38 citations · 103 across the 14 of their papers we have counts for
10 papers · 1 filter
Generalized Decidability via Brouwer Trees
Tom de Jong, Nicolai Kraus, Aref Mohammadzadeh +1
In the setting of constructive mathematics, we suggest and study a framework for decidability of properties, which allows for finer distinctions than just "decidable, semidecidable…
Constructive Ordinal Exponentiation
Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg +1
In classical mathematics, ordinal arithmetic is well-studied; constructively, addition and multiplication are well-known. We study constructive ordinal exponentiation, where ordina…
Set-Theoretic and Type-Theoretic Ordinals Coincide
Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg +1
In constructive set theory, an ordinal is a hereditarily transitive set. In homotopy type theory (HoTT), an ordinal is a type with a transitive, wellfounded, and extensional binary…
Type-Theoretic Approaches to Ordinals
Nicolai Kraus, Fredrik Nordvall Forsberg, Chuangjie Xu
In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate li…
Connecting Constructive Notions of Ordinals in Homotopy Type Theory
Nicolai Kraus, Fredrik Nordvall Forsberg, Chuangjie Xu
In classical set theory, there are many equivalent ways to introduce ordinals. In a constructive setting, however, the different notions split apart, with different advantages and…
Compositional Game Theory, Compositionally
Robert Atkey, Bruno Gavranović, Neil Ghani +3
We present a new compositional approach to compositional game theory (CGT) based upon Arrows, a concept originally from functional programming, closely related to Tambara modules,…
Compositional Game Theory with Mixed Strategies: Probabilistic Open Games Using a Distributive Law
Neil Ghani, Clemens Kupke, Alasdair Lambert +1
We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show th…
Quotient inductive-inductive types
Thorsten Altenkirch, Paolo Capriotti, Gabe Dijkstra +2
Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotien…
Positive Inductive-Recursive Definitions
Neil Ghani, Fredrik Nordvall Forsberg, Lorenzo Malatesta
A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive induc…
Extracting verified decision procedures: DPLL and Resolution
Ulrich Berger, Andrew Lawrence, Fredrik Nordvall Forsberg +1
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability…