Algebraic solutions to recursion schemes
The search for solutions of the set of equations associated with recursion schemes of programs and the description of the set of such solutions constitute one of the principal problems in modern schematics. The paper deals with the algebraic theory of recursion schemes which includes tree algebras and the algebras obtained from congruence on trees. Special attention is paid to the description of denotational semantics for non-determined computations and for communicating processes. Some of the obtained results are of interest within the framework of the abstract data types theory which is intensively developing now. The apparatus of the categorical theory and the mechanisms of the search for fixed points, in particular, minimal and maximal ones, is employed. The review of relevant investigations concerning the outlined problematics is given in the paper together with the previously obtained results.
scientific article; zbMATH DE number 4039262
scientific article