## How to Handle the Incompatible Types Error in Java

##### Table of Contents

## Introduction to Data Types & Type Conversion

**Variables** are memory containers used to store information. In Java, every variable has a **data type** and stores a value of that type. Data types, or types for short, are divided into two categories: **primitive** and **non-primitive**. There are eight primitive types in Java: byte , short , int , long , float , double , boolean and char . These built-in types describe variables that store single values of a predefined format and size. Non-primitive types, also known as **reference types**, hold references to objects stored somewhere in memory. The number of reference types is unlimited, as they are user-defined. A few reference types are already baked into the language and include String , as well as wrapper classes for all primitive types, like Integer for int and Boolean for boolean . All reference types are subclasses of java.lang.Object [1].

In programming, it is commonplace to convert certain data types to others in order to allow for the storing, processing, and exchanging of data between different modules, components, libraries, APIs, etc. Java is a statically typed language, and as such has certain rules and constraints in regard to working with types. While it is possible to convert to and from certain types with relative ease, like converting a char to an int and vice versa with **type casting** [2], it is not very straightforward to convert between other types, such as between certain primitive and reference types, like converting a String to an int , or one user-defined type to another. In fact, many of these cases would be indicative of a logical error and require careful consideration as to what is being converted and how, or whether the conversion is warranted in the first place. Aside from type casting, another common mechanism for performing type conversion is **parsing** [3], and Java has some predefined methods for performing this operation on built-in types.

## Incompatible Types Error: What, Why & How?

The incompatible types error indicates a situation where there is some expression that yields a value of a certain data type different from the one expected. This error implies that **the Java compiler is unable to resolve a value assigned to a variable or returned by a method, because its type is incompatible with the one declared on the variable or method in question**. Incompatible, in this context, means that the source type is both different from and unconvertible (by means of automatic type casting) to the declared type.

This might seem like a syntax error, but it is a logical error discovered in the semantic phase of compilation. The error message generated by the compiler indicates the line and the position where the type mismatch has occurred and specifies the incompatible types it has detected. This error is a generalization of the method X in class Y cannot be applied to given types and the constructor X in class Y cannot be applied to given types errors discussed in [4].

The incompatible types error most often occurs when manual or explicit conversion between types is required, but it can also happen by accident when using an incorrect API, usually involving the use of an incorrect reference type or the invocation of an incorrect method with an identical or similar name.

## Incompatible Types Error Examples

### Explicit type casting

Assigning a value of one primitive type to another can happen in one of two directions. Either from a type of a smaller size to one of a larger size (upcasting), or from a larger-sized type to a smaller-sized type (downcasting). In the case of the former, the data will take up more space but will be intact as the larger type can accommodate any value of the smaller type. So the conversion here is done automatically. However, converting from a larger-sized type to a smaller one necessitates explicit casting because some data may be lost in the process.

Fig. 1(a) shows how attempting to assign the values of the two double variables a and b to the int variables x and y results in the incompatible types error at compile-time. Prefixing the variables on the right-hand side of the assignment with the int data type in parenthesis (lines 10 & 11 in Fig. 1(b)) fixes the issue. Note how both variables lost their decimal part as a result of the conversion, but only one kept its original value—this is exactly why the error message reads possible lossy conversion from double to int and why the incompatible types error is raised in this scenario. By capturing this error, the compiler prevents accidental loss of data and forces the programmer to be deliberate about the conversion. The same principle applies to downcasting reference types, although the process is slightly different as polymorphism gets involved [5].

## Java type conversion exception

short to byte or char

char to byte or short

int to byte , short , or char

long to byte , short , char , or int

float to byte , short , char , int , or long

double to byte , short , char , int , long , or float

A narrowing primitive conversion may lose information about the overall magnitude of a numeric value and may also lose precision and range.

A narrowing primitive conversion from double to float is governed by the IEEE 754 rounding rules (§4.2.4). This conversion can lose precision, but also lose range, resulting in a float zero from a nonzero double and a float infinity from a finite double . A double NaN is converted to a float NaN and a double infinity is converted to the same-signed float infinity.

A narrowing conversion of a signed integer to an integral type T simply discards all but the *n* lowest order bits, where *n* is the number of bits used to represent type T . In addition to a possible loss of information about the magnitude of the numeric value, this may cause the sign of the resulting value to differ from the sign of the input value.

A narrowing conversion of a char to an integral type T likewise simply discards all but the *n* lowest order bits, where *n* is the number of bits used to represent type T . In addition to a possible loss of information about the magnitude of the numeric value, this may cause the resulting value to be a negative number, even though chars represent 16-bit unsigned integer values.

A narrowing conversion of a floating-point number to an integral type T takes two steps:

In the first step, the floating-point number is converted either to a long , if T is long , or to an int , if T is byte , short , char , or int , as follows:

If the floating-point number is NaN (§4.2.3), the result of the first step of the conversion is an int or long 0 .

Otherwise, if the floating-point number is not an infinity, the floating-point value is rounded to an integer value V , rounding toward zero using IEEE 754 round-toward-zero mode (§4.2.3). Then there are two cases:

If T is long , and this integer value can be represented as a long , then the result of the first step is the long value V .

Otherwise, if this integer value can be represented as an int , then the result of the first step is the int value V .

Otherwise, one of the following two cases must be true:

The value must be too small (a negative value of large magnitude or negative infinity), and the result of the first step is the smallest representable value of type int or long .

