Related papers: Orthologic Type Systems
Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
Linear and substructural types are powerful tools, but adding them to standard functional programming languages often means introducing extra annotations and typing machinery. We propose a lightweight substructural type system design that…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical…
Starting with an algorithm to turn lists into full trees which uses non-obvious invariants and partial functions, we progressively encode the invariants in the types of the data, removing most of the burden of a correctness proof. The…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
Working in a variant of the intersection type assignment system of Coppo, Dezani-Ciancaglini and Venneri [1981], we prove several facts about sets of terms having a given intersection type. Our main result is that every strongly normalizing…
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure {\lambda}-calculus, the calculus with explicit substitutions {\lambda}S, and the calculus with explicit…
We intend to investigate the metalogical property of 'omitting types' for a wide variety of quantifier logics (that can also be seen as multimodal logics upon identifying existential quantifiers with modalities syntactically and…
The importance of subtyping to enable a wider range of well-typed programs is undeniable. However, the interaction between subtyping, recursion, and polymorphism is not completely understood yet. In this work, we explore subtyping in a…