Little Circular Networks in Tcl
Theo Verelst
Started this page but claims no rights to keep it unchanged, as usual.
Networks are important, end knowing essentials is even important for programming, and in tcl we can quite well explore what happens with data passing through the smallest imaginable networks, to learn to begin with about what computers are essentially made of, further what networking can do, what object message sending limitations and possible errors are about, and what threads and interprocess communication must deal with.
And it's fun enough to think about the quite large complexity involved in a few 'not-so-black' boxes exchanging information, being 'created', initialized, and how one sensibly can simulate or enforce a communication regime to make the network tick.
In ee, you'd have logical circuit simulators who do such things, but if you don't persue a PhD and still want to think about oo messages, this tcl-inside page should not pose insurmountable problems.
I'm sure, by experience of letting a tcl/tk controller socket-talk a number crunching C program in real time, that the issue is relevant (in that context in windows tcl 8.0+ I think with cygnus socket connection).
Lets start with the idea of a logical function, which is easy enough, and of course done on various pages (boolean logic Finite State Machine).
A procedure to make an NAND as being invert(and(a,b):
proc nand {a b} {return [expr !($a && $b)]}the result is only 1 when both a and b are 0, and0 otherwise. Now we could put two nands on a row and feed the output back to the input, like we would do for an eigenvalue analysis/definition, and play around with what that gives us:
proc nand2 {a b} {return [expr !($a2 && $b)]}
set a 1
set a2 1
for {set i 0} {$i < 10} {incr i} {
set b2 [nand $a $b]
set b [nand2 $a2 $b2]
}
# or:
for {set i 0} {$i < 10} {incr i} {
set b2 [nand $a $b]
set b [nand2 $a2 $b2]
}So the nands are like in series, and then fed round, and the open inputs are set to 1.
The fun is that this circuit can memorize a bit, also in electronical practice, and that as it is, it is like the dining philosophers, or at least it is as yet undefined what it will do: the above minimal initialisation of the eigenvalue problem leaves us with an undefined initial state, no matter what order we make the nands evaluate in.
Now this might seem a touch boring or irrelevant, but it isn't. Its the eigenfunction analysis of a very simple function composition, which has memory, as we'll see, and which is undefined to start with, but completely defined from any resolving point onward, it is easily controllable, and can be practically implemented in various reasonable ways.
We can break through the undefined loop by applying another input signal to one of the inputs set to one thus far, as soon as we do that, the problem enters a defined state, and it depends on which input we make zero instead of one what state that will be: {b2 b} = 01 or 10.
When we in the 'running' network bring both open inputs back to 1, the last state, which was stable, is remembered. Setting the other input to zero forces the inverse state, while a=0 and a2=0 makes both b and b2 1, which cannot be a situation which is remembered.
For simulation, or practical implementation, it doesn't matter how and when we evaluate the functions, as long as for each input change, both get evaluated sufficiently often to propagate the chance into a new stable overall state.
On the bottom of the page I listed the bwise canvas graphics file, followed by the block variable and function file, which can be sourced into a freshly started bwise block environment, and the graphics also in program with a .mw.c canvas exisiting, and some unlikely to fail global variables missing.
Preferably don't use the bwise 'load' button, that will erase the canvas menus first without reinstalling them.
Your canvas should show the logical function block create subnetworks consisting of a generate function and ID incrementor, which can be triggered by running 'funcprop' from the right mouse button popup menu when the mouse is over the genXX yellow block. Each time the subnet will run one circle, creating a new logical function block and preparing a new ID number on the generator block input.
On the bottom part, the and + invertor circuits can be found, with two dummy blocks to hold the a and a2 equivalent input values, and followed by blocks showing their input values for feedback of the function outputs. The two constructed nand functions are fed in circle, but organized in a symmetrical fashion. The popup menu can be used on every block to get a 'data' window which shows all block variables, including *_bfunc which holds the function.
When you try the circuit, only run 'funcproc' or single eval and transfers on the network, or you'l end up with infinite circling of the block evaluator until some stack overflows (though I think that than deliberately happens in tcl).
Also, the funprop keeps an array of block names which have been executed and generated data that hasn't yet been consumed by the connected block, so repeated and alternating funcprop invokations from for instance the starting blocks makes the data ripple through. See the bwise and some other pages.
Alternatively, we can 'run' the blocks in a fixed sequence which we choose ourselves by the filelist procedure, which takes a list of block names and fires them and transfers their data in given order.
A not particularly well formed but illustrative function to do this is:
proc firelist2 { {l} } {
global bfunc t
foreach n $l {
set f {}
append f [blockfunc $n {}]
global $f
eval set fc \$\{$f\}
set t $fc
uplevel #0 $t ;
transfer $l
}
}Which we can call with a list consisting of the block names we want to fire, such as
firelist2 {Proc1 Proc2 and1 inv1 and2 inv2 Text1 Text2}When you used the data windows on the proc1 and proc2 from the below network to set 11 (memorize) 10 (set) 01 (set) or 00 (make no sense), using this command repeatedly will let the data ripple through the network and show the result in the text blocks, normally either text1 or text2 being 1, the other 0.