The value must be too large (a positive value of large magnitude or positive infinity), and the result of the first step is the largest representable value of type int or long .

In the second step:

If T is int or long , the result of the conversion is the result of the first step.

If T is byte , char , or short , the result of the conversion is the result of a narrowing conversion to type T (§5.1.3) of the result of the first step.

**Example 5.1.3-1. Narrowing Primitive Conversion**

This program produces the output:

The results for char , int , and long are unsurprising, producing the minimum and maximum representable values of the type.

The results for byte and short lose information about the sign and magnitude of the numeric values and also lose precision. The results can be understood by examining the low order bits of the minimum and maximum int . The minimum int is, in hexadecimal, 0x80000000 , and the maximum int is 0x7fffffff . This explains the short results, which are the low 16 bits of these values, namely, 0x0000 and 0xffff ; it explains the char results, which also are the low 16 bits of these values, namely, ‘\u0000’ and ‘\uffff’ ; and it explains the byte results, which are the low 8 bits of these values, namely, 0x00 and 0xff .

Despite the fact that overflow, underflow, or other loss of information may occur, a narrowing primitive conversion never results in a run-time exception (§11.1.1).

**Example 5.1.3-2. Narrowing Primitive Conversions that lose information**

This program produces the output:

### 5.1.4. Widening and Narrowing Primitive Conversion

The following conversion combines both widening and narrowing primitive conversions:

First, the byte is converted to an int via widening primitive conversion (§5.1.2), and then the resulting int is converted to a char by narrowing primitive conversion (§5.1.3).

### 5.1.5. Widening Reference Conversion

A *widening reference* conversion exists from any reference type S to any reference type T , provided S is a subtype (§4.10) of T .

Widening reference conversions never require a special action at run time and therefore never throw an exception at run time. They consist simply in regarding a reference as having some other type in a manner that can be proved correct at compile time.

### 5.1.6. Narrowing Reference Conversion

Six kinds of conversions are called the *narrowing reference conversions* :

From any reference type S to any reference type T , provided that S is a proper supertype of T (§4.10).

An important special case is that there is a narrowing reference conversion from the class type Object to any other reference type (§4.12.4).

From any class type C to any non-parameterized interface type K , provided that C is not final and does not implement K .

From any interface type J to any non-parameterized class type C that is not final .

From any interface type J to any non-parameterized interface type K , provided that J is not a subinterface of K .

From the interface types Cloneable and java.io.Serializable to any array type T [] .

From any array type SC [] to any array type TC [] , provided that SC and TC are reference types and there is a narrowing reference conversion from SC to TC .

Such conversions require a test at run time to find out whether the actual reference value is a legitimate value of the new type. If not, then a ClassCastException is thrown.

### 5.1.7. Boxing Conversion

Boxing conversion converts expressions of primitive type to corresponding expressions of reference type. Specifically, the following nine conversions are called the *boxing conversions* :

From type boolean to type Boolean

From type byte to type Byte

From type short to type Short

From type char to type Character

From type int to type Integer

From type long to type Long

From type float to type Float

From type double to type Double

From the null type to the null type

This rule is necessary because the conditional operator (§15.25) applies boxing conversion to the types of its operands, and uses the result in further calculations.

At run time, boxing conversion proceeds as follows:

If p is a value of type boolean , then boxing conversion converts p into a reference r of class and type Boolean , such that r .booleanValue() == p

If p is a value of type byte , then boxing conversion converts p into a reference r of class and type Byte , such that r .byteValue() == p

If p is a value of type char , then boxing conversion converts p into a reference r of class and type Character , such that r .charValue() == p

If p is a value of type short , then boxing conversion converts p into a reference r of class and type Short , such that r .shortValue() == p

If p is a value of type int , then boxing conversion converts p into a reference r of class and type Integer , such that r .intValue() == p

If p is a value of type long , then boxing conversion converts p into a reference r of class and type Long , such that r .longValue() == p

If p is a value of type float then:

If p is not NaN, then boxing conversion converts p into a reference r of class and type Float , such that r .floatValue() evaluates to p

Otherwise, boxing conversion converts p into a reference r of class and type Float such that r .isNaN() evaluates to true

If p is a value of type double , then:

If p is not NaN, boxing conversion converts p into a reference r of class and type Double , such that r .doubleValue() evaluates to p

Otherwise, boxing conversion converts p into a reference r of class and type Double such that r .isNaN() evaluates to true

If p is a value of any other type, boxing conversion is equivalent to an identity conversion (§5.1.1).

If the value p being boxed is true , false , a byte , or a char in the range \u0000 to \u007f , or an int or short number between -128 and 127 (inclusive), then let r_{1} and r_{2} be the results of any two boxing conversions of p . It is always the case that r_{1} == r_{2} .

Ideally, boxing a given primitive value p , would always yield an identical reference. In practice, this may not be feasible using existing implementation techniques. The rules above are a pragmatic compromise. The final clause above requires that certain common values always be boxed into indistinguishable objects. The implementation may cache these, lazily or eagerly. For other values, this formulation disallows any assumptions about the identity of the boxed values on the programmer’s part. This would allow (but not require) sharing of some or all of these references.

This ensures that in most common cases, the behavior will be the desired one, without imposing an undue performance penalty, especially on small devices. Less memory-limited implementations might, for example, cache all char and short values, as well as int and long values in the range of -32K to +32K.

