Type inference for conversion of method groups

Similar to calls of generic methods, type inference must also be applied when a method group M containing a generic method is converted to a given delegate type D (§6.6). Given a method

T_r M<X₁…X_n>(T₁ x₁ … T_m x_m)

and the method group M being assigned to the delegate type D the task of type inference is to find type arguments S₁…S_n so that the expression:

M<S₁…S_n>

becomes compatible (§15.1) with D.

Unlike the type inference algorithm for generic method calls, in this case there are only argument types, no argument expressions. In particular, there are no anonymous functions and hence no need for multiple phases of inference.

Instead, all X_i are considered unfixed, and a lower-bound inference is made from each argument type U_j of D to the corresponding parameter type T_j of M. If for any of the X_i no bounds were found, type inference fails. Otherwise, all X_i are fixed to corresponding S_i, which are the result of type inference.

Finding the best common type of a set of expressions

In some cases, a common type needs to be inferred for a set of expressions. In particular, the element types of implicitly typed arrays and the return types of anonymous functions with block bodies are found in this way.

Intuitively, given a set of expressions E₁…E_m this inference should be equivalent to calling a method

T_r M<X>(X x₁ … X x_m)

with the E_i as arguments.

More precisely, the inference starts out with an unfixed type variable X. Output type inferences are then made from each E_i to X. Finally, X is fixed and, if successful, the resulting type S is the resulting best common type for the expressions. If no such S exists, the expressions have no best common type.

Overload resolution

Overload resolution is a binding-time mechanism for selecting the best function member to invoke given an argument list and a set of candidate function members. Overload resolution selects the function member to invoke in the following distinct contexts within C#:

· Invocation of a method named in an invocation-expression (§7.6.5.1).

· Invocation of an instance constructor named in an object-creation-expression (§7.6.10.1).

· Invocation of an indexer accessor through an element-access (§7.6.6).

· Invocation of a predefined or user-defined operator referenced in an expression (§7.3.3 and §7.3.4).

Each of these contexts defines the set of candidate function members and the list of arguments in its own unique way, as described in detail in the sections listed above. For example, the set of candidates for a method invocation does not include methods marked override (§7.4), and methods in a base class are not candidates if any method in a derived class is applicable (§7.6.5.1).

Once the candidate function members and the argument list have been identified, the selection of the best function member is the same in all cases:

· Given the set of applicable candidate function members, the best function member in that set is located. If the set contains only one function member, then that function member is the best function member. Otherwise, the best function member is the one function member that is better than all other function members with respect to the given argument list, provided that each function member is compared to all other function members using the rules in §7.5.3.2. If there is not exactly one function member that is better than all other function members, then the function member invocation is ambiguous and a binding-time error occurs.

The following sections define the exact meanings of the terms applicable function member and better function member.

Applicable function member

A function member is said to be an applicable function member with respect to an argument list A when all of the following are true:

· Each argument in A corresponds to a parameter in the function member declaration as described in §7.5.1.1, and any parameter to which no argument corresponds is an optional parameter.

· For each argument in A, the parameter passing mode of the argument (i.e., value, ref, or out) is identical to the parameter passing mode of the corresponding parameter, and

o for a value parameter or a parameter array, an implicit conversion (§6.1) exists from the argument to the type of the corresponding parameter, or

o for a ref or out parameter, the type of the argument is identical to the type of the corresponding parameter. After all, a ref or out parameter is an alias for the argument passed.

For a function member that includes a parameter array, if the function member is applicable by the above rules, it is said to be applicable in its normal form. If a function member that includes a parameter array is not applicable in its normal form, the function member may instead be applicable in its expanded form:

· The expanded form is constructed by replacing the parameter array in the function member declaration with zero or more value parameters of the element type of the parameter array such that the number of arguments in the argument list A matches the total number of parameters. If A has fewer arguments than the number of fixed parameters in the function member declaration, the expanded form of the function member cannot be constructed and is thus not applicable.

· Otherwise, the expanded form is applicable if for each argument in A the parameter passing mode of the argument is identical to the parameter passing mode of the corresponding parameter, and

o for a fixed value parameter or a value parameter created by the expansion, an implicit conversion (§6.1) exists from the type of the argument to the type of the corresponding parameter, or

o for a ref or out parameter, the type of the argument is identical to the type of the corresponding parameter.

Better function member

For the purposes of determining the better function member, a stripped-down argument list A is constructed containing just the argument expressions themselves in the order they appear in the original argument list.

Parameter lists for each of the candidate function members are constructed in the following way:

· The expanded form is used if the function member was applicable only in the expanded form.

· Optional parameters with no corresponding arguments are removed from the parameter list

· The parameters are reordered so that they occur at the same position as the corresponding argument in the argument list.

Given an argument list A with a set of argument expressions { E₁, E₂,..., E_N } and two applicable function members M_P and M_Q with parameter types { P₁, P₂,..., P_N } and { Q₁, Q₂,..., Q_N }, M_P is defined to be a better function member than M_Q if

· for each argument, the implicit conversion from E_X to Q_X is not better than the implicit conversion from E_X to P_X, and

· for at least one argument, the conversion from E_X to P_X is better than the conversion from E_X to Q_X.

When performing this evaluation, if M_P or M_Q is applicable in its expanded form, then P_X or Q_X refers to a parameter in the expanded form of the parameter list.

In case the parameter type sequences {P₁, P₂, …, P_N} and {Q₁, Q₂, …, Q_N} are equivalent (i.e. each P_i has an identity conversion to the corresponding Q_i), the following tie-breaking rules are applied, in order, to determine the better function member.

· If M_P is a non-generic method and M_Q is a generic method, then M_P is better than M_Q.

· Otherwise, if M_P is applicable in its normal form and M_Q has a params array and is applicable only in its expanded form, then M_P is better than M_Q.

· Otherwise, if M_P has more declared parameters than M_Q, then M_P is better than M_Q. This can occur if both methods have params arrays and are applicable only in their expanded forms.

· Otherwise if all parameters of M_P have a corresponding argument whereas default arguments need to be substituted for at least one optional parameter in M_Q then M_P is better than M_Q.

· Otherwise, if M_P has more specific parameter types than M_Q, then M_P is better than M_Q. Let {R₁, R₂, …, R_N} and {S₁, S₂, …, S_N} represent the uninstantiated and unexpanded parameter types of M_P and M_Q. M_P’s parameter types are more specific than M_Q’s if, for each parameter, R_X is not less specific than S_X, and, for at least one parameter, R_X is more specific than S_X:

o A type parameter is less specific than a non-type parameter.

o Recursively, a constructed type is more specific than another constructed type (with the same number of type arguments) if at least one type argument is more specific and no type argument is less specific than the corresponding type argument in the other.

o An array type is more specific than another array type (with the same number of dimensions) if the element type of the first is more specific than the element type of the second.

· Otherwise if one member is a non-lifted operator and the other is a lifted operator, the non-lifted one is better.

· Otherwise, neither function member is better.