Upper-bound inferences

An upper-bound inference from a type U to a type V is made as follows:

· If V is one of the unfixed X_i then U is added to the set of upper bounds for X_i.

· Otherwise, sets V₁…V_k and U₁…U_k are determined by checking if any of the following cases apply:

· U is an array type U₁[…]and V is an array type V₁[…]of the same rank

· U is one of IEnumerable<U_e>, ICollection<U_e> or IList<U_e> and V is a one-dimensional array type V_e[]

· U is the type U₁? and V is the type V₁?

· U is constructed class, struct, interface or delegate type C<U₁…U_k> and V is a class, struct, interface or delegate type which is identical to, inherits from (directly or indirectly), or implements (directly or indirectly) a unique type C<V₁…V_k>

(The “uniqueness” restriction means that if we have interface C<T>{} class V<Z>: C<X<Z>>, C<Y<Z>>{}, then no inference is made when inferring from C<U₁> to V<Q>. Inferences are not made from U₁ to either X<Q> or Y<Q>.)

If any of these cases apply then an inference is made from each U_i to the corresponding V_i as follows:

· If U_i is not known to be a reference type then an exact inference is made

· Otherwise, if V is an array type then an upper-bound inference is made

· Otherwise, if U is C<U₁…U_k> then inference depends on the i-th type parameter of C:

· If it is covariant then an upper-bound inference is made.

· If it is contravariant then a lower-bound inference is made.

· If it is invariant then an exact inference is made.

· Otherwise, no inferences are made.

Fixing

An unfixed type variable X_i with a set of bounds is fixed as follows:

· The set of candidate types U_j starts out as the set of all types in the set of bounds for X_i.

· We then examine each bound for X_i in turn: For each exact bound U of X_i all types U_j which are not identical to U are removed from the candidate set. For each lower bound U of X_i all types U_j to which there is not an implicit conversion from U are removed from the candidate set. For each upper bound U of X_i all types U_j from which there is not an implicit conversion to U are removed from the candidate set.

· If among the remaining candidate types U_j there is a unique type V from which there is an implicit conversion to all the other candidate types, then X_i is fixed to V.

· Otherwise, type inference fails.