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            "Programming Language :: Lisp",
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        "description": "\nCalchylus - Lambda calculus with Hy\n===================================\n\nIntro\n-----\n\n``calchylus`` is a computer installable `Hy`_ module that is used to evaluate,\nand furthermore through this documentation, shine light to the basics of Lambda\ncalculus (also written as \u03bb-calculus).\n\n\t`Lambda calculus`_ is a formal system in mathematical logic for expressing\n\tcomputation that is based on function abstraction and application using\n\tvariable binding and substitution.\n\nThe target audience is those who:\n\na) are interested in the theory and the history of the programming languages\nb) may have or are interested to gain some experience in Python and/or Lisp\nc) who wants to narrow the gap between mathematical notation and\n   programming languages, especially by means of logic\n\n`Andrew Bayer`_ writes in his blog post about formal proofs and deduction:\n\n\t*Traditional logic, and to some extent also type theory, hides computation\n\tbehind equality.*\n\nLambda calculus, on the other hand, reveals how the computation in logic is\ndone by manipulation of the Lambda terms. Manipulation rules are simple and\nwere originally made with a paper and a pen, but now we rather use computers for\nthe task. Lambda calculus also addresses the problem, what can be proved and\nsolved and what cannot be computed in a finite time. Formally these are called\nthe `decidability`_ and the `halting problem`_.\n\nBeside evaluating Lambda expressions, ``calchylus`` module can serve as a\nstarting point for a mini programming language. Via `custom macros`_\nrepresenting well known Lambda forms, ``calchylus`` provides all necessary\nelements for boolean, positive integer, and list data types as well as\nconditionals, loops, variable setters, imperative do structure, logical\nconnectives, and arithmetic operators. You can build upon that, for example\n`real numbers`_, even negative complex numbers if that makes any sense. Your\nimagination is really the only limit.\n\nFinally, when investigating the open source ``calchylus`` implementation that is\nhosted on `GitHub`_ , one can expect to get a good understanding of the higher\norder functions and the `combinatory logic`_, not the least of the fixed point\ncombinator or shortly, \u03d2 combinator.\n\n\nQuick start\n-----------\n\nFor people willing to get hands quickly on coding:\n\n**Install**\n\n.. code-block:: bash\n\n\t$ pip install calchylus\n\n**Open Hy**\n\n.. code-block:: bash\n\n\t$ hy\n\n**Import**\n\n.. code-block:: hylang\n\n\t(require [calchylus.lambdas [*]])\n\n**Initialize**\n\n.. code-block:: hylang\n\n\t(with-alpha-conversion-and-macros L ,)\n\n**Lambda dance**\n\n.. code-block:: hylang\n\n\t(L x y , (x (x (x (x (x y))))) a b) ; output: (a (a (a (a (a b)))))\n\n.. code-block:: hylang\n\n\t(FIBONACCI SEVEN x y) ; output: (x (x (x (x (x (x (x (x (x (x (x (x (x y)))))))))))))\n\n\nDocumentation\n-------------\n\nFor full documentation, see: `calchylus.readthedocs.io`_\n\n\n.. |Output:| replace:: [output]\n\n.. _halting problem: http://www.huffingtonpost.com/entry/how-to-describing-alan-turings-halting-problem-to_us_58d1ae08e4b062043ad4add7\n.. _combinatory logic: https://en.wikipedia.org/wiki/Combinatory_logic\n.. _GitHub: https://github.com/markomanninen/calchylus\n.. _real numbers: https://cs.stackexchange.com/questions/2272/representing-negative-and-complex-numbers-using-lambda-calculus?noredirect=1&lq=1\n.. _my favorite programming language: http://www.python.org\n.. _custom macros: http://calchylus.readthedocs.io/en/latest/macros.html\n.. _decidability: https://plato.stanford.edu/entries/computability/#UnsHalPro\n.. _Andrew Bayer: http://math.andrej.com/2016/08/30/formal-proofs-are-not-just-deduction-steps/\n.. _Lambda calculus: https://en.wikipedia.org/wiki/Lambda_calculus\n.. _Hy: http://docs.hylang.org\n.. _calchylus.readthedocs.io: http://calchylus.readthedocs.io/\n",
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