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CLASS is a proof-of-concept general purpose linear programming language, flexibly supporting realistic concurrent programming idioms, and featuring an expressive linear type system ensuring that programs (1) never misuse or leak stateful…
Prototypical Learning is based on the idea that there is a point (which we call prototype) around which the embeddings of a class are clustered. It has shown promising results in scenarios with little labeled data or to design explainable…
As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. Inspired by Hoare Type Theory in classical computing, we propose Quantum Hoare Type Theory (QHTT),…
We describe an application of Prolog: a type checking tool for the Q functional language. Q is a terse vector processing language, a descendant of APL, which is getting more and more popular, especially in financial applications. Q is a…
We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
We present a conservative extension ICaTT of the dependent type theory CaTT for weak $\omega$-categories with a type witnessing coinductive invertibility of cells. This extension allows for a concise description of the "walking equivalence"…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Chain of Thought (CoT) prompting can encourage language models to engage in multi-step logical reasoning. The quality of the provided demonstrations significantly influences the success of downstream inference tasks. Current unsupervised…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
Topic modeling is a powerful technique to discover hidden topics and patterns within a collection of documents without prior knowledge. Traditional topic modeling and clustering-based techniques encounter challenges in capturing contextual…
The $tock$-CSP encoding embeds a rich and flexible approach to modelling discrete timed behaviours in CSP where the event $tock$ is interpreted to mark the passage of time. The model checker FDR provides tailored support for $tock$-CSP,…
This paper describes a method for compiling a constraint-based grammar into a potentially more efficient form for processing. This method takes dependent disjunctions within a constraint formula and factors them into non-interacting groups…
Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a…
In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be…
Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf…
A temporal logic is presented for reasoning about the correctness of timed concurrent constraint programs. The logic is based on modalities which allow one to specify what a process produces as a reaction to what its environment inputs.…