A lean specification for GADTs: system F with first-class equality proofs

Generalized Algebraic Data Types are a generalization of Algebraic Data Types with additional type equality constraints. These found their use in many functional programs, including the development of embedded domain specific programming languages and generic programming. Recently, several authors published novel inference algorithms and corresponding type system specifications. These approaches tend to be more algorithmic than declarative in nature, and tied to a given compiler infrastructure. This results in complex specifications. For a language implementor, adopting such a complex approach is hard, due to conflicting infrastructure and language features. Similarly, type inference is difficult to comprehend for a programmer when the specification is complex. To make the integration of GADTs in languages easier, we thus need a more orthogonal specification. We present an orthogonal specification for GADTs: the language System F∼, consisting of System F augmented with first-class equality proofs. This specification exploits the Church encoding of data types to describe GADT matches in terms of conventional lambda abstractions.