human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "on the versatility of open logical relations continuity automatic differentiation and a containment theorem"):
  Abstract: Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called \emph{open logical relation}, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed $\lambda$-calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any such a collection of functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations.

Includes members:
  Member "a simple differentiable programming language":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a differential form pullback programming language for higher order reverse mode automatic differentiation")
  Member "confusion of tagged perturbations in forward automatic differentiation of higher order functions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "dynamic automatic differentiation of gpu broadcast kernels")
  Member "efficient differentiable programming in a functional array processing language":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "multi layer optimizations for end to end data analytics")
  Member "the simple essence of automatic differentiation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a differential form pullback programming language for higher order reverse mode automatic differentiation")
  Member "automatic differentiation in machine learning a survey":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a workload adaptive mechanism for linear queries under local differential privacy")
  Member "step indexed logical relations for probability":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "relational reasoning for markov chains in a probabilistic guarded lambda calculus")
  Member "abstract effects and proof relevant logical relations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "parametric cubical type theory")
  Member "church scott ptime an application of resource sensitive realizability":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "quantitative classical realizability")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.PL(Programming Languages)