
+                                                     w/ { .1.] : .2.] }
+([4 5 .2.] 2 3 1 -- 3 2      ) (6       -- [6 .2.])
                                                      w/ {2: 6}
-([4 5 .2.] 6 3 1 -- 3        ) (        -- [6 .2.])
+([4 5 .2.] 6 3 1 -- 3        ) (        -- [6 .2.])
 
    
 
    
 
    First rule:
    
-
    ([4 5 .2.] 6 3 1 -- 3 [6 .2.])
+
    ([4 5 .2.] 6 3 1 -- 3 [6 .2.])
 
    
 
    
 
    Re-label:
    
@@ -309,19 +309,19 @@ actually pretty easy. I’ll explain below.
    
 
    
 
    
 
    Re-label:
    
-
    ([4 5 .1.] 2 3 1 -- 3 [2 .1.]) (6 [.2.] -- [6 .2.])
+
    ([4 5 .1.] 2 3 1 -- 3 [2 .1.]) (6 [.2.] -- [6 .2.])
 
    
 
    
 
    Unify:
    
-
    ([4 5 .1.] 2 3 1 -- 3 [2 .1.]) (6 [.2.] -- [6 .2.]  )
-                                                       w/ { .2.] : 2 .1.] }
-([4 5 .1.] 2 3 1 -- 3        ) (6       -- [6 2 .1.])
+
    ([4 5 .1.] 2 3 1 -- 3 [2 .1.]) (6 [.2.] -- [6 .2.]  )
+                                                       w/ { .2.] : 2 .1.] }
+([4 5 .1.] 2 3 1 -- 3        ) (6       -- [6 2 .1.])
                                                        w/ {3: 6}
-([4 5 .1.] 2 6 1 --          ) (        -- [6 2 .1.])
+([4 5 .1.] 2 6 1 --          ) (        -- [6 2 .1.])
 
    
 
    
 
    First or second rule:
    
-
    ([4 5 .1.] 2 6 1 -- [6 2 .1.])
+
    ([4 5 .1.] 2 6 1 -- [6 2 .1.])
 
    
 
    
 
    Clean up the labels:
    
@@ -335,9 +335,9 @@ actually pretty easy. I’ll explain below.
    
 
    
 
    From this stack effect comment it should be possible to construct the
 following Python code:
    
-
    def F(stack):
-    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
-    return (d, (c, S0)), stack
+
    def F(stack):
+    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
+    return (d, (c, S0)), stack
 
    
 
    
 
    
@@ -348,96 +348,96 @@ following Python code:
    
 
    Representing Stack Effect Comments in Python
    
 
    I’m going to use pairs of tuples of type descriptors, which will be
 integers or tuples of type descriptors:
    
-
    roll_dn = (1, 2, 3), (2, 3, 1)
+
    roll_dn = (1, 2, 3), (2, 3, 1)
 
-pop = (1,), ()
+pop = (1,), ()
 
-swap = (1, 2), (2, 1)
+swap = (1, 2), (2, 1)
 
    
 
    
 
    
 
    
 
    compose()
    
-
    def compose(f, g):
+
    def compose(f, g):
 
-    (f_in, f_out), (g_in, g_out) = f, g
+    (f_in, f_out), (g_in, g_out) = f, g
 
-    # First rule.
-    #
-    #       (a -- b) (-- d)
-    #    ---------------------
-    #         (a -- b d)
+    # First rule.
+    #
+    #       (a -- b) (-- d)
+    #    ---------------------
+    #         (a -- b d)
 
-    if not g_in:
+    if not g_in:
 
-        fg_in, fg_out = f_in, f_out + g_out
+        fg_in, fg_out = f_in, f_out + g_out
 
-    # Second rule.
-    #
-    #       (a --) (c -- d)
-    #    ---------------------
-    #         (c a -- d)
+    # Second rule.
+    #
+    #       (a --) (c -- d)
+    #    ---------------------
+    #         (c a -- d)
 
-    elif not f_out:
+    elif not f_out:
 
-        fg_in, fg_out = g_in + f_in, g_out
+        fg_in, fg_out = g_in + f_in, g_out
 
-    else: # Unify, update, recur.
+    else: # Unify, update, recur.
 
-        fo, gi = f_out[-1], g_in[-1]
+        fo, gi = f_out[-1], g_in[-1]
 
-        s = unify(gi, fo)
+        s = unify(gi, fo)
 
-        if s == False:  # s can also be the empty dict, which is ok.
-            raise TypeError('Cannot unify %r and %r.' % (fo, gi))
+        if s == False:  # s can also be the empty dict, which is ok.
+            raise TypeError('Cannot unify %r and %r.' % (fo, gi))
 
-        f_g = (f_in, f_out[:-1]), (g_in[:-1], g_out)
+        f_g = (f_in, f_out[:-1]), (g_in[:-1], g_out)
 
-        if s: f_g = update(s, f_g)
+        if s: f_g = update(s, f_g)
 
-        fg_in, fg_out = compose(*f_g)
+        fg_in, fg_out = compose(*f_g)
 
-    return fg_in, fg_out
+    return fg_in, fg_out
 
    
 
    
 
    
 
    
 
    unify()
    
-
    def unify(u, v, s=None):
-    if s is None:
-        s = {}
+
    def unify(u, v, s=None):
+    if s is None:
+        s = {}
 
-    if isinstance(u, int):
-        s[u] = v
-    elif isinstance(v, int):
-        s[v] = u
-    else:
-        s = False
+    if isinstance(u, int):
+        s[u] = v
+    elif isinstance(v, int):
+        s[v] = u
+    else:
+        s = False
 
-    return s
+    return s
 
    
 
    
 
    
 
    
 
    update()
    
-
    def update(s, term):
-    if not isinstance(term, tuple):
-        return s.get(term, term)
-    return tuple(update(s, inner) for inner in term)
+
    def update(s, term):
+    if not isinstance(term, tuple):
+        return s.get(term, term)
+    return tuple(update(s, inner) for inner in term)
 
    
 
    
 
    
 
    
 
    relabel()
    
-
    def relabel(left, right):
-    return left, _1000(right)
+
    def relabel(left, right):
+    return left, _1000(right)
 
-def _1000(right):
-    if not isinstance(right, tuple):
-        return 1000 + right
-    return tuple(_1000(n) for n in right)
+def _1000(right):
+    if not isinstance(right, tuple):
+        return 1000 + right
+    return tuple(_1000(n) for n in right)
 
-relabel(pop, swap)
+relabel(pop, swap)
 
    
 
    
 
    (((1,), ()), ((1001, 1002), (1002, 1001)))
@@ -446,21 +446,21 @@ integers or tuples of type descriptors:
    
 
    
 
    
 
    delabel()
    
-
    def delabel(f):
-    s = {u: i for i, u in enumerate(sorted(_unique(f)))}
-    return update(s, f)
+
    def delabel(f):
+    s = {u: i for i, u in enumerate(sorted(_unique(f)))}
+    return update(s, f)
 
-def _unique(f, seen=None):
-    if seen is None:
-        seen = set()
-    if not isinstance(f, tuple):
-        seen.add(f)
-    else:
-        for inner in f:
-            _unique(inner, seen)
-    return seen
+def _unique(f, seen=None):
+    if seen is None:
+        seen = set()
+    if not isinstance(f, tuple):
+        seen.add(f)
+    else:
+        for inner in f:
+            _unique(inner, seen)
+    return seen
 
-delabel(relabel(pop, swap))
+delabel(relabel(pop, swap))
 
    
 
    
 
    (((0,), ()), ((1, 2), (2, 1)))
@@ -472,39 +472,39 @@ integers or tuples of type descriptors:
    
 
    At last we put it all together in a function C() that accepts two
 stack effect comments and returns their composition (or raises and
 exception if they can’t be composed due to type conflicts.)
    
-
    def C(f, g):
-    f, g = relabel(f, g)
-    fg = compose(f, g)
-    return delabel(fg)
+
    def C(f, g):
+    f, g = relabel(f, g)
+    fg = compose(f, g)
+    return delabel(fg)
 
    
 
    
 
    Let’s try it out.
    
-
    C(pop, swap)
+
    C(pop, swap)
 
    
 
    
 
    ((1, 2, 0), (2, 1))
 
    
 
    
-
    C(C(pop, swap), roll_dn)
+
    C(C(pop, swap), roll_dn)
 
    
 
    
 
    ((3, 1, 2, 0), (2, 1, 3))
 
    
 
    
-
    C(swap, roll_dn)
+
    C(swap, roll_dn)
 
    
 
    
 
    ((2, 0, 1), (1, 0, 2))
 
    
 
    
-
    C(pop, C(swap, roll_dn))
+
    C(pop, C(swap, roll_dn))
 
    
 
    
 
    ((3, 1, 2, 0), (2, 1, 3))
 
    
 
    
-
    poswrd = reduce(C, (pop, swap, roll_dn))
-poswrd
+
    poswrd = reduce(C, (pop, swap, roll_dn))
+poswrd
 
    
 
    
 
    ((3, 1, 2, 0), (2, 1, 3))
@@ -516,12 +516,12 @@ exception if they can’t be composed due to type conflicts.)
    
 
    Here’s that trick to represent functions like rest and cons that
 manipulate stacks. We use a cons-list of tuples and give the tails their
 own numbers. Then everything above already works.
    
-
    rest = ((1, 2),), (2,)
+
    rest = ((1, 2),), (2,)
 
-cons = (1, 2), ((1, 2),)
+cons = (1, 2), ((1, 2),)
 
    
 
    
-
    C(poswrd, rest)
+
    C(poswrd, rest)
 
    
 
    
 
    (((3, 4), 1, 2, 0), (2, 1, 4))
@@ -542,9 +542,9 @@ own numbers. Then everything above already works.
    
 }
 
    
 
    
-
    F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons))
+
    F = reduce(C, (pop, swap, roll_dn, rest, rest, cons, cons))
 
-F
+F
 
    
 
    
 
    (((3, (4, 5)), 1, 2, 0), ((2, (1, 5)),))
@@ -560,13 +560,13 @@ own numbers. Then everything above already works.
    
 
    Dealing with cons and uncons
    
 
    However, if we try to compose e.g. cons and uncons it won’t
 work:
    
-
    uncons = ((1, 2),), (1, 2)
+
    uncons = ((1, 2),), (1, 2)
 
    
 
    
-
    try:
-    C(cons, uncons)
-except Exception, e:
-    print e
+
    try:
+    C(cons, uncons)
+except Exception, e:
+    print e
 
    
 
    
 
    Cannot unify (1, 2) and (1001, 1002).
@@ -577,36 +577,36 @@ work:
    
 
    The problem is that the unify() function as written doesn’t handle
 the case when both terms are tuples. We just have to add a clause to
 deal with this recursively:
    
-
    def unify(u, v, s=None):
-    if s is None:
-        s = {}
-    elif s:
-        u = update(s, u)
-        v = update(s, v)
+
    def unify(u, v, s=None):
+    if s is None:
+        s = {}
+    elif s:
+        u = update(s, u)
+        v = update(s, v)
 
-    if isinstance(u, int):
-        s[u] = v
+    if isinstance(u, int):
+        s[u] = v
 
-    elif isinstance(v, int):
-        s[v] = u
+    elif isinstance(v, int):
+        s[v] = u
 
-    elif isinstance(u, tuple) and isinstance(v, tuple):
+    elif isinstance(u, tuple) and isinstance(v, tuple):
 
-        if len(u) != 2 or len(v) != 2:
-            # Not a type error, caller passed in a bad value.
-            raise ValueError(repr((u, v)))  # FIXME this message sucks.
+        if len(u) != 2 or len(v) != 2:
+            # Not a type error, caller passed in a bad value.
+            raise ValueError(repr((u, v)))  # FIXME this message sucks.
 
-        (a, b), (c, d) = u, v
-        s = unify(a, c, s)
-        if s != False:
-            s = unify(b, d, s)
-    else:
-        s = False
+        (a, b), (c, d) = u, v
+        s = unify(a, c, s)
+        if s != False:
+            s = unify(b, d, s)
+    else:
+        s = False
 
-    return s
+    return s
 
    
 
    
-
    C(cons, uncons)
+
    C(cons, uncons)
 
    
 
    
 
    ((0, 1), (0, 1))
@@ -618,13 +618,13 @@ deal with this recursively:
    
 
    
 
    Part III: Compiling Yin Functions
    
 
    Now consider the Python function we would like to derive:
    
-
    def F_python(stack):
-    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
-    return (d, (c, S0)), stack
+
    def F_python(stack):
+    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
+    return (d, (c, S0)), stack
 
    
 
    
 
    And compare it to the input stack effect comment tuple we just computed:
    
-
    F[0]
+
    F[0]
 
    
 
    
 
    ((3, (4, 5)), 1, 2, 0)
@@ -646,7 +646,7 @@ stack effect comment tuple, just in the reverse order:
    
 
    
 
    Eh?
    
