Cf. `“Bananas, Lenses, & Barbed
Wire” <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__

`Hylomorphism <https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>`__
====================================================================================

A
`hylomorphism <https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29>`__
``H :: A -> B`` converts a value of type A into a value of type B by
means of:

-  A generator ``G :: A -> (A, B)``
-  A combiner ``F :: (B, B) -> B``
-  A predicate ``P :: A -> Bool`` to detect the base case
-  A base case value ``c :: B``
-  Recursive calls (zero or more); it has a “call stack in the form of a
   cons list”.

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

.. code:: ipython2

    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))
            return result
    
        return H

Finding `Triangular Numbers <https://en.wikipedia.org/wiki/Triangular_number>`__
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As a concrete example let’s use a function that, given a positive
integer, returns the sum of all positive integers less than that one.
(In this case the types A and B are both ``int``.) ### With ``range()``
and ``sum()``

.. code:: ipython2

    r = range(10)
    r




.. parsed-literal::

    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]



.. code:: ipython2

    sum(r)




.. parsed-literal::

    45



.. code:: ipython2

    range_sum = lambda n: sum(range(n))
    range_sum(10)




.. parsed-literal::

    45



As a hylomorphism
~~~~~~~~~~~~~~~~~

.. code:: ipython2

    G = lambda n: (n - 1, n - 1)
    F = lambda a, b: a + b
    P = lambda n: n <= 1
    
    H = hylomorphism(0, F, P, G)

.. code:: ipython2

    H(10)




.. parsed-literal::

    45



If you were to run the above code in a debugger and check out the call
stack you would find that the variable ``b`` in each call to ``H()`` is
storing the intermediate values as ``H()`` recurses. This is what was
meant by “call stack in the form of a cons list”.

Joy Preamble
~~~~~~~~~~~~

.. code:: ipython2

    from notebook_preamble import D, DefinitionWrapper, J, V, define

Hylomorphism in Joy
-------------------

We can define a combinator ``hylomorphism`` that will make a
hylomorphism combinator ``H`` from constituent parts.

::

   H == c [F] [P] [G] hylomorphism

The function ``H`` is recursive, so we start with ``ifte`` and set the
else-part to some function ``J`` that will contain a quoted copy of
``H``. (The then-part just discards the leftover ``a`` and replaces it
with the base case value ``c``.)

::

   H == [P] [pop c] [J] ifte

The else-part ``J`` gets just the argument ``a`` on the stack.

::

   a J
   a G              The first thing to do is use the generator G
   aa b             which produces b and a new aa
   aa b [H] dip     we recur with H on the new aa
   aa H b F         and run F on the result.

This gives us a definition for ``J``.

::

   J == G [H] dip F

Plug it in and convert to genrec.

::

   H == [P] [pop c] [G [H] dip F] ifte
   H == [P] [pop c] [G]   [dip F] genrec

This is the form of a hylomorphism in Joy, which nicely illustrates that
it is a simple specialization of the general recursion combinator.

::

   H == [P] [pop c] [G] [dip F] genrec

Derivation of ``hylomorphism``
------------------------------

Now we just need to derive a definition that builds the ``genrec``
arguments out of the pieces given to the ``hylomorphism`` combinator.

::

   H == [P] [pop c]              [G]                  [dip F] genrec
        [P] [c]    [pop] swoncat [G]        [F] [dip] swoncat genrec
        [P] c unit [pop] swoncat [G]        [F] [dip] swoncat genrec
        [P] c [G] [F] [unit [pop] swoncat] dipd [dip] swoncat genrec

Working in reverse: - Use ``swoncat`` twice to decouple ``[c]`` and
``[F]``. - Use ``unit`` to dequote ``c``. - Use ``dipd`` to untangle
``[unit [pop] swoncat]`` from the givens.

At this point all of the arguments (givens) to the hylomorphism are to
the left so we have a definition for ``hylomorphism``:

::

   hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec

The order of parameters is different than the one we started with but
that hardly matters, you can rearrange them or just supply them in the
expected order.

::

   [P] c [G] [F] hylomorphism == H

.. code:: ipython2

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

Demonstrate summing a range of integers from 0 to n-1.

-  ``[P]`` is ``[0 <=]``
-  ``c`` is ``0``
-  ``[G]`` is ``[1 - dup]``
-  ``[F]`` is ``[+]``

So to sum the positive integers less than five we can do this.

.. code:: ipython2

    V('5 [0 <=] 0 [1 - dup] [+] hylomorphism')


.. parsed-literal::

                                                                                   . 5 [0 <=] 0 [1 - dup] [+] hylomorphism
                                                                                 5 . [0 <=] 0 [1 - dup] [+] hylomorphism
                                                                          5 [0 <=] . 0 [1 - dup] [+] hylomorphism
                                                                        5 [0 <=] 0 . [1 - dup] [+] hylomorphism
                                                              5 [0 <=] 0 [1 - dup] . [+] hylomorphism
                                                          5 [0 <=] 0 [1 - dup] [+] . hylomorphism
                                                          5 [0 <=] 0 [1 - dup] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec
                                     5 [0 <=] 0 [1 - dup] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec
                                                                        5 [0 <=] 0 . unit [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                        5 [0 <=] 0 . [] cons [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                     5 [0 <=] 0 [] . cons [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                      5 [0 <=] [0] . [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                5 [0 <=] [0] [pop] . swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                5 [0 <=] [0] [pop] . swap concat [1 - dup] [+] [dip] swoncat genrec
                                                                5 [0 <=] [pop] [0] . concat [1 - dup] [+] [dip] swoncat genrec
                                                                  5 [0 <=] [pop 0] . [1 - dup] [+] [dip] swoncat genrec
                                                        5 [0 <=] [pop 0] [1 - dup] . [+] [dip] swoncat genrec
                                                    5 [0 <=] [pop 0] [1 - dup] [+] . [dip] swoncat genrec
                                              5 [0 <=] [pop 0] [1 - dup] [+] [dip] . swoncat genrec
                                              5 [0 <=] [pop 0] [1 - dup] [+] [dip] . swap concat genrec
                                              5 [0 <=] [pop 0] [1 - dup] [dip] [+] . concat genrec
                                                5 [0 <=] [pop 0] [1 - dup] [dip +] . genrec
        5 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte
    5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [5] [0 <=] . infra first choice i
                                                                                 5 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] swaack first choice i
                                                                               5 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] swaack first choice i
                                                                             False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] swaack first choice i
       False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] . swaack first choice i
       5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i
         5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i
                       5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i
                                                                                 5 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                                                               5 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                                                                 4 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                                                               4 4 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                     4 4 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip +
                                                                                 4 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 4 +
                                                                          4 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 4 +
                                                                  4 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 4 +
                                                        4 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 4 +
                                                4 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 4 +
        4 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 4 +
    4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [4] [0 <=] . infra first choice i 4 +
                                                                                 4 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] swaack first choice i 4 +
                                                                               4 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] swaack first choice i 4 +
                                                                             False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] swaack first choice i 4 +
       False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] . swaack first choice i 4 +
       4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 4 +
         4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 4 +
                       4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 4 +
                                                                                 4 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 +
                                                                               4 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 +
                                                                                 3 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 +
                                                                               3 3 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 +
                                     3 3 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 4 +
                                                                                 3 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 3 + 4 +
                                                                          3 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 3 + 4 +
                                                                  3 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 3 + 4 +
                                                        3 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 3 + 4 +
                                                3 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 3 + 4 +
        3 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 3 + 4 +
    3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [3] [0 <=] . infra first choice i 3 + 4 +
                                                                                 3 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] swaack first choice i 3 + 4 +
                                                                               3 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] swaack first choice i 3 + 4 +
                                                                             False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] swaack first choice i 3 + 4 +
       False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] . swaack first choice i 3 + 4 +
       3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 3 + 4 +
         3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 3 + 4 +
                       3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 3 + 4 +
                                                                                 3 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 +
                                                                               3 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 +
                                                                                 2 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 +
                                                                               2 2 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 +
                                     2 2 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 3 + 4 +
                                                                                 2 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 2 + 3 + 4 +
                                                                          2 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 2 + 3 + 4 +
                                                                  2 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 2 + 3 + 4 +
                                                        2 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 2 + 3 + 4 +
                                                2 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 2 + 3 + 4 +
        2 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 2 + 3 + 4 +
    2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [2] [0 <=] . infra first choice i 2 + 3 + 4 +
                                                                                 2 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] swaack first choice i 2 + 3 + 4 +
                                                                               2 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] swaack first choice i 2 + 3 + 4 +
                                                                             False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] swaack first choice i 2 + 3 + 4 +
       False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] . swaack first choice i 2 + 3 + 4 +
       2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 2 + 3 + 4 +
         2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 2 + 3 + 4 +
                       2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 2 + 3 + 4 +
                                                                                 2 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 +
                                                                               2 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 +
                                                                                 1 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 +
                                                                               1 1 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 +
                                     1 1 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 2 + 3 + 4 +
                                                                                 1 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 1 + 2 + 3 + 4 +
                                                                          1 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 1 + 2 + 3 + 4 +
                                                                  1 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 1 + 2 + 3 + 4 +
                                                        1 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 1 + 2 + 3 + 4 +
                                                1 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 1 + 2 + 3 + 4 +
        1 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 1 + 2 + 3 + 4 +
    1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [1] [0 <=] . infra first choice i 1 + 2 + 3 + 4 +
                                                                                 1 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] swaack first choice i 1 + 2 + 3 + 4 +
                                                                               1 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] swaack first choice i 1 + 2 + 3 + 4 +
                                                                             False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] swaack first choice i 1 + 2 + 3 + 4 +
       False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] . swaack first choice i 1 + 2 + 3 + 4 +
       1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 1 + 2 + 3 + 4 +
         1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 1 + 2 + 3 + 4 +
                       1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 1 + 2 + 3 + 4 +
                                                                                 1 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 +
                                                                               1 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 +
                                                                                 0 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 +
                                                                               0 0 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 +
                                     0 0 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 1 + 2 + 3 + 4 +
                                                                                 0 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 0 + 1 + 2 + 3 + 4 +
                                                                          0 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 0 + 1 + 2 + 3 + 4 +
                                                                  0 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 0 + 1 + 2 + 3 + 4 +
                                                        0 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 0 + 1 + 2 + 3 + 4 +
                                                0 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 0 + 1 + 2 + 3 + 4 +
        0 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 0 + 1 + 2 + 3 + 4 +
    0 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [0] [0 <=] . infra first choice i 0 + 1 + 2 + 3 + 4 +
                                                                                 0 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] swaack first choice i 0 + 1 + 2 + 3 + 4 +
                                                                               0 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] swaack first choice i 0 + 1 + 2 + 3 + 4 +
                                                                              True . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] swaack first choice i 0 + 1 + 2 + 3 + 4 +
        True [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] . swaack first choice i 0 + 1 + 2 + 3 + 4 +
        0 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [True] . first choice i 0 + 1 + 2 + 3 + 4 +
          0 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] True . choice i 0 + 1 + 2 + 3 + 4 +
                                                                         0 [pop 0] . i 0 + 1 + 2 + 3 + 4 +
                                                                                 0 . pop 0 0 + 1 + 2 + 3 + 4 +
                                                                                   . 0 0 + 1 + 2 + 3 + 4 +
                                                                                 0 . 0 + 1 + 2 + 3 + 4 +
                                                                               0 0 . + 1 + 2 + 3 + 4 +
                                                                                 0 . 1 + 2 + 3 + 4 +
                                                                               0 1 . + 2 + 3 + 4 +
                                                                                 1 . 2 + 3 + 4 +
                                                                               1 2 . + 3 + 4 +
                                                                                 3 . 3 + 4 +
                                                                               3 3 . + 4 +
                                                                                 6 . 4 +
                                                                               6 4 . +
                                                                                10 . 


