Definability and Full Abstraction

  title={Definability and Full Abstraction},
  author={Pierre-Louis Curien},
  journal={Electron. Notes Theor. Comput. Sci.},
  • P. Curien
  • Published 1 April 2007
  • Computer Science
  • Electron. Notes Theor. Comput. Sci.
Notes on game semantics
Applications of game semantics to model-checking and abstract interpretation are being developed, which opens the way for connecting the uses of games in semantics and in verification.
Dynamic game semantics
This work gives game semantics of a higher-order programming language that distinguishes programmes with the same value yet different algorithms and the hiding operation on strategies that precisely corresponds to the (small-step) operational semantics of the language.
Some Programming Languages Suggested by Game Models (Extended Abstract)
Game semantics and realizability for classical logic
This thesis investigates two realizability models for classical logic built on HO game semantics. The main motivation is to have a direct computational interpretation of classical logic, arithmetic
Game semantics of Martin-Löf type theory, part III: its consistency with Church's thesis
This work proves consistency of intensional Martin-Lof type theory with formal Church's thesis (CT) by novel realizability a la game semantics, which is based on the author's previous work.
Dynamic Games and Strategies
A new game semantics of a prototypical programming language that distinguishes terms with the same value yet different algorithms, capturing intensionality of computation is given, equipped with the hiding operation on strategies that exactly corresponds to the (small-step) operational semantics of the programming language.
A game-semantic model of computation
This work shows, as a main technical achievement, that viable strategies in game semantics are Turing complete and has given a mathematical foundation of computation in the same sense as Turing machines but beyond computation on natural numbers, e.g., higher-order computation, in a more abstract fashion.
Focusing in Asynchronous Games
Interestingly, it is shown that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic.
On the reification of semantic linearity
This work proposes a PCF-like language imposing linear constraints on the use of variable to program only linear functions, and exploits the denotational linearity to provide an efficient evaluation semantics SECD-like, that avoids theUse of closures.
Full abstraction for nominal Scott domains
A full abstraction result is proved for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model.


Game semantics and subtyping
  • J. Chroboczek
  • Computer Science
    Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)
  • 2000
It is shown how the simple device of explicitly introducing error values in the syntax of the calculus leads to a notion of subtyping for game semantics, thus yielding an interpretation of bounded quantification.
Stable Models of Typed lambda-Calculi
It is shown that Milner's fully abstract model of Plotkin's PCP language only contains stable functions, and new model constructions from a notion of stable function are presented.
Angelic semantics of fine-grained concurrency
A fully abstract game semantics for finite nondeterminism
This model is shown to be fully abstract, with respect to an equivalence based on both safety and liveness properties, by means of a factorization theorem which states that every nondeterministic strategy is the composite of a deterministic strategy with a nondetergetic oracle.
Kripke Logical Relations and PCF
It is shown that one may achieve full abstraction at all types using a form of "Kripke logical relations" introduced by Jung and Tiuryn to characterize λ-definability.
Games and full abstraction for FPC
  • G. McCusker
  • Computer Science
    Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
  • 1996
A model of the language FPC, a sequential functional language with just this type structure, in /spl epsi/ is described and shown to be fully abstract.
The regular-language semantics of second-order idealized ALGOL
Hereditarily Sequential Functionals
In order to define models of simply typed functional programming languages being closer to the operational semantics of these languages, the notions of sequentiality, stability and seriality were
Mechanizing Logical Relations
We give an algorithm for deciding whether there exists a definable element of a finite model of an applied typed lambda calculus that passes certain tests, in the special case when all the constants
Linearity, Sharing and State: a fully abstract game semantics for Idealized Algol with active expressions