 
    And the return tuple
    
-
    F[1]
+
    F[1]
 
    
 
    
 
    ((2, (1, 5)),)
@@ -666,21 +666,21 @@ effect.)
    
 
    Python Identifiers
    
 
    We want to substitute Python identifiers for the integers. I’m going to
 repurpose joy.parser.Symbol class for this:
    
-
    from collections import defaultdict
-from joy.parser import Symbol
+
    from collections import defaultdict
+from joy.parser import Symbol
 
 
-def _names_for():
-    I = iter(xrange(1000))
-    return lambda: Symbol('a%i' % next(I))
+def _names_for():
+    I = iter(xrange(1000))
+    return lambda: Symbol('a%i' % next(I))
 
 
-def identifiers(term, s=None):
-    if s is None:
-        s = defaultdict(_names_for())
-    if isinstance(term, int):
-        return s[term]
-    return tuple(identifiers(inner, s) for inner in term)
+def identifiers(term, s=None):
+    if s is None:
+        s = defaultdict(_names_for())
+    if isinstance(term, int):
+        return s[term]
+    return tuple(identifiers(inner, s) for inner in term)
 
    
 
    
 
    
@@ -690,36 +690,36 @@ repurpose joy.parse
 effect comment tuples to reasonable text format. There are some details
 in how this code works that related to stuff later in the notebook, so
 you should skip it for now and read it later if you’re interested.
    
-
    def doc_from_stack_effect(inputs, outputs):
-    return '(%s--%s)' % (
-        ' '.join(map(_to_str, inputs + ('',))),
-        ' '.join(map(_to_str, ('',) + outputs))
-    )
+
    def doc_from_stack_effect(inputs, outputs):
+    return '(%s--%s)' % (
+        ' '.join(map(_to_str, inputs + ('',))),
+        ' '.join(map(_to_str, ('',) + outputs))
+    )
 
 
-def _to_str(term):
-    if not isinstance(term, tuple):
-        try:
-            t = term.prefix == 's'
-        except AttributeError:
-            return str(term)
-        return '[.%i.]' % term.number if t else str(term)
+def _to_str(term):
+    if not isinstance(term, tuple):
+        try:
+            t = term.prefix == 's'
+        except AttributeError:
+            return str(term)
+        return '[.%i.]' % term.number if t else str(term)
 
-    a = []
-    while term and isinstance(term, tuple):
-        item, term = term
-        a.append(_to_str(item))
+    a = []
+    while term and isinstance(term, tuple):
+        item, term = term
+        a.append(_to_str(item))
 
-    try:
-        n = term.number
-    except AttributeError:
-        n = term
-    else:
-        if term.prefix != 's':
-            raise ValueError('Stack label: %s' % (term,))
+    try:
+        n = term.number
+    except AttributeError:
+        n = term
+    else:
+        if term.prefix != 's':
+            raise ValueError('Stack label: %s' % (term,))
 
-    a.append('.%s.' % (n,))
-    return '[%s]' % ' '.join(a)
+    a.append('.%s.' % (n,))
+    return '[%s]' % ' '.join(a)
 
    
 
    
 
    
@@ -728,25 +728,25 @@ you should skip it for now and read it later if you’re interested.
    
 
    Now we can write a compiler function to emit Python source code. (The
 underscore suffix distiguishes it from the built-in compile()
 function.)
    
-
    def compile_(name, f, doc=None):
-    if doc is None:
-        doc = doc_from_stack_effect(*f)
-    inputs, outputs = identifiers(f)
-    i = o = Symbol('stack')
-    for term in inputs:
-        i = term, i
-    for term in outputs:
-        o = term, o
-    return '''def %s(stack):
-    """%s"""
-    %s = stack
-    return %s''' % (name, doc, i, o)
+
    def compile_(name, f, doc=None):
+    if doc is None:
+        doc = doc_from_stack_effect(*f)
+    inputs, outputs = identifiers(f)
+    i = o = Symbol('stack')
+    for term in inputs:
+        i = term, i
+    for term in outputs:
+        o = term, o
+    return '''def %s(stack):
+    """%s"""
+    %s = stack
+    return %s''' % (name, doc, i, o)
 
    
 
    
 
    Here it is in action:
    
-
    source = compile_('F', F)
+
    source = compile_('F', F)
 
-print source
+print source
 
    
 
    
 
    def F(stack):
@@ -756,31 +756,31 @@ function.)
    
 
    
 
    
 
    Compare:
    
-
    def F_python(stack):
-    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
-    return ((d, (c, S0)), stack)
+
    def F_python(stack):
+    (_, (d, (c, ((a, (b, S0)), stack)))) = stack
+    return ((d, (c, S0)), stack)
 
    
 
    
 
    Next steps:
    
-
    L = {}
+
    L = {}
 
-eval(compile(source, '__main__', 'single'), {}, L)
+eval(compile(source, '__main__', 'single'), {}, L)
 
-L['F']
+L['F']
 
    
 
    
 
    <function F>
 
    
 
    
 
    Let’s try it out:
    
-
    from notebook_preamble import D, J, V
-from joy.library import SimpleFunctionWrapper
+
    from notebook_preamble import D, J, V
+from joy.library import SimpleFunctionWrapper
 
    
 
    
-
    D['F'] = SimpleFunctionWrapper(L['F'])
+
    D['F'] = SimpleFunctionWrapper(L['F'])
 
    
 
    
-
    J('[4 5 ...] 2 3 1 F')
+
    J('[4 5 ...] 2 3 1 F')
 
    
 
    
 
    [3 2 ...]
@@ -800,33 +800,33 @@ this might be less helpful.
    
 
    Compiling Library Functions
    
 
    We can use compile_() to generate many primitives in the library
 from their stack effect comments:
    
-
    def defs():
+
    def defs():
 
-    rolldown = (1, 2, 3), (2, 3, 1)
+    rolldown = (1, 2, 3), (2, 3, 1)
 
-    rollup = (1, 2, 3), (3, 1, 2)
+    rollup = (1, 2, 3), (3, 1, 2)
 
-    pop = (1,), ()
+    pop = (1,), ()
 
-    swap = (1, 2), (2, 1)
+    swap = (1, 2), (2, 1)
 
-    rest = ((1, 2),), (2,)
+    rest = ((1, 2),), (2,)
 
-    rrest = C(rest, rest)
+    rrest = C(rest, rest)
 
-    cons = (1, 2), ((1, 2),)
+    cons = (1, 2), ((1, 2),)
 
-    uncons = ((1, 2),), (1, 2)
+    uncons = ((1, 2),), (1, 2)
 
-    swons = C(swap, cons)
+    swons = C(swap, cons)
 
-    return locals()
+    return locals()
 
    
 
    
-
    for name, stack_effect_comment in sorted(defs().items()):
-    print
-    print compile_(name, stack_effect_comment)
-    print
+
    for name, stack_effect_comment in sorted(defs().items()):
+    print
+    print compile_(name, stack_effect_comment)
+    print
 
    
 
    
 
    def cons(stack):
@@ -966,57 +966,57 @@ and t
 Python class hierarchy of Joy types and use the issubclass() method
 to establish domain ordering, as well as other handy behaviour that will
 make it fairly easy to reuse most of the code above.
    
-
    class AnyJoyType(object):
+
    class AnyJoyType(object):
 
-    prefix = 'a'
+    prefix = 'a'
 
-    def __init__(self, number):
-        self.number = number
+    def __init__(self, number):
+        self.number = number
 
-    def __repr__(self):
-        return self.prefix + str(self.number)
+    def __repr__(self):
+        return self.prefix + str(self.number)
 
-    def __eq__(self, other):
-        return (
-            isinstance(other, self.__class__)
-            and other.prefix == self.prefix
-            and other.number == self.number
-        )
+    def __eq__(self, other):
+        return (
+            isinstance(other, self.__class__)
+            and other.prefix == self.prefix
+            and other.number == self.number
+        )
 
-    def __ge__(self, other):
-        return issubclass(other.__class__, self.__class__)
+    def __ge__(self, other):
+        return issubclass(other.__class__, self.__class__)
 
-    def __add__(self, other):
-        return self.__class__(self.number + other)
-    __radd__ = __add__
+    def __add__(self, other):
+        return self.__class__(self.number + other)
+    __radd__ = __add__
 
-    def __hash__(self):
-        return hash(repr(self))
+    def __hash__(self):
+        return hash(repr(self))
 
 
-class NumberJoyType(AnyJoyType): prefix = 'n'
-class FloatJoyType(NumberJoyType): prefix = 'f'
-class IntJoyType(FloatJoyType): prefix = 'i'
+class NumberJoyType(AnyJoyType): prefix = 'n'
+class FloatJoyType(NumberJoyType): prefix = 'f'
+class IntJoyType(FloatJoyType): prefix = 'i'
 
 
-class StackJoyType(AnyJoyType):
-    prefix = 's'
+class StackJoyType(AnyJoyType):
+    prefix = 's'
 
 
-_R = range(10)
-A = map(AnyJoyType, _R)
-N = map(NumberJoyType, _R)
-S = map(StackJoyType, _R)
+_R = range(10)
+A = map(AnyJoyType, _R)
+N = map(NumberJoyType, _R)
+S = map(StackJoyType, _R)
 
    
 
    
 
    Mess with it a little:
    
-
    from itertools import permutations
+
    from itertools import permutations
 
    
 
    
 
    “Any” types can be specialized to numbers and stacks, but not vice
 versa:
    
-
    for a, b in permutations((A[0], N[0], S[0]), 2):
-    print a, '>=', b, '->', a >= b
+
    for a, b in permutations((A[0], N[0], S[0]), 2):
+    print a, '>=', b, '->', a >= b
 
    
 
    
 
    a0 >= n0 -> True
@@ -1030,8 +1030,8 @@ versa:
    
 
    Our crude Numerical
 Tower of numbers >
 floats > integers works as well (but we’re not going to use it yet):
    
-
    for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2):
-    print a, '>=', b, '->', a >= b
+
    for a, b in permutations((A[0], N[0], FloatJoyType(0), IntJoyType(0)), 2):
+    print a, '>=', b, '->', a >= b
 
    
 
    
 
    a0 >= n0 -> True
@@ -1051,18 +1051,18 @@ Tower of numbers >
 
    
 
    
 
    Typing sqr
    
-
    dup = (A[1],), (A[1], A[1])
+
    dup = (A[1],), (A[1], A[1])
 
-mul = (N[1], N[2]), (N[3],)
+mul = (N[1], N[2]), (N[3],)
 
    
 
    
-
    dup
+
    dup
 
    
 
    
 
    ((a1,), (a1, a1))
 
    
 
    
-
    mul
+
    mul
 
    
 
    
 
    ((n1, n2), (n3,))
@@ -1072,9 +1072,9 @@ Tower of numbers >
 
    
 
    Modifying the Inferencer
    
 
    Re-labeling still works fine:
    
-
    foo = relabel(dup, mul)
+
    foo = relabel(dup, mul)
 
-foo
+foo
 
    
 
    
 
    (((a1,), (a1, a1)), ((n1001, n1002), (n1003,)))
@@ -1084,28 +1084,28 @@ Tower of numbers >
 
    delabel() version 2
    
 
    The delabel() function needs an overhaul. It now has to keep track
 of how many labels of each domain it has “seen”.
    
-
    from collections import Counter
+
    from collections import Counter
 
 
-def delabel(f, seen=None, c=None):
-    if seen is None:
-        assert c is None
-        seen, c = {}, Counter()
+def delabel(f, seen=None, c=None):
+    if seen is None:
+        assert c is None
+        seen, c = {}, Counter()
 
-    try:
-        return seen[f]
-    except KeyError:
-        pass
+    try:
+        return seen[f]
+    except KeyError:
+        pass
 
-    if not isinstance(f, tuple):
-        seen[f] = f.__class__(c[f.prefix] + 1)
-        c[f.prefix] += 1
-        return seen[f]
+    if not isinstance(f, tuple):
+        seen[f] = f.__class__(c[f.prefix] + 1)
+        c[f.prefix] += 1
+        return seen[f]
 
-    return tuple(delabel(inner, seen, c) for inner in f)
+    return tuple(delabel(inner, seen, c) for inner in f)
 
    
 
    
-
    delabel(foo)
+
    delabel(foo)
 
    
 
    
 
    (((a1,), (a1, a1)), ((n1, n2), (n3,)))
@@ -1114,120 +1114,120 @@ of how many labels of each domain it has “seen”.
    
 
    
 
    
 
    unify() version 3
    
-
    def unify(u, v, s=None):
-    if s is None:
-        s = {}
-    elif s:
-        u = update(s, u)
-        v = update(s, v)
+
    def unify(u, v, s=None):
+    if s is None:
+        s = {}
+    elif s:
+        u = update(s, u)
+        v = update(s, v)
 
-    if u == v:
-        return s
+    if u == v:
+        return s
 
-    if isinstance(u, AnyJoyType) and isinstance(v, AnyJoyType):
-        if u >= v:
-            s[u] = v
-            return s
-        if v >= u:
-            s[v] = u
-            return s
-        raise TypeError('Cannot unify %r and %r.' % (u, v))
+    if isinstance(u, AnyJoyType) and isinstance(v, AnyJoyType):
+        if u >= v:
+            s[u] = v
+            return s
+        if v >= u:
+            s[v] = u
+            return s
+        raise TypeError('Cannot unify %r and %r.' % (u, v))
 
-    if isinstance(u, tuple) and isinstance(v, tuple):
-        if len(u) != len(v) != 2:
-            raise TypeError(repr((u, v)))
-        for uu, vv in zip(u, v):
-            s = unify(uu, vv, s)
-            if s == False: # (instead of a substitution dict.)
-                break
-        return s
+    if isinstance(u, tuple) and isinstance(v, tuple):
+        if len(u) != len(v) != 2:
+            raise TypeError(repr((u, v)))
+        for uu, vv in zip(u, v):
+            s = unify(uu, vv, s)
+            if s == False: # (instead of a substitution dict.)
+                break
+        return s
 
-    if isinstance(v, tuple):
-        if not stacky(u):
-            raise TypeError('Cannot unify %r and %r.' % (u, v))
-        s[u] = v
-        return s
+    if isinstance(v, tuple):
+        if not stacky(u):
+            raise TypeError('Cannot unify %r and %r.' % (u, v))
+        s[u] = v
+        return s
 
-    if isinstance(u, tuple):
-        if not stacky(v):
-            raise TypeError('Cannot unify %r and %r.' % (v, u))
-        s[v] = u
-        return s
+    if isinstance(u, tuple):
+        if not stacky(v):
+            raise TypeError('Cannot unify %r and %r.' % (v, u))
+        s[v] = u
+        return s
 
-    return False
+    return False
 
 
-def stacky(thing):
-    return thing.__class__ in {AnyJoyType, StackJoyType}
+def stacky(thing):
+    return thing.__class__ in {AnyJoyType, StackJoyType}
 
    
 
    
 
    Rewrite the stack effect comments:
    
-
    def defs():
+
    def defs():
 
-    rolldown = (A[1], A[2], A[3]), (A[2], A[3], A[1])
+    rolldown = (A[1], A[2], A[3]), (A[2], A[3], A[1])
 
-    rollup = (A[1], A[2], A[3]), (A[3], A[1], A[2])
+    rollup = (A[1], A[2], A[3]), (A[3], A[1], A[2])
 
-    pop = (A[1],), ()
+    pop = (A[1],), ()
 
-    popop = (A[2], A[1],), ()
+    popop = (A[2], A[1],), ()
 
-    popd = (A[2], A[1],), (A[1],)
+    popd = (A[2], A[1],), (A[1],)
 
-    popdd = (A[3], A[2], A[1],), (A[2], A[1],)
+    popdd = (A[3], A[2], A[1],), (A[2], A[1],)
 
-    swap = (A[1], A[2]), (A[2], A[1])
+    swap = (A[1], A[2]), (A[2], A[1])
 
-    rest = ((A[1], S[1]),), (S[1],)
+    rest = ((A[1], S[1]),), (S[1],)
 
-    rrest = C(rest, rest)
+    rrest = C(rest, rest)
 
-    cons = (A[1], S[1]), ((A[1], S[1]),)
+    cons = (A[1], S[1]), ((A[1], S[1]),)
 
-    ccons = C(cons, cons)
+    ccons = C(cons, cons)
 
-    uncons = ((A[1], S[1]),), (A[1], S[1])
+    uncons = ((A[1], S[1]),), (A[1], S[1])
 
-    swons = C(swap, cons)
+    swons = C(swap, cons)
 
-    dup = (A[1],), (A[1], A[1])
+    dup = (A[1],), (A[1], A[1])
 
-    dupd = (A[2], A[1]), (A[2], A[2], A[1])
+    dupd = (A[2], A[1]), (A[2], A[2], A[1])
 
-    mul = (N[1], N[2]), (N[3],)
+    mul = (N[1], N[2]), (N[3],)
 
-    sqrt = C(dup, mul)
+    sqrt = C(dup, mul)
 
-    first = ((A[1], S[1]),), (A[1],)
+    first = ((A[1], S[1]),), (A[1],)
 
-    second = C(rest, first)
+    second = C(rest, first)
 
-    third = C(rest, second)
+    third = C(rest, second)
 
-    tuck = (A[2], A[1]), (A[1], A[2], A[1])
+    tuck = (A[2], A[1]), (A[1], A[2], A[1])
 
-    over = (A[2], A[1]), (A[2], A[1], A[2])
+    over = (A[2], A[1]), (A[2], A[1], A[2])
 
-    succ = pred = (N[1],), (N[2],)
+    succ = pred = (N[1],), (N[2],)
 
-    divmod_ = pm = (N[2], N[1]), (N[4], N[3])
+    divmod_ = pm = (N[2], N[1]), (N[4], N[3])
 
-    return locals()
+    return locals()
 
    
 
    
-
    DEFS = defs()
+
    DEFS = defs()
 
    
 
    
-
    for name, stack_effect_comment in sorted(DEFS.items()):
-    print name, '=', doc_from_stack_effect(*stack_effect_comment)
+
    for name, stack_effect_comment in sorted(DEFS.items()):
+    print name, '=', doc_from_stack_effect(*stack_effect_comment)
 
    
 
    
-
    ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
-cons = (a1 [.1.] -- [a1 .1.])
+
    ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
+cons = (a1 [.1.] -- [a1 .1.])
 divmod_ = (n2 n1 -- n4 n3)
 dup = (a1 -- a1 a1)
 dupd = (a2 a1 -- a2 a2 a1)
-first = ([a1 .1.] -- a1)
+first = ([a1 .1.] -- a1)
 mul = (n1 n2 -- n3)
 over = (a2 a1 -- a2 a1 a2)
 pm = (n2 n1 -- n4 n3)
@@ -1236,68 +1236,68 @@ of how many labels of each domain it has “seen”.
    
 popdd = (a3 a2 a1 -- a2 a1)
 popop = (a2 a1 --)
 pred = (n1 -- n2)
-rest = ([a1 .1.] -- [.1.])
+rest = ([a1 .1.] -- [.1.])
 rolldown = (a1 a2 a3 -- a2 a3 a1)
 rollup = (a1 a2 a3 -- a3 a1 a2)
-rrest = ([a1 a2 .1.] -- [.1.])
-second = ([a1 a2 .1.] -- a2)
+rrest = ([a1 a2 .1.] -- [.1.])
+second = ([a1 a2 .1.] -- a2)
 sqrt = (n1 -- n2)
 succ = (n1 -- n2)
 swap = (a1 a2 -- a2 a1)
-swons = ([.1.] a1 -- [a1 .1.])
-third = ([a1 a2 a3 .1.] -- a3)
+swons = ([.1.] a1 -- [a1 .1.])
+third = ([a1 a2 a3 .1.] -- a3)
 tuck = (a2 a1 -- a1 a2 a1)
-uncons = ([a1 .1.] -- a1 [.1.])
+uncons = ([a1 .1.] -- a1 [.1.])
 
    
 
    
-
    globals().update(DEFS)
+
    globals().update(DEFS)
 
    
 
    
 
    
 
    
 
    Compose dup and mul
    
-
    C(dup, mul)
+
    C(dup, mul)
 
    
 
    
 
    ((n1,), (n2,))
 
    
 
    
 
    Revisit the F function, works fine.
    
-
    F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
-F
+
    F = reduce(C, (pop, swap, rolldown, rest, rest, cons, cons))
+F
 
    
 
    
 
    (((a1, (a2, s1)), a3, a4, a5), ((a4, (a3, s1)),))
 
    
 
    
-
    print doc_from_stack_effect(*F)
+
    print doc_from_stack_effect(*F)
 
    
 
    
-
    ([a1 a2 .1.] a3 a4 a5 -- [a4 a3 .1.])
+
    ([a1 a2 .1.] a3 a4 a5 -- [a4 a3 .1.])
 
    
 
    
 
    Some otherwise inefficient functions are no longer to be feared. We can
 also get the effect of combinators in some limited cases.
    
-
    def neato(*funcs):
-    print doc_from_stack_effect(*reduce(C, funcs))
+
    def neato(*funcs):
+    print doc_from_stack_effect(*reduce(C, funcs))
 
    
 
    
-
    # e.g. [swap] dip
-neato(rollup, swap, rolldown)
+
    # e.g. [swap] dip
+neato(rollup, swap, rolldown)
 
    
 
    
 
    (a1 a2 a3 -- a2 a1 a3)
 
    
 
    
-
    # e.g. [popop] dipd
-neato(popdd, rolldown, pop)
+
    # e.g. [popop] dipd
+neato(popdd, rolldown, pop)
 
    
 
    
 
    (a1 a2 a3 a4 -- a3 a4)
 
    
 
    
-
    # Reverse the order of the top three items.
-neato(rollup, swap)
+
    # Reverse the order of the top three items.
+neato(rollup, swap)
 
    
 
    
 
    (a1 a2 a3 -- a3 a2 a1)
@@ -1308,22 +1308,22 @@ also get the effect of combinators in some limited cases.
    
 
    compile_() version 2
    
 
    Because the type labels represent themselves as valid Python identifiers
 the compile_() function doesn’t need to generate them anymore:
    
-
    def compile_(name, f, doc=None):
-    inputs, outputs = f
-    if doc is None:
-        doc = doc_from_stack_effect(inputs, outputs)
-    i = o = Symbol('stack')
-    for term in inputs:
-        i = term, i
-    for term in outputs:
-        o = term, o
-    return '''def %s(stack):
-    """%s"""
-    %s = stack
-    return %s''' % (name, doc, i, o)
+
    def compile_(name, f, doc=None):
+    inputs, outputs = f
+    if doc is None:
+        doc = doc_from_stack_effect(inputs, outputs)
+    i = o = Symbol('stack')
+    for term in inputs:
+        i = term, i
+    for term in outputs:
+        o = term, o
+    return '''def %s(stack):
+    """%s"""
+    %s = stack
+    return %s''' % (name, doc, i, o)
 
    
 
    
-
    print compile_('F', F)
+
    print compile_('F', F)
 
    
 
    
 
    def F(stack):
@@ -1334,7 +1334,7 @@ the compile_()
 
    But it cannot magically create new functions that involve e.g. math and
 such. Note that this is not a sqr function implementation:
    
-
    print compile_('sqr', C(dup, mul))
+
    print compile_('sqr', C(dup, mul))
 
    
 
    
 
    def sqr(stack):
@@ -1356,38 +1356,38 @@ functions (at least) are already wrappers it should be straightforward.)
    
 
    The functions that can be compiled are the ones that have only
 AnyJoyType and StackJoyType labels in their stack effect
 comments. We can write a function to check that:
    
-
    from itertools import imap
+
    from itertools import imap
 
 
-def compilable(f):
-    return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f)
+def compilable(f):
+    return isinstance(f, tuple) and all(imap(compilable, f)) or stacky(f)
 
    
 
    
-
    for name, stack_effect_comment in sorted(defs().items()):
-    if compilable(stack_effect_comment):
-        print name, '=', doc_from_stack_effect(*stack_effect_comment)
+
    for name, stack_effect_comment in sorted(defs().items()):
+    if compilable(stack_effect_comment):
+        print name, '=', doc_from_stack_effect(*stack_effect_comment)
 
    
 
    
-
    ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
-cons = (a1 [.1.] -- [a1 .1.])
+
    ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
+cons = (a1 [.1.] -- [a1 .1.])
 dup = (a1 -- a1 a1)
 dupd = (a2 a1 -- a2 a2 a1)
-first = ([a1 .1.] -- a1)
+first = ([a1 .1.] -- a1)
 over = (a2 a1 -- a2 a1 a2)
 pop = (a1 --)
 popd = (a2 a1 -- a1)
 popdd = (a3 a2 a1 -- a2 a1)
 popop = (a2 a1 --)
-rest = ([a1 .1.] -- [.1.])
+rest = ([a1 .1.] -- [.1.])
 rolldown = (a1 a2 a3 -- a2 a3 a1)
 rollup = (a1 a2 a3 -- a3 a1 a2)
-rrest = ([a1 a2 .1.] -- [.1.])
-second = ([a1 a2 .1.] -- a2)
+rrest = ([a1 a2 .1.] -- [.1.])
+second = ([a1 a2 .1.] -- a2)
 swap = (a1 a2 -- a2 a1)
-swons = ([.1.] a1 -- [a1 .1.])
-third = ([a1 a2 a3 .1.] -- a3)
+swons = ([.1.] a1 -- [a1 .1.])
+third = ([a1 a2 a3 .1.] -- a3)
 tuck = (a2 a1 -- a1 a2 a1)
-uncons = ([a1 .1.] -- a1 [.1.])
+uncons = ([a1 .1.] -- a1 [.1.])
 
