src/CTT/ctt.thy

   Eqtype    :: "[t,t]=>prop"        ("(3_ =/ _)" [10,10] 5)
   Elem      :: "[i, t]=>prop"       ("(_ /: _)" [10,10] 5)
   Eqelem    :: "[i,i,t]=>prop"      ("(3_ =/ _ :/ _)" [10,10,10] 5)
   Reduce    :: "[i,i]=>prop"        ("Reduce[_,_]")
   (*Types*)
-  "@PROD"   :: "[id,t,t]=>t"        ("(3PROD _:_./ _)" 10)
-  "@SUM"    :: "[id,t,t]=>t"        ("(3SUM _:_./ _)" 10)
+  "@PROD"   :: "[idt,t,t]=>t"       ("(3PROD _:_./ _)" 10)
+  "@SUM"    :: "[idt,t,t]=>t"       ("(3SUM _:_./ _)" 10)
   "+"       :: "[t,t]=>t"           (infixr 40)
   (*Invisible infixes!*)
   "@-->"    :: "[t,t]=>t"           ("(_ -->/ _)" [31,30] 30)
   "@*"      :: "[t,t]=>t"           ("(_ */ _)" [51,50] 50)
   (*Functions*)

   (*Pairing*)
   pair      :: "[i,i]=>i"           ("(1<_,/_>)")
 
 translations
   "PROD x:A. B" => "Prod(A, %x. B)"
+  "A --> B"     => "Prod(A, _K(B))"
   "SUM x:A. B"  => "Sum(A, %x. B)"
+  "A * B"       => "Sum(A, _K(B))"
 
 rules
 
   (*Reduction: a weaker notion than equality;  a hack for simplification.
     Reduce[a,b] means either that  a=b:A  for some A or else that "a" and "b"

 end
 
 
 ML
 
-val parse_translation =
-  [("@-->", ndependent_tr "Prod"), ("@*", ndependent_tr "Sum")];
-
 val print_translation =
   [("Prod", dependent_tr' ("@PROD", "@-->")),
    ("Sum", dependent_tr' ("@SUM", "@*"))];