BETA is an object-oriented programming language that was created in the 1980s by Bjarne Däcker, a professor of computer science at the University of Aarhus in Denmark. The language was designed to be a modern alternative to languages like Simula and Smalltalk, and it has been used in a wide range of applications, including modeling and simulation, real-time control systems, and artificial intelligence.

History:

BETA was first developed in the mid-1980s by Bjarne Däcker and his colleagues at the University of Aarhus. The language was influenced by earlier object-oriented languages like Simula and Smalltalk, but it was designed to be more modern and flexible. The name BETA was chosen to suggest that the language was still under development and open to improvement.

Syntax:

BETA is a strongly-typed language, which means that every variable has a specific type that is determined at compile time. The language also supports dynamic binding, which allows objects to be bound to variables at runtime. BETA uses a syntax that is similar to that of other object-oriented languages, with classes, objects, methods, and inheritance. Here's an example of a simple BETA program:

```
class Point
  fields
    x: @real;
    y: @real;
  methods
    setX(value: @real)
      x := value;
    setY(value: @real)
      y := value;
    getX(): @real
      return x;
    getY(): @real
      return y;
end
```

This program defines a class called Point, which represents a point in two-dimensional space. The class has two fields, x and y, which are both of type @real. It also has four methods: setX and setY, which set the values of the x and y fields, and getX and getY, which return the values of the x and y fields.

Examples:

Here's an example of a more complex BETA program that uses inheritance and polymorphism:

```
class Shape
  methods
    draw()
      % abstract method
end

class Circle is Shape
  fields
    center: Point;
    radius: @real;
  methods
    draw()
      % draw circle
end

class Rectangle is Shape
  fields
    topLeft: Point;
    bottomRight: Point;
  methods
    draw()
      % draw rectangle
end

main()
  shapes: array[3] of Shape;
  shapes[1] := Circle(center: Point(x: 0.0, y: 0.0), radius: 1.0);
  shapes[2] := Rectangle(topLeft: Point(x: -1.0, y: 1.0), bottomRight: Point(x: 1.0, y: -1.0));
  shapes[3] := Circle(center: Point(x: 2.0, y: 2.0), radius: 0.5);
  for shape in shapes do
    shape.draw();
  end;
end
```

This program defines a base class called Shape, which has an abstract method called draw. It also defines two subclasses, Circle and Rectangle, which inherit from Shape and implement the draw method. The main function creates an array of three Shape objects, which are initialized as two circles and a rectangle, and then iterates over the array and calls the draw method on each object.

Applications:

BETA has been used in a wide range of applications, including modeling and simulation, real-time control systems, and artificial intelligence. One of the key strengths of BETA is its support for abstraction and mod