Anamorphism
===========

An anamorphism can be defined as a hylomorphism that uses ``[]`` for
``c`` and ``swons`` for ``F``.

::

   [P] [G] anamorphism == [P] [] [G] [swons] hylomorphism == A

This allows us to define an anamorphism combinator in terms of the
hylomorphism combinator.

::

   [] swap [swons] hylomorphism == anamorphism

Partial evaluation gives us a “pre-cooked” form.

::

   [P] [G] . anamorphism
   [P] [G] . [] swap [swons] hylomorphism
   [P] [G] [] . swap [swons] hylomorphism
   [P] [] [G] . [swons] hylomorphism
   [P] [] [G] [swons] . hylomorphism
   [P] [] [G] [swons] . [unit [pop] swoncat] dipd [dip] swoncat genrec
   [P] [] [G] [swons] [unit [pop] swoncat] . dipd [dip] swoncat genrec
   [P] [] . unit [pop] swoncat [G] [swons] [dip] swoncat genrec
   [P] [[]] [pop] . swoncat [G] [swons] [dip] swoncat genrec
   [P] [pop []] [G] [swons] [dip] . swoncat genrec

   [P] [pop []] [G] [dip swons] genrec

(We could also have just substituted for ``c`` and ``F`` in the
definition of ``H``.)

::

   H == [P] [pop c ] [G] [dip F    ] genrec
   A == [P] [pop []] [G] [dip swons] genrec

The partial evaluation is overkill in this case but it serves as a
reminder that this sort of program specialization can, in many cases, be
carried out automatically.)

Untangle ``[G]`` from ``[pop []]`` using ``swap``.

::

   [P] [G] [pop []] swap [dip swons] genrec

All of the arguments to ``anamorphism`` are to the left, so we have a
definition for it.

::

   anamorphism == [pop []] swap [dip swons] genrec

An example of an anamorphism is the range function.

::

   range == [0 <=] [1 - dup] anamorphism

Catamorphism
============

A catamorphism can be defined as a hylomorphism that uses
``[uncons swap]`` for ``[G]`` and ``[[] =]`` for the predicate ``[P]``.

::

   c [F] catamorphism == [[] =] c [uncons swap] [F] hylomorphism == C

This allows us to define a ``catamorphism`` combinator in terms of the
``hylomorphism`` combinator.

::

   [[] =] roll> [uncons swap] swap hylomorphism == catamorphism

Partial evaluation doesn’t help much.

::

   c [F] . catamorphism
   c [F] . [[] =] roll> [uncons swap] swap hylomorphism
   c [F] [[] =] . roll> [uncons swap] swap hylomorphism
   [[] =] c [F] [uncons swap] . swap hylomorphism
   [[] =] c [uncons swap] [F] . hylomorphism
   [[] =] c [uncons swap] [F] [unit [pop] swoncat] . dipd [dip] swoncat genrec
   [[] =] c . unit [pop] swoncat [uncons swap] [F] [dip] swoncat genrec
   [[] =] [c] [pop] . swoncat [uncons swap] [F] [dip] swoncat genrec
   [[] =] [pop c] [uncons swap] [F] [dip] . swoncat genrec
   [[] =] [pop c] [uncons swap] [dip F] genrec

Because the arguments to catamorphism have to be prepared (unlike the
arguments to anamorphism, which only need to be rearranged slightly)
there isn’t much point to “pre-cooking” the definition.

::

   catamorphism == [[] =] roll> [uncons swap] swap hylomorphism

An example of a catamorphism is the sum function.

::

   sum == 0 [+] catamorphism

“Fusion Law” for catas (UNFINISHED!!!)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I’m not sure exactly how to translate the “Fusion Law” for catamorphisms
into Joy.

I know that a ``map`` composed with a cata can be expressed as a new
cata:

::

   [F] map b [B] cata == b [F B] cata

But this isn’t the one described in “Bananas…”. That’s more like:

A cata composed with some function can be expressed as some other cata:

::

   b [B] catamorphism F == c [C] catamorphism

Given:

::

   b F == c

   ...

   B F == [F] dip C

   ...

   b[B]cata F == c[C]cata

   F(B(head, tail)) == C(head, F(tail))

   1 [2 3] B F         1 [2 3] F C


   b F == c
   B F == F C

   b [B] catamorphism F == c [C] catamorphism
   b [B] catamorphism F == b F [C] catamorphism

   ...

Or maybe,

::

   [F] map b [B] cata == c [C] cata     ???

   [F] map b [B] cata == b [F B] cata    I think this is generally true, unless F consumes stack items
                                           instead of just transforming TOS.  Of course, there's always [F] unary.
   b [F] unary [[F] unary B] cata

   [10 *] map 0 swap [+] step == 0 swap [10 * +] step

For example:

::

   F == 10 *
   b == 0
   B == +
   c == 0
   C == F +

   b F    == c
   0 10 * == 0

   B F    == [F]    dip C
   + 10 * == [10 *] dip F +
   + 10 * == [10 *] dip 10 * +

   n m + 10 * == 10(n+m)

   n m [10 *] dip 10 * +
   n 10 * m 10 * +
   10n m 10 * +
   10n 10m +
   10n+10m

   10n+10m = 10(n+m)

Ergo:

::

   0 [+] catamorphism 10 * == 0 [10 * +] catamorphism

The ``step`` combinator will usually be better to use than ``catamorphism``.
----------------------------------------------------------------------------

::

   sum == 0 swap [+] step
   sum == 0 [+] catamorphism

anamorphism catamorphism == hylomorphism
========================================

Here is (part of) the payoff.

An anamorphism followed by (composed with) a catamorphism is a
hylomorphism, with the advantage that the hylomorphism does not create
the intermediate list structure. The values are stored in either the
call stack, for those implementations that use one, or in the pending
expression (“continuation”) for the Joypy interpreter. They still have
to be somewhere, converting from an anamorphism and catamorphism to a
hylomorphism just prevents using additional storage and doing additional
processing.

::

       range == [0 <=] [1 - dup] anamorphism
         sum == 0 [+] catamorphism

   range sum == [0 <=] [1 - dup] anamorphism 0 [+] catamorphism
             == [0 <=] 0 [1 - dup] [+] hylomorphism

We can let the ``hylomorphism`` combinator build ``range_sum`` for us or
just substitute ourselves.

::

           H == [P]    [pop c] [G]       [dip F] genrec
   range_sum == [0 <=] [pop 0] [1 - dup] [dip +] genrec

.. code:: ipython2

    defs = '''
    anamorphism == [pop []] swap [dip swons] genrec
    hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec
    catamorphism == [[] =] roll> [uncons swap] swap hylomorphism
    range == [0 <=] [1 - dup] anamorphism
    sum == 0 [+] catamorphism
    range_sum == [0 <=] 0 [1 - dup] [+] hylomorphism
    '''
    
    DefinitionWrapper.add_definitions(defs, D)

.. code:: ipython2

    J('10 range')


.. parsed-literal::

    [9 8 7 6 5 4 3 2 1 0]


.. code:: ipython2

    J('[9 8 7 6 5 4 3 2 1 0] sum')


.. parsed-literal::

    45


.. code:: ipython2

    V('10 range sum')


.. parsed-literal::

