This article gives an overview of recent work on the theory of selection functions. We explain
the intuition behind these higher type objects, and define a general notion of sequential …

Simple type theories, ubiquitous in the study of programming language theory, augment
algebraic theories with higher-order, variable-binding structure. This motivates the definition …

We introduce a new foundation for game theory based on so-called open games. Unlike
existing approaches open games are fully compositional: games are built using algebraic …

Algorithms for solid modeling, ie, Computer-Aided Design (CAD) and computer graphics,
are often specified on real numbers and then implemented with finite-precision arithmetic …

This paper extends Escardo and Oliva's selection monad to the selection monad
transformer, a general monadic framework for expressing backtracking search algorithms in …

Using techniques from higher-type computability theory and proof theory we extend the well-
known game-theoretic technique of backward induction to certain general classes of …

We study temporal properties over infinite binary red-blue trees in the setting of constructive
type theory. We consider several familiar path-based properties, typical to linear-time and …

In applied game theory the modelling of each player's intentions and motivations is a key
aspect. In classical game theory these are encoded in the payoff functions. In previous work …

This paper explores a novel approach to selection functions through the introduction of a
generalised selection monad. The foundation is laid with the conventional selection monad …

We present a method of backward induction for computing approximate subgame perfect
Nash equilibria of infinitely repeated games with discounted payoffs. This uses the selection …