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Generalized Algebraic Data Types and Object-Oriented Programming

Generalized algebraic data types (GADTs) have received much attention recently in the functional programming community. They generalize the type-parameterized datatypes of ML and Haskell by permitting constructors to produce different type-instantiations of the same datatype. GADTs have a number of applications, including strongly typed evaluators, generic pretty-printing, generic traversals and queries, and typed LR parsing. We show that existing object-oriented programming languages such as Java and C# can express GADT definitions, and a large class of GADT-manipulating programs, through the use of generics, subclassing, and virtual dispatch. However, some programs can be written only through the use of redundant run-time casts. We propose a generalization of the type constraint mechanisms of C# and Java to avoid the need for such casts, present a Visitor pattern for GADTs, and describe a switch construct as an alternative to virtual dispatch on datatypes. We formalize both extensions and prove a type soundness result.

Keywords: generalised algebraic data types, patterns, generics, C#, Java, virtual methods, constraints, polymorphism, existential types