                                                                                                                                   . 10 range sum
                                                                                                                                10 . range sum
                                                                                                                                10 . [0 <=] [1 - dup] anamorphism sum
                                                                                                                         10 [0 <=] . [1 - dup] anamorphism sum
                                                                                                               10 [0 <=] [1 - dup] . anamorphism sum
                                                                                                               10 [0 <=] [1 - dup] . [pop []] swap [dip swons] genrec sum
                                                                                                      10 [0 <=] [1 - dup] [pop []] . swap [dip swons] genrec sum
                                                                                                      10 [0 <=] [pop []] [1 - dup] . [dip swons] genrec sum
                                                                                          10 [0 <=] [pop []] [1 - dup] [dip swons] . genrec sum
                                             10 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte sum
                                        10 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [10] [0 <=] . infra first choice i sum
                                                                                                                                10 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 10] swaack first choice i sum
                                                                                                                              10 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 10] swaack first choice i sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 10] swaack first choice i sum
                                            False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 10] . swaack first choice i sum
                                            10 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i sum
                                              10 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i sum
                                                             10 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i sum
                                                                                                                                10 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons sum
                                                                                                                              10 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons sum
                                                                                                                                 9 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons sum
                                                                                                                               9 9 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons sum
                                                                                9 9 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons sum
                                                                                                                                 9 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 9 swons sum
                                                                                                                          9 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 9 swons sum
                                                                                                                 9 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 9 swons sum
                                                                                                       9 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 9 swons sum
                                                                                           9 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 9 swons sum
                                              9 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 9 swons sum
                                          9 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [9] [0 <=] . infra first choice i 9 swons sum
                                                                                                                                 9 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 9] swaack first choice i 9 swons sum
                                                                                                                               9 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 9] swaack first choice i 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 9] swaack first choice i 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 9] . swaack first choice i 9 swons sum
                                             9 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 9 swons sum
                                               9 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 9 swons sum
                                                              9 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 9 swons sum
                                                                                                                                 9 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 9 swons sum
                                                                                                                               9 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 9 swons sum
                                                                                                                                 8 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 9 swons sum
                                                                                                                               8 8 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 9 swons sum
                                                                                8 8 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 9 swons sum
                                                                                                                                 8 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 8 swons 9 swons sum
                                                                                                                          8 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 8 swons 9 swons sum
                                                                                                                 8 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 8 swons 9 swons sum
                                                                                                       8 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 8 swons 9 swons sum
                                                                                           8 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 8 swons 9 swons sum
                                              8 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 8 swons 9 swons sum
                                          8 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [8] [0 <=] . infra first choice i 8 swons 9 swons sum
                                                                                                                                 8 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 8] swaack first choice i 8 swons 9 swons sum
                                                                                                                               8 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 8] swaack first choice i 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 8] swaack first choice i 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 8] . swaack first choice i 8 swons 9 swons sum
                                             8 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 8 swons 9 swons sum
                                               8 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 8 swons 9 swons sum
                                                              8 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 8 swons 9 swons sum
                                                                                                                                 8 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 8 swons 9 swons sum
                                                                                                                               8 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 8 swons 9 swons sum
                                                                                                                                 7 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 8 swons 9 swons sum
                                                                                                                               7 7 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 8 swons 9 swons sum
                                                                                7 7 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 8 swons 9 swons sum
                                                                                                                                 7 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 7 swons 8 swons 9 swons sum
                                                                                                                          7 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 7 swons 8 swons 9 swons sum
                                                                                                                 7 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 7 swons 8 swons 9 swons sum
                                                                                                       7 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 7 swons 8 swons 9 swons sum
                                                                                           7 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 7 swons 8 swons 9 swons sum
                                              7 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 7 swons 8 swons 9 swons sum
                                          7 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [7] [0 <=] . infra first choice i 7 swons 8 swons 9 swons sum
                                                                                                                                 7 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 7] swaack first choice i 7 swons 8 swons 9 swons sum
                                                                                                                               7 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 7] swaack first choice i 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 7] swaack first choice i 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 7] . swaack first choice i 7 swons 8 swons 9 swons sum
                                             7 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 7 swons 8 swons 9 swons sum
                                               7 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 7 swons 8 swons 9 swons sum
                                                              7 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 7 swons 8 swons 9 swons sum
                                                                                                                                 7 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 7 swons 8 swons 9 swons sum
                                                                                                                               7 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 7 swons 8 swons 9 swons sum
                                                                                                                                 6 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 7 swons 8 swons 9 swons sum
                                                                                                                               6 6 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 7 swons 8 swons 9 swons sum
                                                                                6 6 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 7 swons 8 swons 9 swons sum
                                                                                                                                 6 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          6 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 6 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       6 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 6 swons 7 swons 8 swons 9 swons sum
                                                                                           6 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 6 swons 7 swons 8 swons 9 swons sum
                                              6 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 6 swons 7 swons 8 swons 9 swons sum
                                          6 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [6] [0 <=] . infra first choice i 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 6 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 6] swaack first choice i 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               6 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 6] swaack first choice i 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 6] swaack first choice i 6 swons 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 6] . swaack first choice i 6 swons 7 swons 8 swons 9 swons sum
                                             6 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 6 swons 7 swons 8 swons 9 swons sum
                                               6 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 6 swons 7 swons 8 swons 9 swons sum
                                                              6 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 6 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               6 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 5 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               5 5 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                5 5 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 5 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          5 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 5 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       5 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                           5 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              5 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                          5 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [5] [0 <=] . infra first choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 5 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 5] swaack first choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               5 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 5] swaack first choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 5] swaack first choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 5] . swaack first choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             5 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                               5 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                              5 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 5 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               5 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 4 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               4 4 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                4 4 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 4 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          4 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 4 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       4 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                           4 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              4 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                          4 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [4] [0 <=] . infra first choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 4 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 4] swaack first choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               4 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 4] swaack first choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 4] swaack first choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 4] . swaack first choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             4 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                               4 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                              4 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 4 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               4 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 3 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               3 3 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                3 3 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 3 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          3 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 3 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       3 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                           3 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              3 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                          3 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [3] [0 <=] . infra first choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 3 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 3] swaack first choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               3 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 3] swaack first choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 3] swaack first choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 3] . swaack first choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             3 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                               3 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                              3 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 3 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               3 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 2 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               2 2 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                2 2 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 2 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          2 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 2 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       2 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                           2 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              2 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                          2 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [2] [0 <=] . infra first choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 2 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               2 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 2] . swaack first choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             2 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                               2 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                              2 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 2 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               2 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 1 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               1 1 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                1 1 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 1 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          1 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 1 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       1 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                           1 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              1 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                          1 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [1] [0 <=] . infra first choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 1 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               1 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             False . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             False [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 1] . swaack first choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                             1 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                               1 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] False . choice i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                              1 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . i 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 1 . 1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               1 1 . - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 0 . dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               0 0 . [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                0 0 [[0 <=] [pop []] [1 - dup] [dip swons] genrec] . dip swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 0 . [0 <=] [pop []] [1 - dup] [dip swons] genrec 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                          0 [0 <=] . [pop []] [1 - dup] [dip swons] genrec 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                 0 [0 <=] [pop []] . [1 - dup] [dip swons] genrec 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                       0 [0 <=] [pop []] [1 - dup] . [dip swons] genrec 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                           0 [0 <=] [pop []] [1 - dup] [dip swons] . genrec 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              0 [0 <=] [pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] . ifte 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                          0 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [0] [0 <=] . infra first choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 0 . 0 <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 0] swaack first choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               0 0 . <= [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 0] swaack first choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                              True . [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 0] swaack first choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              True [[pop []] [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] 0] . swaack first choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                              0 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] [True] . first choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                0 [1 - dup [[0 <=] [pop []] [1 - dup] [dip swons] genrec] dip swons] [pop []] True . choice i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                        0 [pop []] . i 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                 0 . pop [] 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                   . [] 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                                [] . 0 swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                              [] 0 . swons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                              [] 0 . swap cons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                              0 [] . cons 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                               [0] . 1 swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             [0] 1 . swons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             [0] 1 . swap cons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             1 [0] . cons 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                             [1 0] . 2 swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                           [1 0] 2 . swons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                           [1 0] 2 . swap cons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                           2 [1 0] . cons 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                           [2 1 0] . 3 swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                         [2 1 0] 3 . swons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                         [2 1 0] 3 . swap cons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                         3 [2 1 0] . cons 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                         [3 2 1 0] . 4 swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                       [3 2 1 0] 4 . swons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                       [3 2 1 0] 4 . swap cons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                       4 [3 2 1 0] . cons 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                       [4 3 2 1 0] . 5 swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                     [4 3 2 1 0] 5 . swons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                     [4 3 2 1 0] 5 . swap cons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                     5 [4 3 2 1 0] . cons 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                     [5 4 3 2 1 0] . 6 swons 7 swons 8 swons 9 swons sum
                                                                                                                   [5 4 3 2 1 0] 6 . swons 7 swons 8 swons 9 swons sum
                                                                                                                   [5 4 3 2 1 0] 6 . swap cons 7 swons 8 swons 9 swons sum
                                                                                                                   6 [5 4 3 2 1 0] . cons 7 swons 8 swons 9 swons sum
                                                                                                                   [6 5 4 3 2 1 0] . 7 swons 8 swons 9 swons sum
                                                                                                                 [6 5 4 3 2 1 0] 7 . swons 8 swons 9 swons sum
                                                                                                                 [6 5 4 3 2 1 0] 7 . swap cons 8 swons 9 swons sum
                                                                                                                 7 [6 5 4 3 2 1 0] . cons 8 swons 9 swons sum
                                                                                                                 [7 6 5 4 3 2 1 0] . 8 swons 9 swons sum
                                                                                                               [7 6 5 4 3 2 1 0] 8 . swons 9 swons sum
                                                                                                               [7 6 5 4 3 2 1 0] 8 . swap cons 9 swons sum
                                                                                                               8 [7 6 5 4 3 2 1 0] . cons 9 swons sum
                                                                                                               [8 7 6 5 4 3 2 1 0] . 9 swons sum
                                                                                                             [8 7 6 5 4 3 2 1 0] 9 . swons sum
                                                                                                             [8 7 6 5 4 3 2 1 0] 9 . swap cons sum
                                                                                                             9 [8 7 6 5 4 3 2 1 0] . cons sum
                                                                                                             [9 8 7 6 5 4 3 2 1 0] . sum
                                                                                                             [9 8 7 6 5 4 3 2 1 0] . 0 [+] catamorphism
                                                                                                           [9 8 7 6 5 4 3 2 1 0] 0 . [+] catamorphism
                                                                                                       [9 8 7 6 5 4 3 2 1 0] 0 [+] . catamorphism
                                                                                                       [9 8 7 6 5 4 3 2 1 0] 0 [+] . [[] =] roll> [uncons swap] swap hylomorphism
                                                                                                [9 8 7 6 5 4 3 2 1 0] 0 [+] [[] =] . roll> [uncons swap] swap hylomorphism
