Empowering Union and Intersection Types with Integrated Subtyping

Empowering Union and Intersection Types with Integrated Subtyping Fabian Muehlboeck and Ross Tate

Union Types Intersection Types Algol 68 Coppo, Dezani-Ciancaglini, Sallé, Pottinger, late 1970 s

Unions and Intersections Ceylon Racket

Nullability in Ceylon

Nullability in Ceylon

Nullability in Ceylon filter. Nulls(nstrs);

Nullability in Ceylon filter. Nulls(nstrs);

Nullability in Ceylon filter. Nulls(nstrs); (Disjointness) (Distributivity)

Nullability in Ceylon filter. Nulls(nstrs); (Disjointness) (Distributivity)

Subtyping Extension “Textbook” Subtyping Integrated Subtyping Our Framework

Textbook Subtyping “Literals”

Textbook Subtyping

Textbook Subtyping

Textbook Subtyping • Syntax-Directed • Well-founded

Textbook Subtyping

Textbook Subtyping

“Textbook” Subtyping Decision Procedure Our Framework

Nullability in Ceylon filter. Nulls(nstrs); (Disjointness) (Distributivity)

Distributivity In dnf DNF

Disjunctive Normal Form Promotion

Preserving DNF Still in dnf In dnf

Preserving DNF Not necessarily in dnf In dnf

Integrating DNF into the Subtyping Algorithm Re-Establish dnf

“Textbook” Subtyping Decision +Distributivity Procedure Our Framework

Nullability in Ceylon filter. Nulls(nstrs); (Disjointness) (Distributivity)

Subtyping Extension “Textbook” Subtyping +Distributivity Our Framework

Integrated Subtyping Additional Subtyping Relationships

Integrated Subtyping

Integrated Subtyping

Integrated Subtyping

Integrated Subtyping

Integrated Subtyping

Integrated Subtyping Promotion

Integrated Subtyping Algorithm

Subtyping Extension “Textbook” Subtyping Integrated +Distributivity Subtyping Our Framework

Subtyping Extension “Textbook” Subtyping Our Framework

Composition “Textbook” Subtyping Integrated Subtyping Our Framework

Composition

More Ceylon Extensions Classes with Enumerated Cases Object or Null Principal Instantiations

Extensions for Other Languages

Composition “Textbook” Subtyping Integrated Subtyping Our Framework www. cs. cornell. edu/~ross/empower