72 Subtypes of abstract types

Abstract types provide a basis for open variants, because concrete types may declare themselves to be subtypes of an abstract type.

A subtype is declared using isa with a non-empty list of supertypes. For example:

value Circle isa Shape
{
    Point centre;
    Real radius;
    → perimeter = 2 * pi * radius;
    → area = pi * radius * radius;
}

A value type cannot subtype an entity type, and an entity type cannot subtype a value type.

A subtype inherits the predicates of its supertypes and may define additional structure.

An existing concrete type may be declared a subtype of an abstract type after its definition, even in a different component:

// Component A
value Polygon
{
    Point vertex*;
}

// Component B
abstract value Shape {};

// Component C, with dependencies on A and B
using A { Polygon };
using B { Shape };

Polygon isa Shape;