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Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
Session types express and enforce safe communication in concurrent message-passing systems by statically capturing the interaction protocols between processes in the type. Recent works extend session types with arithmetic refinements, which…
Answering complex questions often requires multi-step reasoning in order to obtain the final answer. Most research into decompositions of complex questions involves open-domain systems, which have shown success in using these decompositions…
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…
This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order…
This paper discusses the processes by which conversants in a dialogue can infer whether their assertions and proposals have been accepted or rejected by their conversational partners. It expands on previous work by showing that logical…
The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a…
Resolution and superposition are common techniques which have seen widespread use with propositional and first-order logic in modern theorem provers. In these cases, resolution proof production is a key feature of such tools; however, the…
We introduce a new compile-time notion of type subsumption based on type simulation. We show how to apply this static subsumption relation to support a more intuitive, object oriented approach to generic programming of reusable, high…
Linear type systems need to keep track of how programs use their resources. The standard approach is to use context splits specifying how resources are (disjointly) split across subterms. In this approach, context splits redundantly echo…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
Session types statically prescribe bidirectional communication protocols for message-passing processes. However, simple session types cannot specify properties beyond the type of exchanged messages. In this paper we extend the type system…
Pronouns are frequently omitted in pro-drop languages, such as Chinese, generally leading to significant challenges with respect to the production of complete translations. Recently, Wang et al. (2018) proposed a novel reconstruction-based…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
Compositional, structured models are appealing because they explicitly decompose problems and provide interpretable intermediate outputs that give confidence that the model is not simply latching onto data artifacts. Learning these models…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
Scripting code may present maintenance problems in the long run. There is, then, the call for methodologies that make it possible to control the properties of programs written in dynamic languages in an automatic fashion. We introduce…
Disentanglement is a runtime property of parallel programs guaranteeing that parallel tasks remain oblivious to each other's allocations. As demonstrated in the MaPLe compiler and run-time system, disentanglement can be exploited for fast…