                                                                                                [9 8 7 6 5 4 3 2 1 0] [[] =] 0 [+] . [uncons swap] swap hylomorphism
                                                                                  [9 8 7 6 5 4 3 2 1 0] [[] =] 0 [+] [uncons swap] . swap hylomorphism
                                                                                  [9 8 7 6 5 4 3 2 1 0] [[] =] 0 [uncons swap] [+] . hylomorphism
                                                                                  [9 8 7 6 5 4 3 2 1 0] [[] =] 0 [uncons swap] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec
                                                             [9 8 7 6 5 4 3 2 1 0] [[] =] 0 [uncons swap] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec
                                                                                                    [9 8 7 6 5 4 3 2 1 0] [[] =] 0 . unit [pop] swoncat [uncons swap] [+] [dip] swoncat genrec
                                                                                                    [9 8 7 6 5 4 3 2 1 0] [[] =] 0 . [] cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec
                                                                                                 [9 8 7 6 5 4 3 2 1 0] [[] =] 0 [] . cons [pop] swoncat [uncons swap] [+] [dip] swoncat genrec
                                                                                                  [9 8 7 6 5 4 3 2 1 0] [[] =] [0] . [pop] swoncat [uncons swap] [+] [dip] swoncat genrec
                                                                                            [9 8 7 6 5 4 3 2 1 0] [[] =] [0] [pop] . swoncat [uncons swap] [+] [dip] swoncat genrec
                                                                                            [9 8 7 6 5 4 3 2 1 0] [[] =] [0] [pop] . swap concat [uncons swap] [+] [dip] swoncat genrec
                                                                                            [9 8 7 6 5 4 3 2 1 0] [[] =] [pop] [0] . concat [uncons swap] [+] [dip] swoncat genrec
                                                                                              [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] . [uncons swap] [+] [dip] swoncat genrec
                                                                                [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] . [+] [dip] swoncat genrec
                                                                            [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [+] . [dip] swoncat genrec
                                                                      [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [+] [dip] . swoncat genrec
                                                                      [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [+] [dip] . swap concat genrec
                                                                      [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip] [+] . concat genrec
                                                                        [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec
                            [9 8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte
    [9 8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[9 8 7 6 5 4 3 2 1 0]] [[] =] . infra first choice i
                                                                                                             [9 8 7 6 5 4 3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [9 8 7 6 5 4 3 2 1 0]] swaack first choice i
                                                                                                          [9 8 7 6 5 4 3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [9 8 7 6 5 4 3 2 1 0]] swaack first choice i
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [9 8 7 6 5 4 3 2 1 0]] swaack first choice i
                           False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [9 8 7 6 5 4 3 2 1 0]] . swaack first choice i
                           [9 8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i
                             [9 8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i
                                           [9 8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i
                                                                                                             [9 8 7 6 5 4 3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +
                                                                                                             9 [8 7 6 5 4 3 2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +
                                                                                                             [8 7 6 5 4 3 2 1 0] 9 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +
                                                               [8 7 6 5 4 3 2 1 0] 9 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip +
                                                                                                               [8 7 6 5 4 3 2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 9 +
                                                                                                        [8 7 6 5 4 3 2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 9 +
                                                                                                [8 7 6 5 4 3 2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 9 +
                                                                                  [8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 9 +
                                                                          [8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 9 +
                              [8 7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 9 +
        [8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[8 7 6 5 4 3 2 1 0]] [[] =] . infra first choice i 9 +
                                                                                                               [8 7 6 5 4 3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [8 7 6 5 4 3 2 1 0]] swaack first choice i 9 +
                                                                                                            [8 7 6 5 4 3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [8 7 6 5 4 3 2 1 0]] swaack first choice i 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [8 7 6 5 4 3 2 1 0]] swaack first choice i 9 +
                             False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [8 7 6 5 4 3 2 1 0]] . swaack first choice i 9 +
                             [8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 9 +
                               [8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 9 +
                                             [8 7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 9 +
                                                                                                               [8 7 6 5 4 3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 9 +
                                                                                                               8 [7 6 5 4 3 2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 9 +
                                                                                                               [7 6 5 4 3 2 1 0] 8 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 9 +
                                                                 [7 6 5 4 3 2 1 0] 8 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 9 +
                                                                                                                 [7 6 5 4 3 2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 8 + 9 +
                                                                                                          [7 6 5 4 3 2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 8 + 9 +
                                                                                                  [7 6 5 4 3 2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 8 + 9 +
                                                                                    [7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 8 + 9 +
                                                                            [7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 8 + 9 +
                                [7 6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 8 + 9 +
            [7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[7 6 5 4 3 2 1 0]] [[] =] . infra first choice i 8 + 9 +
                                                                                                                 [7 6 5 4 3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [7 6 5 4 3 2 1 0]] swaack first choice i 8 + 9 +
                                                                                                              [7 6 5 4 3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [7 6 5 4 3 2 1 0]] swaack first choice i 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [7 6 5 4 3 2 1 0]] swaack first choice i 8 + 9 +
                               False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [7 6 5 4 3 2 1 0]] . swaack first choice i 8 + 9 +
                               [7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 8 + 9 +
                                 [7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 8 + 9 +
                                               [7 6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 8 + 9 +
                                                                                                                 [7 6 5 4 3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 8 + 9 +
                                                                                                                 7 [6 5 4 3 2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 8 + 9 +
                                                                                                                 [6 5 4 3 2 1 0] 7 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 8 + 9 +
                                                                   [6 5 4 3 2 1 0] 7 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 8 + 9 +
                                                                                                                   [6 5 4 3 2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 7 + 8 + 9 +
                                                                                                            [6 5 4 3 2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 7 + 8 + 9 +
                                                                                                    [6 5 4 3 2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 7 + 8 + 9 +
                                                                                      [6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 7 + 8 + 9 +
                                                                              [6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 7 + 8 + 9 +
                                  [6 5 4 3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 7 + 8 + 9 +
                [6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[6 5 4 3 2 1 0]] [[] =] . infra first choice i 7 + 8 + 9 +
                                                                                                                   [6 5 4 3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [6 5 4 3 2 1 0]] swaack first choice i 7 + 8 + 9 +
                                                                                                                [6 5 4 3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [6 5 4 3 2 1 0]] swaack first choice i 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [6 5 4 3 2 1 0]] swaack first choice i 7 + 8 + 9 +
                                 False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [6 5 4 3 2 1 0]] . swaack first choice i 7 + 8 + 9 +
                                 [6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 7 + 8 + 9 +
                                   [6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 7 + 8 + 9 +
                                                 [6 5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 7 + 8 + 9 +
                                                                                                                   [6 5 4 3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 7 + 8 + 9 +
                                                                                                                   6 [5 4 3 2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 7 + 8 + 9 +
                                                                                                                   [5 4 3 2 1 0] 6 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 7 + 8 + 9 +
                                                                     [5 4 3 2 1 0] 6 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 7 + 8 + 9 +
                                                                                                                     [5 4 3 2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 6 + 7 + 8 + 9 +
                                                                                                              [5 4 3 2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 6 + 7 + 8 + 9 +
                                                                                                      [5 4 3 2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 6 + 7 + 8 + 9 +
                                                                                        [5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 6 + 7 + 8 + 9 +
                                                                                [5 4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 6 + 7 + 8 + 9 +
                                    [5 4 3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 6 + 7 + 8 + 9 +
                    [5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[5 4 3 2 1 0]] [[] =] . infra first choice i 6 + 7 + 8 + 9 +
                                                                                                                     [5 4 3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [5 4 3 2 1 0]] swaack first choice i 6 + 7 + 8 + 9 +
                                                                                                                  [5 4 3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [5 4 3 2 1 0]] swaack first choice i 6 + 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [5 4 3 2 1 0]] swaack first choice i 6 + 7 + 8 + 9 +
                                   False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [5 4 3 2 1 0]] . swaack first choice i 6 + 7 + 8 + 9 +
                                   [5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 6 + 7 + 8 + 9 +
                                     [5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 6 + 7 + 8 + 9 +
                                                   [5 4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 6 + 7 + 8 + 9 +
                                                                                                                     [5 4 3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                                                                                                     5 [4 3 2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                                                                                                     [4 3 2 1 0] 5 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                                                       [4 3 2 1 0] 5 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 6 + 7 + 8 + 9 +
                                                                                                                       [4 3 2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                                                                                [4 3 2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                                                                        [4 3 2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                                                          [4 3 2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                                                  [4 3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 5 + 6 + 7 + 8 + 9 +
                                      [4 3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 5 + 6 + 7 + 8 + 9 +
                        [4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[4 3 2 1 0]] [[] =] . infra first choice i 5 + 6 + 7 + 8 + 9 +
                                                                                                                       [4 3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [4 3 2 1 0]] swaack first choice i 5 + 6 + 7 + 8 + 9 +
                                                                                                                    [4 3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [4 3 2 1 0]] swaack first choice i 5 + 6 + 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [4 3 2 1 0]] swaack first choice i 5 + 6 + 7 + 8 + 9 +
                                     False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [4 3 2 1 0]] . swaack first choice i 5 + 6 + 7 + 8 + 9 +
                                     [4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 5 + 6 + 7 + 8 + 9 +
                                       [4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 5 + 6 + 7 + 8 + 9 +
                                                     [4 3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 5 + 6 + 7 + 8 + 9 +
                                                                                                                       [4 3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                                                                                                       4 [3 2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                                                                                                       [3 2 1 0] 4 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                                                         [3 2 1 0] 4 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 5 + 6 + 7 + 8 + 9 +
                                                                                                                         [3 2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                  [3 2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                          [3 2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                            [3 2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                    [3 2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                        [3 2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 4 + 5 + 6 + 7 + 8 + 9 +
                            [3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[3 2 1 0]] [[] =] . infra first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                         [3 2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3 2 1 0]] swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                      [3 2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3 2 1 0]] swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3 2 1 0]] swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                       False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [3 2 1 0]] . swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                       [3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                         [3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                       [3 2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                         [3 2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                         3 [2 1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                         [2 1 0] 3 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                           [2 1 0] 3 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                           [2 1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                    [2 1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                            [2 1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                              [2 1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                      [2 1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                          [2 1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                [2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[2 1 0]] [[] =] . infra first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                           [2 1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 1 0]] swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                        [2 1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 1 0]] swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 1 0]] swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                         False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [2 1 0]] . swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                         [2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                           [2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                         [2 1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                           [2 1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                           2 [1 0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                           [1 0] 2 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                             [1 0] 2 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             [1 0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                      [1 0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                              [1 0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                [1 0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                        [1 0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                            [1 0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                    [1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[1 0]] [[] =] . infra first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             [1 0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [1 0]] swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                          [1 0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [1 0]] swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [1 0]] swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                           False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [1 0]] . swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                           [1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                             [1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                           [1 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             [1 0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             1 [0] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             [0] 1 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                               [0] 1 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               [0] . [[] =] [pop 0] [uncons swap] [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                        [0] [[] =] . [pop 0] [uncons swap] [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                [0] [[] =] [pop 0] . [uncons swap] [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                  [0] [[] =] [pop 0] [uncons swap] . [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                          [0] [[] =] [pop 0] [uncons swap] [dip +] . genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                              [0] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                        [0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[0]] [[] =] . infra first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               [0] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [0]] swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                            [0] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [0]] swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             False . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [0]] swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                             False [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [0]] . swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                             [0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [False] . first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                               [0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] False . choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                             [0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               [0] . uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                              0 [] . swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                              [] 0 . [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                [] 0 [[[] =] [pop 0] [uncons swap] [dip +] genrec] . dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                [] . [[] =] [pop 0] [uncons swap] [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                         [] [[] =] . [pop 0] [uncons swap] [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                 [] [[] =] [pop 0] . [uncons swap] [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                   [] [[] =] [pop 0] [uncons swap] . [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                           [] [[] =] [pop 0] [uncons swap] [dip +] . genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                               [] [[] =] [pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] . ifte 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                          [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [[]] [[] =] . infra first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                [] . [] = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] []] swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                             [] [] . = [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] []] swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                              True . [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] []] swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                               True [[pop 0] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] []] . swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                               [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] [True] . first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                 [] [uncons swap [[[] =] [pop 0] [uncons swap] [dip +] genrec] dip +] [pop 0] True . choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                        [] [pop 0] . i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                [] . pop 0 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                   . 0 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                 0 . 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               0 0 . + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                 0 . 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               0 1 . + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                 1 . 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               1 2 . + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                 3 . 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               3 3 . + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                 6 . 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                                                               6 4 . + 5 + 6 + 7 + 8 + 9 +
                                                                                                                                10 . 5 + 6 + 7 + 8 + 9 +
                                                                                                                              10 5 . + 6 + 7 + 8 + 9 +
                                                                                                                                15 . 6 + 7 + 8 + 9 +
                                                                                                                              15 6 . + 7 + 8 + 9 +
                                                                                                                                21 . 7 + 8 + 9 +
                                                                                                                              21 7 . + 8 + 9 +
                                                                                                                                28 . 8 + 9 +
                                                                                                                              28 8 . + 9 +
                                                                                                                                36 . 9 +
                                                                                                                              36 9 . +
                                                                                                                                45 . 


