Date of Award

2013

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Computer and Information Science

First Advisor

Steve Zdancewic

Abstract

Session types and typestate both promise a type system that can reason about protocol

adherence. The complexity budgets of most programming languages, however, do not

allow for new forms of types aimed at specific problem domains--even domains as broad

as these.

Classical F◦ --read "F-pop"--is a typed λ-calculus based on classical (i.e., full) linear

logic, wherein session types arise naturally from the interaction between the usual sums,

products, and implications of linear logic and a simple process model, with the dualizing

negation of classical logic naturally accounting for how a protocol is seen by each of a

channel's endpoints. Classical F◦ expressions evaluate to processes, reminiscent of those

in the π-calculus, that communicate over channels, but source expressions, rather than

including processes and channels, employ only two novel control operators that account

for process creation and communication.

F◦ is introduced by way of its intuitionistic fragment, which even on its own can account

for typestate: the combination of linearity and polymorphism leads to natural encodings

of many programmer-specified protocols. In fact, any protocol expressible as a regular

language can be encoded in an intuitionistic F◦ type. F◦ distinguishes between linear

and unrestricted types by using kinds together with a notion of subkinding, avoiding

the pitfalls of approaches based on type qualifiers or modalities; kinds are related by a

subkinding order that allows unrestricted types to be treated as though they were linear.

Soundness for intuitionistic and classical F◦ is proved both in the standard operational

sense of preservation and progress and for an augmented semantics that shows more

directly that the expected properties of linearity are preserved. This establishes the absence

of deadlocks in closed, well-typed F◦ programs; it also guarantees that such programs will

not "leak" processes as long as their result types are unrestricted.

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