# Notes on game semantics

@inproceedings{Curien2006NotesOG, title={Notes on game semantics}, author={Pierre-Louis Curien}, year={2006} }

The subject called game semantics grew out as a coherent body of work from two seminal works of the early 1990’s, with forerunners in logic, recursion theory, and semantics. Game semantics allows to provide precise and also natural, interactive semantics to most of the classical features of programming such as functions, control, references. The precision is measured by definability and in some cases by full abstraction results. Applications of game semantics to model-checking and abstract…

## 15 Citations

### Imperative Programs as Proofs via Game Semantics

- Computer Science, Philosophy2011 IEEE 26th Annual Symposium on Logic in Computer Science
- 2011

### Game Semantics and Normalization by Evaluation

- Computer ScienceFoSSaCS
- 2015

We show that Hyland and Ong’s game semantics for PCF can be presented using normalization by evaluation (nbe). We use the bijective correspondence between innocent well-bracketed strategies and PCF…

### Game semantics of Martin-Löf type theory, part III: its consistency with Church's thesis

- Computer ScienceArXiv
- 2020

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.

### Plays as Resource Terms via Non-idempotent Intersection Types

- Mathematics2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2016

It is shown that both relational interpretations of resource terms and of plays are injective, have the same image, and respect composition.

### On the Meaning of Logical Completeness

- MathematicsTLCA
- 2009

This work considers an extension of the original ludics with contraction and universal nondeterminism in order to capture a polarized fragment of linear logic and thus a constructive variant of classical propositional logic and proves a completeness theorem for proofs in this extended setting.

### Game Semantics for Martin-Löf Type Theory

- Computer ScienceArXiv
- 2016

A category with families of a novel variant of games is proposed, which induces a surjective and injective interpretation of the intensional variant of MLTT equipped with unit-, empty-, N-, dependent product, dependent sum and Id-types as well as the cumulative hierarchy of universes for the first time in the literature.

### A new approach to semantics of procedures in categorical terms

- Computer Science2015 IEEE 13th International Scientific Conference on Informatics
- 2015

A new approach to structural operational semantics of procedures is presented: semantics of non-recursive procedures is defined as a farm of categories interconnected by functors that enables the repeated call of procedures with different arguments and also nesting of procedure calls.

### Interpreting Localized Computational Effects Using Operators of Higher Type

- Mathematics
- 2008

We outline a general approach to providing intensional models for languages with computational effects, whereby the problem of interpreting a given effect reduces to that of finding an operator of…

### Interpreting Localized Computational Effects Using Operators of Higher Type

- MathematicsCiE
- 2008

We outline a general approach to providing intensional models for languages with computational effects, whereby the problem of interpreting a given effect reduces to that of finding an operator of…

### Categorical model of structural operational semantics for imperative language

- Computer Science
- 2016

A new approach to structural operational semantics of imperative programming languages is presented, which model behavior of programs in category of states, where objects are states, an abstraction of computer memory and morphisms model state changes, execution of a program in elementary steps.

## References

SHOWING 1-10 OF 88 REFERENCES

### Game semantics and subtyping

- Computer ScienceProceedings 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.

### Asynchronous games 2: The true concurrency of innocence

- Computer ScienceTheor. Comput. Sci.
- 2004

### The regular-language semantics of second-order idealized ALGOL

- Computer ScienceTheor. Comput. Sci.
- 2003

### Game semantics and abstract machines

- Computer ScienceProceedings 11th Annual IEEE Symposium on Logic in Computer Science
- 1996

There is a simple and natural embedding of AJM-games to HO-games, mapping strategies to strategies and reducing AJM definability (or full abstraction) property to HO's one.

### A fully abstract game semantics for general references

- Computer ScienceProceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)
- 1998

A games model of a programming language with higher-order store in the style of ML-references is introduced and is shown to be fully abstract by means of factorization arguments which reduce the question of definability for the language withHigher- order store to that for its purely functional fragment.

### Linearity, Sharing and State: a fully abstract game semantics for Idealized Algol with active expressions

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 1996

### Games and full completeness for multiplicative linear logic

- Computer ScienceJournal of Symbolic Logic
- 1994

It is shown that this semantics yields a categorical model of Linear Logic and proves full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cut-free proof net.

### Game Theoretic Analysis of Call-by-Value Computation

- Computer ScienceICALP
- 1997

We present a general semantic universe of call-by-value computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for…

### A fully abstract game semantics for finite nondeterminism

- Computer ScienceProceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)
- 1999

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.