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Lambda Calculus & A++ 
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ARS Based Programming is built on three principles:
Abstraction, Reference and Synthesis (ARS) which are
derived from the Lambda Calculus. This approach to programming
is covered in detail in the book `Programmierung pur'
(`Undiluted Programming') which has been published in April 2003
by the S.ToecheMittler Verlag in Darmstadt, Germany.
This site introduces ARS Based Programming and three tools intended to help learning and applying this approach:
A++ standing for `abstraction plus reference plus synthesis' is used as a name for the smallest programming language in the world that is built on ARS. It's definition follows below and more detailed information is available in the description of 'Programmierung pur' here ARS is an abstraction from the Lambda Calculus, taking its three basic operations, and giving them a more general meaning. Whereas the Lambda Calculus gives functional programming its theoretical foundation, ARS is capable to provide a theoretical base for all three major programming paradigms, i.e. functional, object oriented and imperative programming.
ARS is a generalized form of the basic operations
of the Lambda Calculus in that respect, that the definition
of abstraction retains the full meaning of the word (`give something a name')
and that all three operations can be applied anywhere in a program
without restrictions.
The following definitions in EBNF notation define A++ as a programming language in contrast to the Lambda Calculus.
For further details on A++ see description of 'Programmierung pur' on this site or on the official A++ website. EBNF Notation:
The generalizations of the Lambda Calculus are threefold:

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