Input                  Should be parsed as             Derived constraint
                                                       on precedence
--------------------------------------------------------------------------------
\lambda x.x y          ((\lambda x.x) y)               lambda > apply
S x = y                  (= (S x) y)                   apply  > infix operators
\forall x.x=x	       (\forall x.(= x x))	       infix operators > binders
\lambda x.x \to x    \lambda. (x \to x)                \to > \lambda
--------------------------------------------------------------------------------

Precedence total order:

  \to > lambda > apply > infix operators > binders

where binders are all binders except lambda (i.e. \forall, \pi, \exists)

to test:
  
./test_parser term << EOT 
  \lambda x.x y
  S x = y
  \forall x.x=x
  \lambda x.x \to x
EOT
  
should respond with:
  
  (\lambda x.x y)
  (eq (S x) y)
  \forall x.(eq x x)
  \lambda x.(x \to x)