Abstract

Note: Talk cancelled for today – speaker cannot make it. troduces logical assumptions in the type system, which breaks type soundness in the presence of full reduction. Even though programming languages use weak reduction strategies, typically call-by-value, we believe that type soundness for full reduction in the underlying effect-free core calculus is important and gives the programmer a more abstract understanding of program fragments. We propose an expressive type system with implicit coercions and both coherent and incoherent abstraction over coercions. This allows a fine-grained control of dependencies between computations and the logical hypotheses they depend on while preserving the implicit use of hypotheses and confluence. Combining implicit hypotheses and full reduction leads to a better understanding of GAD Ts, provides a better continuum between explicit and implicit type information, and would be a good setting for studying extraction of computational contents from proofs in proof assistants.

Adding GADTs to a language such as ML or System F in