# Fundamentals of Programming Languages. Data Types Lecture 07 sl. dr. ing. Ciprian-Bogdan Chirila

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1 Fundamentals of Programming Languages Data Types Lecture 07 sl. dr. ing. Ciprian-Bogdan Chirila

2 Predefined types Programmer defined types Scalar types Structured data types Cartesian product Finite projection Sequence Recurrence Variable reunions Sets Pointer type Type Compatibility Lecture outline

3 Data types A set of objects and A set of operations to Create Destroy Modify Predefined types a certain set of objects specified at language definition Unitary construction of objects in advanced PLs structure operations

4 Predefined Types The base of the typing system of a language Reflects the system functioning at the hardware level Values and operations related to low level data and machine operations

5 Predefined Types Numerical base types int in Algol 68 integer in Pascal real in Algol 68 and Pascal float in Ada short int, long int, double Mathematical operations +,-,*,/ For integers and reals Polymorphic operators - overloaded

6 Predefined Types boolean enumeration type with values true false bool in Algol 68 boolean in Pascal, Java, Ada char in Algol 68, Java, Pascal character in Ada ASCII EBCDIC Extended Binary Coded Decimal Interchange Code

7 Programmer defined types The most powerful feature of a typing system is to create new types Named type tab=array[1..10] of integer; Anonymous var t:array[1..10] of integer;

8 Scalar types Scalar type objects are simple constants which can not be decomposed further Integer, real, character, boolean are scalar types The programmer can define its own scalar types

9 Enumeration type The user specifies in a list the type values type days=(sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday); Started in Pascal Present in the majority of the PLs

10 Other scalar types Important from the portability point of view in Ada type eps is digits 10; a floating point number with a minimum number of 10 significant decimals The precision will be preserved independently of the platform

11 Subdomains In Pascal type working_day=monday..friday; small_caps= a.. z ; index=0..90; In Ada type eps_1 is new eps range ;

12 Structured data types PLs offer mechanisms for description and manipulation of data structures containing scalars other structures Structuring mechanism features allowing to build structures starting from its components Selection mechanism features allowing access to a structure component

13 Cartesian product Structured objects Composed out of a fixed number of components Components are of different types The type of the structured objects is the Cartesian product of the sets corresponding to components If the types of the components are represented by sets C1, C2, C3,, Cn Each element of structured type will be: T=C1 x C2 x x Cn

14 Cartesian product Named also Articles Structures In Pascal and Ada - record In Algol 68 and C structure To describe the type of each component To select a component means to specify the object and the name of the selected field

15 Cartesian product example Ada type complex is record re,im:real; end record; c:complex; c.re:=1; c.im:=0; c:=(1,0);

16 Finite projection Is a function defined on IT set with values on ET set IT index type ET element type var a:array[1..100] of char; It is a projection of {1,2,3,,100} set on the characters set The array components called elements are selected through the indexing mechanism To the array name we add an index value to select a certain element

17 Finite projection a[k] selects the k index element from array a can be regarded as a application of function a with argument k resulting the value of the element In Algol, Ada Selection can be made on a slice not just a single element a[10..19]=(0,1,2,3,4,5,6,7,8,9);

18 The key moment of binding the set of indexes Fixed at compile time Writing the code which establishes the index set Can not be modified during program execution It is the case for Fortran, C, Pascal Fixed at run time In the moment of array object creation The size can be unknown at compile time Can depend on program variables It is the case for Algol 60, Basic or Ada In languages with dynamic memory allocation like C pointers are used for dynamic arrays access

19 The key moment of binding the set of indexes Flexible at run time The index set can be modified The size of the array can be modified It is the case for Snobol4 and Algol 68

20 Sequence Is a structure formed out of a random number of components of the same type Anytime a component can be added Virtually unlimited In PLs Strings of characters Sequential file

21 Sequence For strings In PL/I, Ada, Basic, Pascal When declaring a string the maximum length must be known Operations PL dependent Catenation First character selection Last character selection Substring selection etc

22 Recursion A type T is recursive if one of its components is of type T Typical examples are Lists Trees The objects can have arbitrary shapes and sizes

23 Recursion in pseudocode type node=record info : info_type; left, right : node; end;

24 Recursion in practice pointers must be used a recursive object of type T must have a reference of a T object not an object itself C, Pascal, Ada, Algol 68 In Lisp lists and trees does not need pointers type node=record info : info_type; left, right : ^node; end;

25 Variable reunions Allow specifying structures which can have several alternatives The set of all possible structures represents the reunion of alternative sets

26 Variable reunions In C union { float radius; float rectangle_sides[2]; float triangle_sides[3]; } shape;

27 Variable reunions at one time shape variable can have only float radius or two float array or three float array in an article all fields coexist in a union there will be only one of the alternative fields

28 Variable reunions More evolved unions are in Pascal and Ada The union is a part of an article with variants type figure=(circle, triangle, rectangle); shape=record length, area:real; case shape:figure of circle: (radius:real); rectangle: (rectangle_sides:array[1..2] of real); triangle: (triangle_sides:array[1..3] of real); end

29 Variable reunions Are dangerous The correct variant must be used All responsibility is left on programmers shoulders (C) No compile time checking possible No runtime checking possible Ada and Pascal cases will be detailed later

30 Sets T is the base type Variables of set(t) can have as value any subset generated by values of T including void set Operations Reunion Intersection Difference Inclusion tests belonging tests

31 Sets Pascal Has a set type When no such mechanism is present Can be implemented by the programmer by Boolean arrays Bit arrays Lists Trees

32 The pointer type A pointer is a reference to an object The usual mean to implement recursive data structures In C the only way of transmitting parameters by address

33 Problems with pointers Type compatibility violations Pseudonyms False references

34 Type compatibility violations In PL/I a pointer variable can refer any object At compile time is impossible to know the object type and to do appropriate type checking runtime checking is possible but they are expensive In Pascal, Ada pointers have assigned the object types they may refer In C we have the void* generic pointers

35 Pseudonyms The very same object is referred by several names Their presence in the code affects its readability var a,b:^t; a:=new(t); b:=a; a and b are pseudonyms

36 False references When a pointer refers an object no longer alive Its access is an error var a,b:^t; a:=new(t); b:=a; dispose(a); b is a false reference even a is set to nil

37 In C int *p; void f() { int x; p=&x; } f(); False references

38 Type compatibility T1 and T2 are compatible types if A value of type T1 can be assigned to a variable of type T2 (and vice versa) A parameter of type T1 corresponds to an actual of type T2 (and vice versa)

39 Example type var t=array[1..100] of integer; t1=array[1..100] of integer; t2=t1; a,b:array[1..100] of integer; c:t; d:t; e,f:t1; g:t2;

40 Theoretical type compatibilities Name equivalence Structural equivalence

41 Name equivalence when 2 variables declared together or using the same name for the type In the example a and b are compatible c and d are compatible e and f are compatible a or b with c or d are not compatible

42 Structural equivalence two variables have compatible types if they have the same structure as type checking we will replace the name of the type by its definition recursive process ends when all user defined type are replaced Two types are compatible if they have the same description In our example a, b, c, d, e, f, g are all compatible

43 Comparison Structural equivalence simplicity of the implementation Name equivalence Complex operations in order to determine type compatibility Allows refined abstractions type price=integer; students_no=integer; cost:price; effective:student_no;

44 Comparison Variables cost and effective structurally equivalent assigning values from cost to effective or viceversa is a semantic error Structural equivalence Algol 68 C - structure and union different types even they have identical structures Name equivalence Ada Pascal - equivalence not specified, implementation dependent

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