The Essence of Principal Typings

Wells, J. B.

doi:10.1007/3-540-45465-9_78

Cited by 66 publications

(69 citation statements)

References 28 publications

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“…In this section we show that every command does indeed have a principal Flow Core-pc typing in this sense. More formally, the most general definition of principal typing is due to Wells [Wel02]. We do not use Wells' definition in the current paper but it is a simple corollary of Theorem 2 (see below) that our principal typings are indeed principal according to that definition.…”

Section: Principal Typingsmentioning

confidence: 99%

From Exponential to Polynomial-Time Security Typing via Principal Types

Hunt

Sands

2011

Programming Languages and Systems

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Abstract. Hunt and Sands (POPL'06) studied a flow sensitive type (FST) system for multi-level security, parametric in the choice of lattice of security levels. Choosing the powerset of program variables as the security lattice yields a system which was shown to be equivalent to Amtoft and Banerjee's Hoare-style independence logic (SAS'04). Moreover, using the powerset lattice, it was shown how to derive a principal type from which all other types (for all choices of lattice) can be simply derived. Both of these earlier works gave "algorithmic" formulations of the type system/program logic, but both algorithms are of exponential complexity due to the iterative typing of While loops. Later work by Hunt and Sands (ESOP'08) adapted the FST system to provide an erasure type system which determines whether some input is correctly erased at a designated time. This type system is inherently exponential, requiring a double typing of the erasure-labelled input command. In this paper we start by developing the FST work in two key ways: (1) We specialise the FST system to a form which only derives principal types; the resulting type system has a simple algorithmic reading, yielding principal security types in polynomial time. (2) We show how the FST system can be simply extended to check for various degrees of termination sensitivity (the original FST system is completely termination insensitive, while the erasure type system is fully termination sensitive). We go on to demonstrate the power of these techniques by combining them to develop a type system which is shown to correctly implement erasure typing in polynomial time. Principality is used in an essential way to reduce type derivation size from exponential to linear.

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Section: Principal Typingsmentioning

confidence: 99%

From Exponential to Polynomial-Time Security Typing via Principal Types

Hunt

Sands

2011

Programming Languages and Systems

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“…This implies that the possible typings for M in ML and M β ML in shallow-polymorphic X are essentially the same. Since Wells proves in [12] that ML does not in general have principal typings (i.e. when the basis of assumptions is unspecified, there is no pair of basis and type which represents all other possible typings), this immediately implies that the same is the case of our shallow polymorphic version of X .…”

Section: Definition 23 (Shallow Polymorphic Type Assignment For X )mentioning

confidence: 90%

“…In [11] a notion of principal contexts (principal typings, in the language of [12]) is defined by providing an algorithm pC that, given an X -term P , returns a context Γ ; ∆ , with the following properties:…”

Section: Theorem 8 (Witness Reduction [10]) If P · · · γ ∆ and Pmentioning

confidence: 99%

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Approaches to Polymorphism in Classical Sequent Calculus

Summers

Bakel

2006

Programming Languages and Systems

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Abstract. X is a relatively new calculus, invented to give a Curry-Howard correspondence with Classical Implicative Sequent Calculus. It is already known to provide a very expressive language; embeddings have been defined of the λ-calculus, Bloo and Rose's λx, Parigot's λµ and Curien and Herbelin's λµμ.We investigate various notions of polymorphism in the context of the Xcalculus. In particular, we examine the first class polymorphism of System F, and the shallow polymorphism of ML. We define analogous systems based on the X -calculus, and show that these are suitable for embedding the original calculi.In the case of shallow polymorphism we obtain a more general calculus than ML, while retaining its useful properties. A type-assignment algorithm is defined for this system, which generalises Milner's W.

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“…Thus, we now define a syntactically restricted type system for which we do prove that principal types exist. Allowing only modest and discrete types yields principal typings (defined in [21]):…”

Section: Proposition 18 Every Term P Has a Type (Although The Type Mamentioning

confidence: 99%

Polya:True Type Polymorphism for Mobile Ambients

Amtoft

Makholm²,

Wells³

IFIP International Federation for Information Processing

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Previous type systems for mobility calculi (the original Mobile Ambients, its variants and descendants, e.g., Boxed Ambients and Safe Ambients, and other related systems) offer little support for generic mobile agents. Previous systems either do not handle communication at all or globally assign fixed communication types to ambient names that do not change as an ambient moves around or interacts with other ambients. This makes it hard to type examples such as a messenger ambient that uses communication primitives to collect a message of non-predetermined type and deliver it to a non-predetermined destination.In contrast, we present our new type system PolyA. Instead of assigning communication types to ambient names, PolyA assigns a type to each process P that gives upper bounds on (1) the possible ambient nesting shapes of any process P to which P can evolve, (2) the values that may be communicated at each location, and (3) the capabilities that can be used at each location. Because PolyA can type generic mobile agents, we believe PolyA is the first type system for a mobility calculus that provides type polymorphism comparable in power to polymorphic type systems for the λ-calculus. PolyA is easily extended to ambient calculus variants. A restriction of PolyA has principal typings.

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The Essence of Principal Typings

Cited by 66 publications

References 28 publications

From Exponential to Polynomial-Time Security Typing via Principal Types

From Exponential to Polynomial-Time Security Typing via Principal Types

Approaches to Polymorphism in Classical Sequent Calculus

Polya:True Type Polymorphism for Mobile Ambients

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