Type System and Polymorphism in Programming Languages, Study notes of Programming Languages

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1

Programming Languages

Tevfik Koşar

Lecture - XV March 14th, 2006

2

Roadmap

• Data Types
• Type Checking
• Polymorphism
• Type Equivalence
• Polymorphism

3

Data Types

Types provide implicit context for many operations

• a+b
  • Types of a and b determine which addition function to use
  • eg. integer addition, or floating point addition
• new p
  • will allocate storage from the heap right size to hold the object pointed by p

4

Data Types

Types limit set of operations

• prevents illegal or meaningless operations:
  • adding a record and a char
  • passing a file as parameter to a functions which expects an int
  • taking sinus of a pointer

7

Type Checking

• Every definition of an object must specify the object’s type (statically types lang.)
• In type checking, three important notions:
  • type equivalence
  • type compatibility
  • type inference

8

Type Equivalence

Two principal ways of defining type equivalence:

• Structural equivalence: Two types are equal if they consist of the same components

1. type foo1 = record a, b: integer end;
2. type foo2 = record a , b: integer end;
3. type foo3 = record a: integer; b: integer; end;
4. type foo4 = record b: integer; a: integer; end;

• The last one is equal to the rest in most languages, but not in ML!

9

Type Equivalence

• Structural equivalence: Example 2:

1. type str1 = array [1..10] of char;

2. type str2 = array [1..2*5] of char;

3. type str3 = array [0..9] of char;

• The second one is equal to the first one, but not the third one! (length of the array is same, but index values are different)

10

Type Equivalence

• Name equivalence: Each definition introduces a new type.

1. type foo1 = record a, b: integer end;
2. type foo2 = record a, b: integer end;

foo1 and foo2 are considered as different types!