Related papers: Substructural Parametricity
Usually a name of the category is inherited from the name of objects. However more relevant for a category of objects and morphisms is an algebra of morphisms. Therefore we prefer to say a category of graphs if every morphism is a graph. In…
Linear Logic and Defeasible Logic have been adopted to formalise different features relevant to agents: consumption of resources, and reasoning with exceptions. We propose a framework to combine sub-structural features, corresponding to the…
Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…
It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with…
Design patterns are distilled from many real systems to catalog common programming practice. However, some object-oriented design patterns are distorted or overly complicated because of the lack of supporting programming language constructs…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
Parametricity states that polymorphic functions behave the same regardless of how they are instantiated. When developing polymorphic programs, Wadler's free theorems can serve as free specifications, which can turn otherwise partial…
We consider the problem of extending an acyclic binary relation that is invariant under a given family of transformations into an invariant preference. We show that when a family of transformations is commutative, every acyclic invariant…
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…
We introduce a monoid structure on a certain set of labelled binary trees, by a process similar to the construction of the plactic monoid. This leads to a new interpretation of the algebra of planar binary trees of Loday-Ronco.
We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are: (a) being atomic, i.e. not being…