Fully reflexive intensional type analysis

Abstract

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.

Principled Scavenging

“…In fact, an early paper of Wang and Appel [21] was titled "safe garbage collection = regions + intensional type analysis;" but they failed to make it work, and they subsequently gave up on using ITA and ended up opting for the lower-tech solution mentioned above [23]. Saha et al [15,19] also tried to use ITA to write the copy function, but their attempt is missing crucial details and didn't really work either.…”

“…2. It extends λ CLOS with regions [17] and intensional type analysis [8,19]. Functions are also fully closed and use CPS but they can additionally be polymorphic over tags and regions.…”

“…Tags represent the runtime type descriptors and map very directly to source-level types without any region annotations. The only different between λCLOS types and λGC tags is the addition of tag functions λt.τ and tag applications τ1τ2, which are needed for type analysis of existentials [19]. To do the actual analysis of tags, terms include a refining typecase construct, i.e.…”

“…• We show how to use intensional type analysis (ITA) [19,8] to accurately describe the contract between the mutator and the collector and how the same framework can be applied to construct various different type-safe GCs.…”

“…• Using ITA to typecheck GC may seem to be an obvious idea (at least to some people), however, none of the previous work [21,15,19] have succeeded in getting it to work. Indeed, Wang and Appel [23] subsequently gave up on using ITA.…”