A boxing conversion may result in an OutOfMemoryError if a new instance of one of the wrapper classes ( Boolean , Byte , Character , Short , Integer , Long , Float , or Double ) needs to be allocated and insufficient storage is available.

### 5.1.8. Unboxing Conversion

Unboxing conversion converts expressions of reference type to corresponding expressions of primitive type. Specifically, the following eight conversions are called the *unboxing conversions* :

From type Boolean to type boolean

From type Byte to type byte

From type Short to type short

From type Character to type char

From type Integer to type int

From type Long to type long

From type Float to type float

From type Double to type double

At run time, unboxing conversion proceeds as follows:

If r is a reference of type Boolean , then unboxing conversion converts r into r .booleanValue()

If r is a reference of type Byte , then unboxing conversion converts r into r .byteValue()

If r is a reference of type Character , then unboxing conversion converts r into r .charValue()

If r is a reference of type Short , then unboxing conversion converts r into r .shortValue()

If r is a reference of type Integer , then unboxing conversion converts r into r .intValue()

If r is a reference of type Long , then unboxing conversion converts r into r .longValue()

If r is a reference of type Float , unboxing conversion converts r into r .floatValue()

If r is a reference of type Double , then unboxing conversion converts r into r .doubleValue()

If r is null , unboxing conversion throws a NullPointerException

A type is said to be *convertible to a numeric type* if it is a numeric type (§4.2), or it is a reference type that may be converted to a numeric type by unboxing conversion.

A type is said to be *convertible to an integral type* if it is an integral type, or it is a reference type that may be converted to an integral type by unboxing conversion.

### 5.1.9. Unchecked Conversion

Let G name a generic type declaration with *n* type parameters.

There is an *unchecked conversion* from the raw class or interface type (§4.8) G to any parameterized type of the form G T_{1} . T_{n} > .

There is an *unchecked conversion* from the raw array type G [] to any array type type of the form G T_{1} . T_{n} > [] .

Use of an unchecked conversion causes a compile-time *unchecked warning* unless G . > is a parameterized type in which all type arguments are unbounded wildcards (§4.5.1), or the unchecked warning is suppressed by the SuppressWarnings annotation (§9.6.3.5).

Unchecked conversion is used to enable a smooth interoperation of legacy code, written before the introduction of generic types, with libraries that have undergone a conversion to use genericity (a process we call generification). In such circumstances (most notably, clients of the Collections Framework in java.util ), legacy code uses raw types (e.g. Collection instead of Collection ). Expressions of raw types are passed as arguments to library methods that use parameterized versions of those same types as the types of their corresponding formal parameters.

Such calls cannot be shown to be statically safe under the type system using generics. Rejecting such calls would invalidate large bodies of existing code, and prevent them from using newer versions of the libraries. This in turn, would discourage library vendors from taking advantage of genericity. To prevent such an unwelcome turn of events, a raw type may be converted to an arbitrary invocation of the generic type declaration to which the raw type refers. While the conversion is unsound, it is tolerated as a concession to practicality. An unchecked warning is issued in such cases.

### 5.1.10. Capture Conversion

Let G name a generic type declaration (§8.1.2, §9.1.2) with *n* type parameters A_{1} . A_{n} with corresponding bounds U_{1} . U_{n} .

There exists a *capture conversion* from a parameterized type G T_{1} . T_{n} > (§4.5) to a parameterized type G S_{1} . S_{n} > , where, for 1 ≤ *i* ≤ *n* :

If T_{i} is a wildcard type argument (§4.5.1) of the form ? , then S_{i} is a fresh type variable whose upper bound is U_{i} [ A_{1} := S_{1} . A_{n} := S_{n} ] and whose lower bound is the null type (§4.1).

If T_{i} is a wildcard type argument of the form ? extends B_{i} , then S_{i} is a fresh type variable whose upper bound is glb( B_{i} , U_{i} [ A_{1} := S_{1} . A_{n} := S_{n} ] ) and whose lower bound is the null type.

It is a compile-time error if, for any two classes (not interfaces) V_{i} and V_{j} , V_{i} is not a subclass of V_{j} or vice versa.

If T_{i} is a wildcard type argument of the form ? super B_{i} , then S_{i} is a fresh type variable whose upper bound is U_{i} [ A_{1} := S_{1} . A_{n} := S_{n} ] and whose lower bound is B_{i} .

Capture conversion on any type other than a parameterized type (§4.5) acts as an identity conversion (§5.1.1).

Capture conversion is not applied recursively.

Capture conversion never requires a special action at run time and therefore never throws an exception at run time.

Capture conversion is designed to make wildcards more useful. To understand the motivation, let’s begin by looking at the method java.util.Collections.reverse() :

The method reverses the list provided as a parameter. It works for any type of list, and so the use of the wildcard type List as the type of the formal parameter is entirely appropriate.

Now consider how one would implement reverse() :

The implementation needs to copy the list, extract elements from the copy, and insert them into the original. To do this in a type-safe manner, we need to give a name, T , to the element type of the incoming list. We do this in the private service method rev() . This requires us to pass the incoming argument list, of type List , as an argument to rev() . In general, List is a list of unknown type. It is not a subtype of List , for any type T . Allowing such a subtype relation would be unsound. Given the method:

the following code would undermine the type system:

So, without some special dispensation, we can see that the call from reverse() to rev() would be disallowed. If this were the case, the author of reverse() would be forced to write its signature as:

This is undesirable, as it exposes implementation information to the caller. Worse, the designer of an API might reason that the signature using a wildcard is what the callers of the API require, and only later realize that a type safe implementation was precluded.

