.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/vm/foundations/plot_06_forth.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_vm_foundations_plot_06_forth.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_vm_foundations_plot_06_forth.py:


Forth: programming with stack words (Moore 1970)
================================================

Charles Moore's Forth has no named variables in expressions: words such as
``DUP``, ``DROP``, ``SWAP``, ``OVER`` and ``ROT`` rearrange the stack, and each
word is documented by its *stack diagram*: ``OVER ( a b -- a b a )``. Small,
fast and easy to implement, Forth ran telescopes and spacecraft. Bitcoin
Script is described as Forth-like, and the EVM's ``DUP`` and ``SWAP`` families
serve the same purpose.

What to look for
----------------

Each stack word matches its diagram. The polynomial ``a x**2 + b x + c``
is computed by Horner's rule with stack words only, and gives the same
values as Python for every input.

The history behind this experiment: :doc:`/history/vm_breakthroughs`.
See :doc:`/exercises/vm` for a worked solution to the exercise.

.. GENERATED FROM PYTHON SOURCE LINES 24-26

Check every stack diagram
-------------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-41

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    diagrams = {
        "DUP": ((1,), (1, 1)),
        "DROP": ((1, 2), (1,)),
        "SWAP": ((1, 2), (2, 1)),
        "OVER": ((1, 2), (1, 2, 1)),
        "ROT": ((1, 2, 3), (2, 3, 1)),
    }
    for word, (before, after) in diagrams.items():
        assert bk.vm.execute([(word, None)], arguments=before).stack == after
        print(f"{word:4s} ( {' '.join(map(str, before))} -- {' '.join(map(str, after))} )")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    DUP  ( 1 -- 1 1 )
    DROP ( 1 2 -- 1 )
    SWAP ( 1 2 -- 2 1 )
    OVER ( 1 2 -- 1 2 1 )
    ROT  ( 1 2 3 -- 2 3 1 )




.. GENERATED FROM PYTHON SOURCE LINES 42-45

Horner's rule without variables
-------------------------------
( x -- a*x*x + b*x + c ) as ((a * x) + b) * x + c, keeping x with OVER.

.. GENERATED FROM PYTHON SOURCE LINES 45-65

.. code-block:: Python

    a, b, c = 3, 5, 7
    horner = bk.vm.assemble(f"""
        PUSH {a}
        OVER
        MUL         # x a*x
        PUSH {b}
        ADD         # x a*x+b
        MUL         # (a*x+b)*x
        PUSH {c}
        ADD
    """)
    xs = list(range(0, 11))
    values = [bk.vm.execute(horner, arguments=(x,)).stack[0] for x in xs]
    assert values == [a * x * x + b * x + c for x in xs]

    fig, ax = plt.subplots(figsize=(6, 4))
    ax.plot(xs, values, "o")
    ax.set(xlabel="x", ylabel="result", title=f"{a}x² + {b}x + {c} from stack words")
    fig.tight_layout()




.. image-sg:: /api/gallery/vm/foundations/images/sphx_glr_plot_06_forth_001.png
   :alt: 3x² + 5x + 7 from stack words
   :srcset: /api/gallery/vm/foundations/images/sphx_glr_plot_06_forth_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 66-70

Exercise
--------
Define ``NIP ( a b -- b )`` and ``TUCK ( a b -- b a b )`` from the five
words above and check them with ``bk.vm.execute``.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.095 seconds)


.. _sphx_glr_download_api_gallery_vm_foundations_plot_06_forth.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/vm/foundations/plot_06_forth.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_06_forth.ipynb <plot_06_forth.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_06_forth.py <plot_06_forth.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_06_forth.zip <plot_06_forth.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_