Higher-order functions

A higher-order function is a type of function that either takes another function as an input parameter or returns a function as its output. These functions are able to receive and manipulate other functions as data, allowing for more complex and flexible programming.From: Dictionary of Computer Science, Engineering, and Technology [2017], Solving Partially Observable Environments with Universal Search Using Dataflow Graph-Based Programming Model [2021]

Functions

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Published in Janet Woodcock, Software Engineering Mathematics, 1988

Janet Woodcock

dom is a function from the set of relations from X to Y to (P X): we apply it to a function and it returns a set. This is an example of what is called a higher order function, since it takes a function as an argument. Some people make a lot of fuss about this, but since we regard functions merely as sets with knobs on, dom is just taking a set as its argument.

Solving Partially Observable Environments with Universal Search Using Dataflow Graph-Based Programming Model

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Published in IETE Journal of Research, 2021

Swarna Kamal Paul, Parama Bhaumik

Programs are evaluated in lazy style. The execution starts from the terminal node of a program and all the parent nodes are called recursively until the initial node is reached. Memoization is applied on each node and the output value is cached during the course of the execution. The output value is copied on respective edges on each subsequent call. As illustrated in Figure 2(a), execution starts from node h and corresponding parent nodes are called recursively. After execution of each node, output data is copied over outgoing edges. Atomic primitive functions are directly evaluated by applying the functions on the arguments whereas higher-order functions are evaluated by substitution and reduction. Higher-order functions receive another function as argument and apply some form of computation on the function received as input data. Nodes having stored function as a program subgraph are also evaluated by substitution and reduction strategy. Figure 2(b) illustrates execution by substitution and reduction where node f is substituted with its function definition – and reduced by evaluation.

Higher-order functions

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Solving Partially Observable Environments with Universal Search Using Dataflow Graph-Based Programming Model