# Intensionality, Definability and Computation

## TL;DR

This paper explores the concept of intensionality in computation through game semantics, highlighting its role in modeling programming languages and its potential for developing a mathematical theory of intensional structures.

## Contribution

It reviews how game semantics characterizes sequential functional processes and discusses its potential for creating a formal theory of intensional structures.

## Key findings

- Game semantics effectively models sequential functional processes.
- It provides methods for constructing fully abstract models of programming languages.
- Potential for developing a positive mathematical theory of intensional structures.

## Abstract

We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully abstract models of programming languages, with applications in program analysis and verification. In a broader context, we can regard game semantics as a first step towards developing a positive theory of intensional structures with a robust mathematical structure, and finding the right notions of invariance for these structures.