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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_fib.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_fib.py:


Fibonacci numbers example
=========================

.. GENERATED FROM PYTHON SOURCE LINES 5-29





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    </g>
    <!-- fib&#45;5871781006564002453&#45;value -->
    <g id="node24" class="node">
    <title>fib&#45;5871781006564002453&#45;value</title>
    <g id="a_node24"><a xlink:title="fib&#45;5871781006564002453&#45;value: fib&#45;5871781006564002453&#45;value">
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    <text text-anchor="start" x="904" y="-107.3" font-family="Helvetica,sans-Serif" font-size="14.00">1</text>
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    </a>
    </g>
    </g>
    <!-- i64&#45;17615343019692007359 -->
    <g id="node25" class="node">
    <title>i64&#45;17615343019692007359</title>
    <g id="a_node25"><a xlink:title="i64&#45;17615343019692007359: i64&#45;17615343019692007359">
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    </a>
    </g>
    </g>
    <!-- fib&#45;17615343019692007359 -->
    <g id="node26" class="node">
    <title>fib&#45;17615343019692007359</title>
    <g id="a_node26"><a xlink:title="fib&#45;17615343019692007359&#45;value: fib&#45;17615343019692007359">
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    <text text-anchor="start" x="1081.5" y="-107.3" font-family="Helvetica,sans-Serif" font-size="14.00">fib</text>
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    </a>
    </g>
    </g>
    <!-- fib&#45;17615343019692007359&#45;value -->
    <g id="node27" class="node">
    <title>fib&#45;17615343019692007359&#45;value</title>
    <g id="a_node27"><a xlink:title="fib&#45;17615343019692007359&#45;value: fib&#45;17615343019692007359&#45;value">
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    </a>
    </g>
    </g>
    </g>
    </svg>

    </div>
    <br />
    <br />

.. code-block:: Python

    from __future__ import annotations

    from egglog import *

    egraph = EGraph()


    @egraph.function
    def fib(x: i64Like) -> i64:  # type: ignore[empty-body]
        ...


    f0, f1, x = vars_("f0 f1 x", i64)
    egraph.register(
        set_(fib(0)).to(i64(1)),
        set_(fib(1)).to(i64(1)),
        rule(
            eq(f0).to(fib(x)),
            eq(f1).to(fib(x + 1)),
        ).then(set_(fib(x + 2)).to(f0 + f1)),
    )
    egraph.run(7)
    egraph.check(eq(fib(i64(7))).to(i64(21)))
    egraph


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

   **Total running time of the script:** (0 minutes 0.174 seconds)


.. _sphx_glr_download_auto_examples_fib.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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