    
 
    
 
    
@@ -1465,36 +1465,36 @@ first two rules’ 
 the “truthiness” of StackJoyType to false to let e.g.
 joy.utils.stack.concat work with our stack effect comment cons-list
 tuples.)
    
-
    def compose(f, g):
-    (f_in, f_out), (g_in, g_out) = f, g
-    s = unify(g_in, f_out)
-    if s == False:  # s can also be the empty dict, which is ok.
-        raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-    return update(s, (f_in, g_out))
+
    def compose(f, g):
+    (f_in, f_out), (g_in, g_out) = f, g
+    s = unify(g_in, f_out)
+    if s == False:  # s can also be the empty dict, which is ok.
+        raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
+    return update(s, (f_in, g_out))
 
    
 
    
 
    I don’t want to rewrite all the defs myself, so I’ll write a little
 conversion function instead. This is programmer’s laziness.
    
-
    def sequence_to_stack(seq, stack=StackJoyType(23)):
-    for item in seq: stack = item, stack
-    return stack
+
    def sequence_to_stack(seq, stack=StackJoyType(23)):
+    for item in seq: stack = item, stack
+    return stack
 
-NEW_DEFS = {
-    name: (sequence_to_stack(i), sequence_to_stack(o))
-    for name, (i, o) in DEFS.iteritems()
-}
-NEW_DEFS['stack'] = S[0], (S[0], S[0])
-NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1])
-globals().update(NEW_DEFS)
+NEW_DEFS = {
+    name: (sequence_to_stack(i), sequence_to_stack(o))
+    for name, (i, o) in DEFS.iteritems()
+}
+NEW_DEFS['stack'] = S[0], (S[0], S[0])
+NEW_DEFS['swaack'] = (S[1], S[0]), (S[0], S[1])
+globals().update(NEW_DEFS)
 
    
 
    
-
    C(stack, uncons)
+
    C(stack, uncons)
 
    
 
    
 
    ((a1, s1), (s1, (a1, (a1, s1))))
 
    
 
    
-
    reduce(C, (stack, uncons, uncons))
+
    reduce(C, (stack, uncons, uncons))
 
    
 
    
 
    ((a1, (a2, s1)), (s1, (a2, (a1, (a1, (a2, s1))))))
@@ -1506,63 +1506,63 @@ conversion function instead. This is programmer’s laziness.
    
 
    
 
    doc_from_stack_effect() version 2
    
 
    Clunky junk, but it will suffice for now.
    
-
    def doc_from_stack_effect(inputs, outputs):
-    switch = [False]  # Do we need to display the '...' for the rest of the main stack?
-    i, o = _f(inputs, switch), _f(outputs, switch)
-    if switch[0]:
-        i.append('...')
-        o.append('...')
-    return '(%s--%s)' % (
-        ' '.join(reversed([''] + i)),
-        ' '.join(reversed(o + [''])),
-    )
+
    def doc_from_stack_effect(inputs, outputs):
+    switch = [False]  # Do we need to display the '...' for the rest of the main stack?
+    i, o = _f(inputs, switch), _f(outputs, switch)
+    if switch[0]:
+        i.append('...')
+        o.append('...')
+    return '(%s--%s)' % (
+        ' '.join(reversed([''] + i)),
+        ' '.join(reversed(o + [''])),
+    )
 
 
-def _f(term, switch):
-    a = []
-    while term and isinstance(term, tuple):
-        item, term = term
-        a.append(item)
-    assert isinstance(term, StackJoyType), repr(term)
-    a = [_to_str(i, term, switch) for i in a]
-    return a
+def _f(term, switch):
+    a = []
+    while term and isinstance(term, tuple):
+        item, term = term
+        a.append(item)
+    assert isinstance(term, StackJoyType), repr(term)
+    a = [_to_str(i, term, switch) for i in a]
+    return a
 
 
-def _to_str(term, stack, switch):
-    if not isinstance(term, tuple):
-        if term == stack:
-            switch[0] = True
-            return '[...]'
-        return (
-            '[.%i.]' % term.number
-            if isinstance(term, StackJoyType)
-            else str(term)
-        )
+def _to_str(term, stack, switch):
+    if not isinstance(term, tuple):
+        if term == stack:
+            switch[0] = True
+            return '[...]'
+        return (
+            '[.%i.]' % term.number
+            if isinstance(term, StackJoyType)
+            else str(term)
+        )
 
-    a = []
-    while term and isinstance(term, tuple):
-        item, term = term
-        a.append(_to_str(item, stack, switch))
-    assert isinstance(term, StackJoyType), repr(term)
-    if term == stack:
-        switch[0] = True
-        end = '...'
-    else:
-        end = '.%i.' % term.number
-    a.append(end)
-    return '[%s]' % ' '.join(a)
+    a = []
+    while term and isinstance(term, tuple):
+        item, term = term
+        a.append(_to_str(item, stack, switch))
+    assert isinstance(term, StackJoyType), repr(term)
+    if term == stack:
+        switch[0] = True
+        end = '...'
+    else:
+        end = '.%i.' % term.number
+    a.append(end)
+    return '[%s]' % ' '.join(a)
 
    
 
    
-
    for name, stack_effect_comment in sorted(NEW_DEFS.items()):
-    print name, '=', doc_from_stack_effect(*stack_effect_comment)
+
    for name, stack_effect_comment in sorted(NEW_DEFS.items()):
+    print name, '=', doc_from_stack_effect(*stack_effect_comment)
 
    
 
    
-
    ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
-cons = (a1 [.1.] -- [a1 .1.])
+
    ccons = (a1 a2 [.1.] -- [a1 a2 .1.])
+cons = (a1 [.1.] -- [a1 .1.])
 divmod_ = (n2 n1 -- n4 n3)
 dup = (a1 -- a1 a1)
 dupd = (a2 a1 -- a2 a2 a1)
-first = ([a1 .1.] -- a1)
+first = ([a1 .1.] -- a1)
 mul = (n1 n2 -- n3)
 over = (a2 a1 -- a2 a1 a2)
 pm = (n2 n1 -- n4 n3)
@@ -1571,26 +1571,26 @@ conversion function instead. This is programmer’s laziness.
    
 popdd = (a3 a2 a1 -- a2 a1)
 popop = (a2 a1 --)
 pred = (n1 -- n2)
-rest = ([a1 .1.] -- [.1.])
+rest = ([a1 .1.] -- [.1.])
 rolldown = (a1 a2 a3 -- a2 a3 a1)
 rollup = (a1 a2 a3 -- a3 a1 a2)
-rrest = ([a1 a2 .1.] -- [.1.])
-second = ([a1 a2 .1.] -- a2)
+rrest = ([a1 a2 .1.] -- [.1.])
+second = ([a1 a2 .1.] -- a2)
 sqrt = (n1 -- n2)
 stack = (... -- ... [...])
 succ = (n1 -- n2)
-swaack = ([.1.] -- [.0.])
+swaack = ([.1.] -- [.0.])
 swap = (a1 a2 -- a2 a1)
-swons = ([.1.] a1 -- [a1 .1.])
-third = ([a1 a2 a3 .1.] -- a3)
+swons = ([.1.] a1 -- [a1 .1.])
+third = ([a1 a2 a3 .1.] -- a3)
 tuck = (a2 a1 -- a1 a2 a1)
-uncons = ([a1 .1.] -- a1 [.1.])
+uncons = ([a1 .1.] -- a1 [.1.])
 
    
 
    
-
    print ; print doc_from_stack_effect(*stack)
-print ; print doc_from_stack_effect(*C(stack, uncons))
-print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, uncons)))
-print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, cons)))
+
    print ; print doc_from_stack_effect(*stack)
+print ; print doc_from_stack_effect(*C(stack, uncons))
+print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, uncons)))
+print ; print doc_from_stack_effect(*reduce(C, (stack, uncons, cons)))
 
    
 
    
 
    (... -- ... [...])
@@ -1602,15 +1602,15 @@ conversion function instead. This is programmer’s laziness.
    
 (... a1 -- ... a1 [a1 ...])
 
    
 
    
-
    print doc_from_stack_effect(*C(ccons, stack))
+
    print doc_from_stack_effect(*C(ccons, stack))
 
    
 
    
-
    (... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])
+
    (... a2 a1 [.1.] -- ... [a2 a1 .1.] [[a2 a1 .1.] ...])
 
    
 
    
-
    Q = C(ccons, stack)
+
    Q = C(ccons, stack)
 
-Q
+Q
 
    
 
    
 
    ((s1, (a1, (a2, s2))), (((a2, (a1, s1)), s2), ((a2, (a1, s1)), s2)))
@@ -1620,17 +1620,17 @@ conversion function instead. This is programmer’s laziness.
    
 
    compile_() version 3
    
 
    This makes the compile_() function pretty simple as the stack effect
 comments are now already in the form needed for the Python code:
    
-
    def compile_(name, f, doc=None):
-    i, o = f
-    if doc is None:
-        doc = doc_from_stack_effect(i, o)
-    return '''def %s(stack):
-    """%s"""
-    %s = stack
-    return %s''' % (name, doc, i, o)
+
    def compile_(name, f, doc=None):
+    i, o = f
+    if doc is None:
+        doc = doc_from_stack_effect(i, o)
+    return '''def %s(stack):
+    """%s"""
+    %s = stack
+    return %s''' % (name, doc, i, o)
 
    
 
    
-
    print compile_('Q', Q)
+
    print compile_('Q', Q)
 
    
 
    
 
    def Q(stack):
@@ -1639,35 +1639,35 @@ comments are now already in the form needed for the Python code:
    
     return (((a2, (a1, s1)), s2), ((a2, (a1, s1)), s2))
 
    
 
    
-
    unstack = (S[1], S[0]), S[1]
-enstacken = S[0], (S[0], S[1])
+
    unstack = (S[1], S[0]), S[1]
+enstacken = S[0], (S[0], S[1])
 
    
 
    
-
    print doc_from_stack_effect(*unstack)
+
    print doc_from_stack_effect(*unstack)
 
    
 
    
-
    ([.1.] --)
+
    ([.1.] --)
 
    
 
    
-
    print doc_from_stack_effect(*enstacken)
+
    print doc_from_stack_effect(*enstacken)
 
    
 
    
-
    (-- [.0.])
+
    (-- [.0.])
 
    
 
    
-
    print doc_from_stack_effect(*C(cons, unstack))
+
    print doc_from_stack_effect(*C(cons, unstack))
 
    
 
    
-
    (a1 [.1.] -- a1)
+
    (a1 [.1.] -- a1)
 
    
 
    
-
    print doc_from_stack_effect(*C(cons, enstacken))
+
    print doc_from_stack_effect(*C(cons, enstacken))
 
    
 
    
-
    (a1 [.1.] -- [[a1 .1.] .2.])
+
    (a1 [.1.] -- [[a1 .1.] .2.])
 
