Related papers: On Isomorphism of "Functional" Intersection and Un…
Configuring consists in simulating the realization of a complex product from a catalog of component parts, using known relations between types, and picking values for object attributes. This highly combinatorial problem in the field of…
Function association is a useful process for binary reverse engineers. Search tools exist to perform association at scale, but they do not utilize the full range of capabilities that AI-enabled search provides. Prior work has explored the…
We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
The space complexity of functional programs is not well understood. In particular, traditional implementation techniques are tailored to time efficiency, and space efficiency induces time inefficiencies, as it prefers re-computing to…
The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.
Many object-oriented dynamic languages allow programmers to _extract methods_ from objects and treat them as functions. This allows for flexible programming patterns, but presents challenges for type systems. In particular, a simple…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
In this paper we define several notions of term expansion, used to define terms with less sharing, but with the same computational properties of terms typable in an intersection type system. Expansion relates terms typed by associative,…
We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…
We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we…
Imperative session types provide an imperative interface to session-typed communication. In such an interface, channel references are first-class objects with operations that change the typestate of the channel. Compared to functional…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
In Programming by Example, a system attempts to infer a program from input and output examples, generally by searching for a composition of certain base functions. Performing a naive brute force search is infeasible for even mildly involved…
Programming with dependent types is a blessing and a curse. It is a blessing to be able to bake invariants into the definition of data-types: we can finally write correct-by-construction software. However, this extreme accuracy is also a…