Related papers: Proofs for Free in the $\lambda\Pi$-Calculus Modul…
We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Structural subtyping and parametric polymorphism provide similar flexibility and reusability to programmers. For example, both features enable the programmer to provide a wider record as an argument to a function that expects a narrower…
For a rational map $\phi: X \to G$ from a normal algebraic variety $X$ to a commutative algebraic group $G$, we define the modulus of $\phi$ as an effective divisor on $X$. We study the properties of the modulus. This work generalizes the…
Working with a rather general notion of independence, we provide a transference method which allows to compare the p-norm of sums of independent copies with the p-norm of sums of free copies. Our main technique is to construct explicit…
This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
This paper studies useful sharing, which is a sophisticated optimization for lambda-calculi, in the context of call-by-need evaluation in presence of open terms. Useful sharing turns out to be harder in call-by-need than in call-by-name or…
The Stratified Foundations are a restriction of naive set theory where the comprehension scheme is restricted to stratifiable propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory.…
We study unimodality for free multiplicative convolution with free normal distributions $\{\lambda_t\}_{t>0}$ on the unit circle. We give four results on unimodality for $\mu\boxtimes\lambda_t$: (1) if $\mu$ is a symmetric unimodal…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
In this paper, we show how to interpret a language featuring concurrency, references and replication into proof nets, which correspond to a fragment of differential linear logic. We prove a simulation and adequacy theorem. A key element in…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
This paper elaborates on a new approach of the question of the proof-theoretic study of concurrent interaction called "proofs as schedules". Observing that proof theory is well suited to the description of confluent systems while…
Initiated by Abramsky [1994], the Proofs as Processes agenda is to establish a solid foundation for the study of concurrent languages, by researching the connection between linear logic and the $\pi$-calculus. To date, Proofs as Processes…
This paper surveys some applications of moduli theory to issues concerning the distribution of rational points on algebraic varieties. It will appear on the proceedings of the Fano Conference.
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
For unitary groups associated to a ramified quadratic extension of a $p$-adic field, we define various regular formal moduli spaces of $p$-divisible groups with parahoric levels, characterize exceptional special divisors on them, and…
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…