The applicative approach to the synthesis of a data structure with the given combinatory characteristic

Abstract

The paper shows that the use of a composition of objects representing a data structure, in fact, means the creation of a kind of information channels on their basis, along which the computation process spreads. In the case of applying the applicative computational technology, the computation process is started by means of the operation of applying the function object to the argument object. Two ways are presented to generate function objects — to use either lambda expressions or combinators to represent them. The first method uses an abstraction meta-operator and associated variables, which leads to the use of substitution systems with the potential for side effects. In the second method, only constant combinator objects participate in the construction of the function, and their application to the argument triggers a conversion based on rewriting rules, which does not cause a side effect. A practical solution to the problem of synthesizing a compositional data structure can be mixed, when both lambda terms and combinators are involved in the computations, which reduces the length of expressions. As a result, a data structure appears, which is composed of compositions of argument objects, equipped with a generated set of supporting function objects.