.. code:: ipython2

    V('10 range_sum')


.. parsed-literal::

                                                                                     . 10 range_sum
                                                                                  10 . range_sum
                                                                                  10 . [0 <=] 0 [1 - dup] [+] hylomorphism
                                                                           10 [0 <=] . 0 [1 - dup] [+] hylomorphism
                                                                         10 [0 <=] 0 . [1 - dup] [+] hylomorphism
                                                               10 [0 <=] 0 [1 - dup] . [+] hylomorphism
                                                           10 [0 <=] 0 [1 - dup] [+] . hylomorphism
                                                           10 [0 <=] 0 [1 - dup] [+] . [unit [pop] swoncat] dipd [dip] swoncat genrec
                                      10 [0 <=] 0 [1 - dup] [+] [unit [pop] swoncat] . dipd [dip] swoncat genrec
                                                                         10 [0 <=] 0 . unit [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                         10 [0 <=] 0 . [] cons [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                      10 [0 <=] 0 [] . cons [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                       10 [0 <=] [0] . [pop] swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                 10 [0 <=] [0] [pop] . swoncat [1 - dup] [+] [dip] swoncat genrec
                                                                 10 [0 <=] [0] [pop] . swap concat [1 - dup] [+] [dip] swoncat genrec
                                                                 10 [0 <=] [pop] [0] . concat [1 - dup] [+] [dip] swoncat genrec
                                                                   10 [0 <=] [pop 0] . [1 - dup] [+] [dip] swoncat genrec
                                                         10 [0 <=] [pop 0] [1 - dup] . [+] [dip] swoncat genrec
                                                     10 [0 <=] [pop 0] [1 - dup] [+] . [dip] swoncat genrec
                                               10 [0 <=] [pop 0] [1 - dup] [+] [dip] . swoncat genrec
                                               10 [0 <=] [pop 0] [1 - dup] [+] [dip] . swap concat genrec
                                               10 [0 <=] [pop 0] [1 - dup] [dip] [+] . concat genrec
                                                 10 [0 <=] [pop 0] [1 - dup] [dip +] . genrec
         10 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte
    10 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [10] [0 <=] . infra first choice i
                                                                                  10 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 10] swaack first choice i
                                                                                10 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 10] swaack first choice i
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 10] swaack first choice i
        False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 10] . swaack first choice i
        10 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i
          10 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i
                        10 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i
                                                                                  10 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                                                                10 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                                                                   9 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                                                                 9 9 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +
                                       9 9 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip +
                                                                                   9 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 9 +
                                                                            9 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 9 +
                                                                    9 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 9 +
                                                          9 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 9 +
                                                  9 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 9 +
          9 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 9 +
      9 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [9] [0 <=] . infra first choice i 9 +
                                                                                   9 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 9] swaack first choice i 9 +
                                                                                 9 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 9] swaack first choice i 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 9] swaack first choice i 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 9] . swaack first choice i 9 +
         9 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 9 +
           9 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 9 +
                         9 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 9 +
                                                                                   9 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 9 +
                                                                                 9 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 9 +
                                                                                   8 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 9 +
                                                                                 8 8 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 9 +
                                       8 8 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 9 +
                                                                                   8 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 8 + 9 +
                                                                            8 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 8 + 9 +
                                                                    8 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 8 + 9 +
                                                          8 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 8 + 9 +
                                                  8 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 8 + 9 +
          8 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 8 + 9 +
      8 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [8] [0 <=] . infra first choice i 8 + 9 +
                                                                                   8 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 8] swaack first choice i 8 + 9 +
                                                                                 8 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 8] swaack first choice i 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 8] swaack first choice i 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 8] . swaack first choice i 8 + 9 +
         8 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 8 + 9 +
           8 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 8 + 9 +
                         8 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 8 + 9 +
                                                                                   8 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 8 + 9 +
                                                                                 8 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 8 + 9 +
                                                                                   7 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 8 + 9 +
                                                                                 7 7 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 8 + 9 +
                                       7 7 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 8 + 9 +
                                                                                   7 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 7 + 8 + 9 +
                                                                            7 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 7 + 8 + 9 +
                                                                    7 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 7 + 8 + 9 +
                                                          7 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 7 + 8 + 9 +
                                                  7 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 7 + 8 + 9 +
          7 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 7 + 8 + 9 +
      7 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [7] [0 <=] . infra first choice i 7 + 8 + 9 +
                                                                                   7 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 7] swaack first choice i 7 + 8 + 9 +
                                                                                 7 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 7] swaack first choice i 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 7] swaack first choice i 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 7] . swaack first choice i 7 + 8 + 9 +
         7 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 7 + 8 + 9 +
           7 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 7 + 8 + 9 +
                         7 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 7 + 8 + 9 +
                                                                                   7 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 7 + 8 + 9 +
                                                                                 7 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 7 + 8 + 9 +
                                                                                   6 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 7 + 8 + 9 +
                                                                                 6 6 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 7 + 8 + 9 +
                                       6 6 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 7 + 8 + 9 +
                                                                                   6 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 6 + 7 + 8 + 9 +
                                                                            6 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 6 + 7 + 8 + 9 +
                                                                    6 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 6 + 7 + 8 + 9 +
                                                          6 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 6 + 7 + 8 + 9 +
                                                  6 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 6 + 7 + 8 + 9 +
          6 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 6 + 7 + 8 + 9 +
      6 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [6] [0 <=] . infra first choice i 6 + 7 + 8 + 9 +
                                                                                   6 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 6] swaack first choice i 6 + 7 + 8 + 9 +
                                                                                 6 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 6] swaack first choice i 6 + 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 6] swaack first choice i 6 + 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 6] . swaack first choice i 6 + 7 + 8 + 9 +
         6 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 6 + 7 + 8 + 9 +
           6 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 6 + 7 + 8 + 9 +
                         6 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 6 + 7 + 8 + 9 +
                                                                                   6 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                                                                 6 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                                                                   5 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                                                                 5 5 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 6 + 7 + 8 + 9 +
                                       5 5 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 6 + 7 + 8 + 9 +
                                                                                   5 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                                            5 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                                    5 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                          5 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 5 + 6 + 7 + 8 + 9 +
                                                  5 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 5 + 6 + 7 + 8 + 9 +
          5 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 5 + 6 + 7 + 8 + 9 +
      5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [5] [0 <=] . infra first choice i 5 + 6 + 7 + 8 + 9 +
                                                                                   5 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] swaack first choice i 5 + 6 + 7 + 8 + 9 +
                                                                                 5 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] swaack first choice i 5 + 6 + 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] swaack first choice i 5 + 6 + 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 5] . swaack first choice i 5 + 6 + 7 + 8 + 9 +
         5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 5 + 6 + 7 + 8 + 9 +
           5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 5 + 6 + 7 + 8 + 9 +
                         5 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 5 + 6 + 7 + 8 + 9 +
                                                                                   5 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                                                                 5 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                                                                   4 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                                                                 4 4 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 5 + 6 + 7 + 8 + 9 +
                                       4 4 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 5 + 6 + 7 + 8 + 9 +
                                                                                   4 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                                            4 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                                    4 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                          4 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 4 + 5 + 6 + 7 + 8 + 9 +
                                                  4 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 4 + 5 + 6 + 7 + 8 + 9 +
          4 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 4 + 5 + 6 + 7 + 8 + 9 +
      4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [4] [0 <=] . infra first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   4 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 4 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 4] . swaack first choice i 4 + 5 + 6 + 7 + 8 + 9 +
         4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 4 + 5 + 6 + 7 + 8 + 9 +
           4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 4 + 5 + 6 + 7 + 8 + 9 +
                         4 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   4 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 4 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   3 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 3 3 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                       3 3 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   3 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                            3 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                    3 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                          3 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                  3 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 3 + 4 + 5 + 6 + 7 + 8 + 9 +
          3 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 3 + 4 + 5 + 6 + 7 + 8 + 9 +
      3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [3] [0 <=] . infra first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   3 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 3 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 3] . swaack first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
         3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
           3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                         3 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   3 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 3 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   2 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 2 2 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                       2 2 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   2 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                            2 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                    2 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                          2 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                  2 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
          2 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
      2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [2] [0 <=] . infra first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   2 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 2 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 2] . swaack first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
         2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
           2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                         2 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   2 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 2 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   1 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 1 1 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                       1 1 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   1 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                            1 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                    1 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                          1 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                  1 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
          1 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
      1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [1] [0 <=] . infra first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   1 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 1 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                               False . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
         False [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 1] . swaack first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
         1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [False] . first choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
           1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] False . choice i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                         1 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . i 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   1 . 1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 1 1 . - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   0 . dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 0 0 . [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                       0 0 [[0 <=] [pop 0] [1 - dup] [dip +] genrec] . dip + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   0 . [0 <=] [pop 0] [1 - dup] [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                            0 [0 <=] . [pop 0] [1 - dup] [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                    0 [0 <=] [pop 0] . [1 - dup] [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                          0 [0 <=] [pop 0] [1 - dup] . [dip +] genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                  0 [0 <=] [pop 0] [1 - dup] [dip +] . genrec 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
          0 [0 <=] [pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] . ifte 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
      0 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [0] [0 <=] . infra first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   0 . 0 <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 0 0 . <= [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                True . [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
          True [[pop 0] [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] 0] . swaack first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
          0 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] [True] . first choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
            0 [1 - dup [[0 <=] [pop 0] [1 - dup] [dip +] genrec] dip +] [pop 0] True . choice i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                           0 [pop 0] . i 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   0 . pop 0 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                     . 0 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   0 . 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 0 0 . + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   0 . 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 0 1 . + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   1 . 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 1 2 . + 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   3 . 3 + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 3 3 . + 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                   6 . 4 + 5 + 6 + 7 + 8 + 9 +
                                                                                 6 4 . + 5 + 6 + 7 + 8 + 9 +
                                                                                  10 . 5 + 6 + 7 + 8 + 9 +
                                                                                10 5 . + 6 + 7 + 8 + 9 +
                                                                                  15 . 6 + 7 + 8 + 9 +
                                                                                15 6 . + 7 + 8 + 9 +
                                                                                  21 . 7 + 8 + 9 +
                                                                                21 7 . + 8 + 9 +
                                                                                  28 . 8 + 9 +
                                                                                28 8 . + 9 +
                                                                                  36 . 9 +
                                                                                36 9 . +
                                                                                  45 . 


