Types in Object-Oriented Languages
Most object-oriented languages are type safe (C++ is a notable exception).
In Smalltalk-80, all type checking is done dynamically.
Some object-oriented languages have static type checking, for example
Emerald, Simula, Trellis, Eiffel (except that Eiffel's type system has a
loophole).
Cecil: optional type declarations and static checking
Type = Class?
In a class-based object-oriented language, an obvious thing to do is to
make types be classes. (This is done for example in Simula, the first
object-oriented language.)
Simula example:
begin
class vehicle(destination);
comment 'text' is the name of the string datatype in simula.
the default transmission mode for text is by reference, so this is
overridden below;
value destination;
text destination;
virtual: procedure start;
begin
procedure start;
begin
outtext("vehicle going to "); outtext(destination); outimage;
end;
comment notice that croak is not virtual;
procedure croak;
begin
outtext("this vehicle just died"); outimage;
end;
end vehicle;
vehicle class car;
begin
procedure start;
begin
outtext("vroom"); outimage;
end;
procedure croak;
begin
outtext("broken radiator"); outimage;
end;
end car;
vehicle class bus(max_passengers);
integer max_passengers;
begin
procedure start;
begin
outtext("85 cents, please"); outimage;
end;
comment no procedure definition for croak in bus;
end bus;
bus class articulated_bus(max_angle);
real max_angle;
begin
procedure start;
begin
outtext("move to the back of the bus, please"); outimage;
end;
procedure croak;
begin
outtext("rear section of bus fell off"); outimage;
end;
end articulated_bus;
vehicle class train;
begin
end train;
ref(vehicle) v;
ref(car) c;
ref(train) t;
ref(bus) b1, b2;
ref(articulated_bus) a;
comment construct a new car with destination = downtown;
v :- new car("downtown");
c :- new car("airport");
t :- new train("portland");
b1 :- new bus("ballard",60);
b2 :- new articulated_bus("u-district",100,33.5);
comment invoke associated procedures to see effects;
v.start;
v.croak;
c.start;
c.croak;
t.start;
t.croak;
b1.start;
b1.croak;
b2.start;
b2.croak;
comment and now some examples of legal assignments and accesses;
v :- c;
v :- b1;
b2 :- b1;
comment the following assignment would be illegal without the 'qua';
b2 :- v qua bus;
outtext(c.destination); outimage;
outint(b1.max_passengers, 10); outimage;
comment these assignments and accesses would cause compile-time errors:
c :- v
v.max_passengers
b1.max_angle
;
comment finally, an assignment that is ok at compile time but that
will create a run-time error;
v :- new vehicle("tukwila");
c :- v qua car;
end;
Types as sets of classes
Another definition of "type" sometimes used in type inference systems: a
type is a set of classes (see e.g. Palsberg and Schwartzbach).
Abstract Types in Object-Oriented Languages
It isn't necessary, however, to identify types and classes. In some
languages, we have a notion of an abstract type, which is different from a
class.
Definition of abstract type in an object-oriented language: An abstract
type is a collection of operation signatures, where each signature
consists of the operation name, the types of the arguments, and the
type of the result(s).
We will say that an object is of an abstract type if it has the properties
defined by that type. Abstract types can allow us to do static type
checking in an object-oriented language, while preserving the dynamic
binding of names to operations. For example, we can statically check that
some object will understand a message m, even though we don't know exactly
which method will be invoked.
Example:
The type Point might be defined as follows:
Type Point
x(): Number
y(): Number
set_x(a: Number)
set_y(a: Number)
r(): Number
theta(): Number
set_r(a: Number)
set_theta(a: Number)
+(p: Point): Point
We then might have two classes, CartesianPoint and PolarPoint, both of
which implement the operations specified by the type Point.
Contravariance
The contravariant rule for subtyping is used in Emerald, Cecil, Trellis, etc.
(There is an alternative rule, covariance, which is used in Eiffel, but
it's broken.)
Contravariant rule
S is a subtype of T if:
- S provides all the operations that T does (and maybe some more)
- For each operation in T, the corresponding operation in S has the same
number of arguments and results
- The types of the results of S's operations are subtypes of the types of
the corresponding results of T's operations
- The types of the arguments of T's operations are subtypes of the types
of the corresponding arguments of S's operations
(note the reversal of T and S here)
N.B. If S=T, then S is a subtype of T.
Example
Type Color
Type GrayScaleColor (a subtype of Color)
Type Point
x(): Number
y(): Number
Type ColoredPoint
x(): Number
y(): Number
mycolor() : Color
Type GrayScalePoint
x(): Number
y(): Number
mycolor() : GrayScaleColor
GrayScalePoint is a subtype of ColoredPoint -- anywhere a ColoredPoint is
needed, we can use a GrayScalePoint. (Also ColoredPoint is a subtype of
Point, and GrayScalePoint is a subtype of point.)
p : ColoredPoint;
c : Color
p := GrayScalePoint.new;
c := p.mycolor;
q , r : Point;
a : Number;
q := ColoredPoint.new;
r := GrayScalePoint.new;
a := q.x + r.x;
now add a message with an argument:
Type ColoredPoint
x(): Number
y(): Number
mycolor() : Color
setDotSize(c : Integer);
Type GrayScalePoint
x(): Number
y(): Number
mycolor() : GrayScaleColor
setDotSize(c : Number);
The contravariant rule says that GrayScalePoint is still a subtype of
ColoredPoint.
c : ColoredPoint;
c := GrayScalePoint.new;
c.setDotSize(3);
Now consider:
Type ColoredPoint
x(): Number
y(): Number
mycolor() : Color
setcolor(c : Color);
Type GrayScalePoint
x(): Number
y(): Number
mycolor() : GrayScaleColor
setcolor(c : GrayScaleColor);
Under the contravariant rule there is no longer a subtype relation between
ColoredPoint and GrayScalePoint. Example:
c : ColoredPoint;
c := GrayScalePoint.new; /* not permitted */
c.setcolor(yellow); /* an error would occur if we tried this */
Multiple Inheritance
A type can be a subtype of several other types -- 'multiple inheritance'
for abstract types introduces no additional complications (unlike multiple
implementation inheritance).
Parameterized types
What is the type of array? We want to be able to get reasonable type
information for the element access and set messages.
Statically-typed object-oriented languages usually have some notion of
parameterized types to handle this.
a : Array[Integer]
n : Integer;
...
a[1] := 4;
n := a[1];
For a type Array, we can have something like:
Type Array[T]
at(n : Integer) : T
put(n : Integer, x : T)
Question:What is the type relation between Array[Number]
and Array[Integer]?
Answer: under the contravariant rule, none.
Design Decision: should abstract type and concrete
implementation inheritance be separate or combined? (This question
only makes sense if there are type declarations.)
Reasons for separating them:
- they are different concepts
- allows additional flexibility (for example, multiple implementations of
the same abstract type)
Reasons against:
- it makes the language more complicated
- they usually go together anyway
Example of multiple implementations (two concrete classes with one abstract
type):
abstract type Stack
implementation classes ListStack, ArrayStack
both would conform to the abstract type Stack
Example of inheriting implementation but not abstract type:
Stack inherits from Deque (just masks off extra operations like front)