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We present a graded modal type theory, a dependent type theory with grades that can be used to enforce various properties of the code. The theory has $\Pi$-types, weak and strong $\Sigma$-types, natural numbers, an empty type, and a…
Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assignments (dichotomies) of $p$ points in $n$ dimensions can be…
In this paper we examine the natural interpretation of a ramified type hierarchy into Martin-L\"of type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
The sole purpose of this note is to introduce some elementary results on the structure and functoriality of Reedy model categories. In particular, I give a very useful little criterion to determine whether composition with a morphism of…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…
In the seminal paper Functional unparsing, Olivier Danvy used continuation passing to reanalyse printf-like format strings as combinators. In the intervening decades, the conversation shifted towards a concurrent line of work --…
Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…
Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…
Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that favors simplicity and compositionality. However, some applications require explicit information about the data…
Pipage rounding is a dependent random sampling technique that has several interesting properties and diverse applications. One property that has been particularly useful is negative correlation of the resulting vector. Unfortunately…
This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate…
In this work we completely describe the dynamics of triangle tiling billiards. In the first part of this work, we propose a geometric approach of dynamics by introducing natural foliations associated to it. In the second part, we exploit…
Treewidth is a well-known graph invariant with multiple interesting applications in combinatorics. On the practical side, many NP-complete problems are polynomial-time (sometimes even linear-time) solvable on graphs of bounded treewidth. On…
In Constructive Type Theory, recursive and corecursive definitions are subject to syntactic restrictions which guarantee termination for recursive functions and productivity for corecursive functions. However, many terminating and…
Given a simple recursive function, we show how to extract from it a reversible and an classical iterative part. Those parts can synchronously cooperate under a Producer/Consumer pattern in order to implement the original recursive function.…
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…
By connecting disparate sources of scientific literature, literature\-/based discovery (LBD) methods help to uncover new knowledge and generate new research hypotheses that cannot be found from domain-specific documents alone. Our work…
Although a standard in natural science, reproducibility has been only episodically applied in experimental computer science. Scientific papers often present a large number of tables, plots and pictures that summarize the obtained results,…