Inside functions and equations.

[hlreed]

When I was developing Hal algebra I had to get inside functions and equations. It interested me as a new means of defining them.
Consider functions and equations as input, output devices. Then A = B + C is two inputs and an output. The function A = f(B,C) is the same, but f is left undefined. So every equation is a function in action. The definition is a procedure.
You know that procedures have labels and a sequence like a computer program. Here is a function with the internal variables I, R and O that map to any other outside variables.<p>Function
Read I
Read R
do f ;do anything you can program here.
Write O
goto Function ; Here is what makes data streams.<p>Note that O is undefined while f is undefined. Lets define it with the general equation:
Equation
Read I
Read R
O = I + R ; now we define O
Write O
goto Equation ;do this forever. Make a stream of O<p>Note that this is every two input equation. The number of inputs is the only parameter that describes them.<p>These are definitions now. You still use A = B + C
and Z = f(X,Y) to work in symbols, but I hope they look different now.

[russlk]

Your dissertation reminds me of Whitehead & Russell's attempt to prove that 1+1=2 was logical, except that their book was 2 inches thick!

[bwts]

Following on the output O can also be used as an input for another function/action/machine <p>B)

[hlreed]

Russ,
All the action is down here. Spoken language is not adequate to define functions. By defining them procedurally we make the definition exact and we can see inner detail that can be shown no other way. <p>B,
That is the general idea. Functions and equations can be combined into networks. I call mine Hal trees, of course. With data streams you have a large number of possible operators. Look how many gates there are for bit streams.<p>[ March 25, 2003: Message edited by: Harold ]</p>