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Preamble





In [1]:



    


from notebook_preamble import D, J, V

A long trace





In [2]:



    


V('[23 18] average')



    


















    






                                  . [23 18] average
                          [23 18] . average
                          [23 18] . [sum 1.0 *] [size] cleave /
              [23 18] [sum 1.0 *] . [size] cleave /
       [23 18] [sum 1.0 *] [size] . cleave /
       [23 18] [sum 1.0 *] [size] . [i] app2 [popd] dip /
   [23 18] [sum 1.0 *] [size] [i] . app2 [popd] dip /
[23 18] [[sum 1.0 *] [23 18]] [i] . infra first [[size] [23 18]] [i] infra first [popd] dip /
              [23 18] [sum 1.0 *] . i [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                          [23 18] . sum 1.0 * [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                               41 . 1.0 * [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                           41 1.0 . * [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                             41.0 . [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                   41.0 [[23 18]] . swaack first [[size] [23 18]] [i] infra first [popd] dip /
                   [23 18] [41.0] . first [[size] [23 18]] [i] infra first [popd] dip /
                     [23 18] 41.0 . [[size] [23 18]] [i] infra first [popd] dip /
    [23 18] 41.0 [[size] [23 18]] . [i] infra first [popd] dip /
[23 18] 41.0 [[size] [23 18]] [i] . infra first [popd] dip /
                   [23 18] [size] . i [41.0 [23 18]] swaack first [popd] dip /
                          [23 18] . size [41.0 [23 18]] swaack first [popd] dip /
                          [23 18] . 0 swap [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                        [23 18] 0 . swap [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                        0 [23 18] . [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
               0 [23 18] [pop ++] . step [41.0 [23 18]] swaack first [popd] dip /
                    0 23 [pop ++] . i [18] [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                             0 23 . pop ++ [18] [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                                0 . ++ [18] [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                                1 . [18] [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                           1 [18] . [pop ++] step [41.0 [23 18]] swaack first [popd] dip /
                  1 [18] [pop ++] . step [41.0 [23 18]] swaack first [popd] dip /
                    1 18 [pop ++] . i [41.0 [23 18]] swaack first [popd] dip /
                             1 18 . pop ++ [41.0 [23 18]] swaack first [popd] dip /
                                1 . ++ [41.0 [23 18]] swaack first [popd] dip /
                                2 . [41.0 [23 18]] swaack first [popd] dip /
                 2 [41.0 [23 18]] . swaack first [popd] dip /
                 [23 18] 41.0 [2] . first [popd] dip /
                   [23 18] 41.0 2 . [popd] dip /
            [23 18] 41.0 2 [popd] . dip /
                     [23 18] 41.0 . popd 2 /
                             41.0 . 2 /
                           41.0 2 . /
                             20.5 .

Replacing sum and size with "compiled" versions.

Both sum and size are catamorphisms, they each convert a sequence to a single value.





In [3]:



    


J('[sum] help')



    


















    






Given a quoted sequence of numbers return the sum.

sum == 0 swap [+] step


















In [4]:



    


J('[size] help')



    


















    






0 swap [pop ++] step

We can use "compiled" versions (they're not really compiled in this case, they're hand-written in Python) to speed up evaluation and make the trace more readable. The sum function is already in the library. It gets shadowed by the definition version above during initialize().





In [5]:



    


from joy.library import SimpleFunctionWrapper, primitives
from joy.utils.stack import iter_stack


@SimpleFunctionWrapper
def size(stack):
    '''Return the size of the sequence on the stack.'''
    sequence, stack = stack
    n = 0
    for _ in iter_stack(sequence):
        n += 1
    return n, stack


sum_ = next(p for p in primitives if p.name == 'sum')

Now we replace them old versions in the dictionary with the new versions and re-evaluate the expression.





In [6]:



    


old_sum, D['sum'] = D['sum'], sum_
old_size, D['size'] = D['size'], size

You can see that size and sum now execute in a single step.





In [7]:



    


V('[23 18] average')



    


















    






                                  . [23 18] average
                          [23 18] . average
                          [23 18] . [sum 1.0 *] [size] cleave /
              [23 18] [sum 1.0 *] . [size] cleave /
       [23 18] [sum 1.0 *] [size] . cleave /
       [23 18] [sum 1.0 *] [size] . [i] app2 [popd] dip /
   [23 18] [sum 1.0 *] [size] [i] . app2 [popd] dip /
[23 18] [[sum 1.0 *] [23 18]] [i] . infra first [[size] [23 18]] [i] infra first [popd] dip /
              [23 18] [sum 1.0 *] . i [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                          [23 18] . sum 1.0 * [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                               41 . 1.0 * [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                           41 1.0 . * [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                             41.0 . [[23 18]] swaack first [[size] [23 18]] [i] infra first [popd] dip /
                   41.0 [[23 18]] . swaack first [[size] [23 18]] [i] infra first [popd] dip /
                   [23 18] [41.0] . first [[size] [23 18]] [i] infra first [popd] dip /
                     [23 18] 41.0 . [[size] [23 18]] [i] infra first [popd] dip /
    [23 18] 41.0 [[size] [23 18]] . [i] infra first [popd] dip /
[23 18] 41.0 [[size] [23 18]] [i] . infra first [popd] dip /
                   [23 18] [size] . i [41.0 [23 18]] swaack first [popd] dip /
                          [23 18] . size [41.0 [23 18]] swaack first [popd] dip /
                                2 . [41.0 [23 18]] swaack first [popd] dip /
                 2 [41.0 [23 18]] . swaack first [popd] dip /
                 [23 18] 41.0 [2] . first [popd] dip /
                   [23 18] 41.0 2 . [popd] dip /
            [23 18] 41.0 2 [popd] . dip /
                     [23 18] 41.0 . popd 2 /
                             41.0 . 2 /
                           41.0 2 . /
                             20.5 .

Content source: calroc/joypy

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