By V.E. Wolfengagen
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Extra resources for Combinatory Logic in Programming. Computations with Objects Through Examples and Exercises
Numerals among primary objects in combinatory logic. The point is that the concept of a numeral can be developed independently, by using known combinators. In such a case, numerals present themselves in a somewhat unusual aspect, being objects, which display their arity, depending on the used system of postulates. In the same way, arithmetical operations are successfully developed in the form of combinators. In other words, arithmetical entities are built into combinatory logic. e. an application (arithmetical objects with their rules) is built into a software environment (combinatory logic).
Then, one may read Sections 10, 15–18, introducing a body of concepts for programming by means of combinators with the dynamic system of instructions. Other sections can be added to one’s taste. In particular, a more detailed acquaintance with the categorial abstract machine in Sections 19–22 will require one to refer to the literature cited in the bibliography. Sections 11–14 are aimed at those readers, who want to independently begin reading original research papers in the field of computer science.
Curien, , ) contain the constructing of a special kind of combinatory logic called categorical combinatory logic. It gave 34 C HAPTER 1: P RELIMINARIES a foundation for constructing the abstract machine, which is both an enhanced notion of computation and self standing programming system, aimed to pursue the research in an area of programming. Several supplementary works, given in bibliography, will assist to start with your own research in various applied areas, using the possibilities of applicative computational systems.