Related papers: On Isomorphism of "Functional" Intersection and Un…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
Robotic performance emerges from the coupling of body and controller, yet it remains unclear when morphology-control co-design is necessary. We present a unified framework that embeds morphology and control parameters within a single neural…
Semantic subtyping is an approach to define subtyping relations for type systems featuring union and intersection type connectives. It has been studied only for strict languages, and it is unsound for non-strict semantics. In this work, we…
We study the interaction of structural subtyping with parametric polymorphism and recursively defined type constructors. Although structural subtyping is undecidable in this setting, we describe a notion of parametricity for type…
We study functional and concurrent calculi with non-determinism, along with type systems to control resources based on linearity. The interplay between non-determinism and linearity is delicate: careless handling of branches can discard…
Design patterns are elegant and well-tested solutions to recurrent software development problems. They are the result of software developers dealing with problems that frequently occur, solving them in the same or a slightly adapted way. A…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
In this paper, we study the behaviour of TF-isomorphisms, a natural generalisation of isomorphisms. TF-isomorphisms allow us to simplify the approach to seemingly unrelated problems. In particular, we mention the Neighbourhood…
The characteristic function of row contractions and liftings of row contractions are complete invariants up to unitary equivalence for row contractions and liftings of row contractions, respectively. We provide alternate proofs for these…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
Although intersection homology lacks a ring structure, certain expressions (called uniform) in the intersection homology of an irreducible projective variety $X$ always give the same value, when computed via the decomposition theorem on any…
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…
In stepwise derivations of programs from specifications, data type refinements are common. Many data type refinements involve isomorphic mappings between the more abstract and more concrete data representations. Examples include refinement…
In this paper we consider a type system with a universal type $\omega$ where any term (whether open or closed, $\beta$-normalising or not) has type $\omega$. We provide this type system with a realisability semantics where an atomic type is…
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…
We present a principled theoretical framework for inferring and checking the union types, and show its work in practice on JSON data structures. The framework poses a union type inference as a learning problem from multiple examples. The…