Modern Haskell supports zero-cost coercions, a mechanism where types that share the same run-time representation may be freely converted between. To make sure such conversions are safe and desirable, this feature relies on a mechanism of roles to prohibit invalid coercions. In this work, we show how to incorporate roles into dependent types systems and prove, using the Coq proof assistant, that the resulting system is sound. We have designed this work as a foundation for the addition of dependent types to the Glasgow Haskell Compiler, but we also expect that it will be of use to designers of other dependently-typed languages who might want to adopt Haskell’s safe coercions feature.

Metaprograms are programs that manipulate (generate, analyze and evaluate) other programs. These tasks are greatly facilitated by quasiquotation, a technique to construct and deconstruct program fragments using quoted code templates expressed in the syntax of the manipulated language. We argue that two main flavors of quasiquotes have existed so far: Lisp-style quasiquotes, which can both construct and deconstruct programs but may produce code that contains type mismatches and unbound variables; and MetaML-style quasiquotes, which rely on static typing to prevent these errors, but can only construct programs. In this paper, we show how to combine the advantages of both flavors into a unified framework: we allow the construction, deconstruction and evaluation of program fragments while ensuring that generated programs are well-typed and well-scoped, a combination unseen in previous work. We formalize our approach as λ {} , a multi-stage calculus with code pattern matching and rewriting, and prove its type safety. We also present its realization in Squid, a metaprogramming framework for Scala, leveraging Scala’s expressive type system. To demonstrate the usefulness of our approach, we introduce speculative rewrite rules , a novel code transformation technique that makes decisive use of these capabilities, and we outline how it simplifies the design of some crucial query compiler optimizations.

We propose a core semantics for Dependent Haskell, an extension of Haskell with full-spectrum dependent types. Our semantics consists of two related languages. The first is a Curry-style dependently-typed language with nontermination, irrelevant arguments, and equality abstraction. The second, inspired by the Glasgow Haskell Compiler's core language FC, is its explicitly-typed analogue, suitable for implementation in GHC. All of our results---chiefly, type safety, along with theorems that relate these two languages---have been formalized using the Coq proof assistant. Because our work is backwards compatible with Haskell, our type safety proof holds in the presence of nonterminating computation. However, unlike other full-spectrum dependently-typed languages, such as Coq, Agda or Idris, because of this nontermination, Haskell's term language does not correspond to a consistent logic.