Commenting the definition:

• Like the introduction to the Lambda Calculus the definition of A++ deals with `lambda expressions' and defines three different types: `abstractions', `references' and `syntheses'. This corresponds to the `lambda abstractions', the `variables' and the `applications' in the Lambda Calculus. The few differences in the A++ - approach are the following:
  • The syntax of A++ is different. It is borrowed from Scheme and so simple that it can be described in a few words:
    
    
    This is all there is to the syntax! It can't be simpler. Even the syntax of the Lambda Calculus is a little bit more complex! (e.g. sometimes parentheses are required, sometimes they are optional.)
  • Abstractions may be given a name explicitely, matching the general human understanding of `abstraction' as `to give something a name'.
  • Abstractions may contain more than one lambda expression in the body to be evaluated.
  • Applications may contain more than two lambda abstractions including several arguments passed to the operator.
• The rules for the conversion of lambda expressions defined in the Lambda Calculus are valid in A++ as well. Due to `lazy evaluation' in A++ lambda expressions can be treated the same way as in the Lambda Calculus.

Georg P. Loczewski 2004-03-05

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