Related papers: AdapTT: Functoriality for Dependent Type Casts
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
We investigate correspondence functors, namely the functors from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring.They have various specific properties which do not hold for…
Service composition has become commonplace nowadays, in large part due to the increased complexity of software and supporting networks. Composition can be of many types, for instance sequential, prioritising, non-deterministic. However, a…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
We introduce the Delta-framework, LF-Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union.…
In previous work we have illustrated the benefits that compositional data types (CDTs) offer for implementing languages and in general for dealing with abstract syntax trees (ASTs). Based on Swierstra's data types \'a la carte, CDTs are…
Bernstein blocks of complex representations of p-adic reductive groups have been computed in a large amount of examples, in part thanks to the theory of types a la Bushnell and Kutzko. The output of these purely representation-theoretic…
Session types are a rich type discipline, based on linear types, that lifts the sort of safety claims that come with type systems to communications. However, web-based applications and microservices are often written in a mix of languages,…
Recently we presented a concise survey of the formulation of the induction and coinduction principles, and some concepts related to them, in programming languages type theory and four other mathematical disciplines. The presentation in type…
It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In…
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
The Functional Machine Calculus (FMC, Heijltjes 2022) extends the lambda-calculus with the computational effects of global mutable store, input/output, and probabilistic choice while maintaining confluent reduction and simply-typed strong…
Inspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type…
We propose a process calculus, named AbC, to study the behavioural theory of interactions in collective-adaptive systems by relying on attribute-based communication. An AbC system consists of a set of parallel components each of which is…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
Functional decision theory (FDT) is a fairly new mode of decision theory and a normative viewpoint on how an agent should maximize expected utility. The current standard in decision theory and computer science is causal decision theory…