Related papers: Curry-style type Isomorphisms and Game Semantics
The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
This paper reviews the fully complete hypergames model of system $F$, presented a decade ago in the author's thesis. Instantiating type variables is modelled by allowing ``games as moves''. The uniformity of a quantified type variable…
Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational…
Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of "type" in programming…
The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…
System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…
It is well-known that typability, type inhabitation and type inference are undecidable in the Girard-Reynolds polymorphic system F. It has recently been proven that type inhabitation remains undecidable even in the predicative fragment of…
Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of…
Dependently typed languages are well known for having a problem with code reuse. Traditional non-indexed algebraic datatypes (e.g. lists) appear alongside a plethora of indexed variations (e.g. vectors). Functions are often rewritten for…
In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
We investigate the problem of type isomorphisms in the presence of higher-order references. We first introduce a finitary programming language with sum types and higher-order references, for which we build a fully abstract games model…
This thesis investigates effectful declarative programming with an emphasis on non-determinism as an effect. On the one hand, we are interested in developing applications using non-determinism as underlying implementation idea. We discuss…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…