TypesTypes

Antonio CisterninoAntonio Cisternino

Giuseppe AttardiGiuseppe Attardi

Università di PisaUniversità di Pisa

TypesTypes

Computer hardware is capable of Computer hardware is capable of interpreting bits in memory in several interpreting bits in memory in several different waysdifferent ways

A type limits the set of operations that A type limits the set of operations that may be performed on a value belonging to may be performed on a value belonging to that typethat type

The hardware usually doesn’t enforce the The hardware usually doesn’t enforce the notion of type, though it provides notion of type, though it provides operations for numbers and pointersoperations for numbers and pointers

Programming languages tend to associate Programming languages tend to associate types to values to enforce error-checkingtypes to values to enforce error-checking

Type SystemType System

A type system consists of:A type system consists of:– A mechanism for defining types and

associating them with certain language constructs

– A set of rules for:• type equivalence: two values are the same• type compatibility: a value of a given type can

be used in a given context• type inference: type of an expression given the

type of its constituents

Type checkingType checking

Type checkingType checking is the process of ensuring is the process of ensuring that a program obeys the language’s type that a program obeys the language’s type compatibility rulescompatibility rules

A language is A language is strongly typedstrongly typed (or (or type safetype safe) if ) if it prohibits, in a way that the language it prohibits, in a way that the language implementation can enforce, performing an implementation can enforce, performing an operation on an object that does not support operation on an object that does not support itit

A language is A language is statically typedstatically typed if it is if it is strongly strongly typedtyped and type checking can be performed at and type checking can be performed at compile timecompile time

Programming Languages and type checkingProgramming Languages and type checking

AssemblyAssembly CC PascalPascal C++C++ JavaJava LispLisp PrologProlog MLML

No type checking

Static type checkingNot entirely strongly typed (union, interoperability of pointers and arrays)

Static type checkingNot entirely strongly typed (untagged variant records)

Static type checkingNot entirely strongly typed (as C)Dynamic type checking (virtual methods)

Static type checkingDynamic type checking (virtual methods, upcasting) Strongly typedDynamic type checking Strongly typedDynamic type checking

Strongly typedStatic type checking Strongly typed

Different views for typesDifferent views for types

Denotational:Denotational:– types are set of values (domains)– Application: semantics

Constructive:Constructive:– Built-in types– Composite types (application of type

constructors)

Abstraction-based:Abstraction-based:– Type is an interface consisting of a set of

operations

Language typesLanguage types

booleanboolean int, long, float, double (signed/unsigned)int, long, float, double (signed/unsigned) character (1 byte, 2 bytes)character (1 byte, 2 bytes) EnumerationEnumeration Subrange (Subrange (nn11....nn22)) Composite types:Composite types:

– struct– union– arrays– pointers– list

Type Conversions and Type Conversions and CastsCastsConsider the following definition:Consider the following definition:

int add(int i, int j);

int add2(int i, double j);

And the following calls:And the following calls:add(2, 3); // Exact

add(2, (int)3.0); // Explicit cast

add2(2, 3); // Implicit cast

Memory LayoutMemory Layout

Primitive types on 32 bits Primitive types on 32 bits architectures require from 1 to 8 architectures require from 1 to 8 bytesbytes

Composite types are represented by Composite types are represented by chaining constituent values togetherchaining constituent values together

For performance reasons often For performance reasons often compilers employ padding to align compilers employ padding to align fields to multiple of 4 bytes fields to multiple of 4 bytes addressesaddresses

Memory layout exampleMemory layout example

struct element {struct element {

char name[2];char name[2];

int atomic_number;int atomic_number;

double atomic_weight;double atomic_weight;

char metallic;char metallic;

};};

4 bytes/32 bits

name

atomic_number

atomic_weight

metallic

Optimizing Memory LayoutOptimizing Memory Layout

C requires that fields of struct be placed in C requires that fields of struct be placed in the same order of the declaration the same order of the declaration (essential for working with pointers!)(essential for working with pointers!)

Not all languages behaves like this: for Not all languages behaves like this: for instance ML doesn’t specify any orderinstance ML doesn’t specify any order

If the compiler is free of reorganizing If the compiler is free of reorganizing fields holes can be minimized (in the fields holes can be minimized (in the example by packing example by packing metallicmetallic with with name name saving 4 bytes)saving 4 bytes)

4 bytes/32 bits

name

atomic_number

atomic_weight

metallic

UnionUnion

Union types allow sharing the same memory Union types allow sharing the same memory area among different typesarea among different types

The size of the value is the maximum of the The size of the value is the maximum of the constituentsconstituents

4 bytes/32 bits

numberunion u { struct element e; int number;};

Abstract Data TypesAbstract Data Types

According to the abstraction-based view According to the abstraction-based view of types a type is an interfaceof types a type is an interface

An ADT defines a set of values and the An ADT defines a set of values and the operations allowed on itoperations allowed on it

In their evolution programming languages In their evolution programming languages have included mechanisms to define ADThave included mechanisms to define ADT

Definition of an ADT requires the ability of Definition of an ADT requires the ability of incapsulating values and operationsincapsulating values and operations

Example: a C listExample: a C list

struct node {struct node { int val;int val; struct list *next;struct list *next;};};struct node* next(struct node* l) { return l->next; }struct node* next(struct node* l) { return l->next; }struct node* initNode(struct node* l, int v) {struct node* initNode(struct node* l, int v) { l->val = v; l->next = NULL; return l;l->val = v; l->next = NULL; return l;}}void append(struct node* l, int v) {void append(struct node* l, int v) { struct node p = l;struct node p = l; while (p->next) p = p->next;while (p->next) p = p->next; p->next = p->next = initNode((struct node)malloc(sizeof(struct node)), initNode((struct node)malloc(sizeof(struct node)),

v);v);}}

ADT, Modules and ClassesADT, Modules and Classes

C doesn’t provide any mechanism to hide C doesn’t provide any mechanism to hide the structure of data typesthe structure of data types

A program can access the A program can access the nextnext pointer pointer without using the without using the nextnext function function

The notion of module has been introduced The notion of module has been introduced to define data types and restrict the to define data types and restrict the access to their definitionaccess to their definition

An evolution of module is the class: An evolution of module is the class: values and operations are tied together values and operations are tied together (with the addition of inheritance)(with the addition of inheritance)

Class typeClass type

Class is a Class is a type constructortype constructor like struct and like struct and arrayarray

A class combines other types like structsA class combines other types like structs Class definition contains also methods Class definition contains also methods

which are the operations allowed on the which are the operations allowed on the datadata

The The inheritance inheritance relation is introducedrelation is introduced Two special operations provide control Two special operations provide control

over initialization and finalization of over initialization and finalization of objectsobjects

The Node Type in JavaThe Node Type in Java

class Node {class Node { int val;int val; Node m_next;Node m_next; Node(int v) { val = v; }Node(int v) { val = v; } Node next() { return m_next; }Node next() { return m_next; } void append(int v) {void append(int v) { Node n = this;Node n = this; while (n.m_next != null) n = n.m_next;while (n.m_next != null) n = n.m_next; n.m_next = new Node(v);n.m_next = new Node(v); }}} }

InheritanceInheritance

If the class If the class AA inherits from class inherits from class BB ((A<:BA<:B) when an object of class ) when an object of class BB is is expected an object of class expected an object of class AA can be can be used insteadused instead

Inheritance expresses the idea of Inheritance expresses the idea of adding features to an existing type adding features to an existing type (both methods and attributes)(both methods and attributes)

Inheritance can be single or multipleInheritance can be single or multiple

ExampleExample

class A {class A { int i;int i; int j;int j; int foo() { return i + j; }int foo() { return i + j; }}}class B : A {class B : A { int k;int k; int foo() { return k + super.foo(); }int foo() { return k + super.foo(); }}}

QuestionsQuestions

Consider the following:Consider the following:A a = new A();

A b = new B();

Console.WriteLine(a.foo());

Console.WriteLine(b.foo()); Which version of Which version of foofoo is invoked in the is invoked in the

second print?second print? What is the layout of class What is the layout of class BB??

UpcastingUpcasting

Late binding happens because we convert a Late binding happens because we convert a reference to an object of class B into a reference reference to an object of class B into a reference of its super-class A of its super-class A (upcasting(upcasting))::B b = new B();A a = b;

The runtime should not convert the object: only The runtime should not convert the object: only use the part inherited from Ause the part inherited from A

This is different from the following implicit cast This is different from the following implicit cast where the data is modified in the assignment:where the data is modified in the assignment:int i = 10;long l = i;

DowncastingDowncasting

Once we have a reference of the super-Once we have a reference of the super-class we may want to convert it back:class we may want to convert it back:A a = new B();B b = (B)a;

During During downcastdowncast it is necessary to it is necessary to explicitly indicate which class is the explicitly indicate which class is the target: a class may be the ancestor of target: a class may be the ancestor of many sub-classesmany sub-classes

Again this transformation informs the Again this transformation informs the compiler that the referenced object is of compiler that the referenced object is of type B without changing the object in any type B without changing the object in any wayway

Upcasting, downcastingUpcasting, downcasting

We have shown upcasting and downcasting as We have shown upcasting and downcasting as expressed in languages such as C++, C# and expressed in languages such as C++, C# and Java; though the problem is common to OO Java; though the problem is common to OO languageslanguages

Note that the upcast can be verified at compile Note that the upcast can be verified at compile time whereas the downcast cannottime whereas the downcast cannot

Upcasting and downcasting don’t require runtime Upcasting and downcasting don’t require runtime type checking:type checking:– in Java casts are checked at runtime– C++ simply changes the interpretation of an expression

at compile time without any attempt to check it at runtime

Late BindingLate Binding

The output of the example depends on the The output of the example depends on the language: the second output may be the language: the second output may be the result of invoking result of invoking A::foo()A::foo() or or B::foo()B::foo()

In Java the behavior would result in the In Java the behavior would result in the invocation of invocation of B::fooB::foo

In C++ In C++ A::fooA::foo would be invoked would be invoked The mechanism which associates the The mechanism which associates the

method method B::foo()B::foo() to to b.foo()b.foo() is called is called late late bindingbinding

Late BindingLate Binding

In the example the compiler cannot determine In the example the compiler cannot determine statically the exact type of the object referenced by statically the exact type of the object referenced by bb because of upcastingbecause of upcasting

To allow the invocation of the method of the exact To allow the invocation of the method of the exact type rather than the one known at compile time it is type rather than the one known at compile time it is necessary to pay an overhead at runtimenecessary to pay an overhead at runtime

Programming languages allow the programmer to Programming languages allow the programmer to specify whether to apply late binding in a method specify whether to apply late binding in a method invocationinvocation

In Java the keyword In Java the keyword finalfinal is used to indicate that a is used to indicate that a method cannot be overridden in subclasses: thus method cannot be overridden in subclasses: thus the JVM may avoid late bindingthe JVM may avoid late binding

In C++ only methods declared as In C++ only methods declared as virtualvirtual are are considered for late binding considered for late binding

Late BindingLate Binding

With inheritance it is possible to treat objects in a With inheritance it is possible to treat objects in a generic waygeneric way

The benefit is evident: it is possible to write The benefit is evident: it is possible to write generic operations manipulating objects of types generic operations manipulating objects of types inheriting from a common ancestorinheriting from a common ancestor

OOP languages usually support late binding of OOP languages usually support late binding of methods: which method should be invoked is methods: which method should be invoked is determined at runtimedetermined at runtime

This mechanism involves a small runtime This mechanism involves a small runtime overhead: at runtime the type of an object should overhead: at runtime the type of an object should be determined in order to invoke its methodsbe determined in order to invoke its methods

Example (Java)Example (Java)

class A {class A { final void foo() {…}final void foo() {…} void baz() {…}void baz() {…} void bar() {…}void bar() {…}}}class B extends A {class B extends A { // Suppose it’s possible!// Suppose it’s possible! final void foo() {…}final void foo() {…} void bar();void bar();}}

A a = new A();A a = new A();B b = new B();B b = new B();A c = b;A c = b;

a.foo(); a.foo(); // A::foo()// A::foo()a.baz(); a.baz(); // A::baz()// A::baz()a.bar(); a.bar(); // A::bar()// A::bar()b.foo(); b.foo(); // B::foo()// B::foo()b.bar(); b.bar(); // B::bar()// B::bar()c.foo(); c.foo(); // A::foo()// A::foo()c.bar(); c.bar(); // B::bar()// B::bar()

Abstract classesAbstract classes

Sometimes it is necessary to model a set Sometimes it is necessary to model a set SS of of objects which can be partitioned into subsets (objects which can be partitioned into subsets (AA00, … , … AAnn) such that their union covers ) such that their union covers S:S: x S Ai S, x Ai

If we use classes to model each set it is natural thatIf we use classes to model each set it is natural that A S, A<:S

Each object is an instance of a subclass of Each object is an instance of a subclass of SS and no and no object is an instance of object is an instance of SS..

SS is useful because it abstracts the commonalities is useful because it abstracts the commonalities among its subclasses, allowing to express generic among its subclasses, allowing to express generic properties about its objects.properties about its objects.

ExampleExample

We want to manipulate documents with different We want to manipulate documents with different formatsformats

The set of documents can be partitioned by type: The set of documents can be partitioned by type: docdoc, , pdfpdf, , txttxt, and so on, and so on

For each document type we introduce a class that For each document type we introduce a class that inherits from a class inherits from a class DocDoc that represents the that represents the documentdocument

In the class In the class DocDoc we may store common we may store common properties to all documents (title, location, …)properties to all documents (title, location, …)

Each class is responsible for reading the Each class is responsible for reading the document contentdocument content

It doesn’t make sense to have an instance of It doesn’t make sense to have an instance of DocDoc though it is useful to scan a list of documents to though it is useful to scan a list of documents to readread

Abstract methodsAbstract methods

Often when a class is abstract some of its Often when a class is abstract some of its methods could not be definedmethods could not be defined

Consider the method Consider the method read()read() in the in the previous exampleprevious example

In class In class DocDoc there is no reasonable there is no reasonable implementation for itimplementation for it

We leave it We leave it abstractabstract so that through late so that through late binding the appropriate implementation binding the appropriate implementation will be calledwill be called

SyntaxSyntax

Abstract classes can be declared using the Abstract classes can be declared using the abstract abstract keyword in Java or C#:keyword in Java or C#:abstract class Doc { … }

C++ assumes a class is abstract if it contains an C++ assumes a class is abstract if it contains an abstract methodabstract method– it is impossible to instantiate an abstract class, since it will

lack that method A virtual method is abstract in C++ if its definition is A virtual method is abstract in C++ if its definition is

empty:empty:virtual string Read() = 0;

In Java and C# abstract methods are annotated with In Java and C# abstract methods are annotated with abstractabstract and no body is provided: and no body is provided:abstract String Read();

InheritanceInheritance

Inheritance is a relation among classesInheritance is a relation among classes Often systems impose some restriction on Often systems impose some restriction on

inheritance relation for convenienceinheritance relation for convenience We say that class A is an We say that class A is an interfaceinterface if all its if all its

members are abstract; has no fields and members are abstract; has no fields and may inherit only from one or more may inherit only from one or more interfacesinterfaces

Inheritance can be:Inheritance can be:– Single (A <: B (C. A <: C C = B))– Mix-in (S = {B | A <: B}, 1 BS ¬interface(B))– Multiple (no restriction)

Multiple inheritanceMultiple inheritance

Why systems should impose restrictions on inheritance?Why systems should impose restrictions on inheritance? Multiple inheritance introduces both conceptual and Multiple inheritance introduces both conceptual and

implementation issuesimplementation issues The crucial problem, in its simplest form, is the following:The crucial problem, in its simplest form, is the following:

– B <: A C <: A– D <: B D <: C

In presence of a common ancestor:In presence of a common ancestor:– The instance part from A is shared between B and C– The instance part from A is duplicated

This situation is not infrequent: in C++ This situation is not infrequent: in C++ iosios:>:>istreamistream, , iosios:>:>ostreamostream and and iostreamiostream<:<:istreamistream, , iostreamiostream<:<:ostreamostream

The problem in sharing the ancestor A is that B and C may The problem in sharing the ancestor A is that B and C may change the inherited state in a way that may lead to change the inherited state in a way that may lead to conflictsconflicts

Java and Mix-in Java and Mix-in inheritanceinheritance Both single and mix-in inheritance fix the common Both single and mix-in inheritance fix the common

ancestor problemancestor problem Though single inheritance can be somewhat Though single inheritance can be somewhat

restrictiverestrictive Mix-in inheritance has become popular with Java Mix-in inheritance has become popular with Java

and represents an intermediate solutionand represents an intermediate solution Classes are partitioned into two sets: interfaces and Classes are partitioned into two sets: interfaces and

normal classesnormal classes Interfaces constraints elements of the class to be Interfaces constraints elements of the class to be

only abstract methods: no instance variables are only abstract methods: no instance variables are allowedallowed

A class inherits instance variables only from one of A class inherits instance variables only from one of its ancestors avoiding the diamond problem of its ancestors avoiding the diamond problem of multiple inheritancemultiple inheritance

Implementing Single and Implementing Single and Mix-in inheritanceMix-in inheritance

Consists only in combining the state of Consists only in combining the state of a class and its super-classessa class and its super-classess

A A

B

A B<:A

A

B

C<:B<:A

A

B

D<:C<:B<:A

D

Note that Upcasting and Downcasting comes for free: the pointer at the base of the instance can be seen both as a pointer to an instance of A or B

Implementing multiple Implementing multiple inheritanceinheritanceWith multiple inheritance becomes more With multiple inheritance becomes more

complex than reinterpreting a pointer!complex than reinterpreting a pointer!

A A

B

A B<:A

A

C

C<:A

A

A (C)

A (B)

B

CB

CD

D

D<:B, D<:C D<:B, D<:C

Late bindingLate binding

How to identify which method to invoke?How to identify which method to invoke? Solution: use a Solution: use a v-table v-table for each class that has for each class that has

polymorphic methodspolymorphic methods Each virtual method is assigned a slot in the table Each virtual method is assigned a slot in the table

pointing to the method codepointing to the method code Invoking the method involves looking up in the table Invoking the method involves looking up in the table

at a specific offset to retrieve the address to use in at a specific offset to retrieve the address to use in the the callcall instruction instruction

Each instance holds a pointer to the Each instance holds a pointer to the v-tablev-table Thus late binding incurs an overhead both in time (2 Thus late binding incurs an overhead both in time (2

indirections) and space (one pointer per object)indirections) and space (one pointer per object) The overhead is small and often worth the benefitsThe overhead is small and often worth the benefits

Late binding: an example Late binding: an example (Java)(Java)

class A {class A { void foo() {…}void foo() {…} void f() {…}void f() {…} int ai;int ai;}}class B extends A {class B extends A { void foo() {…}void foo() {…} void g() {…}void g() {…} int bi;int bi;}}

foo

f

foo

f

g

A’s v-table

B’s v-table

ai

V-pointer

ai

V-pointer

bi

A a = new A();a.foo();a.f();

B b = new B();b.foo();b.g();b.f();

A c = b;c.foo();c.f();

a

b

c

Overriding and Overriding and OverloadingOverloadingclass A {class A { void foo() {…}void foo() {…} void f() {…}void f() {…} int ai;int ai;}}class B extends A {class B extends A { void foo(int i) {…}void foo(int i) {…} void g() {…}void g() {…} int bi;int bi;}}

foo()

f

foo()

f

g

A’s v-table

B’s v-table

ai

V-pointer

ai

V-pointer

bi

A a = new A();a.foo();a.f();

B b = new B();b.foo();b.g();b.f();

A c = b;c.foo(3);c.f();

a

b

c

foo(int)

JVM invokevirtualJVM invokevirtual

A call like:A call like:x.equals("test")

is translated into:is translated into:aload_1 ; push local variable 1 (x) onto the operand stackldc "test" ; push string "test" onto the operand stackinvokevirtual

java.lang.Object.equals(Ljava.lang.Object;)Z where where

java.lang.Object.equals(Ljava.lang.Object;)Zjava.lang.Object.equals(Ljava.lang.Object;)Z is a is a method specificationmethod specification

When invokevirtual is executed, the JVM looks at method When invokevirtual is executed, the JVM looks at method specification and determines its # of argsspecification and determines its # of args

From the object reference it retrieves the class, searches From the object reference it retrieves the class, searches the list of methods for one matching the method descriptor.the list of methods for one matching the method descriptor.

If not found, searches its superclassIf not found, searches its superclass

Invokevirtual optimizationInvokevirtual optimization

The Java compiler can arrange every The Java compiler can arrange every subclass method table (mtable) in the subclass method table (mtable) in the same way as its superclass, ensuring that same way as its superclass, ensuring that each method is located at the same offseteach method is located at the same offset

The bytecode can be modified after first The bytecode can be modified after first execution, by replacing with:execution, by replacing with:invokevirtual_quick mtable-offset

Even when called on objects of different Even when called on objects of different types, the method offset will be the sametypes, the method offset will be the same

Virtual Method in InterfaceVirtual Method in Interface

Optimization does not work for interfacesOptimization does not work for interfacesinterface Incrementable { public void interface Incrementable { public void incr(); }incr(); }class Counter implements Incrementable class Counter implements Incrementable {{ public void incr(); }public void incr(); }class Timer implements Incrementable { class Timer implements Incrementable { public void decr();public void decr(); public void inc(); }public void inc(); }Incrementable i;Incrementable i;i.incr();i.incr();

Compiler cannot guarantee that method incr() is Compiler cannot guarantee that method incr() is at the same offset.at the same offset.

Runtime type informationRuntime type information

Execution environments may use the v-table Execution environments may use the v-table pointer as a mean of knowing the exact type pointer as a mean of knowing the exact type of an object at runtimeof an object at runtime

This is what happens in C++ with RTTI, This is what happens in C++ with RTTI, in .NET CLR and JVMin .NET CLR and JVM

Thus the cost of having exact runtime type Thus the cost of having exact runtime type information is allocating the v-pointer to all information is allocating the v-pointer to all objectsobjects

C++ leaves the choice to the programmer: C++ leaves the choice to the programmer: without RTTI no v-pointer is allocated in without RTTI no v-pointer is allocated in classes without virtual methodsclasses without virtual methods

OverloadingOverloading

Overloading is the mechanism that a Overloading is the mechanism that a language may provide to bind more than language may provide to bind more than one object to a nameone object to a name

Consider the following class:Consider the following class:class A { void foo() {…} void foo(int i) {…}}

The name The name foofoo is overloaded and it is overloaded and it identifies two methodsidentifies two methods

Method overloadingMethod overloading Overloading is mostly used for methods because the compiler Overloading is mostly used for methods because the compiler

may infer which version of the method should be invoked by may infer which version of the method should be invoked by looking at argument typeslooking at argument types

Behind the scenes the compiler generates a name for the Behind the scenes the compiler generates a name for the method which includes the type of the signature (not the return method which includes the type of the signature (not the return type!)type!)

This process is known as This process is known as name manglingname mangling In the previous example the name In the previous example the name foo_vfoo_v may be associated to may be associated to

the first method and the first method and foo_ifoo_i to the second to the second When the method is invoked the compiler looks at the types of When the method is invoked the compiler looks at the types of

the arguments used in the call and chooses the appropriate the arguments used in the call and chooses the appropriate version of the methodversion of the method

Sometimes implicit conversions may be involved and the Sometimes implicit conversions may be involved and the resolution process may lead to more than one method: in this resolution process may lead to more than one method: in this case the call is considered ambiguous and a compilation error case the call is considered ambiguous and a compilation error is raisedis raised

Operator overloadingOperator overloading

Syntax for operators such as + and – have Syntax for operators such as + and – have is different from invocation of the function is different from invocation of the function they representthey represent

C++ and other languages (i.e. C#) allow C++ and other languages (i.e. C#) allow overloading these operators in the same overloading these operators in the same way as ordinary functions and methodsway as ordinary functions and methods

Conceptually each invocation of + is Conceptually each invocation of + is reinterpreted as a function invocation so reinterpreted as a function invocation so the standard overloading process appliesthe standard overloading process applies

Example (C++):Example (C++):c = a + b; // operator=(c, operator+(a, b))

Late binding: only on first Late binding: only on first argumentargument

class A {class A { void foo(A a) {…}void foo(A a) {…} void f() {…}void f() {…} int ai;int ai;}}class B extends A {class B extends A { void foo(B b) {…}void foo(B b) {…} void g() {…}void g() {…} int bi;int bi;}}

foo()

f

foo(A)

f

g

A’s v-table

B’s v-table

ai

V-pointer

ai

V-pointer

bi

A a = new A();a.foo();a.f();

B b = new B();b.foo();b.g();b.f();

A c = b;c.foo(c);c.f();

a

b

c

foo(B)