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...oriented languages require the choice of one approach exclusive of the other. For instance in C++ and Object Pascal, inheritance is subtyping, so binary methods will not inherit properly. In PolyTOIL =-=[5]-=- and our Loop language [12], inheritance is not subtyping, so binary methods inherit properly but object subtyping may be limited. Our type inference algorithm is capable of inferring a most general t...

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...a class C with a method incr which increments a protected integer field, and a subclass D of C which adds a decr method to decrement that field. class C { protected var x = 0; def incr: this.type = { x = x + 1; this } } class D extends C { def decr: this.type = { x = x - 1; this } } Then we can chain calls to the incr and decr method, as in val d = new D; d.incr.decr; Without the singleton type this.type, this would not have been possible, since d.incr would be of type C, which does not have a decr member. In that sense, this.type is similar to (covariant uses of) Kim Bruce’s mytype construct [5]. Parameter bounds We now refine the Cell class so that it also provides a method setMax which sets a cell to the maximum of the cell’s current value and a given parameter value. We would like to define setMax so that it works for all cell value types admitting a comparison operation “<”, which is a method of class Ordered. For the moment we assume this class is defined as follows (a more refined generic version of this class is in the standard Scala library). abstract class Ordered { type O; def < (that: O): boolean; def <= (that: O): boolean = this < that ||this == that } Class Ordered has a...

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... a final field. The run-time class of an object specified by a final access path does not change. The dependent type this.class is similar to the MyType (self type) construct of LOOM [3] and PolyTOIL =-=[5]-=-. The key difference is that with MyType, an instance of a subtype of MyType may be assigned to a variable of type MyType. Although MyType is covariant with respect to the subclassing relationship, th...

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... the same type. Similarly, one type is a subtype of another only if its specification declares this and the declaration is legal. In some object-oriented languages, e.g., Emerald [BHJ + 87], PolyTOIL =-=[BSvG95]-=-, and School [RIR93], type relations are derived: two specifications define the same type if they are identical except for the names of the types they are defining, and a type is a subtype of another ...