Decidability of the problems of unboundedness and simultaneous unboundedness (aka. the diagonal problem) for higher-order recursion schemes was established by Clemente, Parys, Salvati, and Walukiewicz (2016). Then a procedure of optimal complexity was presented by Parys (2017); this procedure used a complicated type system, involving multiple flags and markers. We present here a simpler and much more intuitive type system serving the same purpose. We prove that this type system allows to solve the unboundedness problem for a widely considered subclass of recursion schemes, called safe schemes. For unsafe recursion schemes we only have soundness of the type system: if one can establish a type derivation claiming that a recursion scheme is unbounded then it is indeed unbounded. Completeness of the type system for unsafe recursion schemes is left as an open question. Going further, we discuss an extension of the type system that allows to handle the simultaneous unboundedness problem. We also design and implement an algorithm that fully automatically checks unboundedness of a given recursion scheme, completing in a short time for a wide variety of inputs.

Apache Spark is a framework for distributed computing that supports the map-reduce programming model. The SQL module of Spark contains Datasets, i.e., distributed collections of records stored in a serialized low-level format in a manually managed chunk of memory. However, the functions users provide to the map-reduce computations expect Java objects. Datasets perform an additional deserialization step beforehand to support the user-provided function, which increases the overhead. We tackled this problem by replacing map functions with their counterparts that accepted the serialized data. This allowed us to skip the unnecessary part of deserialization and achieve faster data processing speeds.