Factorial Function and Paramorphisms
====================================

A paramorphism ``P :: B -> A`` is a recursion combinator that uses
``dup`` on intermediate values.

::

   n swap [P] [pop] [[F] dupdip G] primrec

With - ``n :: A`` is the “identity” for ``F`` (like 1 for
multiplication, 0 for addition) - ``F :: (A, B) -> A`` - ``G :: B -> B``
generates the next ``B`` value. - and lastly ``P :: B -> Bool`` detects
the end of the series.

For Factorial function (types ``A`` and ``B`` are both integer):

::

   n == 1
   F == *
   G == --
   P == 1 <=

.. code:: ipython2

    define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')

Try it with input 3 (omitting evaluation of predicate):

::

   3 1 swap [1 <=] [pop] [[*] dupdip --] primrec
   1 3      [1 <=] [pop] [[*] dupdip --] primrec

   1 3 [*] dupdip --
   1 3  * 3      --
   3      3      --
   3      2

   3 2 [*] dupdip --
   3 2  *  2      --
   6       2      --
   6       1

   6 1 [1 <=] [pop] [[*] dupdip --] primrec

   6 1 pop
   6

.. code:: ipython2

    J('3 factorial')


.. parsed-literal::

    6


Derive ``paramorphism`` from the form above.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

::

   n swap [P] [pop] [[F] dupdip G] primrec

   n swap [P]       [pop]     [[F] dupdip G]                  primrec
   n [P] [swap] dip [pop]     [[F] dupdip G]                  primrec
   n [P] [[F] dupdip G]                [[swap] dip [pop]] dip primrec
   n [P] [F] [dupdip G]           cons [[swap] dip [pop]] dip primrec
   n [P] [F] [G] [dupdip] swoncat cons [[swap] dip [pop]] dip primrec

   paramorphism == [dupdip] swoncat cons [[swap] dip [pop]] dip primrec

.. code:: ipython2

    define('paramorphism == [dupdip] swoncat cons [[swap] dip [pop]] dip primrec')
    define('factorial == 1 [1 <=] [*] [--] paramorphism')

.. code:: ipython2

    J('3 factorial')


.. parsed-literal::

    6


``tails``
=========

An example of a paramorphism for lists given in the `“Bananas…”
paper <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__
is ``tails`` which returns the list of “tails” of a list.

::

   [1 2 3] tails == [[] [3] [2 3]]

Using ``paramorphism`` we would write:

::

   n == []
   F == rest swons
   G == rest
   P == not

   tails == [] [not] [rest swons] [rest] paramorphism

.. code:: ipython2

    define('tails == [] [not] [rest swons] [rest] paramorphism')

.. code:: ipython2

    J('[1 2 3] tails')


.. parsed-literal::

    [[] [3] [2 3]]


.. code:: ipython2

    J('25 range tails [popop] infra [sum] map')


.. parsed-literal::

    [1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276]


.. code:: ipython2

    J('25 range [range_sum] map')


.. parsed-literal::

    [276 253 231 210 190 171 153 136 120 105 91 78 66 55 45 36 28 21 15 10 6 3 1 0 0]


Factoring ``rest``
~~~~~~~~~~~~~~~~~~

Right before the recursion begins we have:

::

   [] [1 2 3] [not] [pop] [[rest swons] dupdip rest] primrec

But we might prefer to factor ``rest`` in the quote:

::

   [] [1 2 3] [not] [pop] [rest [swons] dupdip] primrec

There’s no way to do that with the ``paramorphism`` combinator as
defined. We would have to write and use a slightly different recursion
combinator that accepted an additional “preprocessor” function ``[H]``
and built:

::

   n swap [P] [pop] [H [F] dupdip G] primrec

Or just write it out manually. This is yet another place where the
*sufficiently smart compiler* will one day automatically refactor the
code. We could write a ``paramorphism`` combinator that checked ``[F]``
and ``[G]`` for common prefix and extracted it.

Patterns of Recursion
=====================

Our story so far…

-  A combiner ``F :: (B, B) -> B``
-  A predicate ``P :: A -> Bool`` to detect the base case
-  A base case value ``c :: B``

Hylo-, Ana-, Cata-
~~~~~~~~~~~~~~~~~~

::

   w/ G :: A -> (A, B)

   H == [P   ] [pop c ] [G          ] [dip F    ] genrec
   A == [P   ] [pop []] [G          ] [dip swons] genrec
   C == [[] =] [pop c ] [uncons swap] [dip F    ] genrec

