Dependently-Typed Programming with Logical Equality Reflection

Abstract

In dependently-typed functional programming languages that allow general recursion, programs used as proofs must be evaluated to retain type soundness. As a result, programmers must make a trade-off between performance and safety. To address this problem, we propose System DE, an explicitly-typed, moded core calculus that supports termination tracking and equality reflection. Programmers can write inductive proofs about potentially diverging programs in a logical sublanguage and reflect those proofs to the type checker, while knowing that such proofs will be erased by the compiler before execution. A key feature of System DE is its use of modes for both termination and relevance tracking, which not only simplifies the design but also leaves it open for future extension. System DE is suitable for use in the Glasgow Haskell Compiler, but could serve as the basis for any general purpose dependently-typed language.