The call from reverse() to rev() is in fact harmless, but it cannot be justified on the basis of a general subtyping relation between List and List . The call is harmless, because the incoming argument is doubtless a list of some type (albeit an unknown one). If we can capture this unknown type in a type variable X , we can infer T to be X . That is the essence of capture conversion. The specification of course must cope with complications, like non-trivial (and possibly recursively defined) upper or lower bounds, the presence of multiple arguments etc.

Mathematically sophisticated readers will want to relate capture conversion to established type theory. Readers unfamiliar with type theory can skip this discussion — or else study a suitable text, such as Types and Programming Languages by Benjamin Pierce, and then revisit this section.

Here then is a brief summary of the relationship of capture conversion to established type theoretical notions. Wildcard types are a restricted form of existential types. Capture conversion corresponds loosely to an opening of a value of existential type. A capture conversion of an expression e can be thought of as an open of e in a scope that comprises the top level expression that encloses e .

The classical open operation on existentials requires that the captured type variable must not escape the opened expression. The open that corresponds to capture conversion is always on a scope sufficiently large that the captured type variable can never be visible outside that scope. The advantage of this scheme is that there is no need for a close operation, as defined in the paper On Variance-Based Subtyping for Parametric Types by Atsushi Igarashi and Mirko Viroli, in the proceedings of the 16th European Conference on Object Oriented Programming (ECOOP 2002). For a formal account of wildcards, see Wild FJ by Mads Torgersen, Erik Ernst and Christian Plesner Hansen, in the 12th workshop on Foundations of Object Oriented Programming (FOOL 2005).

### 5.1.11. String Conversion

Any type may be converted to type String by *string conversion* .

A value x of primitive type T is first converted to a reference value as if by giving it as an argument to an appropriate class instance creation expression (§15.9):

If T is boolean , then use new Boolean( x ) .

If T is char , then use new Character( x ) .

If T is byte , short , or int , then use new Integer( x ) .

If T is long , then use new Long( x ) .

If T is float , then use new Float( x ) .

If T is double , then use new Double( x ) .

This reference value is then converted to type String by string conversion.

Now only reference values need to be considered:

If the reference is null , it is converted to the string » null » (four ASCII characters n , u , l , l ).

Otherwise, the conversion is performed as if by an invocation of the toString method of the referenced object with no arguments; but if the result of invoking the toString method is null , then the string » null » is used instead.

The toString method is defined by the primordial class Object (§4.3.2). Many classes override it, notably Boolean , Character , Integer , Long , Float , Double , and String .

See §5.4 for details of the string conversion context.

### 5.1.12. Forbidden Conversions

Any conversion that is not explicitly allowed is forbidden.

### 5.1.13. Value Set Conversion

*Value set conversion* is the process of mapping a floating-point value from one value set to another without changing its type.

Within an expression that is not FP-strict (§15.4), value set conversion provides choices to an implementation of the Java programming language:

If the value is an element of the float-extended-exponent value set, then the implementation may, at its option, map the value to the nearest element of the float value set. This conversion may result in overflow (in which case the value is replaced by an infinity of the same sign) or underflow (in which case the value may lose precision because it is replaced by a denormalized number or zero of the same sign).

If the value is an element of the double-extended-exponent value set, then the implementation may, at its option, map the value to the nearest element of the double value set. This conversion may result in overflow (in which case the value is replaced by an infinity of the same sign) or underflow (in which case the value may lose precision because it is replaced by a denormalized number or zero of the same sign).

Within an FP-strict expression (§15.4), value set conversion does not provide any choices; every implementation must behave in the same way:

If the value is of type float and is not an element of the float value set, then the implementation must map the value to the nearest element of the float value set. This conversion may result in overflow or underflow.

If the value is of type double and is not an element of the double value set, then the implementation must map the value to the nearest element of the double value set. This conversion may result in overflow or underflow.

Within an FP-strict expression, mapping values from the float-extended-exponent value set or double-extended-exponent value set is necessary only when a method is invoked whose declaration is not FP-strict and the implementation has chosen to represent the result of the method invocation as an element of an extended-exponent value set.

Whether in FP-strict code or code that is not FP-strict, value set conversion always leaves unchanged any value whose type is neither float nor double .

## 5.2. Assignment Conversion

*Assignment conversion* occurs when the value of an expression is assigned (§15.26) to a variable: the type of the expression must be converted to the type of the variable.

Assignment contexts allow the use of one of the following:

an identity conversion (§5.1.1)

a widening primitive conversion (§5.1.2)

a widening reference conversion (§5.1.5)

a boxing conversion (§5.1.7) optionally followed by a widening reference conversion

an unboxing conversion (§5.1.8) optionally followed by a widening primitive conversion.

If, after the conversions listed above have been applied, the resulting type is a raw type (§4.8), unchecked conversion (§5.1.9) may then be applied.

It is a compile-time error if the chain of conversions contains two parameterized types that are not in the subtype relation.

An example of such an illegal chain would be:

The first three elements of the chain are related by widening reference conversion, while the last entry is derived from its predecessor by unchecked conversion. However, this is not a valid assignment conversion, because the chain contains two parameterized types, Comparable and Comparable , that are not subtypes.

In addition, if the expression is a constant expression (§15.28) of type byte , short , char , or int :

A narrowing primitive conversion may be used if the type of the variable is byte , short , or char , and the value of the constant expression is representable in the type of the variable.

A narrowing primitive conversion followed by a boxing conversion may be used if the type of the variable is:

Byte and the value of the constant expression is representable in the type byte .

Short and the value of the constant expression is representable in the type short .

Character and the value of the constant expression is representable in the type char .

The compile-time narrowing of constants means that code such as:

is allowed. Without the narrowing, the fact that the integer literal 42 has type int would mean that a cast to byte would be required:

A value of the null type (the null reference is the only such value) may be assigned to any reference type, resulting in a null reference of that type.

If the type of the expression cannot be converted to the type of the variable by a conversion permitted in an assignment context, then a compile-time error occurs.

If the type of an expression can be converted to the type of a variable by assignment conversion, we say the expression (or its value) is *assignable to* the variable or, equivalently, that the type of the expression is *assignment compatible with* the type of the variable.

If the type of the variable is float or double , then value set conversion (§5.1.13) is applied to the value *v* that is the result of the type conversion:

If *v* is of type float and is an element of the float-extended-exponent value set, then the implementation must map *v* to the nearest element of the float value set. This conversion may result in overflow or underflow.

If *v* is of type double and is an element of the double-extended-exponent value set, then the implementation must map *v* to the nearest element of the double value set. This conversion may result in overflow or underflow.

The only exceptions that an assignment conversion may cause are:

A ClassCastException if, after the type conversions above have been applied, the resulting value is an object which is not an instance of a subclass or subinterface of the erasure (§4.6) of the type of the variable.

This circumstance can only arise as a result of heap pollution (§4.12.2). In practice, implementations need only perform casts when accessing a field or method of an object of parametized type, when the erased type of the field, or the erased result type of the method differ from their unerased type.

An OutOfMemoryError as a result of a boxing conversion.

A NullPointerException as a result of an unboxing conversion on a null reference.

An ArrayStoreException in special cases involving array elements or field access (§10.5, §15.26.1).

**Example 5.2-1. Assignment Conversion for Primitive Types**

This program produces the output:

The following program, however, produces compile-time errors:

because not all short values are char values, and neither are all char values short values.

**Example 5.2-2. Assignment Conversion for Reference Types**

The following test program illustrates assignment conversions on reference values, but fails to compile, as described in its comments. This example should be compared to the preceding one.

**Example 5.2-3. Assignment Conversion for Array Types**

In this example:

The value of veclong cannot be assigned to a Long variable, because Long is a class type other than Object . An array can be assigned only to a variable of a compatible array type, or to a variable of type Object , Cloneable or java.io.Serializable .

The value of veclong cannot be assigned to vecshort , because they are arrays of primitive type, and short and long are not the same primitive type.

The value of cpvec can be assigned to pvec , because any reference that could be the value of an expression of type ColoredPoint can be the value of a variable of type Point . The subsequent assignment of the new Point to a component of pvec then would throw an ArrayStoreException (if the program were otherwise corrected so that it could be compiled), because a ColoredPoint array cannot have an instance of Point as the value of a component.

The value of pvec cannot be assigned to cpvec , because not every reference that could be the value of an expression of type ColoredPoint can correctly be the value of a variable of type Point . If the value of pvec at run time were a reference to an instance of Point[] , and the assignment to cpvec were allowed, a simple reference to a component of cpvec , say, cpvec[0] , could return a Point , and a Point is not a ColoredPoint . Thus to allow such an assignment would allow a violation of the type system. A cast may be used (§5.5, §15.16) to ensure that pvec references a ColoredPoint[] :

## 5.3. Method Invocation Conversion

*Method invocation conversion* is applied to each argument value in a method or constructor invocation (§8.8.7.1, §15.9, §15.12): the type of the argument expression must be converted to the type of the corresponding parameter.

Method invocation contexts allow the use of one of the following:

an identity conversion (§5.1.1)

a widening primitive conversion (§5.1.2)

a widening reference conversion (§5.1.5)

a boxing conversion (§5.1.7) optionally followed by widening reference conversion

an unboxing conversion (§5.1.8) optionally followed by a widening primitive conversion.

If, after the conversions listed above have been applied, the resulting type is a raw type (§4.8), an unchecked conversion (§5.1.9) may then be applied.

It is a compile-time error if the chain of conversions contains two parameterized types that are not in the subtype relation.

A value of the null type (the null reference is the only such value) may be converted to any reference type.

If the type of the expression cannot be converted to the type of the parameter by a conversion permitted in a method invocation context, then a compile-time error occurs.

If the type of an argument expression is either float or double , then value set conversion (§5.1.13) is applied after the type conversion:

If an argument value of type float is an element of the float-extended-exponent value set, then the implementation must map the value to the nearest element of the float value set. This conversion may result in overflow or underflow.

If an argument value of type double is an element of the double-extended-exponent value set, then the implementation must map the value to the nearest element of the double value set. This conversion may result in overflow or underflow.

The only exceptions that an method invocation conversion may cause are:

A ClassCastException if, after the type conversions above have been applied, the resulting value is an object which is not an instance of a subclass or subinterface of the erasure (§4.6) of the corresponding formal parameter type.

This circumstance can only arise as a result of heap pollution (§4.12.2).

An OutOfMemoryError as a result of a boxing conversion.

A NullPointerException as a result of an unboxing conversion on a null reference.

Method invocation conversions specifically do not include the implicit narrowing of integer constants which is part of assignment conversion (§5.2). The designers of the Java programming language felt that including these implicit narrowing conversions would add additional complexity to the overloaded method matching resolution process (§15.12.2).

Thus, the program:

causes a compile-time error because the integer literals 12 and 2 have type int , so neither method m matches under the rules of (§15.12.2). A language that included implicit narrowing of integer constants would need additional rules to resolve cases like this example.

## 5.4. String Conversion

String conversion applies only to an operand of the binary + operator which is not a String when the other operand is a String .

In this single special case, the non- String operand to the + is converted to a String (§5.1.11) and evaluation of the + operator proceeds as specified in §15.18.1.

## 5.5. Casting Conversion

*Casting conversion* is applied to the operand of a cast operator (§15.16): the type of the operand expression must be converted to the type explicitly named by the cast operator.

Casting contexts allow the use of one of:

an identity conversion (§5.1.1)

a widening primitive conversion (§5.1.2)

a narrowing primitive conversion (§5.1.3)

a widening and narrowing primitive conversion (§5.1.4)

a widening reference conversion (§5.1.5) optionally followed by either an unboxing conversion (§5.1.8) or an unchecked conversion (§5.1.9)

a narrowing reference conversion (§5.1.6) optionally followed by either an unboxing conversion (§5.1.8) or an unchecked conversion (§5.1.9)

a boxing conversion (§5.1.7) optionally followed by a widening reference conversion (§5.1.5)

an unboxing conversion (§5.1.8) optionally followed by a widening primitive conversion (§5.1.2).

Value set conversion (§5.1.13) is applied after the type conversion.

The compile-time legality of a casting conversion is as follows:

An expression of a primitive type may undergo casting conversion to another primitive type, by an identity conversion (if the types are the same), or by a widening primitive conversion, or by a narrowing primitive conversion, or by a widening and narrowing primitive conversion.

An expression of a primitive type may undergo casting conversion to a reference type without error, by boxing conversion.

An expression of a reference type may undergo casting conversion to a primitive type without error, by unboxing conversion.

An expression of a reference type may undergo casting conversion to another reference type if no compile-time error occurs given the rules in §5.5.1.

The following tables enumerate which conversions are used in certain casting conversions. Each conversion is signified by a symbol:

— signifies no casting conversion allowed

≈ signifies identity conversion (§5.1.1)

ω signifies widening primitive conversion (§5.1.2)

η signifies narrowing primitive conversion (§5.1.3)

ωη signifies widening and narrowing primitive conversion (§5.1.4)

⇑ signifies widening reference conversion (§5.1.5)

⇓ signifies narrowing reference conversion (§5.1.6)

⊡ signifies boxing conversion (§5.1.7)

⊔ signifies unboxing conversion (§5.1.8)

In the tables, a comma between symbols indicates that a casting conversion uses one conversion followed by another. The type Object means any reference type other than the eight wrapper classes Boolean , Byte , Short , Character , Integer , Long , Float , Double .

**Table 5.1. Casting conversions to primitive types**

To → | byte | short | char | int | long | float | double | boolean |
---|---|---|---|---|---|---|---|---|

From ↓ | ||||||||

byte | ≈ | ω | ωη | ω | ω | ω | ω | — |

short | η | ≈ | η | ω | ω | ω | ω | — |

char | η | η | ≈ | ω | ω | ω | ω | — |

int | η | η | η | ≈ | ω | ω | ω | — |

long | η | η | η | η | ≈ | ω | ω | — |

float | η | η | η | η | η | ≈ | ω | — |

double | η | η | η | η | η | η | ≈ | — |

boolean | — | — | — | — | — | — | — | ≈ |

Byte | ⊔ | ⊔,ω | — | ⊔,ω | ⊔,ω | ⊔,ω | ⊔,ω | — |

Short | — | ⊔ | — | ⊔,ω | ⊔,ω | ⊔,ω | ⊔,ω | — |

Character | — | — | ⊔ | ⊔,ω | ⊔,ω | ⊔,ω | ⊔,ω | — |

Integer | — | — | — | ⊔ | ⊔,ω | ⊔,ω | ⊔,ω | — |

Long | — | — | — | — | ⊔ | ⊔,ω | ⊔,ω | — |

Float | — | — | — | — | — | ⊔ | ⊔,ω | — |

Double | — | — | — | — | — | — | ⊔ | — |

Boolean | — | — | — | — | — | — | — | ⊔ |

Object | ⇓,⊔ | ⇓,⊔ | ⇓,⊔ | ⇓,⊔ | ⇓,⊔ | ⇓,⊔ | ⇓,⊔ | ⇓,⊔ |

**Table 5.2. Casting conversions to reference types**

To → | Byte | Short | Character | Integer | Long | Float | Double | Boolean | Object |
---|---|---|---|---|---|---|---|---|---|

From ↓ | |||||||||

byte | ⊡ | — | — | — | — | — | — | — | ⊡,⇑ |

short | — | ⊡ | — | — | — | — | — | — | ⊡,⇑ |

char | — | — | ⊡ | — | — | — | — | — | ⊡,⇑ |

int | — | — | — | ⊡ | — | — | — | — | ⊡,⇑ |

long | — | — | — | — | ⊡ | — | — | — | ⊡,⇑ |

float | — | — | — | — | — | ⊡ | — | — | ⊡,⇑ |

double | — | — | — | — | — | — | ⊡ | — | ⊡,⇑ |

boolean | — | — | — | — | — | — | — | ⊡ | ⊡,⇑ |

Byte | ≈ | — | — | — | — | — | — | — | ⇑ |

Short | — | ≈ | — | — | — | — | — | — | ⇑ |

Character | — | — | ≈ | — | — | — | — | — | ⇑ |

Integer | — | — | — | ≈ | — | — | — | — | ⇑ |

Long | — | — | — | — | ≈ | — | — | — | ⇑ |

Float | — | — | — | — | — | ≈ | — | — | ⇑ |

Double | — | — | — | — | — | — | ≈ | — | ⇑ |

Boolean | — | — | — | — | — | — | — | ≈ | ⇑ |

Object | ⇓ | ⇓ | ⇓ | ⇓ | ⇓ | ⇓ | ⇓ | ⇓ | ≈ |

### 5.5.1. Reference Type Casting

Given a compile-time reference type S (source) and a compile-time reference type T (target), a casting conversion exists from S to T if no compile-time errors occur due to the following rules.

If S is a class type:

If T is a class type, then either | S | | T |, or | T | | S |. Otherwise, a compile-time error occurs.

Furthermore, if there exists a supertype X of T , and a supertype Y of S , such that both X and Y are provably distinct parameterized types (§4.5), and that the erasures of X and Y are the same, a compile-time error occurs.

If T is an interface type:

If S is not a final class (§8.1.1), then, if there exists a supertype X of T , and a supertype Y of S , such that both X and Y are provably distinct parameterized types, and that the erasures of X and Y are the same, a compile-time error occurs.

Otherwise, the cast is always legal at compile time (because even if S does not implement T , a subclass of S might).

If S is a final class (§8.1.1), then S must implement T , or a compile-time error occurs.

If T is a type variable, then this algorithm is applied recursively, using the upper bound of T in place of T .

If T is an array type, then S must be the class Object , or a compile-time error occurs.

If S is an interface type:

If T is an array type, then S must be the type java.io.Serializable or Cloneable (the only interfaces implemented by arrays), or a compile-time error occurs.

If T is a type that is not final (§8.1.1), then if there exists a supertype X of T , and a supertype Y of S , such that both X and Y are provably distinct parameterized types, and that the erasures of X and Y are the same, a compile-time error occurs.

Otherwise, the cast is always legal at compile time (because even if T does not implement S , a subclass of T might).

If T is a type that is final , then:

If S is not a parameterized type or a raw type, then T must implement S , or a compile-time error occurs.

Otherwise, S is either a parameterized type that is an invocation of some generic type declaration G , or a raw type corresponding to a generic type declaration G . Then there must exist a supertype X of T , such that X is an invocation of G , or a compile-time error occurs.

Furthermore, if S and X are provably distinct parameterized types then a compile-time error occurs.

If S is a type variable, then this algorithm is applied recursively, using the upper bound of S in place of S .

If S is an intersection type A_{1} & . & A_{n} , then it is a compile-time error if there exists an A_{i} (1 ≤ *i* ≤ *n* ) such that S cannot be cast to A_{i} by this algorithm. That is, the success of the cast is determined by the most restrictive component of the intersection type.

If S is an array type SC [] , that is, an array of components of type SC :

If T is a class type, then if T is not Object , then a compile-time error occurs (because Object is the only class type to which arrays can be assigned).

If T is an interface type, then a compile-time error occurs unless T is the type java.io.Serializable or the type Cloneable (the only interfaces implemented by arrays).

If T is a type variable, then:

If the upper bound of T is Object or java.io.Serializable or Cloneable , or a type variable that S could undergo casting conversion to, then the cast is legal (though unchecked).

If the upper bound of T is an array type TC [] , then a compile-time error occurs unless the type SC [] can undergo casting conversion to TC [] .

Otherwise, a compile-time error occurs.

If T is an array type TC [] , that is, an array of components of type TC , then a compile-time error occurs unless one of the following is true:

TC and SC are the same primitive type.

TC and SC are reference types and type SC can undergo casting conversion to TC .

**Example 5.5.1-1. Casting Conversion for Reference Types**

Here, the first compile-time error occurs because the class types Long and Point are unrelated (that is, they are not the same, and neither is a subclass of the other), so a cast between them will always fail.

The second compile-time error occurs because a variable of type EndPoint can never reference a value that implements the interface Colorable . This is because EndPoint is a final type, and a variable of a final type always holds a value of the same run-time type as its compile-time type. Therefore, the run-time type of variable e must be exactly the type EndPoint , and type EndPoint does not implement Colorable .

**Example 5.5.1-2. Casting Conversion for Array Types**

This program compiles without errors and produces the output:

### 5.5.2. Checked Casts and Unchecked Casts

A cast from a type S to a type T is *statically known to be correct* if and only if S T (§4.10).

A cast from a type S to a parameterized type (§4.5) T is *unchecked* unless at least one of the following conditions holds:

All of the type arguments (§4.5.1) of T are unbounded wildcards

T S and S has no subtype X other than T where the type arguments of X are not contained in the type arguments of T .

A cast from a type S to a type variable T is unchecked unless S T .

An unchecked cast from S to T is *completely unchecked* if the cast from | S | to | T | is statically known to be correct. Otherwise, it is *partially unchecked* .

An unchecked cast causes a compile-time unchecked warning, unless suppressed by the SuppressWarnings annotation (§9.6.3.5).

A cast is *checked* if it is not statically known to be correct and it is not unchecked.

If a cast to a reference type is not a compile-time error, there are several cases:

The cast is statically known to be correct.

