############################################################
# 
#  Illustrates Maple mechanism for extending type-checking
#  procedure 'type' to user-defined types.  Similar 
#  mechanisms exist for many other Maple procedures such
#  as 'diff', 'int', 'evalf', etc.
#
############################################################

############################################################
#  Our representation of a tensor will be a four-element
#  list whose first element is the literal `TENSOR`.
############################################################

`type/tensor` := proc(x)
   type(x,list) and (nops(x) = 4) and (x[1] = `TENSOR`)
end:

ttype := proc(x)
   if type(x,tensor) then
      printf(`Object %a IS of type tensor\n`,x);
   else
      printf(`Object %a IS NOT of type tensor\n`,x);
   fi;
end:

t1 := [TENSOR,foo,foo,foo]:
t2 := [VECTOR,foo,foo,foo]:
t3 := [TENSOR,foo,foo]:
t4 := {TENSOR,foo,foo}:

ttype(t1):
ttype(t2):
ttype(t3):
ttype(t4):