Origins of Programming: Discourses on Methodology
The book begins with a detailed discussion of two problems that have played an extremely important role in the emergence of theoretical programming as an independent discipline. The principal goals in this book are to explain the line of thought that was followed in solving these problems, demonstrate the workings of the mathematical way of thinking, carefully analyze the different stages of descriptive analysis and problem formulation, and reveal the aesthetic component in the search for solutions - in other words, to try to turn the reader into a true witness of the process of discovering mathematical results. In the first part of the book the author considers the storage minimization packing, or storage problem schemas. The problem of storage packing is treated as an example that illustrates how to solve an application problem by means of mathematical methods. In the second part the author presents the theory of Yanov program schemas, a classical theory generally recognized as having served as a foundation of the mathematical theory of programming. This is analyzed as a methodological example that illustrates how a fully developed theory can be extended to a new class of phenomena and objects: program schemas and configurations of program schemas.
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abstract objects ALGOL ALGOL 60 algorithmic language applied arbitrary arcs arguments and results assertion assigned axiom binary binary relation Boolean functions bundles calculus chain complete graph concept condition connectivity components consider construction control flow graph cross section data flow graph data paths deducible defined definition denote directed graph disjunction elements equivalence equivalence-preserving example executed Figure formal gluing graph G halt instruction heuristic identity implement incompatibility graph int array internal statement interpretation Lemma linear programs liveness domains logical formulas logical operations loop mathematical means memory location method minimal coloring minus arrow notation obtained once ordinal number pair poles precisely predicate variables present procedure program schema proof properties propositional calculus reader recognizer relation rigorous route rule of inference schema G sequence specified step storage allocation storage packing problem structure Suppose symbols Theorem theory transformations transitive closure tree truth values tuple vertex Yanov schemas