Samson Abramsky

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A metalanguage for denotational semantics is given a logical interpretation: types are interpreted as propositional theories; terms (in an extended typed λ-calculus, denoting elements of types) are embedded in an endogenous program logic, which characterises their behaviour in terms of which properties they satisfy; terms (in an extension of the algebraic(More)
Particular focus in this paper is on quantum information protocols, which exploit quantum-mechanical effects in an essential way. The particular examples we shall use to illustrate our approach will be teleportation (Benett et al., 1993), logic-gate teleportation (Gottesman and Chuang,1999), and entanglement swapping (Zukowski et al., 1993). The ideas(More)
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 to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic(More)
We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the Curry-Howard isomorphism. In the case of Intuitionistic Linear Logic, this leads to a reenement of the lambda calculus, giving ner control over order of evaluation and storage allocation, while maintaining the logical content of(More)
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 full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net. A key role is played(More)
The manipulation of objects with state which changes over time is all-pervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focusses on \Idealized Algol", an elegant synthesis of imperative(More)