Help:=proc(): print(` STAB(VOC,R) , TRA(L), CP1(VOC,L), ALLSQ(VOC,K), ALLSQc(VOC,L), RANCON1(VOC1,L),  RANCON(VOC1,L) , MakePuz(VOC,L,K1)`): end:

read `EV3.txt`:
read `EV4.txt`:
read `EV5.txt`:

#STAB(VOC,R): The starting table of the vocubulary list VOC of length R, returns the set of prefixes followed by the table
STAB:=proc(VOC,R) local S,S1,I1,T,W1:
option remember:

S:={seq([op(1..R,VOC[I1])],I1=1..nops(VOC))}:

for S1 in S do
 T[S1]:={}:
od:

for I1 from 1 to nops(VOC) do
 W1:=VOC[I1]:
 T[[op(1..R,W1)]]:= T[[op(1..R,W1)]] union {W1}:
od:

S,op(T):
end:

TRA:=proc(L) local I1,J1:
[seq([seq(L[J1][I1],J1=1..nops(L))],I1=1..nops(L[1]))]:
end:


#CP1(VOC,L): inputs a vocabulary VOC of words of the same length and a list of words that is promising
#finds the set of promising extensions. Try
#CP1(ENGLISH3,[[a,p,e]]);
CP1:=proc(VOC,L) local I1,M1,L1,ST,CHILD,M:

if convert(L,set) minus convert(VOC,set)<>{} then
 RETURN(FAIL):
fi:

if L=[] then
 {seq([VOC[I1]],I1=1..nops(VOC))}:
fi:

L1:=TRA(L):

ST:=STAB(VOC,nops(L))[1]:


if convert(L1,set) minus ST<>{} then
 RETURN({}):
fi:

ST:=STAB(VOC,nops(L)+1)[1]:

CHILD:={}:

for I1 from 1 to nops(VOC) do
 M:=[op(L),VOC[I1]]:
 M1:=TRA(M):

if convert(M1,set) minus ST={} then
 CHILD:=CHILD union {M}:
fi:
od:
CHILD:

end:



#ALLSQ(VOC,K): all the Word squares of size K
ALLSQ:=proc(VOC,K) local S,I1,N1:
S:={seq([VOC[I1]],I1=1..nops(VOC))}:
for N1 from 2 to K do
 S:={seq(op(CP1(VOC,S[I1])),I1=1..nops(S))}:
od:

S:

end:


#ALLSQc(VOC,L): all the continuations of L
ALLSQc:=proc(VOC,L) local K,N1,I1,S:
K:=nops(L[1]):

S:={L}:
for N1 from nops(L)+1 to K do
 S:={seq(op(CP1(VOC,S[I1])),I1=1..nops(S))}:
od:
S:
end:


#RANCON1(VOC,L): a random contiuation of L
RANCON1:=proc(VOC,L) local NEW1:
 NEW1:=CP1(VOC,L):
 if NEW1={} or NEW1=FAIL then
     RETURN(FAIL):
 fi:
NEW1[rand(1..nops(NEW1))()]:
end:

RANCON:=proc(VOC,L) local K,L1,L2:
K:=nops(VOC[1]):
L1:=L:

while L1<>FAIL and nops(L1)<K do
 L2:=RANCON1(VOC,L1):
  if L2=FAIL then
     RETURN(L1):
  fi:
 L1:=L2:
od:
L1:
end:


#MakePuz(VOC,L,K1): makes a a set of random word squares using the words in VOC, starting with L
MakePuz:=proc(VOC,L,K1)local K2,PU1,PU,I1:
K2:=nops(VOC[1]):

PU:={}:

for I1 from 1 to K1 do
PU1:=RANCON(VOC,L):
if nops(PU1)=K2 then
 PU:=PU union {PU1}:
fi:
od:
PU:
end: