Data Types Data Types

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Every program uses data, either explicitly or implicitly to arrive at a result.

Data in a program is collected into data structures, and is manipulated by algorithms.

Algorithms + Data Structures = Programs

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Most programming languages provide: A set of simple data entities such as Integer Real Boolean Char

Mechanisms for constructing new data entities from these.

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• Finiteness: – Mathematically, integer data is thought of as:

• …, -3, -2, -1, 0, 1, 2, 3, …

• In a computer’s hardware, there is always an upper and lower bound for values of integers.

• This is due to a given representation size in bits of an integer on a specific machine.

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 Different language designs deal with data type information in different ways.

 Some languages mandate that type information be explicit in the programming language. This is used to verify program correctness prior to execution. Example:

 int x;  float y;  char z;

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Scheme is a language with no explicit types or translation-time typing.

Ada is a very strictly-typed language. It performs strict type checking.

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 Some form of static (translation-time) type checking is very useful to:

 Allocate memory efficiently.

 Reduce the amount of code to be compiled.

 Improves both writability and readability.

 Improves security and reliability.

 Removes ambiguities.

 Can be used to prove program correctness.

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A Data Type is a Set of Values

Insufficient Definition!

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A Data Type is a Set of Values

A Set of Operations on Those Values having Certain Properties

9 Data Types Example:

The values of an int range from a lower bound to an upper bound (e.g. MININT to MAXINT)

Operations on int include: + - * / Etc. 10

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Type Checking:

Is the process a translator goes through to determine whether the type information in a program is consistent.

11 Data Types Type Checking:

Example:

x = y + z

Can the type of the result of y + z be stored in x?

The type of y + z depends on the type of y and z

Determining the type of y + z is called type inference. 12 Data Types We can construct more complex user defined types from simple data types:

Example:

An array of ten integers in C/C++: int a[10]

The same array in Ada: a: array (1..10) of integer

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Type definitions: In some languages, we can give new types names.

Example in C: A name given to an int array of ten elements typedef int Array_of_ten_integers[10]; Array_of_ten_integers a;

Just like we declare int a, We can declare Array_of_ten_integers a

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Type definitions: In some languages, we can give new types names.

Example in C: A name given to an int array of ten elements typedef int Array_of_ten_integers[10]; Array_of_ten_integers a;

Just like we declare int a, We can declare Array_of_ten_integers a

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Type definitions: In some languages, we can give new types names.

Example in Ada:

type Array_of_ten_integers is array(1..10) of integer; a: Array_of_ten_integers;

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 Type definitions:

 With new type definitions, we have a problem !

 During type checking, a translator must often compare two types to determine if they are the same.

 Example: The following should be equivalent in type!  int a[10]  Array_of_ten_integers

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Type definitions:

Each language with type declarations has rules for checking equivalence.

These are called rule equivalence algorithms.

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 Strongly Typed Languages:

 If a programming language definition specifies a complete type system that can be applied statically.

 Guarantees that all (unintentional) data-corrupting errors in a program will be detected at the earliest possible point.

 The language is said to be strongly typed.

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Strongly Typed Languages:

All type errors are detected at translation time.

With the exception of a few errors that can only be checked during execution.

E.g. array subscript bounds

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 Strongly Typed Languages:

 Strong typing ensures that:

 Most unsafe programs (programs with data corrupting errors) will be rejected at translation time.

 The unsafe programs that are not rejected at translation time will cause an execution error prior to any data corrupting actions.

 Strong typing can also be a burden on the programmer, having to explicitly specify types all the time.

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Strongly Typed Languages (Examples):

Strong Ada is a strongly typed language.

ML and Haskell

Pascal

C (Considered weakly typed) Weak

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 Untyped Languages:

 Languages without static type checking.

 Also called dynamically typed languages.

 Examples: Scheme, Smalltalk, most scripting languages such as Perl.

 An untyped language does not necessarily allow programs to corrupt data, but rather all safety checking is performed at execution time:

 They will generate runtime errors.

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Type Construction:

How are new types constructed?

We can think of construction as mathematical operations.

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Type Construction:

Cartesian product. Unions. Subsets. Arrays/Functions. Sequences/Lists. Recursive types. No Intersection: types should NOT overlap.

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 Type Construction:

 Cartesian product:

 Finite combinations of previously defined types.  Example: C structs:

struct IntCharReal { A finite combination of int i; those types char c; double r; };

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Type Construction:

Unions: Values belong to ONE of a finite set of types. Example: C unions: union IntOrReal { Only one of those can int i; be used. double r; };

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Type Construction:

Subsets:

A new type may be a subrange of another type.

Example in Ada:

subtype IntDigit_Type is integer range 0..9

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Type Construction:

Subsets:

A new type may be a subrange of another type.

Example in Ada:

subtype IntDigit_Type is integer range 0..9

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Type Construction:

Arrays and Functions:

You can define arrays in most programming languages as a homogeneous collection of a given type.

You can define functions also.

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Type Construction:

Sequences and Lists:

Sequences are like arrays, except that they are potentially infinite. Example: Streams

Lists are like arrays, but can only be accessed by counting down from the first element. Almost all functional languages have lists.

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Type Construction:

Recursive Types: Example:

class node { int value; node next; } Recursive Definition

32 Data Types  Example: Java Type Structure:

Java Types

Primitive Reference

boolean Nume r ic Array class interface

Integral Floating point

char float byte double short int long

33 Data Types  Example: C Type Structure:

C Types

Bas ic Derived

void Nume r ic Pointer Array Function struct union

Integral Floating

float double

(signed) enum long double (unsigned) char int short int long int

34 Data Types  Type Checking:

 Dynamic type checking:  If type information is maintained and checked at runtime.  Interpreters by definition perform dynamic type checking.  Compilers also generate code that maintain type attributes during runtime in table.  Dynamic type checking is required when the types can only be determined at runtime.

 Static type checking:  The types are determined from the text of the program.  Checking is performed before execution.

35 Data Types  Type Checking:

 A strongly typed language must report all type errors as compilation errors that prevent execution.

 A language definition may not specify whether static or dynamic type checking is to be used.

36 Data Types  Type Compatibility:

 Two different types may be combined correctly in certain ways.

 They are called compatible.

 Example: int, short.

 What do we mean by combined correctly in a certain way?  Ranges!

37 Data Types  Implicit Types:

 Sometimes types are implicitly inferred.

 Example: 2 + 3, or x / y

 In C, the following is an implicit int variable  X;

 Also, in C, if functions have no return type indicated, they implicitly return an int.

38 Data Types  Overlapping Types:

 It is sometimes difficult to avoid overlapping of various types.

 Example: In Java, the following types overlap:  int  short  long  byte  All overlap

39 Data Types • Shared Operations:

– The + operator for example may be applied to any combination of int, short, byte, double, float, long.

– The + operator even has a different meaning in: • System.out.println(“My” + “Name” + “Is”);

– The plus operator is said to be overloaded.

40 Data Types  Type Conversion:

 There is always a need to convert from one type to another.

 Conversion can either be implicit (automatic) or explicit (manual).

41 Data Types • Type Conversion:

– Example of implicit type conversion in C/C++: • int x = 3.3; • Although x is an int, 3.3 is truncated to 3, and stored in x.

– Example of implicit type conversion in Java: • double x = 2 + 3; • The expression’s type is automatically promoted to double to be stored in x.

– Implicit conversions are also called coercions.

42 Data Types  Type Conversion:

 When we implicitly convert from int to double for example, the destination is large enough to accommodate any int.

 This is called a widening conversion.

 The opposite is called a narrowing conversion.

43 Polymorphic Type Checking  Most statically typed languages require that explicit type information be given for all names in each declaration.

 It is possible to use an extension of type inference to determine the types of names in a declaration without explicitly giving those types.

 The translator can collect information on uses of a name, and infer from the set of all uses a probable type (the most general type) for which all uses are correct.

 The Hindley-Milner type checking provides this kind of inference. It is a major feature of strongly typed functional languages such as ML and Haskell.

44 Data Types  Type Conversion:

 Explicit conversions involve the writing of directives to explicitly convert from one type to another in the code.

 Example:  int x = 2;  double y = 3.3;  y = (double) x; (type casting)

 Type casting will temporarily change the type of the RHS to that of the cast.