Publication: Equalities between Combinators to Evaluate Expressions
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2021
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© 2020 Elsevier B.V.. All rights reserved.One of the aims of this work is to revise the known issues of how to obtain the value of the expression using an applicative computing system. Computation and/or symbolic transformations have undoubtedly become one of the dominant trends in modern computer science. In particular, this refers to the execution of the processes of inference of an object with given properties, which is studied with the formation of sets of equalities leading to a target computational model. At the same time, the mathematical theory of computation gets a target equational description, making the process of studying its properties and capabilities more suitable. A model structure based on the method of indexed expressions is developed and applied using the notions of evaluation mapping and assignments. As shown, this may not be considered as generic notion, but derived using the combinators. Thus, the semantics of computation can be derived from the construction of a combinator-as-process. This is the embedding into a system of combinators. A linking system of equalities between combinatorsl is established, which serving as a generic computational model. This allows us to look differently at the previous cognitive ideas of the semantics of computation disabling an evaluation map and assignments and enabling their replacement by a set of equalities between combinators.
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Kosikov, S. Equalities between Combinators to Evaluate Expressions / Kosikov, S., Ismailova, L., Wolfengagen, V. // Procedia Computer Science. - 2021. - 190. - P. 332-340. - 10.1016/j.procs.2021.06.058