Para-, ?-, ?-
~~~~~~~~~~~~~

::

   w/ G :: B -> B

   P == c  swap [P   ] [pop] [[F    ] dupdip G          ] primrec
   ? == [] swap [P   ] [pop] [[swons] dupdip G          ] primrec
   ? == c  swap [[] =] [pop] [[F    ] dupdip uncons swap] primrec

Four Generalizations
====================

There are at least four kinds of recursive combinator, depending on two
choices. The first choice is whether the combiner function should be
evaluated during the recursion or pushed into the pending expression to
be “collapsed” at the end. The second choice is whether the combiner
needs to operate on the current value of the datastructure or the
generator’s output.

::

   H ==        [P] [pop c] [G             ] [dip F] genrec
   H == c swap [P] [pop]   [G [F]    dip  ] [i]     genrec
   H ==        [P] [pop c] [  [G] dupdip  ] [dip F] genrec
   H == c swap [P] [pop]   [  [F] dupdip G] [i]     genrec

Consider:

::

   ... a G [H] dip F                w/ a G == a' b
   ... c a G [F] dip H                 a G == b  a'
   ... a [G] dupdip [H] dip F          a G == a'
   ... c a [F] dupdip G H              a G == a'

1
~

::

   H == [P] [pop c] [G] [dip F] genrec

Iterate n times.

::

   ... a [P] [pop c] [G] [dip F] genrec
   ... a  G [H] dip F
   ... a' b [H] dip F
   ... a' H b F
   ... a'  G [H] dip F b F
   ... a'' b [H] dip F b F
   ... a'' H b F b F
   ... a''  G [H] dip F b F b F
   ... a''' b [H] dip F b F b F
   ... a''' H b F b F b F
   ... a''' pop c b F b F b F
   ... c b F b F b F

This form builds up a continuation that contains the intermediate
results along with the pending combiner functions. When the base case is
reached the last term is replaced by the identity value c and the
continuation “collapses” into the final result.

2
~

When you can start with the identity value c on the stack and the
combiner can operate as you go, using the intermediate results
immediately rather than queuing them up, use this form. An important
difference is that the generator function must return its results in the
reverse order.

::

   H == c swap [P] [pop] [G [F] dip] primrec

   ... c a G [F] dip H
   ... c b a' [F] dip H
   ... c b F a' H
   ... c b F a' G [F] dip H
   ... c b F b a'' [F] dip H
   ... c b F b F a'' H
   ... c b F b F a'' G [F] dip H
   ... c b F b F b a''' [F] dip H
   ... c b F b F b F a''' H
   ... c b F b F b F a''' pop
   ... c b F b F b F

The end line here is the same as for above, but only because we didn’t
evaluate ``F`` when it normally would have been.

3
~

If the combiner and the generator both need to work on the current value
then ``dup`` must be used at some point, and the generator must produce
one item instead of two (the b is instead the duplicate of a.)

::

   H == [P] [pop c] [[G] dupdip] [dip F] genrec

   ... a [G] dupdip [H] dip F
   ... a  G a       [H] dip F
   ... a'   a       [H] dip F
   ... a' H a F
   ... a' [G] dupdip [H] dip F a F
   ... a'  G  a'     [H] dip F a F
   ... a''    a'     [H] dip F a F
   ... a'' H  a' F a F
   ... a'' [G] dupdip [H] dip F a' F a F
   ... a''  G  a''    [H] dip F a' F a F
   ... a'''    a''    [H] dip F a' F a F
   ... a''' H  a'' F a' F a F
   ... a''' pop c  a'' F a' F a F
   ...          c  a'' F a' F a F

4
~

And, last but not least, if you can combine as you go, starting with c,
and the combiner needs to work on the current item, this is the form:

::

   W == c swap [P] [pop] [[F] dupdip G] primrec

   ... a c swap [P] [pop] [[F] dupdip G] primrec
   ... c a [P] [pop] [[F] dupdip G] primrec
   ... c a [F] dupdip G W
   ... c a  F a G W
   ... c a  F a'  W
   ... c a  F a'  [F] dupdip G W
   ... c a  F a'   F  a'     G W
   ... c a  F a'   F  a''      W
   ... c a  F a'   F  a''      [F] dupdip G W
   ... c a  F a'   F  a''       F  a''    G W
   ... c a  F a'   F  a''       F  a'''     W
   ... c a  F a'   F  a''       F  a'''     pop
   ... c a  F a'   F  a''       F

Each of the four variations above can be specialized to ana- and
catamorphic forms.

.. code:: ipython2

    def WTFmorphism(c, F, P, G):
        '''Return a hylomorphism function H.'''
    
        def H(a, d=c):
            if P(a):
                result = d
            else:
                a, b = G(a)
                result = H(a, F(d, b))
            return result
    
        return H

.. code:: ipython2

    F = lambda a, b: a + b
    P = lambda n: n <= 1
    G = lambda n: (n - 1, n - 1)
    
    wtf = WTFmorphism(0, F, P, G)
    
    print wtf(5)


.. parsed-literal::

    10


::

   H == [P   ] [pop c ] [G          ] [dip F    ] genrec

.. code:: ipython2

    DefinitionWrapper.add_definitions('''
    P == 1 <=
    Ga == -- dup
    Gb == --
    c == 0
    F == +
    ''', D)

.. code:: ipython2

    V('[1 2 3] [[] =] [pop []] [uncons swap] [dip swons] genrec')


.. parsed-literal::

                                                                                                                 . [1 2 3] [[] =] [pop []] [uncons swap] [dip swons] genrec
                                                                                                         [1 2 3] . [[] =] [pop []] [uncons swap] [dip swons] genrec
                                                                                                  [1 2 3] [[] =] . [pop []] [uncons swap] [dip swons] genrec
                                                                                         [1 2 3] [[] =] [pop []] . [uncons swap] [dip swons] genrec
                                                                           [1 2 3] [[] =] [pop []] [uncons swap] . [dip swons] genrec
                                                               [1 2 3] [[] =] [pop []] [uncons swap] [dip swons] . genrec
              [1 2 3] [[] =] [pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . ifte
    [1 2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [[1 2 3]] [[] =] . infra first choice i
                                                                                                         [1 2 3] . [] = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [1 2 3]] swaack first choice i
                                                                                                      [1 2 3] [] . = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [1 2 3]] swaack first choice i
                                                                                                           False . [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [1 2 3]] swaack first choice i
             False [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [1 2 3]] . swaack first choice i
             [1 2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [False] . first choice i
               [1 2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] False . choice i
                              [1 2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . i
                                                                                                         [1 2 3] . uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons
                                                                                                         1 [2 3] . swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons
                                                                                                         [2 3] 1 . [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons
                                                      [2 3] 1 [[[] =] [pop []] [uncons swap] [dip swons] genrec] . dip swons
                                                                                                           [2 3] . [[] =] [pop []] [uncons swap] [dip swons] genrec 1 swons
                                                                                                    [2 3] [[] =] . [pop []] [uncons swap] [dip swons] genrec 1 swons
                                                                                           [2 3] [[] =] [pop []] . [uncons swap] [dip swons] genrec 1 swons
                                                                             [2 3] [[] =] [pop []] [uncons swap] . [dip swons] genrec 1 swons
                                                                 [2 3] [[] =] [pop []] [uncons swap] [dip swons] . genrec 1 swons
                [2 3] [[] =] [pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . ifte 1 swons
        [2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [[2 3]] [[] =] . infra first choice i 1 swons
                                                                                                           [2 3] . [] = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [2 3]] swaack first choice i 1 swons
                                                                                                        [2 3] [] . = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [2 3]] swaack first choice i 1 swons
                                                                                                           False . [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [2 3]] swaack first choice i 1 swons
               False [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [2 3]] . swaack first choice i 1 swons
               [2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 1 swons
                 [2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] False . choice i 1 swons
                                [2 3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . i 1 swons
                                                                                                           [2 3] . uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons 1 swons
                                                                                                           2 [3] . swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons 1 swons
                                                                                                           [3] 2 . [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons 1 swons
                                                        [3] 2 [[[] =] [pop []] [uncons swap] [dip swons] genrec] . dip swons 1 swons
                                                                                                             [3] . [[] =] [pop []] [uncons swap] [dip swons] genrec 2 swons 1 swons
                                                                                                      [3] [[] =] . [pop []] [uncons swap] [dip swons] genrec 2 swons 1 swons
                                                                                             [3] [[] =] [pop []] . [uncons swap] [dip swons] genrec 2 swons 1 swons
                                                                               [3] [[] =] [pop []] [uncons swap] . [dip swons] genrec 2 swons 1 swons
                                                                   [3] [[] =] [pop []] [uncons swap] [dip swons] . genrec 2 swons 1 swons
                  [3] [[] =] [pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . ifte 2 swons 1 swons
            [3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [[3]] [[] =] . infra first choice i 2 swons 1 swons
                                                                                                             [3] . [] = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [3]] swaack first choice i 2 swons 1 swons
                                                                                                          [3] [] . = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [3]] swaack first choice i 2 swons 1 swons
                                                                                                           False . [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [3]] swaack first choice i 2 swons 1 swons
                 False [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [3]] . swaack first choice i 2 swons 1 swons
                 [3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 2 swons 1 swons
                   [3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] False . choice i 2 swons 1 swons
                                  [3] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . i 2 swons 1 swons
                                                                                                             [3] . uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons 2 swons 1 swons
                                                                                                            3 [] . swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons 2 swons 1 swons
                                                                                                            [] 3 . [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons 2 swons 1 swons
                                                         [] 3 [[[] =] [pop []] [uncons swap] [dip swons] genrec] . dip swons 2 swons 1 swons
                                                                                                              [] . [[] =] [pop []] [uncons swap] [dip swons] genrec 3 swons 2 swons 1 swons
                                                                                                       [] [[] =] . [pop []] [uncons swap] [dip swons] genrec 3 swons 2 swons 1 swons
                                                                                              [] [[] =] [pop []] . [uncons swap] [dip swons] genrec 3 swons 2 swons 1 swons
                                                                                [] [[] =] [pop []] [uncons swap] . [dip swons] genrec 3 swons 2 swons 1 swons
                                                                    [] [[] =] [pop []] [uncons swap] [dip swons] . genrec 3 swons 2 swons 1 swons
                   [] [[] =] [pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] . ifte 3 swons 2 swons 1 swons
              [] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [[]] [[] =] . infra first choice i 3 swons 2 swons 1 swons
                                                                                                              [] . [] = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] []] swaack first choice i 3 swons 2 swons 1 swons
                                                                                                           [] [] . = [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] []] swaack first choice i 3 swons 2 swons 1 swons
                                                                                                            True . [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] []] swaack first choice i 3 swons 2 swons 1 swons
                   True [[pop []] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] []] . swaack first choice i 3 swons 2 swons 1 swons
                   [] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] [True] . first choice i 3 swons 2 swons 1 swons
                     [] [uncons swap [[[] =] [pop []] [uncons swap] [dip swons] genrec] dip swons] [pop []] True . choice i 3 swons 2 swons 1 swons
                                                                                                     [] [pop []] . i 3 swons 2 swons 1 swons
                                                                                                              [] . pop [] 3 swons 2 swons 1 swons
                                                                                                                 . [] 3 swons 2 swons 1 swons
                                                                                                              [] . 3 swons 2 swons 1 swons
                                                                                                            [] 3 . swons 2 swons 1 swons
                                                                                                            [] 3 . swap cons 2 swons 1 swons
                                                                                                            3 [] . cons 2 swons 1 swons
                                                                                                             [3] . 2 swons 1 swons
                                                                                                           [3] 2 . swons 1 swons
                                                                                                           [3] 2 . swap cons 1 swons
                                                                                                           2 [3] . cons 1 swons
                                                                                                           [2 3] . 1 swons
                                                                                                         [2 3] 1 . swons
                                                                                                         [2 3] 1 . swap cons
                                                                                                         1 [2 3] . cons
                                                                                                         [1 2 3] . 


.. code:: ipython2

    V('3 [P] [pop c] [Ga] [dip F] genrec')


.. parsed-literal::

                                                                   . 3 [P] [pop c] [Ga] [dip F] genrec
                                                                 3 . [P] [pop c] [Ga] [dip F] genrec
                                                             3 [P] . [pop c] [Ga] [dip F] genrec
                                                     3 [P] [pop c] . [Ga] [dip F] genrec
                                                3 [P] [pop c] [Ga] . [dip F] genrec
                                        3 [P] [pop c] [Ga] [dip F] . genrec
        3 [P] [pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] . ifte
    3 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] [3] [P] . infra first choice i
                                                                 3 . P [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 3] swaack first choice i
                                                                 3 . 1 <= [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 3] swaack first choice i
                                                               3 1 . <= [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 3] swaack first choice i
                                                             False . [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 3] swaack first choice i
    False [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 3] . swaack first choice i
    3 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] [False] . first choice i
      3 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] False . choice i
                    3 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] . i
                                                                 3 . Ga [[P] [pop c] [Ga] [dip F] genrec] dip F
                                                                 3 . -- dup [[P] [pop c] [Ga] [dip F] genrec] dip F
                                                                 2 . dup [[P] [pop c] [Ga] [dip F] genrec] dip F
                                                               2 2 . [[P] [pop c] [Ga] [dip F] genrec] dip F
                             2 2 [[P] [pop c] [Ga] [dip F] genrec] . dip F
                                                                 2 . [P] [pop c] [Ga] [dip F] genrec 2 F
                                                             2 [P] . [pop c] [Ga] [dip F] genrec 2 F
                                                     2 [P] [pop c] . [Ga] [dip F] genrec 2 F
                                                2 [P] [pop c] [Ga] . [dip F] genrec 2 F
                                        2 [P] [pop c] [Ga] [dip F] . genrec 2 F
        2 [P] [pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] . ifte 2 F
