More on Types

A Little Type Theory

What is a Type?

• A type is considered to have two parts:
1. Set of values
2. Set of operations


• Example: Integers
1. Values: all integers from Integer'First to Integer'Last
2. Operations:
• Arithmetic: +, -, *, /, **, abs
• Declare/Allocation
• I/O
• Attributes: Integer'Image, Integer'First


• Example: Days
1. Values: Sunday, Monday, ..., Saturday
2. Operations:
1. Declare/Allocation - eg d: Day
2. I/O - Create new IO package
3. Attributes: Day'Image, Day'First, Day'Succ

Creating New Types

• When creating a new type, remember the values and operations


• Each kind of type has a way of specifying the values
• type Color is (red, blue, green);
• type Temperature is range 0 .. 100;
• type minutes is mod 60;


• Operations have several sources:
• Many are provided automatically
• Color'succ
• For numeric types the operations are inherited from the underlying type
• Operations can also be defined by user

Benefits of Defining New Types

Benefits of Defining New Types

• Program at level of problem vs level of machine


• Extend language to make it more expressive


• Abstraction


• Reliability:
• Stronger type checking
• Easier to validate input
• Errors detected earlier
• More readable


• One of the most important features of a language is its type system