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Summary: A Step-Indexed Model of Substructural State
Amal Ahmed
Harvard University
amal@eecs.harvard.edu
Matthew Fluet
Cornell University
fluet@cs.cornell.edu
Greg Morrisett
Harvard University
greg@eecs.harvard.edu
Abstract
The concept of a "unique" object arises in many emerging programming languages such as Clean, CQual, Cyclone,
TAL, and Vault. In each of these systems, unique objects make it possible to perform operations that would otherwise
be prohibited (e.g., deallocating an object) or to ensure that some obligation will be met (e.g., an opened file will be
closed). However, different languages provide different interpretations of "uniqueness" and have different rules regarding
how unique objects interact with the rest of the language.
Our goal is to establish a common model that supports each of these languages, by allowing us to encode and study
the interactions of the different forms of uniqueness. The model we provide is based on a substructural variant of the
polymorphic -calculus, augmented with four kinds of mutable references: unrestricted, relevant, affine, and linear. The
language has a natural operational semantics that supports deallocation of references, strong (type-varying) updates, and
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