    
 
    
-
    C(cons, unstack)
+
    C(cons, unstack)
 
    
 
    
 
    ((s1, (a1, s2)), (a1, s1))
@@ -1679,23 +1679,23 @@ comments are now already in the form needed for the Python code:
    
 
    
 
    Part VI: Multiple Stack Effects
    
 
    …
    
-
    class IntJoyType(NumberJoyType): prefix = 'i'
+
    class IntJoyType(NumberJoyType): prefix = 'i'
 
 
-F = map(FloatJoyType, _R)
-I = map(IntJoyType, _R)
+F = map(FloatJoyType, _R)
+I = map(IntJoyType, _R)
 
    
 
    
-
    muls = [
-     ((I[2], (I[1], S[0])), (I[3], S[0])),
-     ((F[2], (I[1], S[0])), (F[3], S[0])),
-     ((I[2], (F[1], S[0])), (F[3], S[0])),
-     ((F[2], (F[1], S[0])), (F[3], S[0])),
-]
+
    muls = [
+     ((I[2], (I[1], S[0])), (I[3], S[0])),
+     ((F[2], (I[1], S[0])), (F[3], S[0])),
+     ((I[2], (F[1], S[0])), (F[3], S[0])),
+     ((F[2], (F[1], S[0])), (F[3], S[0])),
+]
 
    
 
    
-
    for f in muls:
-    print doc_from_stack_effect(*f)
+
    for f in muls:
+    print doc_from_stack_effect(*f)
 
    
 
    
 
    (i1 i2 -- i3)
@@ -1704,42 +1704,42 @@ comments are now already in the form needed for the Python code:
    
 (f1 f2 -- f3)
 
    
 
    
-
    for f in muls:
-    try:
-        e = C(dup, f)
-    except TypeError:
-        continue
-    print doc_from_stack_effect(*dup), doc_from_stack_effect(*f), doc_from_stack_effect(*e)
+
    for f in muls:
+    try:
+        e = C(dup, f)
+    except TypeError:
+        continue
+    print doc_from_stack_effect(*dup), doc_from_stack_effect(*f), doc_from_stack_effect(*e)
 
    
 
    
 
    (a1 -- a1 a1) (i1 i2 -- i3) (i1 -- i2)
 (a1 -- a1 a1) (f1 f2 -- f3) (f1 -- f2)
 
    
 
    
-
    from itertools import product
+
    from itertools import product
 
 
-def meta_compose(F, G):
-    for f, g in product(F, G):
-        try:
-            yield C(f, g)
-        except TypeError:
-            pass
+def meta_compose(F, G):
+    for f, g in product(F, G):
+        try:
+            yield C(f, g)
+        except TypeError:
+            pass
 
 
-def MC(F, G):
-    return sorted(set(meta_compose(F, G)))
+def MC(F, G):
+    return sorted(set(meta_compose(F, G)))
 
    
 
    
-
    for f in MC([dup], [mul]):
-    print doc_from_stack_effect(*f)
+
    for f in MC([dup], [mul]):
+    print doc_from_stack_effect(*f)
 
    
 
    
 
    (n1 -- n2)
 
    
 
    
-
    for f in MC([dup], muls):
-    print doc_from_stack_effect(*f)
+
    for f in MC([dup], muls):
+    print doc_from_stack_effect(*f)
 
    
 
    
 
    (f1 -- f2)
@@ -1768,173 +1768,173 @@ to return all universes (represented by their substitution dicts, the
 “unifiers”) that don’t lead to type conflicts.
    
 
    Consider unifying two stacks (the lowercase letters are any type
 variables of the kinds we have defined so far):
    
-
    [a A* b .0.] U [c d .1.]
+
    [a A* b .0.] U [c d .1.]
                           w/ {c: a}
-[  A* b .0.] U [  d .1.]
+[  A* b .0.] U [  d .1.]
 
    
 
    
 
    Now we have to split universes to unify A*. In the first universe it
 disappears:
    
-
    [b .0.] U [d .1.]
-                   w/ {d: b, .1.: .0.}
+
    [b .0.] U [d .1.]
+                   w/ {d: b, .1.: .0.}
      [] U []
 
    
 
    
 
    While in the second it spawns an A, which we will label e:
    
-
    [e A* b .0.] U [d .1.]
+
    [e A* b .0.] U [d .1.]
                         w/ {d: e}
-[  A* b .0.] U [  .1.]
-                        w/ {.1.: A* b .0.}
-[  A* b .0.] U [  A* b .0.]
+[  A* b .0.] U [  .1.]
+                        w/ {.1.: A* b .0.}
+[  A* b .0.] U [  A* b .0.]
 
    
 
    
 
    Giving us two unifiers:
    
-
    {c: a,  d: b,  .1.:      .0.}
-{c: a,  d: e,  .1.: A* b .0.}
+
    {c: a,  d: b,  .1.:      .0.}
+{c: a,  d: e,  .1.: A* b .0.}
 
    
 
    
-
    class KleeneStar(object):
+
    class KleeneStar(object):
 
-    kind = AnyJoyType
+    kind = AnyJoyType
 
-    def __init__(self, number):
-        self.number = number
-        self.count = 0
-        self.prefix = repr(self)
+    def __init__(self, number):
+        self.number = number
+        self.count = 0
+        self.prefix = repr(self)
 
-    def __repr__(self):
-        return '%s%i*' % (self.kind.prefix, self.number)
+    def __repr__(self):
+        return '%s%i*' % (self.kind.prefix, self.number)
 
-    def another(self):
-        self.count += 1
-        return self.kind(10000 * self.number + self.count)
+    def another(self):
+        self.count += 1
+        return self.kind(10000 * self.number + self.count)
 
-    def __eq__(self, other):
-        return (
-            isinstance(other, self.__class__)
-            and other.number == self.number
-        )
+    def __eq__(self, other):
+        return (
+            isinstance(other, self.__class__)
+            and other.number == self.number
+        )
 
-    def __ge__(self, other):
-        return self.kind >= other.kind
+    def __ge__(self, other):
+        return self.kind >= other.kind
 
-    def __add__(self, other):
-        return self.__class__(self.number + other)
-    __radd__ = __add__
+    def __add__(self, other):
+        return self.__class__(self.number + other)
+    __radd__ = __add__
 
-    def __hash__(self):
-        return hash(repr(self))
+    def __hash__(self):
+        return hash(repr(self))
 
-class AnyStarJoyType(KleeneStar): kind = AnyJoyType
-class NumberStarJoyType(KleeneStar): kind = NumberJoyType
-#class FloatStarJoyType(KleeneStar): kind = FloatJoyType
-#class IntStarJoyType(KleeneStar): kind = IntJoyType
-class StackStarJoyType(KleeneStar): kind = StackJoyType
+class AnyStarJoyType(KleeneStar): kind = AnyJoyType
+class NumberStarJoyType(KleeneStar): kind = NumberJoyType
+#class FloatStarJoyType(KleeneStar): kind = FloatJoyType
+#class IntStarJoyType(KleeneStar): kind = IntJoyType
+class StackStarJoyType(KleeneStar): kind = StackJoyType
 
 
-As = map(AnyStarJoyType, _R)
-Ns = map(NumberStarJoyType, _R)
-Ss = map(StackStarJoyType, _R)
+As = map(AnyStarJoyType, _R)
+Ns = map(NumberStarJoyType, _R)
+Ss = map(StackStarJoyType, _R)
 
    
 
    
 
    
 
    unify() version 4
    
 
    Can now return multiple results…
    
-
    def unify(u, v, s=None):
-    if s is None:
-        s = {}
-    elif s:
-        u = update(s, u)
-        v = update(s, v)
+
    def unify(u, v, s=None):
+    if s is None:
+        s = {}
+    elif s:
+        u = update(s, u)
+        v = update(s, v)
 
-    if u == v:
-        return s,
+    if u == v:
+        return s,
 
-    if isinstance(u, AnyJoyType) and isinstance(v, AnyJoyType):
-        if u >= v:
-            s[u] = v
-            return s,
-        if v >= u:
-            s[v] = u
-            return s,
-        raise TypeError('Cannot unify %r and %r.' % (u, v))
+    if isinstance(u, AnyJoyType) and isinstance(v, AnyJoyType):
+        if u >= v:
+            s[u] = v
+            return s,
+        if v >= u:
+            s[v] = u
+            return s,
+        raise TypeError('Cannot unify %r and %r.' % (u, v))
 
-    if isinstance(u, tuple) and isinstance(v, tuple):
-        if len(u) != len(v) != 2:
-            raise TypeError(repr((u, v)))
+    if isinstance(u, tuple) and isinstance(v, tuple):
+        if len(u) != len(v) != 2:
+            raise TypeError(repr((u, v)))
 
-        a, b = v
-        if isinstance(a, KleeneStar):
-            # Two universes, in one the Kleene star disappears and unification
-            # continues without it...
-            s0 = unify(u, b)
+        a, b = v
+        if isinstance(a, KleeneStar):
+            # Two universes, in one the Kleene star disappears and unification
+            # continues without it...
+            s0 = unify(u, b)
 
-            # In the other it spawns a new variable.
-            s1 = unify(u, (a.another(), v))
+            # In the other it spawns a new variable.
+            s1 = unify(u, (a.another(), v))
 
-            t = s0 + s1
-            for sn in t:
-                sn.update(s)
-            return t
+            t = s0 + s1
+            for sn in t:
+                sn.update(s)
+            return t
 
-        a, b = u
-        if isinstance(a, KleeneStar):
-            s0 = unify(v, b)
-            s1 = unify(v, (a.another(), u))
-            t = s0 + s1
-            for sn in t:
-                sn.update(s)
-            return t
+        a, b = u
+        if isinstance(a, KleeneStar):
+            s0 = unify(v, b)
+            s1 = unify(v, (a.another(), u))
+            t = s0 + s1
+            for sn in t:
+                sn.update(s)
+            return t
 
-        ses = unify(u[0], v[0], s)
-        results = ()
-        for sn in ses:
-            results += unify(u[1], v[1], sn)
-        return results
+        ses = unify(u[0], v[0], s)
+        results = ()
+        for sn in ses:
+            results += unify(u[1], v[1], sn)
+        return results
 
-    if isinstance(v, tuple):
-        if not stacky(u):
-            raise TypeError('Cannot unify %r and %r.' % (u, v))
-        s[u] = v
-        return s,
+    if isinstance(v, tuple):
+        if not stacky(u):
+            raise TypeError('Cannot unify %r and %r.' % (u, v))
+        s[u] = v
+        return s,
 
-    if isinstance(u, tuple):
-        if not stacky(v):
-            raise TypeError('Cannot unify %r and %r.' % (v, u))
-        s[v] = u
-        return s,
+    if isinstance(u, tuple):
+        if not stacky(v):
+            raise TypeError('Cannot unify %r and %r.' % (v, u))
+        s[v] = u
+        return s,
 
-    return ()
+    return ()
 
 
-def stacky(thing):
-    return thing.__class__ in {AnyJoyType, StackJoyType}
+def stacky(thing):
+    return thing.__class__ in {AnyJoyType, StackJoyType}
 
    
 
    
-
    a = (As[1], S[1])
-a
+
    a = (As[1], S[1])
+a
 
    
 
    
 
    (a1*, s1)
 
    
 
    
-
    b = (A[1], S[2])
-b
+
    b = (A[1], S[2])
+b
 
    
 
    
 
    (a1, s2)
 
    
 
    
-
    for result in unify(b, a):
-    print result, '->', update(result, a), update(result, b)
+
    for result in unify(b, a):
+    print result, '->', update(result, a), update(result, b)
 
    
 
    
 
    {s1: (a1, s2)} -> (a1*, (a1, s2)) (a1, s2)
 {a1: a10001, s2: (a1*, s1)} -> (a1*, s1) (a10001, (a1*, s1))
 
    
 
    
-
    for result in unify(a, b):
-    print result, '->', update(result, a), update(result, b)
+
    for result in unify(a, b):
+    print result, '->', update(result, a), update(result, b)
 
    
 
    
 
    {s1: (a1, s2)} -> (a1*, (a1, s2)) (a1, s2)
@@ -1948,24 +1948,24 @@ disappears:
    
 (a1*, s1)       [a1*]       (a2, (a1*, s1)) [a2 a1*]
 
    
 
    
-
    sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0])
+
    sum_ = ((Ns[1], S[1]), S[0]), (N[0], S[0])
 
-print doc_from_stack_effect(*sum_)
+print doc_from_stack_effect(*sum_)
 
    
 
    
-
    ([n1* .1.] -- n0)
+
    ([n1* .1.] -- n0)
 
    
 
    
-
    f = (N[1], (N[2], (N[3], S[1]))), S[0]
+
    f = (N[1], (N[2], (N[3], S[1]))), S[0]
 
-print doc_from_stack_effect(S[0], f)
+print doc_from_stack_effect(S[0], f)
 
    
 
    
-
    (-- [n1 n2 n3 .1.])
+
    (-- [n1 n2 n3 .1.])
 
    
 
    
-
    for result in unify(sum_[0], f):
-    print result, '->', update(result, sum_[1])
+
    for result in unify(sum_[0], f):
+    print result, '->', update(result, sum_[1])
 
    
 
    
 
    {s1: (n1, (n2, (n3, s1)))} -> (n0, s0)
@@ -1978,88 +1978,88 @@ disappears:
    
 
    
 
    compose() version 3
    
 
    This function has to be modified to yield multiple results.
    
