Faithful Translations between Polyvariant Flows and Polymorphic Types

Abstract

Recent work has shown equivalences between various type systems and flow logics. Ideally, the translations upon which such equivalences are based should be faithful in the sense that information is not lost in round (1) it expresses call-string based polyvariance (such as k-CFA) as well as argument based polyvariance; (2) it enjoys a subject reduction property for flows as well as for types; and (3) it supports a flow-oriented perspective rather than a type-oriented one.

Instant Polymorphic Type Systems for Mobile Process Calculi: Just Add Reduction Rules and Close

“…It inherits from PolyA the difference from most other type systems for mobility calculi that the emphasis is on types for processes rather than types for (ambient or channel) names. 3 In fact, types for names have completely vanished: A name has no intrinsic type of its own, but is distinguished solely by the way it can be used to form processes. Poly✶ works by approximating the set of terms a given term can possibly evolve to using the given reduction rules.…”

“…This is different from, and 1 These fine tuning options are omitted from this paper due to lack of space, but they are described in detail in the implementation's documentation. 2 Indeed it is well known [20,3] that the difference between an advanced flow analysis and an advanced type system is often just a question of different perspectives on the same underlying machinery. The presentation of Poly✶ is closer to the data-flow viewpoint than is common for type systems, though this of course does not make Poly✶ any less a type system.…”

“…The presentation of Poly✶ is closer to the data-flow viewpoint than is common for type systems, though this of course does not make Poly✶ any less a type system. 3 There are a number of type systems for process calculi without an explicit notion of locations which assign types to processes rather than names, for example [4,14,27,11]. Fig.…”

Branching Types

“…They can characterize the behavior of λ-terms more precisely, and can be used to express exactly the results of many program analyses [13,1,25,26]. Type polymorphism with intersection types is also more flexible.…”

“…First, this approach needs intersection types to be associative, commutative, and idempotent (ACI). Recent research suggests that non-ACI intersection types are needed to faithfully encode flow analyses [1]. Second, this approach arranges the type information inconveniently because it must be found from enclosing type variable bindings by a tree-walking process.…”