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3 Webbles of Recursive Function Theory
As described in section 2, the recursive function theory is accompanied by writing
terms to describe certain functions. Instead of writing formulas, functions can
appear as media objects as described in [1,7,8]. This section provides an overview
of this previous work about Webbles of Recursive Function Theory.
First, the implementation of the six basic functions (see section 2) as media
objects using the webble environment was performed. The three initial functions
1. constant; 2. projection; 3. successor, the two primitive operators 4. substitu-
tion; 5.primitive recursion with free slots for media objects (corresponds to the
input functions) and 6. the minimum operator (see figure 1).
Fig. 1.
The six basic primitve recursion webbles (PRF-webbles)
Each media object can be directly manipulated (see section 4), so its easily
possible to change the values and properties of each operator. For example a
substitution operator, which substitutes one unary function into another one,
can be directly manipulated into a substitution operator, which substitutes one
binary function into a unary one, within seconds by simply editing one property
of the media object.
A major advantage of these media objects to terms and term equations is
the possibility to directly manipulate the formula by simply plugging some func-
tion objects into the operator object. The result is a new media object which
describes a new function. To understand the new formula you can enter some
values into the media object. In addition defect formulas are avoided because its
only possible to construct correct formulas with the media objects. Another ad-
vantage is the possibility of hiding parts of the formula by grouping some media
objects.
