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 restoring confluence. Combining implicit hypotheses and full reduction leads to a better understanding of GADTs, 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.
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