Deriving structures from structures
This paper introduces a new mathematical approach to transformations of structures, where the concept of "structure" is extremely general. Many structures and transformations that arise in biology as well as computer science are special cases of our concepts. A structure may be changed by finding an occurrence of a pattern and replacing it by another pattern as specified by a rule. To prove theorems about long sequences of applications of complicated rules, we need precise and tractable mathematical definitions of rules and how to apply them. This paper presents such definitions and some fundamental theorems, together with brief remarks on applications to record handling, evaluation of recursively defined functions, and control flow analysis for optimizing compilers.
KeywordsDirect Derivation Full Subcategory Colored Structure Graph Grammar Unary Predicate
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