Abstract: An outer event stream can be modeled to represent duration for an event with an inner event stream. The inner event stream can be generated to represent duration of at least one event from the outer event stream. By modeling the outer event stream to include duration, coincidence between two or more events can be determined. More specifically, the modeling of the outer event stream enables use of operators to identify coincidence between events from event streams.

Abstract: In non-limiting examples of the present disclosure, systems and methods for rewriting expressions utilizing cooperative visitors are provided. A data request may be received by a computing device, which may then be represented in a data structure, e.g., an expression tree, representative of the data request. A node within the data structure representative of the data request may be visited. Metadata associated with at least one cooperative visitor may be extracted from the node, and the node may then be transformed by applying the at least one cooperative visitor to the node.

Abstract: An outer event stream can be modeled to represent duration for an event with an inner event stream. The inner event stream can be generated to represent duration of at least one event from the outer event stream. By modeling the outer event stream to include duration, coincidence between two or more events can be determined. More specifically, the modeling of the outer event stream enables use of operators to identify coincidence between events from event streams.

Abstract: An outer event stream can be modeled to represent duration for an event with an inner event stream. The inner event stream can be generated to represent duration of at least one event from the outer event stream. By modeling the outer event stream to include duration, coincidence between two or more events can be determined. More specifically, the modeling of the outer event stream enables use of operators to identify coincidence between events from event streams.

Abstract: In non-limiting examples of the present disclosure, systems and methods for interning expression trees are provided. Hash code for a plurality of expression tree nodes is recursively computed and a determination is made as to whether hash code for each of a plurality of expression tree nodes is stored in a cached intern pool. Upon determining that at least one of a plurality of expression tree nodes is not stored in a cached intern pool, one or more functions may be run on at least one of a plurality of expression tree nodes for determining whether at least one of a plurality of expression tree nodes should be stored in a cached intern pool. Normalization of expression trees may also be employed to effectuate effective sharing of expression tree nodes.

Abstract: Higher-order operators are subject to checkpointing as well as recovery. The state of a higher-order operator, comprising an outer subscription and one or more inner subscriptions, is captured and subsequently utilized to recover the operator. In one instance, a data representation of code that can produce an inner subscription is saved. In other instance, an outer subscription is decoupled from inner subscriptions of a higher-order operator.

Abstract: A pageable query can be generated based on an event-processing query. The pageable query is a form of the event-processing query that supports swapping the event-processing query into and out of memory. For instance, page-in and page-out triggers can be inserted. After detection of a page-in trigger, the event-processing query can be loaded into the memory, and after detection of a page-out trigger, the event-processing query can be unloaded from memory.

Abstract: A multidimensional object, such as a language-integrated query (LINQ) object, can be generated based upon a grouping set operator and zero or more key selectors. The object can be utilized to query over a non-relational data source. The object can include a sequence of functions corresponding to each grouping related to the grouping set operator in order to provide multidimensional grouping representation. Furthermore, the object includes nested structures for optimized execution of the grouping set operator.

Abstract: Computation can be encoded in a lightweight and optionally typed data representation. The data representation can be specified in a prefix-based notation potentially including nested function-argument pairs. Further, the data representation can comprise optional static type information associated with at least a portion of computation. Still further, the data representation can be programming language and platform independent or surfaced in a particular programming language or platform.

Abstract: Methods and devices are provided for analyzing a multi-output query. A data stream associated with a direct input and/or an indirect input related to a multi-output query is phased into a plurality of connectable resources. A plurality of nodes is identified within the plurality of connectable resources, and the plurality of nodes is processed to produce a data output. Additionally, a user interface is provided for building at least one multi-output query. A multi-output query input is received, at least one data stream is generated in response to the multi-output query, and nodes are identified that define data sub-streams within the at least one data stream. The nodes are processed to produce a data output responsive to the multi-output query, and a data sub-stream responsive to the at least one multi-output query is displayed through the graphical user interface.

Abstract: In non-limiting examples of the present disclosure, systems and methods for rewriting expressions utilizing cooperative visitors are provided. A data request may be received by a computing device, which may then be represented in a data structure, e.g., an expression tree, representative of the data request. A node within the data structure representative of the data request may be visited. Metadata associated with at least one cooperative visitor may be extracted from the node, and the node may then be transformed by applying the at least one cooperative visitor to the node.

Abstract: In non-limiting examples of the present disclosure, systems and methods for interning expression trees are provided. Hash code for a plurality of expression tree nodes is recursively computed and a determination is made as to whether hash code for each of a plurality of expression tree nodes is stored in a cached intern pool. Upon determining that at least one of a plurality of expression tree nodes is not stored in a cached intern pool, one or more functions may be run on at least one of a plurality of expression tree nodes for determining whether at least one of a plurality of expression tree nodes should be stored in a cached intern pool. Normalization of expression trees may also be employed to effectuate effective sharing of expression tree nodes.

Abstract: An outer event stream can be modeled to represent duration for an event with an inner event stream. The inner event stream can be generated to represent duration of at least one event from the outer event stream. By modeling the outer event stream to include duration, coincidence between two or more events can be determined. More specifically, the modeling of the outer event stream enables use of operators to identify coincidence between events from event streams.

Abstract: An outer event stream can be modeled to represent duration for an event with an inner event stream. The inner event stream can be generated to represent duration of at least one event from the outer event stream. By modeling the outer event stream to include duration, coincidence between two or more events can be determined. More specifically, the modeling of the outer event stream enables use of operators to identify coincidence between events from event streams.

Abstract: Higher-order operators are subject to checkpointing as well as recovery. The state of a higher-order operator, comprising an outer subscription and one or more inner subscriptions, is captured and subsequently utilized to recover the operator. In one instance, a data representation of code that can produce an inner subscription is saved. In other instance, an outer subscription is decoupled from inner subscriptions of a higher-order operator.

Abstract: A scheduler timeline comprising a sequence of time stamped scheduling activities associated with scheduling execution of a computer program is exposed. The timeline can subsequently be modified in a variety of ways and utilized to schedule activities. For instance, activities can be added, removed, or reordered in a timeline. The timeline can be manipulated to enable code examination including testing and monitoring.

Abstract: A pageable query can be generated based on an event-processing query. The pageable query is a form of the event-processing query that supports swapping the event-processing query into and out of memory. For instance, page-in and page-out triggers can be inserted. After detection of a page-in trigger, the event-processing query can be loaded into the memory, and after detection of a page-out trigger, the event-processing query can be unloaded from memory.

Abstract: Reactive programming is facilitated. Reactive expressions can be generated automatically from non-reactive expressions or in other words standard expressions. Additionally or alternatively, reactive expressions can be optimized in a number of different ways to minimize computational work.

Abstract: A query specified in a source programming language can be analyzed as a function of a type-based state machine that encodes query constraints of a target programming language. The type-based state machine can encode such constraints as types representing states and methods representing transitions between states or types.

Abstract: Computation can be encoded in a lightweight and optionally typed data representation. The data representation can be specified in a prefix-based notation potentially including nested function-argument pairs. Further, the data representation can comprise optional static type information associated with at least a portion of computation. Still further, the data representation can be programming language and platform independent or surfaced in a particular programming language or platform.