# Games and Weak-Head Reduction for Classical PCF

@inproceedings{Herbelin1997GamesAW, title={Games and Weak-Head Reduction for Classical PCF}, author={Hugo Herbelin}, booktitle={TLCA}, year={1997} }

We present a game model for classical PCF, a finite version of PCF extended by a catch/throw mechanism. This model is build from E-dialogues, a kind of two-players game defined by Lorenzen. In the E-dialogues for classical PCF, the strategies of the first player are isomorphic to the Bhohm trees of the language.

## 16 Citations

Abstract machines for dialogue games

- Computer ScienceArXiv
- 2007

This paper revisits the notion of abstract Boehm tree, providing more syntactic support and more examples (like call-by-value evaluation) illustrating the generality of the underlying computing device.

A JM's games model is a model of classical Linear Logic.

- Computer Science
- 1997

A subcategory of saturated strategies, closed under all possible codings in copy games, is shown to model reduction in classical Linear Logic.

Believe it or not, AJM's games model is a model of classical linear logic

- Computer ScienceProceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science
- 1997

A subcategory of saturated strategies, closed under all possible codings in copy games, is shown to model reduction in classical linear logic.

Game semantics for first-order logic

- Philosophy, Computer ScienceLog. Methods Comput. Sci.
- 2010

A Church style extension of Parigot's lambda-mu-calculus is used to represent proofs of first-order classical logic and some relations with Krivine's classical realizability and applications to type isomorphisms are presented.

Notes on game semantics

- Computer Science
- 2006

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.

The Anatomy of Innocence

- MathematicsCSL
- 2001

A direct definability theorem of general innocent strategies is proved with respect to a simply typed language of extended Bohm trees, which gives an operational meaning to rigidity in call-byname.

A semantic analysis of control

- Computer Science
- 1999

This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages, and establishes decidability of observational equivalence for finitary PCF, contrasting with the undecidable of the analogous relation in pure PCF.

On Classical PCF, Linear Logic and the MIX Rule

- Computer ScienceCSL
- 2015

A refinement of the relational model of classical PCF in which programs of type integer are single valued is proposed, and this model rejects the MIX syntactical constructs (and the Mix rule of Linear Logic).

The Anatomy of Innocence Revisited

- MathematicsFSTTCS
- 2006

Improved factorization results for bracketing and rigidity that can be combined in any order are presented and Hyland-Ong game semantics is refined.

On the Unity of Logic: a Sequential, Unpolarized Approach

- Computer ScienceArXiv
- 2019

The vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that the linear refinement of classical logic (CL) coincides with (classical) linear logic (LL), and its intuitionistic restrictions with the linear refine of intuitionistic logic (IL) into intuitionistic LL (ILL).

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