Compilers for polymorphic languages can use runtime type inspection to support advanced implementation techniques such as tagless garbage collection, polymorphic marshalling, and flattened data structures. Intensional type analysis is a type-theoretic framework for expressing and certifying such type-analyzing computations. Unfortunately, existing approaches to intensional analysis do not work well on types with universal, existential, or fixpoint quantifiers. This makes it impossible to code applications such as garbage collection, persistence, or marshalling which must be able to examine the type of any runtime value.We present a typed intermediate language that supports fully reflexive intensional type analysis. By fully reflexive, we mean that type-analyzing operations are applicable to the type of any runtime value in the language. In particular, we provide both type-level and term-level constructs for analyzing quantified types. Our system supports structural induction on quantified types yet type checking remains decidable. We show how to use reflexive type analysis to support type-safe marshalling and how to generate certified type-analyzing object code.
A polymorphic, constraint-based type inference algorithm for an object-oriented language is defined. A generalized form of type, polymorphic recursively constrained types, are inferred. These types are expressive enough for typing objects, since they generalize recursive types and F-bounded polymorphism. The well-known tradeoff between inheritance and subtyping is mitigated by the type inference mechanism. Soundness and completeness of type inference are established.
A certified binary is a value together with a proof that the value satisfies a given specification. Existing compilers that generate certified code have focused on simple memory and control-flow safety rather than more advanced properties. In this paper, we present a general framework for explicitly representing complex propositions and proofs in typed intermediate and assembly languages. The new framework allows us to reason about certified programs that involve effects while still maintaining decidable typechecking. We show how to integrate an entire proof system (the calculus of inductive constructions) into a compiler intermediate language and how the intermediate language can undergo complex transformations (CPS and closure conversion) while preserving proofs represented in the type system. Our work provides a foundation for the process of automatically generating certified binaries in a typetheoretic framework.
Important strides toward developing expressive yet semantically sound type systems for object-oriented programming languages have recently been made by Cook, Bruce, Mitchell, and others. This paper focusses on how the theoretical work using F-bounded quantification may be brought more into the realm of actual language implementations while preserving rigorous soundness properties. We simultaneously address three of the more significant problems: adding a notion of global state, proving type-checking is decidable, and integrating the more widely implemented view that subclasses correspond to subtypes with the F-bounded view.
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