To experiment with different schemes of activating the blocks (and transfering output data over the right hand side connected wires), I made a little script which lets you form a list of blocks by simply tapping on the yellow blocks and having an entry build a list as you click. An empty button let you make a new list, and a Run button executes the blocks in order of the list.
toplevel .p
entry .p.e
pack .p.e
.p.e conf -textvar rr
$mc bind block <Button-1> {global rr; set rr [$mc itemcget current -tags]}
pack .p.e -expand y -fill x
$mc bind block <Button-1> {global rr; lappend rr [lindex [$mc itemcget current -tags] 0]}
pack .p.r [button .p.r -text empty -command {global rr; set rr {}}] -side bottom -expand n -fill x
pack [button .p.f -text run -command {global rr; firelist2 $rr}] -side bottom -expand n -fill x # canlogic2.tcl
global bcount scopeindex wireindex shellindex drumindex
set bcount 0
set scopeindex 0
set wireindex 20
set shellindex 0
set drumindex 0
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.mw.c create text 385.0 213.0 -activefill {} -activestipple {} -anchor nw -disabledfill {} -disabledstipple {} -fill navy -font {courier 10} -justify left -offset 0,0 -state {} -stipple {} -tags {Text2 textfield} -text Text2 -width 0
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.mw.c create line 325.0 223.0 359.0 223.0 -activedash {} -activefill {} -activestipple {} -activewidth 0.0 -arrow none -arrowshape {8 10 3} -capstyle butt -fill darkblue -dash {} -dashoffset 0 -disableddash {} -disabledfill {} -disabledstipple {} -disabledwidth 0.0 -joinstyle round -offset 0,0 -smooth 0 -splinesteps 12 -state {} -stipple {} -tags {wire19 connect wire inv2 q Text2 in} -width 1.0 # varlogic2.tcl
set genor.bfunc {newproc "set or${genor.n}.q \[expr (\${or${genor.n}.a} || \${or${genor.n}.b})\]" or${genor.n} {a b} q ;set genor.nlast ${genor.n}}
set genor.bfunc_init {}
set genor.n {1}
set genor.nlast {1}
set genand.bfunc {newproc "set and${genand.n}.q \[expr (\${and${genand.n}.a} && \${and${genand.n}.b})\]" and${genand.n} {a b} q ;set genand.nlast ${genand.n}}
set genand.bfunc_init {}
set genand.n {3}
set genand.nlast {2}
set geninv.bfunc {newproc "set inv${geninv.n}.q \[expr !(\${inv${geninv.n}.a})\]" inv${geninv.n} {a} q ;set geninv.nlast ${geninv.n}}
set geninv.bfunc_init {}
set geninv.n {3}
set geninv.nlast {2}
set genincr.bfunc {newproc "set incr${genincr.n}.o \[expr 1+(\${incr${genincr.n}.i})\]" incr${genincr.n} {i} o ;set genincr.nlast ${genincr.n}}
set genincr.bfunc_init {}
set genincr.n {5}
set genincr.nlast {5}
set incr1.bfunc {set incr1.o [expr 1+(${incr1.i})]}
set incr1.bfunc_init {}
set incr1.i {5}
set incr1.o {6}
set incr2.bfunc {set incr2.o [expr 1+(${incr2.i})]}
set incr2.bfunc_init {}
set incr2.i {1}
set incr2.o {2}
set incr3.bfunc {set incr3.o [expr 1+(${incr3.i})]}
set incr3.bfunc_init {}
set incr3.i {2}
set incr3.o {3}
set incr4.bfunc {set incr4.o [expr 1+(${incr4.i})]}
set incr4.bfunc_init {}
set incr4.i {2}
set incr4.o {3}
set inv1.a {}
set inv1.bfunc {set inv1.q [expr !(${inv1.a})]}
set inv1.bfunc_init {}
set inv1.q {}
set and1.a {0}
set and1.b {1}
set and1.bfunc {set and1.q [expr (${and1.a} && ${and1.b})]}
set and1.bfunc_init {}
set and1.q {}
set inv2.a {}
set inv2.bfunc {set inv2.q [expr !(${inv2.a})]}
set inv2.bfunc_init {}
set inv2.q {}
set and2.a {}
set and2.b {1}
set and2.bfunc {set and2.q [expr (${and2.a} && ${and2.b})]}
set and2.bfunc_init {}
set and2.q {}
set Proc1.bfunc { set Proc1.out ${Proc1.in} }
set Proc1.bfunc_init {}
set Proc1.in {1}
set Proc1.out {1}
set Proc2.bfunc { set Proc2.out ${Proc2.in} }
set Proc2.bfunc_init {}
set Proc2.in {1}
set Proc2.out {1}
set Text1.bfunc {global mc; $mc itemco [tag_and { Text1 textfield }] -text ${Text1.in} }
set Text1.bfunc_init {}
set Text1.in {}
set Text2.bfunc {global mc; $mc itemco [tag_and { Text2 textfield }] -text ${Text2.in} }
set Text2.bfunc_init {}
set Text2.in {}