Help3:=proc(): print(`AP(L,a), CAT(L1,L2), REV(L), HP(n) , NEXT(w), PREV(w) `):end:

CAT:=proc(L1,L2): [op(L1),op(L2)]:end:

#AP(L,a): Appending a to every member of the list L
AP:=proc(L,a) local i:
[seq([op(L[i]),a],i=1..nops(L))]:
end:

#REV(L): the reverse of L
REV:=proc(L) local i:[seq(L[-i],i=1..nops(L))]:end:

HP:=proc(n) local L:
option remember:

if n=0 then
RETURN([[]]):
else
L:=HP(n-1):
CAT(AP(L,0),AP(REV(L),1)):
fi:

end:

NEXT:=proc(w) local n,w1:
option remember:
n:=nops(w):
if n=0 then
 RETURN(FAIL):
fi:

w1:=[op(1..n-1,w)]:

if w[n]=0 then
 if NEXT(w1)<>FAIL then
  RETURN([op(NEXT(w1)),0]):
 else
  RETURN([op(w1),1]):
 fi:
else

if PREV(w1)<>FAIL then
  RETURN([op(PREV(w1)),1]):
 else
 RETURN(FAIL):
fi:
fi:

end:


PREV:=proc(w) local n,w1:
option remember:
n:=nops(w):
if n=0 then
 RETURN(FAIL):
fi:

w1:=[op(1..n-1,w)]:

if w[n]=0 then
 if PREV(w1)<>FAIL then
  RETURN([op(PREV(w1)),0]):
 else
  RETURN(FAIL):
 fi:
else

if NEXT(w1)<>FAIL then
  RETURN([op(NEXT(w1)),1]):
 else
 RETURN([op(w1),0]):
fi:
fi:

end: