Metadata-Version: 1.1
Name: calchylus
Version: 0.1.16
Summary: Calchylus - Lambda Calculus with Hy
Home-page: https://github.com/markomanninen/calchylus
Author: Marko Manninen
Author-email: elonmedia@gmail.com
License: UNKNOWN
Download-URL: https://github.com/markomanninen/calchylus/archive/v0.1.16.tar.gz
Description: 
        Calchylus - Lambda calculus with Hy
        ===================================
        
        Intro
        -----
        
        ``calchylus`` is a computer installable `Hy`_ module that is used to evaluate,
        and furthermore through this documentation, shine light to the basics of Lambda
        calculus (also written as λ-calculus).
        
        	`Lambda calculus`_ is a formal system in mathematical logic for expressing
        	computation that is based on function abstraction and application using
        	variable binding and substitution.
        
        The target audience is those who:
        
        a) are interested in the theory and the history of the programming languages
        b) may have or are interested to gain some experience in Python and/or Lisp
        c) who wants to narrow the gap between mathematical notation and
           programming languages, especially by means of logic
        
        `Andrew Bayer`_ writes in his blog post about formal proofs and deduction:
        
        	*Traditional logic, and to some extent also type theory, hides computation
        	behind equality.*
        
        Lambda calculus, on the other hand, reveals how the computation in logic is
        done by manipulation of the Lambda terms. Manipulation rules are simple and
        were originally made with a paper and a pen, but now we rather use computers for
        the task. Lambda calculus also addresses the problem, what can be proved and
        solved and what cannot be computed in a finite time. Formally these are called
        the `decidability`_ and the `halting problem`_.
        
        Beside evaluating Lambda expressions, ``calchylus`` module can serve as a
        starting point for a mini programming language. Via `custom macros`_
        representing well known Lambda forms, ``calchylus`` provides all necessary
        elements for boolean, positive integer, and list data types as well as
        conditionals, loops, variable setters, imperative do structure, logical
        connectives, and arithmetic operators. You can build upon that, for example
        `real numbers`_, even negative complex numbers if that makes any sense. Your
        imagination is really the only limit.
        
        Finally, when investigating the open source ``calchylus`` implementation that is
        hosted on `GitHub`_ , one can expect to get a good understanding of the higher
        order functions and the `combinatory logic`_, not the least of the fixed point
        combinator or shortly, ϒ combinator.
        
        
        Quick start
        -----------
        
        For people willing to get hands quickly on coding:
        
        **Install**
        
        .. code-block:: bash
        
        	$ pip install hy calchylus
        
        **Open Hy**
        
        .. code-block:: bash
        
        	$ hy
        
        **Import**
        
        .. code-block:: hylang
        
        	(require [calchylus.lambdas [*]])
        
        **Initialize**
        
        .. code-block:: hylang
        
        	(with-alpha-conversion-and-macros L ,)
        
        **Lambda dance**
        
        .. code-block:: hylang
        
        	(L x y , (x (x (x (x (x y))))) a b) ; output: (a (a (a (a (a b)))))
        
        .. code-block:: hylang
        
        	(FIBONACCI SEVEN) ; output: (x (x (x (x (x (x (x (x (x (x (x (x (x y)))))))))))))
        
        
        Documentation
        -------------
        
        For full documentation, see: `calchylus.readthedocs.io`_
        
        
        .. |Output:| replace:: [output]
        
        .. _halting problem: http://www.huffingtonpost.com/entry/how-to-describing-alan-turings-halting-problem-to_us_58d1ae08e4b062043ad4add7
        .. _combinatory logic: https://en.wikipedia.org/wiki/Combinatory_logic
        .. _GitHub: https://github.com/markomanninen/calchylus
        .. _real numbers: https://cs.stackexchange.com/questions/2272/representing-negative-and-complex-numbers-using-lambda-calculus?noredirect=1&lq=1
        .. _my favorite programming language: http://www.python.org
        .. _custom macros: http://calchylus.readthedocs.io/en/latest/macros.html
        .. _decidability: https://plato.stanford.edu/entries/computability/#UnsHalPro
        .. _Andrew Bayer: http://math.andrej.com/2016/08/30/formal-proofs-are-not-just-deduction-steps/
        .. _Lambda calculus: https://en.wikipedia.org/wiki/Lambda_calculus
        .. _Hy: http://docs.hylang.org
        .. _calchylus.readthedocs.io: http://calchylus.readthedocs.io/
        
Keywords: hylang,python,lisp,macros,dsl,lambda calculus,functional language
Platform: any
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Developers
Classifier: License :: OSI Approved :: MIT License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Lisp
Classifier: Topic :: Software Development :: Libraries