-
    def compose(f, g):
-    (f_in, f_out), (g_in, g_out) = f, g
-    s = unify(g_in, f_out)
-    if not s:
-        raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
-    for result in s:
-        yield update(result, (f_in, g_out))
+
    def compose(f, g):
+    (f_in, f_out), (g_in, g_out) = f, g
+    s = unify(g_in, f_out)
+    if not s:
+        raise TypeError('Cannot unify %r and %r.' % (f_out, g_in))
+    for result in s:
+        yield update(result, (f_in, g_out))
 
    
 
    
-
    def meta_compose(F, G):
-    for f, g in product(F, G):
-        try:
-            for result in C(f, g):
-                yield result
-        except TypeError:
-            pass
+
    def meta_compose(F, G):
+    for f, g in product(F, G):
+        try:
+            for result in C(f, g):
+                yield result
+        except TypeError:
+            pass
 
 
-def C(f, g):
-    f, g = relabel(f, g)
-    for fg in compose(f, g):
-        yield delabel(fg)
+def C(f, g):
+    f, g = relabel(f, g)
+    for fg in compose(f, g):
+        yield delabel(fg)
 
    
 
    
-
    for f in MC([dup], muls):
-    print doc_from_stack_effect(*f)
+
    for f in MC([dup], muls):
+    print doc_from_stack_effect(*f)
 
    
 
    
 
    (f1 -- f2)
 (i1 -- i2)
 
    
 
    
-
    for f in MC([dup], [sum_]):
-    print doc_from_stack_effect(*f)
+
    for f in MC([dup], [sum_]):
+    print doc_from_stack_effect(*f)
 
    
 
    
-
    ([n1* .1.] -- [n1* .1.] n1)
+
    ([n1* .1.] -- [n1* .1.] n1)
 
    
 
    
-
    for f in MC([cons], [sum_]):
-    print doc_from_stack_effect(*f)
+
    for f in MC([cons], [sum_]):
+    print doc_from_stack_effect(*f)
 
    
 
    
-
    (a1 [.1.] -- n1)
-(n1 [n1* .1.] -- n2)
+
    (a1 [.1.] -- n1)
+(n1 [n1* .1.] -- n2)
 
    
 
    
-
    sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
-print doc_from_stack_effect(*cons),
-print doc_from_stack_effect(*sum_),
+
    sum_ = (((N[1], (Ns[1], S[1])), S[0]), (N[0], S[0]))
+print doc_from_stack_effect(*cons),
+print doc_from_stack_effect(*sum_),
 
-for f in MC([cons], [sum_]):
-    print doc_from_stack_effect(*f)
+for f in MC([cons], [sum_]):
+    print doc_from_stack_effect(*f)
 
    
 
    
-
    (a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2)
+
    (a1 [.1.] -- [a1 .1.]) ([n1 n1* .1.] -- n0) (n1 [n1* .1.] -- n2)
 
    
 
    
-
    a = (A[4], (As[1], (A[3], S[1])))
-a
+
    a = (A[4], (As[1], (A[3], S[1])))
+a
 
    
 
    
 
    (a4, (a1*, (a3, s1)))
 
    
 
    
-
    b = (A[1], (A[2], S[2]))
-b
+
    b = (A[1], (A[2], S[2]))
+b
 
    
 
    
 
    (a1, (a2, s2))
 
    
 
    
-
    for result in unify(b, a):
-    print result
+
    for result in unify(b, a):
+    print result
 
    
 
    
 
    {a1: a4, s2: s1, a2: a3}
 {a1: a4, s2: (a1*, (a3, s1)), a2: a10003}
 
    
 
    
-
    for result in unify(a, b):
-    print result
+
    for result in unify(a, b):
+    print result
 
    
 
    
 
    {s2: s1, a2: a3, a4: a1}
@@ -2075,11 +2075,11 @@ disappears:
    
 have the quoted programs they expect available. In the most general
 case, the i combinator, you can’t say anything about its stack
 effect other than it expects one quote:
    
-
    i (... [.1.] -- ... .1.)
+
    i (... [.1.] -- ... .1.)
 
    
 
    
 
    Or
    
-
    i (... [A* .1.] -- ... A*)
+
    i (... [A* .1.] -- ... A*)
 
    
 
    
 
    Consider the type of:
    
@@ -2087,7 +2087,7 @@ effect other than it expects one quote:
    
 
    
 
    
 
    Obviously it would be:
    
-
    (a1 [..1] a2 -- [a1 ..1] a2)
+
    (a1 [..1] a2 -- [a1 ..1] a2)
 
    
 
    
 
    dip itself could have:
    
@@ -2111,19 +2111,19 @@ stack effect we have to “split universes” again and return both.
    
 
    We need a type variable for Joy functions that can go in our expressions
 and be used by the hybrid inferencer/interpreter. They have to store a
 name and a list of stack effects.
    
-
    class FunctionJoyType(AnyJoyType):
+
    class FunctionJoyType(AnyJoyType):
 
-    def __init__(self, name, sec, number):
-        self.name = name
-        self.stack_effects = sec
-        self.number = number
+    def __init__(self, name, sec, number):
+        self.name = name
+        self.stack_effects = sec
+        self.number = number
 
-    def __add__(self, other):
-        return self
-    __radd__ = __add__
+    def __add__(self, other):
+        return self
+    __radd__ = __add__
 
-    def __repr__(self):
-        return self.name
+    def __repr__(self):
+        return self.name
 
    
 
    
 
    
@@ -2131,47 +2131,47 @@ name and a list of stack effects.
    
 
    Specialized for Simple Functions and Combinators
    
 
    For non-combinator functions the stack effects list contains stack
 effect comments (represented by pairs of cons-lists as described above.)
    
-
    class SymbolJoyType(FunctionJoyType):
-    prefix = 'F'
+
    class SymbolJoyType(FunctionJoyType):
+    prefix = 'F'
 
    
 
    
 
    For combinators the list contains Python functions.
    
-
    class CombinatorJoyType(FunctionJoyType):
+
    class CombinatorJoyType(FunctionJoyType):
 
-    prefix = 'C'
+    prefix = 'C'
 
-    def __init__(self, name, sec, number, expect=None):
-        super(CombinatorJoyType, self).__init__(name, sec, number)
-        self.expect = expect
+    def __init__(self, name, sec, number, expect=None):
+        super(CombinatorJoyType, self).__init__(name, sec, number)
+        self.expect = expect
 
-    def enter_guard(self, f):
-        if self.expect is None:
-            return f
-        g = self.expect, self.expect
-        new_f = list(compose(f, g, ()))
-        assert len(new_f) == 1, repr(new_f)
-        return new_f[0][1]
+    def enter_guard(self, f):
+        if self.expect is None:
+            return f
+        g = self.expect, self.expect
+        new_f = list(compose(f, g, ()))
+        assert len(new_f) == 1, repr(new_f)
+        return new_f[0][1]
 
    
 
    
 
    For simple combinators that have only one effect (like dip) you only
 need one function and it can be the combinator itself.
    
-
    import joy.library
+
    import joy.library
 
-dip = CombinatorJoyType('dip', [joy.library.dip], 23)
+dip = CombinatorJoyType('dip', [joy.library.dip], 23)
 
    
 
    
 
    For combinators that can have more than one effect (like branch) you
 have to write functions that each implement the action of one of the
 effects.
    
-
    def branch_true(stack, expression, dictionary):
-    (then, (else_, (flag, stack))) = stack
-    return stack, concat(then, expression), dictionary
+
    def branch_true(stack, expression, dictionary):
+    (then, (else_, (flag, stack))) = stack
+    return stack, concat(then, expression), dictionary
 
-def branch_false(stack, expression, dictionary):
-    (then, (else_, (flag, stack))) = stack
-    return stack, concat(else_, expression), dictionary
+def branch_false(stack, expression, dictionary):
+    (then, (else_, (flag, stack))) = stack
+    return stack, concat(else_, expression), dictionary
 
-branch = CombinatorJoyType('branch', [branch_true, branch_false], 100)
+branch = CombinatorJoyType('branch', [branch_true, branch_false], 100)
 
    
 
    
 
    You can also provide an optional stack effect, input-side only, that
@@ -2189,54 +2189,54 @@ that expression.
    
 updated along with the stack effects after doing unification or we risk
 losing useful information. This was a straightforward, if awkward,
 modification to the call structure of meta_compose() et. al.
    
-
    ID = S[0], S[0]  # Identity function.
+
    ID = S[0], S[0]  # Identity function.
 
 
-def infer(*expression):
-    return sorted(set(_infer(list_to_stack(expression))))
+def infer(*expression):
+    return sorted(set(_infer(list_to_stack(expression))))
 
 
-def _infer(e, F=ID):
-    _log_it(e, F)
-    if not e:
-        return [F]
+def _infer(e, F=ID):
+    _log_it(e, F)
+    if not e:
+        return [F]
 
-    n, e = e
+    n, e = e
 
-    if isinstance(n, SymbolJoyType):
-        eFG = meta_compose([F], n.stack_effects, e)
-        res = flatten(_infer(e, Fn) for e, Fn in eFG)
+    if isinstance(n, SymbolJoyType):
+        eFG = meta_compose([F], n.stack_effects, e)
+        res = flatten(_infer(e, Fn) for e, Fn in eFG)
 
-    elif isinstance(n, CombinatorJoyType):
-        fi, fo = n.enter_guard(F)
-        res = flatten(_interpret(f, fi, fo, e) for f in n.stack_effects)
+    elif isinstance(n, CombinatorJoyType):
+        fi, fo = n.enter_guard(F)
+        res = flatten(_interpret(f, fi, fo, e) for f in n.stack_effects)
 
-    elif isinstance(n, Symbol):
-        assert n not in FUNCTIONS, repr(n)
-        func = joy.library._dictionary[n]
-        res = _interpret(func, F[0], F[1], e)
+    elif isinstance(n, Symbol):
+        assert n not in FUNCTIONS, repr(n)
+        func = joy.library._dictionary[n]
+        res = _interpret(func, F[0], F[1], e)
 
-    else:
-        fi, fo = F
-        res = _infer(e, (fi, (n, fo)))
+    else:
+        fi, fo = F
+        res = _infer(e, (fi, (n, fo)))
 
-    return res
+    return res
 
 
-def _interpret(f, fi, fo, e):
-    new_fo, ee, _ = f(fo, e, {})
-    ee = update(FUNCTIONS, ee)  # Fix Symbols.
-    new_F = fi, new_fo
-    return _infer(ee, new_F)
+def _interpret(f, fi, fo, e):
+    new_fo, ee, _ = f(fo, e, {})
+    ee = update(FUNCTIONS, ee)  # Fix Symbols.
+    new_F = fi, new_fo
+    return _infer(ee, new_F)
 
 
-def _log_it(e, F):
-    _log.info(
-        u'%3i %s ∘ %s',
-        len(inspect_stack()),
-        doc_from_stack_effect(*F),
-        expression_to_string(e),
-        )
+def _log_it(e, F):
+    _log.info(
+        u'%3i %s ∘ %s',
+        len(inspect_stack()),
+        doc_from_stack_effect(*F),
+        expression_to_string(e),
+        )
 
    
 
    
 
    
@@ -2249,18 +2249,18 @@ module (FIXME link to its docs here!) should be explained… There is
 cruft to convert the definitions in DEFS to the new
 SymbolJoyType objects, and some combinators. Here is an example of
 output from the current code :
    
-
    1/0  # (Don't try to run this cell!  It's not going to work.  This is "read only" code heh..)
+
    1/0  # (Don't try to run this cell!  It's not going to work.  This is "read only" code heh..)
 
-logging.basicConfig(format='%(message)s', stream=sys.stdout, level=logging.INFO)
+logging.basicConfig(format='%(message)s', stream=sys.stdout, level=logging.INFO)
 
-globals().update(FUNCTIONS)
+globals().update(FUNCTIONS)
 
-h = infer((pred, s2), (mul, s3), (div, s4), (nullary, (bool, s5)), dipd, branch)
+h = infer((pred, s2), (mul, s3), (div, s4), (nullary, (bool, s5)), dipd, branch)
 
-print '-' * 40
+print '-' * 40
 
-for fi, fo in h:
-    print doc_from_stack_effect(fi, fo)
+for fi, fo in h:
+    print doc_from_stack_effect(fi, fo)
 
    
 
    
 
    ---------------------------------------------------------------------------
@@ -2366,14 +2366,14 @@ relational nature of the stack effect comments to “compute in reverse”
 as it were. There’s a working demo of this at the end of the types
 module. But if you’re interested in all that you should just use Prolog!
    
