#C4.txt, 9/19/2016
Help:=proc(): print(` ChildOf(Dict,Dict1,a)   `): end:

#CWGF(A,Dict,t): Inputs a finite set of letters A (the alphabet), a finite set
#set of "dirty words", Dict (set of lists of words in the alphabet A)
#(we assume that none is properly contained another), and a variable t
#outputs a rational function that is the generating function for
#all CLEAN words (words in A not containing ANY of the members of Dict)
CWGF:=proc(A,Dict,t)
CWGF1(A,Dict, {}, t):
end:

#ChildOf(Dict,Dict1,a):If you have a word in the alphabet A and a list of
#"dirty words" Dict, and another list Dict1, and you look at a typical
#word avoiding any of the dirty words AND avoiding words in Dict1 at the start
#and starting with a, what is the new Dict1?
ChildOf:=proc(Dict,Dict1,a) local S,w:

S:={}:

for w in Dict union Dict1 do
 if w[1]=a then
   S:=S union {w[2..nops(w)]}:
 fi:
od:

S:
end:

#BuildEqs(A,Dict,t): inputs an alphabet A, a set of "dirty words" , Dict, and a variable t
#returns a seq of equations and a set of variables for the various Dict1 that shows up
BuildEqs:=proc(A,Dict,t,J) local var,eq, StillToDo, AlreadyDone,Dict1,eq1,a,yonah:

var:={J[{}]}:
eq:={}:
StillToDo:={{}}:

while StillToDo<>{} do
 Dict1:=StillToDo[1]:
 AlreadyDone:=AlreadyDone union {Dict1}:
 StillToDo:=StillToDo minus {Dict1}:
 var:=var union {J[Dict1]}:
 eq1:=J[Dict1]:

 for a in A do
  yonah:=ChildOf(Dict,Dict1,a):
 od:  
od:

end: