1. 1 COMP313A Programming Languages Data Types (2)

2. 2 Overview Type Constructors Type Equivalence Type Checking Type Conversion

3. 3 Constructors – Mapping (arrays) The array constructor defines mappings as data aggregates Mapping from an array index to the value stored in that position in the array The domain is the values of the index The range is the values stored in the array

4. 4 Constructors Mapping (arrays) C/C++ typedef int little_people_num[3]; little_people_num gollum_city = {0, 0, 0} gollum_city[3] = 5 typedef int matrix[10][20];

5. 5 Constructors – Mapping (arrays)… Pascal ADA Type intarray = array[2..5] of integer; little_people = (dwarf, elf, goblin); little_people_num = array[little_people] of integer; intmatrix = array[1..10, 1..20] of integer; x:array(INTEGER range 2.6) of INTEGER := (0,2,0,5,-33)

6. 6 Constructors Union Cartesian products – conjunction of fields Union – disjunction of fields Discriminated or undiscriminated

7. 7 Constructors Unions Undiscriminated C/C++ typedef union { short int offset; long unsigned int absolute; } address;

8. 8 Constructors Union… Discriminated typedef struct { address location; descriptor kind; } safe_address; enum descriptor{rel, abs}; safe_address an_address; if (an_address == rel) an_address.location.offset = 255;

9. 9 Pascal Variant Record type address_range = 0..maxint; address_type = (absolute, offset); safe_address = record case kind: address_type of absolute: (abs_addr:address_range); offset: (off_addr: integer); end

10. 10 Constructors Pointer and Recursive Types Recursion used to define aggregates whose size can grow arbitrarily Recursive datatype T is defined as a structure that can contain components of type T Implemented via pointers

11. 11 Constructors Pointer and Recursive Types… Linked list of integers typedef struct { int val; int_list* next; } int_list; int-list* head C/C++Ada type int_list_node; type int_list_ref is access node int_list_node; type int_list_node is record val: integer; next: int_list_ref; end; head: int_list_ref

12. 12 Constructors Pointer and Recursive Types Lacks ……. typedef struct { int val; int_list* next; } int_list; int-list* head

13. 13 Constructors Pointer and Recursive Types Think of the the different possibilities for an int_list as: {emptylist} U int U (int X int) U (int X int X int)…

14. 14 Constructors Pointer and Recursive Types Some languages (Pascal, Ada) require pointers to be typed PL/1 treated pointers as untyped data objects What is the significance of this for a type checker? C pointers are typed but C allows arithmetic operations on them unlike Pascal and Ada

15. 15 Type Equivalence When are two types the same Structural equivalence Declaration equivalence Name equivalence

16. 16 Structural Equivalence Two types are the same if they have the same structure i.e. they are constructed in exactly the same way using the same type constructors from the same simple types

17. 17 Structural Equivalence typedef int A[5] typedef A B; typedef int C[5]; typedef int D[10];

18. 18 Structural Type Equivalence typedef int anarray[10]; typedef struct { anarray x; int y;} struct1; typedef struct { int x[10]; int y; }struct2; typedef int anarray[10]; typedef struct { anarray a; int b; }struct3; typedef int anarray[10]; typedef struct { int b; anarray a; }struct4; (Note we are just using the syntax of C as an example. C does NOT use structural equivalence for structs

19. 19 Structural Equivalence Check representing types as trees –Check equivalence recursively on subtrees Consider… Dynamic arrays Type array1 = array[-1..9] of integer; array2 = array[0..10] of integer; Array (INTEGER range <>) of INTEGER