 
    Anyhow, type checking is a few easy steps away.
    
-
    def _ge(self, other):
-    return (issubclass(other.__class__, self.__class__)
-            or hasattr(self, 'accept')
-            and isinstance(other, self.accept))
+
    def _ge(self, other):
+    return (issubclass(other.__class__, self.__class__)
+            or hasattr(self, 'accept')
+            and isinstance(other, self.accept))
 
-AnyJoyType.__ge__ = _ge
-AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
-StackJoyType.accept = tuple
+AnyJoyType.__ge__ = _ge
+AnyJoyType.accept = tuple, int, float, long, str, unicode, bool, Symbol
+StackJoyType.accept = tuple
 
    
 
    
 
    
@@ -2465,7 +2465,7 @@ module. But if you’re interested in all that you should just use Prolog!
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/Zipper.html b/docs/sphinx_docs/_build/html/notebooks/Zipper.html
index 72ff9f1..7eec7cd 100644
--- a/docs/sphinx_docs/_build/html/notebooks/Zipper.html
+++ b/docs/sphinx_docs/_build/html/notebooks/Zipper.html
@@ -42,7 +42,7 @@ the original paper: 
    from notebook_preamble import J, V, define
+
    from notebook_preamble import J, V, define
 
    
 
    
 
    
@@ -52,7 +52,7 @@ strings, Symbols (strings that are names of functions) and sequences
 (aka lists, aka quoted literals, aka aggregates, etc…), but we can build
 trees out
 of sequences.
    
-
    J('[1 [2 [3 4 25 6] 7] 8]')
+
    J('[1 [2 [3 4 25 6] 7] 8]')
 
    
 
    
 
    [1 [2 [3 4 25 6] 7] 8]
@@ -75,13 +75,13 @@ datastructure used to keep track of these items is the zipper.)
    
 show the trace so you can see how it works. If we were going to use
 these a lot it would make sense to write Python versions for efficiency,
 but see below.
    
-
    define('z-down == [] swap uncons swap')
-define('z-up == swons swap shunt')
-define('z-right == [swons] cons dip uncons swap')
-define('z-left == swons [uncons swap] dip swap')
+
    define('z-down == [] swap uncons swap')
+define('z-up == swons swap shunt')
+define('z-right == [swons] cons dip uncons swap')
+define('z-left == swons [uncons swap] dip swap')
 
    
 
    
-
    V('[1 [2 [3 4 25 6] 7] 8] z-down')
+
    V('[1 [2 [3 4 25 6] 7] 8] z-down')
 
    
 
    
 
                              . [1 [2 [3 4 25 6] 7] 8] z-down
@@ -93,7 +93,7 @@ but see below.
    
 [] [[2 [3 4 25 6] 7] 8] 1 .
 
    
 
    
-
    V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')
+
    V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')
 
    
 
    
 
                                      . [] [[2 [3 4 25 6] 7] 8] 1 z-right
@@ -113,43 +113,43 @@ but see below.
    
          [1] [8] [2 [3 4 25 6] 7] .
 
    
 
    
-
    J('[1] [8] [2 [3 4 25 6] 7] z-down')
+
    J('[1] [8] [2 [3 4 25 6] 7] z-down')
 
    
 
    
 
    [1] [8] [] [[3 4 25 6] 7] 2
 
    
 
    
-
    J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')
+
    J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')
 
    
 
    
 
    [1] [8] [2] [7] [3 4 25 6]
 
    
 
    
-
    J('[1] [8] [2] [7] [3 4 25 6] z-down')
+
    J('[1] [8] [2] [7] [3 4 25 6] z-down')
 
    
 
    
 
    [1] [8] [2] [7] [] [4 25 6] 3
 
    
 
    
-
    J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')
+
    J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')
 
    
 
    
 
    [1] [8] [2] [7] [3] [25 6] 4
 
    
 
    
-
    J('[1] [8] [2] [7] [3] [25 6] 4 z-right')
+
    J('[1] [8] [2] [7] [3] [25 6] 4 z-right')
 
    
 
    
 
    [1] [8] [2] [7] [4 3] [6] 25
 
    
 
    
-
    J('[1] [8] [2] [7] [4 3] [6] 25 sqr')
+
    J('[1] [8] [2] [7] [4 3] [6] 25 sqr')
 
    
 
    
 
    [1] [8] [2] [7] [4 3] [6] 625
 
    
 
    
-
    V('[1] [8] [2] [7] [4 3] [6] 625 z-up')
+
    V('[1] [8] [2] [7] [4 3] [6] 625 z-up')
 
    
 
    
 
                                  . [1] [8] [2] [7] [4 3] [6] 625 z-up
@@ -168,13 +168,13 @@ but see below.
    
   [1] [8] [2] [7] [3 4 625 6] .
 
    
 
    
-
    J('[1] [8] [2] [7] [3 4 625 6] z-up')
+
    J('[1] [8] [2] [7] [3 4 625 6] z-up')
 
    
 
    
 
    [1] [8] [2 [3 4 625 6] 7]
 
    
 
    
-
    J('[1] [8] [2 [3 4 625 6] 7] z-up')
+
    J('[1] [8] [2 [3 4 625 6] 7] z-up')
 
    
 
    
 
    [1 [2 [3 4 625 6] 7] 8]
@@ -185,7 +185,7 @@ but see below.
    
 
    dip and infra
    
 
    In Joy we have the dip and infra combinators which can “target”
 or “address” any particular item in a Joy tree structure.
    
-
    V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')
+
    V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')
 
    
 
    
 
                                                                    . [1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra
@@ -236,11 +236,11 @@ been embedded in a nested series of quoted programs, e.g.:
    
 
    
 
    
 
    The Z function isn’t hard to make.
    
-
    define('Z == [[] cons cons] step i')
+
    define('Z == [[] cons cons] step i')
 
    
 
    
 
    Here it is in action in a simplified scenario.
    
-
    V('1 [2 3 4] Z')
+
    V('1 [2 3 4] Z')
 
    
 
    
 
                                 . 1 [2 3 4] Z
@@ -273,7 +273,7 @@ been embedded in a nested series of quoted programs, e.g.:
    
 
    
 
    
 
    And here it is doing the main thing.
    
-
    J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')
+
    J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')
 
    
 
    
 