No run-time action is performed for such a cast.

The cast is a completely unchecked cast.

No run-time action is performed for such a cast.

The cast is a partially unchecked cast.

Such a cast requires a run-time validity check. The check is performed as if the cast had been a checked cast between | S | and | T |, as described below.

The cast is a checked cast.

Such a cast requires a run-time validity check. If the value at run time is null , then the cast is allowed. Otherwise, let R be the class of the object referred to by the run-time reference value, and let T be the erasure (§4.6) of the type named in the cast operator. A cast conversion must check, at run time, that the class R is assignment compatible with the type T , via the algorithm in §5.5.3.

Note that R cannot be an interface when these rules are first applied for any given cast, but R may be an interface if the rules are applied recursively because the run-time reference value may refer to an array whose element type is an interface type.

### 5.5.3. Checked Casts at Run Time

Here is the algorithm to check whether the run-time type R of an object is assignment compatible with the type T which is the erasure (§4.6) of the type named in the cast operator. If a run-time exception is thrown, it is a ClassCastException .

If R is an ordinary class (not an array class):

If T is a class type, then R must be either the same class (§4.3.4) as T or a subclass of T , or a run-time exception is thrown.

If T is an interface type, then R must implement (§8.1.5) interface T , or a run-time exception is thrown.

If T is an array type, then a run-time exception is thrown.

If R is an interface:

If T is a class type, then T must be Object (§4.3.2), or a run-time exception is thrown.

If T is an interface type, then R must be either the same interface as T or a subinterface of T , or a run-time exception is thrown.

If T is an array type, then a run-time exception is thrown.

If R is a class representing an array type RC [] , that is, an array of components of type RC :

If T is a class type, then T must be Object (§4.3.2), or a run-time exception is thrown.

If T is an interface type, then a run-time exception is thrown unless T is the type java.io.Serializable or the type Cloneable (the only interfaces implemented by arrays).

This case could slip past the compile-time checking if, for example, a reference to an array were stored in a variable of type Object .

If T is an array type TC [] , that is, an array of components of type TC , then a run-time exception is thrown unless one of the following is true:

TC and RC are the same primitive type.

TC and RC are reference types and type RC can be cast to TC by a recursive application of these run-time rules for casting.

**Example 5.5.3-1. Incompatible Types at Run Time**

This program uses casts to compile, but it throws exceptions at run time, because the types are incompatible.

## 5.6. Numeric Promotions

*Numeric promotion* is applied to the operands of an arithmetic operator.

Numeric promotion contexts allow the use of:

an identity conversion (§5.1.1)

a widening primitive conversion (§5.1.2)

an unboxing conversion (§5.1.8)

Numeric promotions are used to convert the operands of a numeric operator to a common type so that an operation can be performed. The two kinds of numeric promotion are unary numeric promotion (§5.6.1) and binary numeric promotion (§5.6.2).

### 5.6.1. Unary Numeric Promotion

Some operators apply *unary numeric promotion* to a single operand, which must produce a value of a numeric type:

If the operand is of compile-time type Byte , Short , Character , or Integer , it is subjected to unboxing conversion (§5.1.8). The result is then promoted to a value of type int by a widening primitive conversion (§5.1.2) or an identity conversion (§5.1.1).

Otherwise, if the operand is of compile-time type Long , Float , or Double , it is subjected to unboxing conversion (§5.1.8).

Otherwise, if the operand is of compile-time type byte , short , or char , it is promoted to a value of type int by a widening primitive conversion (§5.1.2).

Otherwise, a unary numeric operand remains as is and is not converted.

In any case, value set conversion (§5.1.13) is then applied.

Unary numeric promotion is performed on expressions in the following situations:

Each dimension expression in an array creation expression (§15.10)

The index expression in an array access expression (§15.13)

The operand of a unary plus operator + (§15.15.3)

The operand of a unary minus operator — (§15.15.4)

The operand of a bitwise complement operator

Each operand, separately, of a shift operator >> , >>> , or (§15.19).

A long shift distance (right operand) does not promote the value being shifted (left operand) to long .

**Example 5.6.1-1. Unary Numeric Promotion**

This program produces the output:

### 5.6.2. Binary Numeric Promotion

When an operator applies *binary numeric promotion* to a pair of operands, each of which must denote a value that is convertible to a numeric type, the following rules apply, in order:

If any operand is of a reference type, it is subjected to unboxing conversion (§5.1.8).

Widening primitive conversion (§5.1.2) is applied to convert either or both operands as specified by the following rules:

If either operand is of type double , the other is converted to double .

Otherwise, if either operand is of type float , the other is converted to float .

Otherwise, if either operand is of type long , the other is converted to long .

Otherwise, both operands are converted to type int .

After the type conversion, if any, value set conversion (§5.1.13) is applied to each operand.

Binary numeric promotion is performed on the operands of certain operators:

The multiplicative operators * , / and % (§15.17)

The addition and subtraction operators for numeric types + and — (§15.18.2)

The numerical comparison operators , , > , and >= (, and >=»>§15.20.1)

The numerical equality operators == and != (§15.21.1)

The integer bitwise operators & , ^ , and | (§15.22.1)

In certain cases, the conditional operator ? : (§15.25)

**Example 5.6.2-1. Binary Numeric Promotion**

This program produces the output:

The example converts the ASCII character G to the ASCII control-G (BEL), by masking off all but the low 5 bits of the character. The 7 is the numeric value of this control character.