System FC is an explicitly typed language that serves as the target language for Haskell source programs. System FC is based on System F with the addition of erasable but explicit type equality proof witnesses. This paper improves FC in two directions: The first contribution is extending term-level functions with the ability to return equality proof witnesses, which allows the smooth integration of equality superclasses and indexed constraint synonyms, features currently absent from Haskell. We show how to ensure soundness and satisfy the zero-cost requirement for equality witnesses using a familiar mechanism, already present in GHC: that of unlifted types. Our second contribution is an equality proof simplification algorithm, which greatly reduces the size of the target System FC terms.

This paper was completely rewritten and reborn as two separate papers Equality proofs and deferred type errors and Evidence normalization in System FC.