HAL Algebra

A cable carries a data stream.
A cable can have any number of sockets.
A cable has width (w) .
HalNode is an operator or a function and has a cycle time (c).
O, I, R are headers on nodes and connect to sockets which are data cable variables.

-,+, o, a,>, -    are operators.
d and i           are functions.
> and z           are special functions.
=                 is transfer operator. (May be read as ‘becomes’)
;                 is a comment delimiter.

OP  HalNode  Notation  Function
 -  C Node   O = L - R   O is difference of L,R
 +  P Node   O = L + R  O is sum of L,R
 o  O Node  O = L o R    O is Max(L,R)
 a  A Node   O = L a R    O is Min(L,R)
 >  GT Node  O = L > R  O is R if L > R else O is 0
 <   LT Node  O = L < R   O is R if L < R else O is 0
 is  IS Node  O = L is R  O is R if L = R else O is 0
 g  G Node  O = I g R  O is R if I > 0 else O is 0
 l  L Node  O = I l R  O is R if I < 0 else O is 0
 z  Z Node  O = I z R  O is R while I = 0 else O is 0
 -  N Node  O =  -I  O is 0 - I
 d   D Node  O = d(I)   O is derivative  of   I
 i  I Node   O = i(I)-R  O is integral  of  I
 f  F Node  O = f(I)  O is frequency of I
 B Node   O = I + 80H  Converts integer <-> offset bin
 In Node  O = X  Interface to hardware from sensor
 Out Node  X = O   Interface to hardware to motor

There are hundreds of variations and additions that can be made.

In a HalNode - cable system like X = Z - Y, as X becomes Z - Y, complexity is reduced and dimension is reduced. If Z and Y are ramps (complexity[1]), then X is a constant (complexity[0]). X is a point. Z and Y are a line.

Data cable variables can be integers of any size.

(Copyright 2004, Harold L. Reed)

CNode, PNode, ONode, ANode, GTNode, LTNode, ISNode, ZNode, NNode, BNode, DNode, INode and FNode are trademarks of Hal Brain Design and Harold L. Reed

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04/22/06