2022-02-10: Jérémy Ledent (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Jérémy Ledent (MSP)

An informal introduction to Game Semantics

Abstract

Denotational semantics specifies the meaning of a computer program by associating it with an abstract mathematical object (its denotation), which represents its behaviour. In the case of game semantics, a program is interpreted as a two-player game, played between the program and its environment. More precisely, types are modelled by arenas (on which the game is played), while the programs themselves are modelled by strategies played on those arenas. Game semantics originated in the 1990's to solve the full abstraction problem for PCF (i.e., λ-calculus with a fixpoint operator); but the framework is very flexible, and many variants have been proposed to describe control, state, probability, concurrency, and many other program constructs.

In this talk, I will start with a (very) brief introduction to denotational semantics in general, and define the concept of full abstraction. Then, I will present the game semantics model for PCF (à la Hyland-Ong), and if time allows, show how to extend it to model mutable references. I aim to keep the presentation intuitive and informal, relying mostly on examples and pictures.

2022-02-10 14:00:00 UTC
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