    [1 [2 [3 4 625 6] 7] 8]
@@ -389,7 +389,7 @@ i d i d i d d Bingo!
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/notebooks/index.html b/docs/sphinx_docs/_build/html/notebooks/index.html
index e742b6c..26bd28c 100644
--- a/docs/sphinx_docs/_build/html/notebooks/index.html
+++ b/docs/sphinx_docs/_build/html/notebooks/index.html
@@ -251,7 +251,7 @@
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/objects.inv b/docs/sphinx_docs/_build/html/objects.inv
index 136209a..10dedf8 100644
Binary files a/docs/sphinx_docs/_build/html/objects.inv and b/docs/sphinx_docs/_build/html/objects.inv differ
diff --git a/docs/sphinx_docs/_build/html/parser.html b/docs/sphinx_docs/_build/html/parser.html
index 99c6be7..1de95b8 100644
--- a/docs/sphinx_docs/_build/html/parser.html
+++ b/docs/sphinx_docs/_build/html/parser.html
@@ -161,7 +161,7 @@ Any unbalanced square brackets will raise a ParseError.
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/pretty.html b/docs/sphinx_docs/_build/html/pretty.html
index b43aaef..8d609eb 100644
--- a/docs/sphinx_docs/_build/html/pretty.html
+++ b/docs/sphinx_docs/_build/html/pretty.html
@@ -182,7 +182,7 @@ trace of the evaluation
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/py-modindex.html b/docs/sphinx_docs/_build/html/py-modindex.html
index 7c96010..3a3c124 100644
--- a/docs/sphinx_docs/_build/html/py-modindex.html
+++ b/docs/sphinx_docs/_build/html/py-modindex.html
@@ -146,7 +146,7 @@
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/search.html b/docs/sphinx_docs/_build/html/search.html
index cb9bd5d..3c0ea74 100644
--- a/docs/sphinx_docs/_build/html/search.html
+++ b/docs/sphinx_docs/_build/html/search.html
@@ -120,7 +120,7 @@
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/searchindex.js b/docs/sphinx_docs/_build/html/searchindex.js
index a270cf5..24de0c6 100644
--- a/docs/sphinx_docs/_build/html/searchindex.js
+++ b/docs/sphinx_docs/_build/html/searchindex.js
@@ -1 +1 @@
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,17,18,19,20,21,24,25],txt:[],type:[0,1,4,8,11,13,16,21,22,23,24],typeerror:19,typeless:19,typic:[2,3,12,13],u:[18,19],uh:19,ui:8,ulam:[0,15],unari:8,unarybuiltinwrapp:3,unbalanc:[11,22],unbound:25,unchang:[3,11],uncompil:19,uncon:[3,7,8,11,13,17,20,25],under:[2,3,8,11],underli:[5,16,19],underscor:19,understand:[0,11],undistinguish:11,undocu:8,unfinish:5,unfortun:24,unicod:19,unif:[19,21],unifi:18,union:5,uniqu:[3,5,11,19],unit:[3,8,13,16,25],univers:[0,8,16,19],unknownsymbolerror:1,unlik:16,unnecessari:21,unnecesssari:19,unpack:[2,3,11,24],unpair:6,unquot:[8,15,17,22],unread:[0,15],unrol:5,unstack:19,unswon:[3,25],untangl:13,until:[5,7,16],unus:6,unusu:11,unwrap:5,up:[1,2,3,6,7,8,11,13,14,15,16,19,20,24],updat:[0,18,21,25],uppercas:5,upward:16,us:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,20,21,22,24,25],usag:8,user:17,usual:[0,2,13],util:[0,3,14,18,19],uu:19,v0:25,v:[2,6,7,9,11,12,13,14,15,17,20,21],valid:19,valu:[0,1,2,3,6,8,9,12,13,14,15,16,17,19,21,22,24,25],value_n:11,valueerror:[5,19,24],variabl:[19,21],variant:11,variat:[13,16,21],varieti:[4,8],variou:0,ve:[11,15,19],vener:24,verbos:4,veri:[0,1,4,5,8,11,15,24],versa:[2,19],version:[0,1,2,5,7,10,17,20,21],vi:21,via:8,vice:[2,19],view:[11,21],viewer:[1,8,10,23],vii:21,visibl:19,von:[0,2,3,4,13],vs:19,vv:19,w:[3,11,13,17,19],wa:[2,6,8,11,15,16,19,24],waaaai:5,wai:[0,2,3,4,5,6,8,13,14,15,16,19],wait:16,want:[2,6,7,9,11,13,19],warranti:[3,8],wash:8,wast:8,we:[2,5,6,7,8,9,10,12,13,14,15,16,19,20,21,24],web:24,websit:[0,6],welcom:8,well:[0,4,8,9,11,19,22],went:19,were:[8,19,20],what:[2,3,4,5,8,11,13,16,17,19,23],whatev:[2,3,13,17,24],when:[6,7,8,11,13,16,19,20,22,24,25],where:[2,3,5,8,11,13,15,19,21,24],whether:[3,13],which:[0,1,3,5,6,8,9,11,15,16,17,19,20,22,24,25],whole:[2,3,6,13,17,19],whose:7,why:[9,16,17],wiki:11,wikipedia:[0,11,20],wildli:8,wind:8,wire:13,within:[8,11,14,21],without:[2,8,11,12,15,16,19],won:[11,19,24],word:[0,3,6,8,13,20],work:[0,3,5,6,7,8,9,11,12,13,15,16,17,20,21,24,25],worker:16,worri:16,worth:6,would:[2,6,7,8,9,11,13,16,19,20,24],wrap:[3,8],wrapper:19,write:[4,5,9,11,13,15,16,17,19,20,21,24],written:[0,1,9,11,14,19,24],wrong:2,wrote:19,x:[0,3,5,6,8,9,16,20,21],xor:3,xrang:19,y:[2,3,5,15,16],yang:19,yeah:16,year:[8,19],yet:[11,16,19,20],yield:[2,3,13,19,24],yin:21,you:[0,2,3,5,6,7,8,10,11,12,13,14,15,16,17,19,20,23,24,25],your:[2,3,8,13,19],yourself:[5,8,11],z:[3,5,16,19,21],zero:[3,5,11,13,16,17,19,22,24],zerodivisionerror:19,zip:[3,5,6,19],zip_:3,zipper:[0,21],zstr:20},titles:["Thun 0.4.1 Documentation","Joy Interpreter","Functions Grouped by, er, Function with Examples","Function Reference","Categorical Programming","\u2202RE","Developing a Program in Joy","Using x to Generate Values","Thun: Joy in Python","Newton\u2019s method","No Updates","Treating Trees I: Ordered Binary Trees","Quadratic formula","Recursion Combinators","Replacing Functions in the Dictionary","Square Spiral Example Joy Code","The Four Fundamental Operations of Definite Action","Treating Trees II: treestep","Type Checking","The Blissful Elegance of Typing Joy","Traversing Datastructures with Zippers","Essays about Programming in Joy","Parsing Text into Joy Expressions","Tracing Joy Execution","Stack or Quote or Sequence or List\u2026","Type Inference of Joy Expressions"],titleterms:{"0":[0,13],"01":5,"1":[0,13],"11":5,"111":5,"2":[7,12,19],"2a":12,"3":[6,19],"4":[0,12,19],"466":7,"5":6,"\u03bb":5,"\u03d5":5,"boolean":15,"case":[9,11],"do":17,"function":[2,3,5,8,9,11,13,14,16,17,19],"long":14,"new":11,"p\u00f6ial":19,"try":5,"void":2,"while":[2,16],A:[5,6,7,9,11,14],If:11,In:[11,17],No:[5,10],Not:15,One:[7,11],The:[6,8,11,13,15,16,17,19],There:8,With:[5,17],about:21,action:16,ad:11,add:[2,11],address:20,al:13,alphabet:5,altern:17,an:[6,7,8,11,13,18,19,20],ana:13,analysi:6,anamorph:[2,13],app1:2,app2:2,app3:2,appendix:[11,13,19],appli:16,approxim:9,ar:11,argument:19,auto:3,averag:2,b:[2,12],base:[9,11],binari:[2,11,17],bliss:19,both:11,branch:[2,11,15,16],brzozowski:5,c:[12,19],can:11,cata:13,catamorph:13,categor:4,chatter:2,check:18,child:11,choic:2,clear:2,cleav:[2,16],cmp:11,code:[0,8,11,15],combin:[2,11,13,19],comment:19,compact:5,compar:11,comparison:2,compil:[7,19],compile_:19,compos:19,comput:9,con:[2,19],concat:2,conclus:[13,15,19],consecut:9,continu:8,current:11,datastructur:[5,8,11,20],deal:19,decrement:15,defin:[11,17],definit:[12,16],delabel:19,delet:11,deriv:[5,12,13,17],design:13,determin:20,develop:6,diagram:5,dialect:0,dictionari:14,dip:[2,20],dipd:2,dipdd:2,direco:7,disenstacken:2,distinguish:19,div:2,doc_from_stack_effect:19,document:0,doe:11,down_to_zero:2,drive:5,drop:2,dup:[2,19],dupd:2,dupdip:2,e:17,effect:19,eleg:19,els:11,empti:11,enstacken:2,equal:11,er:2,essai:21,et:13,euler:[6,7],eval:8,even:7,exampl:[0,2,8,11,13,15,17,18],execut:23,explor:5,express:[5,8,22,25],extract:17,f:11,factori:13,fail:18,fibonacci:7,filter:6,find:[9,11,13],finish:16,finit:5,first:[2,6,15,16,19],five:7,flatten:2,flexibl:17,floordiv:2,form:15,formula:12,found:11,four:[13,16],from:13,fsm:5,fulmin:16,fun:13,fundament:16,further:6,gcd:2,gener:[3,5,6,7,9,13,15],genrec:2,get:[11,17],getitem:2,given:[13,17],greater:11,group:2,h1:13,h2:13,h3:13,h4:13,handl:16,have:[11,17],help:2,highest:11,host:0,how:[6,7],hybrid:19,hylo:13,hylomorph:13,i:[2,5,11,19],identifi:19,ift:[2,16],ii:[17,19],iii:19,implement:[5,19],increment:15,indic:0,infer:[19,25],inferenc:19,inform:0,infra:[2,20],integ:[6,13],interest:7,interlud:11,intern:22,interpret:[1,8,19],item:20,iter:[6,11],iv:19,joi:[0,1,3,6,8,13,15,19,20,21,22,23,24,25],join:16,just:6,kei:11,kind:16,languag:0,larger:5,least_fract:2,left:11,less:11,let:[5,6],letter:5,librari:[3,8,19],like:11,list:[2,13,24],literari:8,littl:6,logic:[2,19],loop:[2,8,16],lower:11,lshift:2,machin:5,make:[7,9],mani:6,map:[2,16],match:5,math:2,memoiz:5,method:9,min:2,miscellan:2,mod:2,modifi:19,modulu:2,more:11,most:11,mul:[2,19],multipl:[6,7,19],must:11,n:13,name:12,ne:2,neg:[2,15],newton:9,next:9,node:11,non:11,now:11,nullari:2,nulli:5,number:[13,19],one:8,onli:8,oper:16,order:[11,17],origin:15,osdn:0,other:16,our:11,out:5,over:2,p:17,pack:6,pam:[2,16],para:13,paradigm:19,parallel:16,parameter:[11,17],pars:[2,22],parser:[8,22],part:19,pass:8,path:20,pattern:13,per:11,piec:15,pop:[2,19],popd:2,popop:2,pow:2,power:7,pred:2,predic:[6,9,11,15,17],pretty_print:23,primit:13,primrec:2,print:8,problem:[6,7],process:11,product:2,program:[4,6,12,17,21],progress:19,project:[0,6,7],pure:8,put:[11,12,15,17],python:[8,14,19],quadrat:12,quick:0,quot:[2,24],rang:[2,6,13],range_to_zero:2,re:[5,11],read:8,recur:[9,11],recurs:[11,13,17],redefin:[11,17],refactor:[6,11],refer:3,regular:[5,8],reimplement:17,relabel:19,rem:2,remaind:2,remov:2,render:6,repl:8,replac:[11,14],repres:[5,19],represent:5,reset:7,rest:[2,19],revers:[2,5,18],right:[11,20],rightmost:11,roll:[2,19],rolldown:2,rollup:2,rshift:2,rule:[5,19],run:[2,7],s:[5,6,9,11,19],second:[2,19],select:2,sequenc:[7,16,19,24],set:[9,11],shorter:14,should:8,shunt:2,simpl:19,simplest:6,size:[2,14],sourc:11,special:[13,19],spiral:15,sqr:[2,19],sqrt:[2,12],squar:15,stack:[2,8,19,24],start:0,state:5,step:[2,13,17],straightforward:12,stream:5,string:5,structur:11,style:8,sub:[2,11],subtyp:19,succ:2,sum:[2,6],swaack:2,swap:[2,19],swon:2,swoncat:2,symbol:[8,13],t:17,tabl:0,tail:13,take:2,term:[6,7,17],ternari:2,text:22,than:11,them:12,thi:11,third:[2,19],three:7,thun:[0,8],time:[2,7],togeth:[11,12,15,17],token:8,toler:9,trace:[14,23],traceprint:8,trampolin:5,translat:15,travers:[11,17,20],treat:[11,17],tree:[11,17,20],treegrind:17,treestep:17,triangular:13,truediv:2,truthi:2,tuck:2,turn:15,two:[5,7],type:[18,19,25],unari:2,unbound:19,uncon:[2,19],unif:18,unifi:19,unit:2,unnecessari:6,unquot:2,unstack:2,up:9,updat:[10,19],us:[7,19],util:[23,24,25],v:19,valu:[7,11],variabl:12,variat:7,version:[6,11,14,19],vi:19,view:8,vii:19,we:[11,17],which:13,within:9,word:2,work:[18,19],write:12,x:[2,7,15],xor:2,yin:19,z:20,zero:7,zip:2,zipper:20}})
\ No newline at end of file
diff --git a/docs/sphinx_docs/_build/html/stack.html b/docs/sphinx_docs/_build/html/stack.html
index ab153d5..2d6ad97 100644
--- a/docs/sphinx_docs/_build/html/stack.html
+++ b/docs/sphinx_docs/_build/html/stack.html
@@ -280,7 +280,7 @@ won’t work because Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.
     
    
 
   
diff --git a/docs/sphinx_docs/_build/html/types.html b/docs/sphinx_docs/_build/html/types.html
index a7e9539..e0f9ec1 100644
--- a/docs/sphinx_docs/_build/html/types.html
+++ b/docs/sphinx_docs/_build/html/types.html
@@ -49,25 +49,25 @@ information is available.)
    
 
    joy.utils.types
    
 
    Curently (asterix after name indicates a function that can be
 auto-compiled to Python):
    
-
    _Tree_add_Ee = ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) *
-_Tree_delete_R0 = ([a2 ...1] a1 -- [a2 ...1] a2 a1 a1) *
-_Tree_delete_clear_stuff = (a3 a2 [a1 ...1] -- [...1]) *
-_Tree_get_E = ([a3 a4 ...1] a2 a1 -- a4) *
+
    _Tree_add_Ee = ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) *
+_Tree_delete_R0 = ([a2 ...1] a1 -- [a2 ...1] a2 a1 a1) *
+_Tree_delete_clear_stuff = (a3 a2 [a1 ...1] -- [...1]) *
+_Tree_get_E = ([a3 a4 ...1] a2 a1 -- a4) *
 add = (n1 n2 -- n3)
 and = (b1 b2 -- b3)
 bool = (a1 -- b1)
-ccons = (a2 a1 [...1] -- [a2 a1 ...1]) *
-cons = (a1 [...0] -- [a1 ...0]) *
+ccons = (a2 a1 [...1] -- [a2 a1 ...1]) *
+cons = (a1 [...0] -- [a1 ...0]) *
 div = (n1 n2 -- n3)
 divmod = (n2 n1 -- n4 n3)
 dup = (a1 -- a1 a1) *
 dupd = (a2 a1 -- a2 a2 a1) *
 dupdd = (a3 a2 a1 -- a3 a3 a2 a1) *
 eq = (n1 n2 -- b1)
-first = ([a1 ...1] -- a1) *
-first_two = ([a1 a2 ...1] -- a1 a2) *
+first = ([a1 ...1] -- a1) *
+first_two = ([a1 a2 ...1] -- a1 a2) *
 floordiv = (n1 n2 -- n3)
-fourth = ([a1 a2 a3 a4 ...1] -- a4) *
+fourth = ([a1 a2 a3 a4 ...1] -- a4) *
 ge = (n1 n2 -- b1)
 gt = (n1 n2 -- b1)
 le = (n1 n2 -- b1)
@@ -88,27 +88,27 @@ auto-compiled to Python):
    
 popopdd = (a4 a3 a2 a1 -- a2 a1) *
 pow = (n1 n2 -- n3)
 pred = (n1 -- n2)
-rest = ([a1 ...0] -- [...0]) *
+rest = ([a1 ...0] -- [...0]) *
 rolldown = (a1 a2 a3 -- a2 a3 a1) *
 rollup = (a1 a2 a3 -- a3 a1 a2) *
-rrest = ([a1 a2 ...1] -- [...1]) *
+rrest = ([a1 a2 ...1] -- [...1]) *
 rshift = (n1 n2 -- n3)
-second = ([a1 a2 ...1] -- a2) *
+second = ([a1 a2 ...1] -- a2) *
 sqrt = (n1 -- n2)
 stack = (... -- ... [...]) *
 stuncons = (... a1 -- ... a1 a1 [...]) *
 stununcons = (... a2 a1 -- ... a2 a1 a1 a2 [...]) *
 sub = (n1 n2 -- n3)
 succ = (n1 -- n2)
-swaack = ([...1] -- [...0]) *
+swaack = ([...1] -- [...0]) *
 swap = (a1 a2 -- a2 a1) *
-swons = ([...1] a1 -- [a1 ...1]) *
-third = ([a1 a2 a3 ...1] -- a3) *
+swons = ([...1] a1 -- [a1 ...1]) *
+third = ([a1 a2 a3 ...1] -- a3) *
 truediv = (n1 n2 -- n3)
 tuck = (a2 a1 -- a1 a2 a1) *
-uncons = ([a1 ...0] -- a1 [...0]) *
+uncons = ([a1 ...0] -- a1 [...0]) *
 unit = (a1 -- [a1 ]) *
-unswons = ([a1 ...1] -- [...1] a1) *
+unswons = ([a1 ...1] -- [...1] a1) *
 
    
 
    
 
    Example output of the infer() function.  The first number on each
@@ -246,7 +246,7 @@ far.
    
 
 
    
 Thun Documentation by Simon Forman is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
    Based on a work at https://osdn.net/projects/joypy/.
-      Created using Sphinx 4.3.0.
+      Created using Sphinx 4.4.0.