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Domain theory
bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of theExpand
A categorical semantics of quantum protocols
  • S. Abramsky, B. Coecke
  • Computer Science, Physics
  • Proceedings of the 19th Annual IEEE Symposium on…
  • 18 February 2004
This paper focuses on quantum information protocols, which exploit quantum-mechanical effects in an essential way and form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation. Expand
Full Abstraction for PCF
An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "history-free" strategies. This model is shown toExpand
Domain Theory in Logical Form
Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics, and the theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics are introduced. Expand
Computational Interpretations of Linear Logic
  • S. Abramsky
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
  • 12 April 1993
Girard's linear logic is studied from the point of view of giving a concrete computational interpretation of the logic, based on the Curry—Howard isomorphism, which opens up a promising new approach to the parallel implementation of functional programming languages. Expand
The lazy lambda calculus
The sheaf-theoretic structure of non-locality and contextuality
It is shown that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections, and a linear algebraic approach to computing these obstructions is described, which allows a systematic treatment of arguments for non- Locality and contextuality. Expand
Games and Full Completeness for Multiplicative Linear Logic
We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove fullExpand
Linearity, Sharing and State: a fully abstract game semantics for Idealized Algol with active expressions
A novel semantics for Idealized Algol is presented using games, which takes into account the irreversibility of changes in state, and makes explicit the difference between copying and sharing of entities. Expand