Encoding, Decoding and Data Refinement
Data refinement is the systematic replacement of a data structure with another one in program development. Data refinement between program statements can on an abstract level be described as a commutativity property where the abstraction relationship between the data structures involved is represented by an abstract statement (a decoding). We generalise the traditional notion of data refinement by defining an encoding operator that describes the least (most abstract) data refinement with respect to a given abstraction. We investigate the categorical and algebraic properties of encoding and describe a number of special cases, which include traditional notions of data refinement. The dual operator of encoding is decoding, which we investigate and give an intuitive interpretation to. Finally we show a number of applications of encoding and decoding.
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