Types, Subtypes, and Type Checking

What is a Type?

• Set of Values + Set of Operations
• Examples - Java: numeric, ...
• Examples - Ada: numeric, ...

What is a Subtype?

• If S is a subtype of T, then
• S has a subset of the values of T
• S has the operations of T

Example Subtypes

• Some example numeric subtypes in Ada:
• subtype Natural is Integer range 0 .. Integer'last
• subtype Positive is ...
• subtype Test_Scores is ...


• All integer operations (eg :=, +, -, 'first, 'last, integer_text_io.put) apply


• Question: Why only 2³¹-1 integers and not twice that?


• FYI: subtypes Positive and Natural are defined in package Standard (along with lots of other stuff).

Subtypes and Type Checking Assignment

• Only valid values can be assigned to a subtype variable
• Examples:

    declare
        n: Natural := 100;
        i: Integer;
    begin
        i := n;  -- does this work? (what kind of conversion)
        n := i;  -- does this work?

        get(i);
        n := i;  -- does this work?
    

Runtime Type Check

• For the assignment in this code:

    declare
        n: Natural := 100;
        i: Integer;
    begin
        get(i);
        p := i;  -- what happens here?
    

• Compiler will generate code to do something like the following

    if i < 0 then
        raise Constraint_Error;
    else
        p := i;
    end if;
    

• Explicit conversions are allowed but not required
• What would that look like?

Subtypes in Java

• Numeric types: byte and int

    int i;
    byte b = s.nextByte();

    i = b;         // what kind of conversion? 

    i = 10;

    // b = i;      // Compile error - what kind of conversion

    // how do we fix the assignment above?
    

Java Class Subtypes

• Subtypes also occur with Inheritance
• Assume class Child inherits from class Parent:

    class Parent{...}
    class Child extends Parent{...}

    Parent p;
    Child c = new Child();

    p = c;  // Does this work?  If not, how to fix?

    c = p;  // Does this work?  If not, how to fix?

    p = new Parent();
    
    c = p;  // Does this work?  If not, how to fix?
    

• Compiler generates code to check value at runtime

Subtypes and Type Checking Arithmetic

• Ada and Java: Numeric subtypes can be mixed
• Examples:

    byte b;
    int i;
    i = i + b;


    i: Integer;
    n: Natural;

    i := i + n;
    

• What happens in these cases?

Bottom Line on Using Subtypes

• A variable whose type is subtype of a parent type can be used anywhere a variable of the parent type is expected
• Sometimes a cast is needed
• In ITEC 324 you learn that this the Liskov Substitution Principle


• Variables of a given type can only hold values of that type
• This is reinforced by a combination of compiler and runtime checks
• The type cast is the programmers way of telling the compiler, I know that there might be a problem here - go ahead and do the assignmnet.
• The compiler says okay, but I'll generate a RT value check, just in case

Motivation for Subtypes

• Some operations are easier
• Example: if i in natural then ...


• Better type checking, with easy mixing of types and subtypes in arithmetic expressions


• Allows programmer to write a the level of the problem - can define and use differnt subtypes instead of using integers for everything


• Later we will see other ways of creating types such as new numeric types and enumerated types