  This paper proposes bimorphic recursion, which is restricted polymorphic
recursion such that every recursive call in the body of a function definition
has the same type. Bimorphic recursion allows us to assign two different types
to a recursively defined function: one is for its recursive calls and the other
is for its calls outside its definition. Bimorphic recursion in this paper can
be nested. This paper shows bimorphic recursion has principal types and
decidable type inference. Hence bimorphic recursion gives us flexible typing
for recursion with decidable type inference. This paper also shows that its
typability becomes undecidable because of nesting of recursions when one
removes the instantiation property from the bimorphic recursion.