    2 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] [2] [P] . infra first choice i 2 F
                                                                 2 . P [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 2] swaack first choice i 2 F
                                                                 2 . 1 <= [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 2] swaack first choice i 2 F
                                                               2 1 . <= [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 2] swaack first choice i 2 F
                                                             False . [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 2] swaack first choice i 2 F
    False [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 2] . swaack first choice i 2 F
    2 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] [False] . first choice i 2 F
      2 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] False . choice i 2 F
                    2 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] . i 2 F
                                                                 2 . Ga [[P] [pop c] [Ga] [dip F] genrec] dip F 2 F
                                                                 2 . -- dup [[P] [pop c] [Ga] [dip F] genrec] dip F 2 F
                                                                 1 . dup [[P] [pop c] [Ga] [dip F] genrec] dip F 2 F
                                                               1 1 . [[P] [pop c] [Ga] [dip F] genrec] dip F 2 F
                             1 1 [[P] [pop c] [Ga] [dip F] genrec] . dip F 2 F
                                                                 1 . [P] [pop c] [Ga] [dip F] genrec 1 F 2 F
                                                             1 [P] . [pop c] [Ga] [dip F] genrec 1 F 2 F
                                                     1 [P] [pop c] . [Ga] [dip F] genrec 1 F 2 F
                                                1 [P] [pop c] [Ga] . [dip F] genrec 1 F 2 F
                                        1 [P] [pop c] [Ga] [dip F] . genrec 1 F 2 F
        1 [P] [pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] . ifte 1 F 2 F
    1 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] [1] [P] . infra first choice i 1 F 2 F
                                                                 1 . P [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 1] swaack first choice i 1 F 2 F
                                                                 1 . 1 <= [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 1] swaack first choice i 1 F 2 F
                                                               1 1 . <= [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 1] swaack first choice i 1 F 2 F
                                                              True . [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 1] swaack first choice i 1 F 2 F
     True [[pop c] [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] 1] . swaack first choice i 1 F 2 F
     1 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] [True] . first choice i 1 F 2 F
       1 [Ga [[P] [pop c] [Ga] [dip F] genrec] dip F] [pop c] True . choice i 1 F 2 F
                                                         1 [pop c] . i 1 F 2 F
                                                                 1 . pop c 1 F 2 F
                                                                   . c 1 F 2 F
                                                                   . 0 1 F 2 F
                                                                 0 . 1 F 2 F
                                                               0 1 . F 2 F
                                                               0 1 . + 2 F
                                                                 1 . 2 F
                                                               1 2 . F
                                                               1 2 . +
                                                                 3 . 


.. code:: ipython2

    V('3 [P] [pop []] [Ga] [dip swons] genrec')


.. parsed-literal::

                                                                             . 3 [P] [pop []] [Ga] [dip swons] genrec
                                                                           3 . [P] [pop []] [Ga] [dip swons] genrec
                                                                       3 [P] . [pop []] [Ga] [dip swons] genrec
                                                              3 [P] [pop []] . [Ga] [dip swons] genrec
                                                         3 [P] [pop []] [Ga] . [dip swons] genrec
                                             3 [P] [pop []] [Ga] [dip swons] . genrec
        3 [P] [pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] . ifte
    3 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] [3] [P] . infra first choice i
                                                                           3 . P [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 3] swaack first choice i
                                                                           3 . 1 <= [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 3] swaack first choice i
                                                                         3 1 . <= [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 3] swaack first choice i
                                                                       False . [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 3] swaack first choice i
    False [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 3] . swaack first choice i
    3 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] [False] . first choice i
      3 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] False . choice i
                     3 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] . i
                                                                           3 . Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons
                                                                           3 . -- dup [[P] [pop []] [Ga] [dip swons] genrec] dip swons
                                                                           2 . dup [[P] [pop []] [Ga] [dip swons] genrec] dip swons
                                                                         2 2 . [[P] [pop []] [Ga] [dip swons] genrec] dip swons
                                  2 2 [[P] [pop []] [Ga] [dip swons] genrec] . dip swons
                                                                           2 . [P] [pop []] [Ga] [dip swons] genrec 2 swons
                                                                       2 [P] . [pop []] [Ga] [dip swons] genrec 2 swons
                                                              2 [P] [pop []] . [Ga] [dip swons] genrec 2 swons
                                                         2 [P] [pop []] [Ga] . [dip swons] genrec 2 swons
                                             2 [P] [pop []] [Ga] [dip swons] . genrec 2 swons
        2 [P] [pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] . ifte 2 swons
    2 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] [2] [P] . infra first choice i 2 swons
                                                                           2 . P [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons
                                                                           2 . 1 <= [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons
                                                                         2 1 . <= [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons
                                                                       False . [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] swaack first choice i 2 swons
    False [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 2] . swaack first choice i 2 swons
    2 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] [False] . first choice i 2 swons
      2 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] False . choice i 2 swons
                     2 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] . i 2 swons
                                                                           2 . Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons 2 swons
                                                                           2 . -- dup [[P] [pop []] [Ga] [dip swons] genrec] dip swons 2 swons
                                                                           1 . dup [[P] [pop []] [Ga] [dip swons] genrec] dip swons 2 swons
                                                                         1 1 . [[P] [pop []] [Ga] [dip swons] genrec] dip swons 2 swons
                                  1 1 [[P] [pop []] [Ga] [dip swons] genrec] . dip swons 2 swons
                                                                           1 . [P] [pop []] [Ga] [dip swons] genrec 1 swons 2 swons
                                                                       1 [P] . [pop []] [Ga] [dip swons] genrec 1 swons 2 swons
                                                              1 [P] [pop []] . [Ga] [dip swons] genrec 1 swons 2 swons
                                                         1 [P] [pop []] [Ga] . [dip swons] genrec 1 swons 2 swons
                                             1 [P] [pop []] [Ga] [dip swons] . genrec 1 swons 2 swons
        1 [P] [pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] . ifte 1 swons 2 swons
    1 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] [1] [P] . infra first choice i 1 swons 2 swons
                                                                           1 . P [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons
                                                                           1 . 1 <= [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons
                                                                         1 1 . <= [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons
                                                                        True . [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 1] swaack first choice i 1 swons 2 swons
     True [[pop []] [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] 1] . swaack first choice i 1 swons 2 swons
     1 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] [True] . first choice i 1 swons 2 swons
       1 [Ga [[P] [pop []] [Ga] [dip swons] genrec] dip swons] [pop []] True . choice i 1 swons 2 swons
                                                                  1 [pop []] . i 1 swons 2 swons
                                                                           1 . pop [] 1 swons 2 swons
                                                                             . [] 1 swons 2 swons
                                                                          [] . 1 swons 2 swons
                                                                        [] 1 . swons 2 swons
                                                                        [] 1 . swap cons 2 swons
                                                                        1 [] . cons 2 swons
                                                                         [1] . 2 swons
                                                                       [1] 2 . swons
                                                                       [1] 2 . swap cons
                                                                       2 [1] . cons
                                                                       [2 1] . 


.. code:: ipython2

    V('[2 1] [[] =] [pop c ] [uncons swap] [dip F] genrec')


.. parsed-literal::

                                                                                                   . [2 1] [[] =] [pop c] [uncons swap] [dip F] genrec
                                                                                             [2 1] . [[] =] [pop c] [uncons swap] [dip F] genrec
                                                                                      [2 1] [[] =] . [pop c] [uncons swap] [dip F] genrec
                                                                              [2 1] [[] =] [pop c] . [uncons swap] [dip F] genrec
                                                                [2 1] [[] =] [pop c] [uncons swap] . [dip F] genrec
                                                        [2 1] [[] =] [pop c] [uncons swap] [dip F] . genrec
            [2 1] [[] =] [pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] . ifte
    [2 1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] [[2 1]] [[] =] . infra first choice i
                                                                                             [2 1] . [] = [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [2 1]] swaack first choice i
                                                                                          [2 1] [] . = [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [2 1]] swaack first choice i
                                                                                             False . [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [2 1]] swaack first choice i
           False [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [2 1]] . swaack first choice i
           [2 1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] [False] . first choice i
             [2 1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] False . choice i
                           [2 1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] . i
                                                                                             [2 1] . uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F
                                                                                             2 [1] . swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F
                                                                                             [1] 2 . [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F
                                               [1] 2 [[[] =] [pop c] [uncons swap] [dip F] genrec] . dip F
                                                                                               [1] . [[] =] [pop c] [uncons swap] [dip F] genrec 2 F
                                                                                        [1] [[] =] . [pop c] [uncons swap] [dip F] genrec 2 F
                                                                                [1] [[] =] [pop c] . [uncons swap] [dip F] genrec 2 F
                                                                  [1] [[] =] [pop c] [uncons swap] . [dip F] genrec 2 F
                                                          [1] [[] =] [pop c] [uncons swap] [dip F] . genrec 2 F
              [1] [[] =] [pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] . ifte 2 F
        [1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] [[1]] [[] =] . infra first choice i 2 F
                                                                                               [1] . [] = [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [1]] swaack first choice i 2 F
                                                                                            [1] [] . = [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [1]] swaack first choice i 2 F
                                                                                             False . [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [1]] swaack first choice i 2 F
             False [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [1]] . swaack first choice i 2 F
             [1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] [False] . first choice i 2 F
               [1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] False . choice i 2 F
                             [1] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] . i 2 F
                                                                                               [1] . uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F 2 F
                                                                                              1 [] . swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F 2 F
                                                                                              [] 1 . [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F 2 F
                                                [] 1 [[[] =] [pop c] [uncons swap] [dip F] genrec] . dip F 2 F
                                                                                                [] . [[] =] [pop c] [uncons swap] [dip F] genrec 1 F 2 F
                                                                                         [] [[] =] . [pop c] [uncons swap] [dip F] genrec 1 F 2 F
                                                                                 [] [[] =] [pop c] . [uncons swap] [dip F] genrec 1 F 2 F
                                                                   [] [[] =] [pop c] [uncons swap] . [dip F] genrec 1 F 2 F
                                                           [] [[] =] [pop c] [uncons swap] [dip F] . genrec 1 F 2 F
               [] [[] =] [pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] . ifte 1 F 2 F
          [] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] [[]] [[] =] . infra first choice i 1 F 2 F
                                                                                                [] . [] = [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] []] swaack first choice i 1 F 2 F
                                                                                             [] [] . = [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] []] swaack first choice i 1 F 2 F
                                                                                              True . [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] []] swaack first choice i 1 F 2 F
               True [[pop c] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] []] . swaack first choice i 1 F 2 F
               [] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] [True] . first choice i 1 F 2 F
                 [] [uncons swap [[[] =] [pop c] [uncons swap] [dip F] genrec] dip F] [pop c] True . choice i 1 F 2 F
                                                                                        [] [pop c] . i 1 F 2 F
                                                                                                [] . pop c 1 F 2 F
                                                                                                   . c 1 F 2 F
                                                                                                   . 0 1 F 2 F
                                                                                                 0 . 1 F 2 F
                                                                                               0 1 . F 2 F
                                                                                               0 1 . + 2 F
                                                                                                 1 . 2 F
                                                                                               1 2 . F
                                                                                               1 2 . +
                                                                                                 3 . 


Appendix - Fun with Symbols
---------------------------

::

   |[ (c, F), (G, P) ]| == (|c, F|) • [(G, P)]

`“Bananas, Lenses, & Barbed
Wire” <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125>`__

::

   (|...|)  [(...)]  [<...>]

I think they are having slightly too much fun with the symbols.

“Too much is always better than not enough.”
